Capricious walk to physics; energy circulation theory

#1 (2022.03.14) （Latest piece）

Introduction - Index

Index

Introduction

What is the energy?
Intrinsic energy and mass
Force working between energies
Fundamental force and energy circulation
Interactions between energy circulations

Cosmic separation to two universes
Universe of 3D surface of 4D sphere
Space energy and spacia
Propagation of an apparent energy
Fundamental constants and varying light speed by time
Space expansion is not accelerating
Beginning of wandering modern physics

Momentum in the hidden dimension
Electric charge and electric force
Prolongation of the hidden-space circulation iS
Rotation of prolonged circulation n-iS
About the light
Elementary circulation and quantum particle
Structure and stability of neutron
β decay of neutron: generation of proton and electron

Wave function showing a location in the real space
Orbiting of an energy circulation
Characteristics of wave function and that for orbiting
Energy of atomic electron
Quantization of atomic orbital and its radius
Wave functions of S and P orbitals
Wave equation giving a wave function
Contradictions of the Schrödinger equation
Summary of the new quantum mechanics
Problems of the existing quantum mechanics
Fiction of the uncertainty principle

Separation and cyclic decomposition of early circulations of universe
Energy expression of a galactic seed
Separation of a galactic seed
Flat interaction of galactic seeds
Orthogonal interaction of galactic seeds
Energy radiation from a galactic seed separation
Gamma-ray burst
Release of stellar seeds from a galactic seed
Circulating velocity of stars in a spiral galactic disc
Cosmic microwave background
Energy circulation theory and the standard cosmology

Division to space energy and apparent energy
Light speed variation over time 1: Time
Light speed variation over time 2: Formula of the light speed
Redshift
Light propagated distance and present distance
Hubble diagram 1: Distance modulus
Hubble diagram 2: K-correction
Hubble diagram of supernovae and expected values

Isolated electric charge or electrostatic force does not exist
What is the electric current?
Propagation model of polarization energy
Polar potential
Definition of the electric current
Current potential
Comparison with standard EM
Magnetic charge
Magnetic charge density
Rotating magnetic charge associated with an electric current
Magnet

Formation of shapes of galaxies: Types of galactic seeds
Types of stellar seed releases
Single galactic seed – Ring releases
Rotating binary galactic seeds – Formation of bar-bulge
Rotating binary galactic seeds – Ring releases
Rotating binary galactic seeds – Binary-end linear releases
Attached galactic seeds - Ring releases
Bulges of a spiral double-disc galaxy
Attached-then-binary rotating galactic seeds – Ring releases

Two ways to express a particle energy
Potential energy
Various energies in a free motion
Novel equation of motion
Kinetic energy
Energy of a static particle under receiving a force
Change of mass of a static particle with altitude above ground
Charge for the gravitational force - Orthogonal energy

Physics is often thought to be logical because it uses the words of mathematics, but it is not logical in terms of proof. In mathematics, one mathematics is formed starting from specific axioms as assumption, and accumulating contents and theorems derived by proving. This mathematics can be applied to an object if it meets the axioms.
In physics, if a certain law is proposed and contents derived from it logically and mathematically meet real measured results, they regard that the law should be correct. There is a pitfall here, whether the law is made up of defined elements. For example, Newton's law of universal gravitation gives a force acting between two masses. But is the mass defined? Newton's law of motion indicates the acceleration that a force exerts on mass. The mass is obtained from the measured values of force and acceleration by this law of motion. In fact, the mass is not defined but self-circulates between the two laws. On the other hand, the theory of relativity states the equivalence of mass and energy. However, the energy is not uniquely defined, and is secondarily derived from mass, acceleration, force, and so on.
It is presumed that what we are conceiving as the mass and energy are the elements of the laws. Therefore, it is speculated that these laws should indicate real physical events. However, in the particle decay, the initial particle state is described by undefined elements. The state after the collapse is described by similar elements, and a law of force and potential that derives this decay process is proposed. The law is claimed as correct because it can derive the experimental results. Actually, this is the end of the story, and the law is obtained so that the experimental results can be derived. If the element that defines the state is real, it is physically meaningful. However, if a completely fantasy element is specified, the law derived from it becomes impossible as a physical law even if it is mathematically possible.
There are too many serious unsolved problems with the existing standard physics. Not only dark matter and dark energy, there are many points that we cannot explain even on the formation of spiral galaxies and gamma-ray bursts. Let's take off the existing concepts temporally and think about the laws of physics, starting with the definition of an element that can be the first starting point.

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#2 (2022.03.15)

What is the energy?

In the existing standard physics, the energy and the matter are distinguished as different while each one can convert to the other. The matter is given a rest mass. The energy seems more fundamental than the matter, but how can we define it?
Let us define the term “energy” as “everything that exists”. Existence means that there is an energy there, and there is nothing that does not fall into energy. There is some interaction between energies, showing diverse distributions and motions of energy. They indicate other physical properties. Contrary to the existing physics, we derive various physical properties from energy. The space of universe is the region where energy exists.
Let’s assume that energy is vibration in multiple dimensions. There is no absolute time, but the dimension that shows the longest period of vibration among the all dimensions can trace movements in the other dimensions, that is, it can function as time. The definition of the “time” is given in Features of time .
The properties and definition of energy are premises that serve as a starting point. Together with the force working between two energies to be considered next, we call them as the Energy Circulation Theory. This theory is just a hypothesis. However, it brings very important consequences and successfully solves the unsolved problems of existing physics. Let us take a walk to a completely novel physics capriciously.

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#3 (2022.03.16) (revision 2024.09.23)

Intrinsic energy and mass

In Newtonian mechanics, the kinetic energy is proportional to the mass and the square of velocity. In the theory of relativity, the total energy is the product of the mass and the square of light speed. If the energy is a vibration in multiple dimensions, it would be regarded as a motion of an intrinsic energy. The energy circulation theory claims that the quantity of energy can be expressed as the product of an intrinsic energy and the square of its velocity as the main principle (hypothesis). \[ E=E_0 v^2 \] The intrinsic energy may be defined as mass. However, the velocity depends on how the target direction is taken, and the same energy can be expressed by a different intrinsic energy and velocity E = E₁v₁² = E₂v₂². If we take a common value of velocity for any intrinsic energies, the total energy and the intrinsic energy get in proportion. We define such intrinsic energies that move at the common velocity c, which is the current light speed, as the “mass” in a narrow sense E = mc².
A linearly moving particle can be expressed as a helical motion of the intrinsic energy (mass) m moving at c. The velocity is the vector sum of the circular component C_r and the linear component v. The same particle can be also expressed as a linear motion of another intrinsic energy M at v. \[ E=m c^2 =m({C_r}^2 +v^2) = Mv^2 \] In the first version of this page, I explained that the energy of a particle is increased when it is accelerated by receiving a force as below. \[ E=m_0 c^2 + E_k = (m_0 + \Delta m)c^2= mc^2 \] However, it was wrong. By receiving a force F, its kinetic energy is increased, but the particle exerts the force -F to the counterpart, resulting in a decrease in potential energy. The total energy does not change even if it receives a force and gets accelerated. \[ E=m_0 c^2 +E_p+ E_k =E_r+ E_k = m_0 c^2 \\ E_k =-E_p \, , \, \, \, E_r=m_0 c^2 +E_p \] The kinetic and potential energies cancel out each other to be zero. The rest energy is defined as the total energy minus the kinetic energy. The potential energy is incorporated in the rest energy as shown by the above formula. For the explanation, please see the summary file “Dynamics by ECT-Summary” and/or the book “Novel dynamics by ECT” for full text.

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#4 (2022.03.17)

Force working between energies

What kind of force works between two energies? Gravity is a known force, which works based on the magnitude of energy. The gravitational force is too weak to control the expansion of the universe or to allow an energy circulation giving elementary particles. I also examined a possibility of the electromagnetic force or nuclear force, but reached to think that there should be a more fundamental and universal force.
I proposed that there is a force that works based on the energy movement, that is, momentum, not the magnitude of energy. This is the other main principle (hypothesis) of the energy circulation theory, and is defined by the following equation. (Momentum is defined from energy and velocity E = pv.)

The force works in the distance direction, and a plus value indicates a repulsive force and a minus force is attractive. _rp denotes the orthogonal component of momentum to the distance direction. The fundamental force is proportional to the inner product of _rp₁ and _rp₂, and inversely proportional to the square of the distance.

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#5 (2022.03.18)

Fundamental force and energy circulation

Two antiparallel energy pieces moving in opposite directions in a plane attract each other by the fundamental force, and tend to make a circular motion. We call a continuous and uniform energy in circle as the "energy circulation". The intrinsic energy M is the sum of local intrinsic energies m in the whole circumference. At a circulating velocity V_c the energy is E = MV_c² and the momentum is p = MV_c. A local area within the circumference receives the following force from the whole circumference. μ is the radius, Δp is the momentum of m. \[ _c F_\perp = -K_f\frac{p \Delta p }{2\pi \mu^2} = -K_f\frac{E \Delta E }{2\pi V_c^2 \mu^2} = -K_f V_c^2 \frac{Mm }{2\pi \mu^2} \] We call this force as the “intra-circulation force”. This centripetal force balances with the centrifugal force and make a circular motion. The radius is proportional to the total energy E (see p18 of Galactic evolution).
An energy circulation disperses its energy on the circumference, and interacts with another energy circulation, which will be explained later. Therefore, an energy circulation can be treated as a particle. We define the term “particle” as an energy circulation. Particles do not shrink to infinitesimal but spread according to the energy value. There exists no black hole, which is expected in the standard physics. What is said to be an observed black hole is an energy circulation with high energy.

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#6 (2022.03.19)

Interactions between energy circulations

Since the energy circulation has momentum at each point on the circumference, plural circulations interact with each other by the fundamental force. This is called the "inter-circulation force". The interaction in a common plane is called the "flat interaction". The coaxial and vertical action is called "orthogonal interaction".
The flat interaction of two circulations in a same direction (angular frequency) is repulsive until they are adjacent to each other, and attractive at a distance beyond that, causing them attached each other. Its example is a nuclear force holding an atomic nucleus together.

Opposite directional circulations (conjugated) show an attractive force until they get adjacent and a repulsive force after that. An example is a decay of a particle. The so-called strong nuclear interaction including the both cases is a flat interaction of energy circulations.
With an orthogonal interaction, opposite directional circulations are attached each other by the attractive force and form a coupled conjugate pair. A quantum particle like nucleons includes a single circulation and / or coupled conjugate pair (double circulation). An example of same-directional interaction is an orthogonal separation of an energy circulation. A high-energy one is a division of a galactic seed (energy circulation to develop to a galaxy) to two seeds. A low-energy example is the decay of the smallest single circulation to a neutrino and an antineutrino, the repulsive force between which is the so-called weak nuclear force.
In standard physics, the mass (energy) of elementary particles cannot be explained and measured values are used. A proton is said to consist of three quarks, but its mass cannot be explained by quarks. The energy circulation theory clearly shows the interactions and structures of quantum particles, and demonstrates in concrete changes in force and potential energy in the process of galactic evolution. Quantum particles　Gamma-ray burst

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#7 (2022.03.20)

Cosmic separation to two universes

The standard model insists that the beginning of the universe was a high-temperature energy explosion, the Big Bang. Pair production from the energy to matter and antimatter occurred, and most of them returned to energy by annihilation. A little more matter was generated than antimatter, and a matter-dominant universe was formed. In a collision experiment of accelerated particles, is non-matter energy really once generated, from which new particles are created? The model introduces particle generation and particle annihilation too conveniently without enough rationale.
In the energy circulation theory, the cosmic evolution begins with the cosmic separation to two universes. The initial energy is vibration in multiple (M) dimensions. The real nature of a one-dimensional vibration is a circulation in a 2-dimensional plane shown by \[ \mu [\;\cos \omega t\;\;\; \sin \omega t \;] = \mu (\cos \omega t + i\sin \omega t) = \mu \varphi \;. \] Its coupled conjugate pair with a circulation φ* of the frequency −ω shows a one-dimensional vibration but is symmetric as circulation. The initial energy can be expressed as M/2 pairs of coupled conjugate energy circulations.
A one-dimensional extension separates two pairs of coupled conjugate circulations. The division in the plain including the 1D extension is a flat separation, and the other is an orthogonal one. Asymmetrical circulations are shown in a total of four dimensions. The pairs in the rest dimensions remain as a coupled pair even after the separation while the energy gets to a half. The symmetrical initial energy separates to two universes, each of which is asymmetric in four dimensions. Vibrations in the rest dimensions are of pair-symmetry and orthogonal to the 4D space. Therefore, they vest intrinsic energies in the 4D space, but do not work the fundamental force since their momentums are zero. The decoupled 4D space expands because the balance with the centrifugal force is broken, while the space of the rest dimensions does not expand with keeping a constant radius. \[ \text{Cosmic separation:}\;\;\; E \mu_{pre} (\varphi_{12} : \varphi_{12}^* + \varphi_{34} : \varphi_{34}^*)\;\; \rightarrow \;\; \frac{E}{2}\mu (\varphi_{12} + \varphi_{34}) + \frac{E}{2}\mu (\varphi_{12}^* + \varphi_{34}^*) \]

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#8 (2022.03.21)

Universe of 3D surface of 4D sphere

The two energy circulations (frequency ω) generated by the cosmic separation can be expressed in 4D polar coordinates as follows. \[ \textbf{x} = [\; \mu_u \;\;\; \theta_1 \;\;\; \theta_2 \;\;\; \theta_3 \;] = [\; \mu_u \;\;\; \omega t \;\;\; \theta_2 \;\;\; \omega t \;] \] If we express it in 4D Cartesian coordinates, it becomes as below. \[ \textbf{x} = \mu_u [\; \cos \omega t \;\;\; \sin \omega t \cos \theta_2 \;\;\; \sin \omega t \sin \theta_2 \cos \omega t \;\;\; \sin \omega t \sin \theta_2 \sin \omega t \;] \] Taking base vectors e₀ for the radial direction and e₁ for the arc direction with respect to the circulation of θ₁, the energy distribution can be expressed in 3D Cartesian coordinates as follows. \[ \textbf{x} = \; \mu_u (\omega t \textbf{e}_1 \cos \theta_2 + \sin \theta_2 (j\cos \omega t + k\sin \omega t) ) \] e₁, j and k constitute a 3D Cartesian coordinate system. The above formula indicates that the cosmic energy is distributed in a 3D surface of a 4D sphere and its motion. e₁ is linear in the 3D space but an arc in the 4D space. θ₂ expands continuously from 0 to π, and its specific value is one of parameters to show a location.
Due to the expansion of the cosmic radius, the energy circulation becomes unable to maintain a continuous energy distribution. It repeats separation and cyclic decomposition that decomposes to local circulations at the same time over the whole circumference. At this time, it is not the case that the all energy of the universe is separated or decomposed, but pairs of conjugate circulations in the rest dimensions other than the expanding 4 dimensions are uniformly dispersed in the space of the universe. We divide the energy of the universe to the symmetric part as the "space energy" and the asymmetric part as the "apparent energy" (explanation in p44). The space energy spreads uniformly in the 3D space, and the apparent energy shows the initial circulation shown by the above equation, then separates and decomposes with the space expansion.

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#9 (2022.03.22)

Space energy and spacia

The space energy is the rest energy part of the cosmic energy, consisting of conjugate pairs of energy circulations in the rest dimensions other than the 4D dimensions. They fill the 3D space and are stationary. Because each one is a coupled pair of conjugate circulations, the circular momentum is zero and it does not receive the fundamental force. The kinetic energy part of the cosmic energy is the apparent energy, which can be regarded as vibrations in the medium; space energy. What we observe is an apparent energy, and we cannot observe the space energy; the medium. (Refer for details to p44) Let us take the coupled conjugate pairs in the rest dimensions as the intrinsic energy, and express the space energy as its motion in the 4D space. The 3D surface space mentioned in the previous page has the thickness in the 4D space in the radial direction e₀ due to circulations of the intrinsic energy derived from the rest dimensions. We define the space energy in a unit region of the 4D sphere with the thickness as the "spacia". With the space expansion, the radius of the spacia μ₀ does not change, and the number of spacias increases. We call the radial direction e₀ of the 4D sphere as the "hidden dimension" and the 3D surface as the "space dimension". Considering the nature of the space energy as a medium as well as its distribution, let us express a spacia as a coupled pair of conjugate circulations in hidden-space dimensions. The imaginary part shows the location in the hidden dimension H, and the real part shows that in the space dimension X. \[ \text{Spacia :}\;\;\; E_\mu [\; X \;\;\; H \;] = E_\mu \mu_0 (\varphi_0 + \varphi_0^*)\;, \;\;\; \varphi_0 = \cos \omega_0 t + i\sin \omega_0 t \] There is only one layer of spacias in the hidden H dimension, but there are enormous numbers in the space dimensions. X in the above equation can be in any direction in the 3D space, and even divided to plural directions. Energy circulates in as the whole of space dimensions with H.

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#10 (2022.03.23)

Propagation of an apparent energy

As described in the previous page, the spacia is the circulation of the intrinsic energy with the radius μ₀ and the frequency ±ω₀. The circulating velocity is v_c = ± μ₀ω₀. An apparent energy is given by additional circulation of an intrinsic energy in a spacia. If the additional circulation is of an integral multiple of ω₀, it can be stationary in spacias. The minimum additional circulation of energy to be quantized is called the "single circulation". The intrinsic energy of one circulation among two conjugate ones is additionally circulating, and is referred to as m₀. The circulating velocity of a single circulation is v_c = μ₀ω₀ same as that of a spacia. There are two kinds of circulation planes; hidden-space dimensional and space-space dimensional. The energy distribution and quantity are given as follows. \[ E_{(iS)}[\;X \;\;\; H \;] = E_{(iS)}\mu_0(\cos \omega_0 t + i\sin \omega_0 t) \] \[ E_{(S)}[\;X \;\;\; Y \;] = E_{(S)}\mu_0(\cos \omega_0 t + i\sin \omega_0 t) \] \[ E_{(iS)} = E_{(S)} = m_0 v_c^2 = m_0 \mu_0^2 \omega_0^2 = m_0 c^2 \] The imaginary unit i is a unit vector for the hidden-dimensional direction H or a space-dimensional direction Y, and shows a position in the real space. The circulating velocity v_c is equal to the light speed c. These single circulations iS and S are an elementary circulation composing a quantum particle. A coupled pair of conjugate single circulations is called as the "double circulation" iD or D.
Energy with a lower frequency than ω₀ cannot be quantized as a static circulation. It instead makes the next spacia rotate with stopping the circulation in the original spacia. This is repeated and the energy propagates in the space energy. The propagation speed is the circulating velocity of the spacia, which becomes the phase velocity of the space energy as a medium. A circulation in hidden-space dimensions with a lower frequency than ω₀ breaks and propagates in the space direction, which is the light. The light speed is equal to the circulating velocity of the spacia.
In a propagation of a space-space dimensional circulation, the intrinsic energy moves helically at the speed c, which breaks down into the circular and linear components. The linear component is the propagation speed. The propagation velocity of a neutrino, which is the lowest energy, is close to the light speed. In the case of a galactic seed of high energy, various ratios of the liner and circular components are possible.

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#11 (2022.03.24)

Fundamental constants and varying light speed by time

What are the fundamental constants that do not change by the time course, that is, the space expansion? In the existing standard physics, there are the gravitational constant G, the light speed c, Planck constant h and so on. Are they really basic and invariant by time?
As the space expansion, the volume increases and the energy density decreases, that is, the number of spacias increases and the energy of a spacia decreases. We may consider two possibilities; one is the case that the circulating velocity of the intrinsic energy decreases, and the other is that the intrinsic energy of a spacia decreases. However, there is a problem with the later. The intrinsic energy cannot change continuously because it is quantized as a coupled pair of conjugate circulations in the rest dimensions. Since the space of the universe is expanding almost continuously, we can conclude that the intrinsic energy is invariant and its circulating velocity is decreasing.
The circulating velocity of the spacia is given by v_c = μ₀ω₀, in which μ₀ is invariant and the angular frequency ω₀ changes with the cosmic radius. When the cosmic radius becomes n times, the number of spacias becomes n³ times. The frequency and circulating velocity get 1/n^3/2 times since the energy is proportional to the square of the circulating velocity. Therefore, the light speed c = v_c is a varying quantity by the radius of the universe. This change of light speed is consistent to the general phenomena of waves that the phase propagation velocity is in proportion to the square root of the medium density. (For details, refer to Light speed) (Additional explanation in p46)
In the energy m₀μ₀²ω₀² of an elementary circulation iS or S, the intrinsic energy corresponds to that of a spacia at a specific ratio. Therefore, m₀ is invariant by the space expansion. The energy of a quantum particle decreases by the space expansion like that of the spacia does.
Based on the energy circulation theory, we raise the radius μ₀ of the spacia and the intrinsic energy m₀ of an elementary single circulation as the fundamental constants that do not change by time. The fundamental force constant K_f depends on the speed of intrinsic energy, and is a function of the ratio of the circulating velocity over the light speed. The Planck constant is an invariant constant by time, but is secondary as expressed by m₀ and μ₀ as h = 2π²m₀μ₀² (ref. Light radiation). The elementary charge e is expressed by m₀ and the light speed.

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#12 (2022.03.25)

Space expansion is not accelerating

One of the most important unsolved problems of the existing standard physics is the acceleration of the space expansion speed. It is assumed that there should be a repulsive force that accelerates the expansion and an energy that produces it (dark energy). However, no such energy has been found.
The interpretation of the acceleration of the space expansion is based on the premise that the light speed has been constant since the beginning to the present. As mentioned in the previous page, the light speed is decreasing with the space expansion. The energy circulation theory gives the light speed equation with the cosmic radius as a variable. The observed data (Hubble diagram) of redshift and brightness of supernovae showed an excellent fit to the graph line by the equation for the current radius as 0.7 of the maximum. By the original time (based on relative frequencies in multiple dimensions), the space expansion is decelerating, and by the Observed Time, which is the radius of the universe, the expansion speed is constant (refer to p16 of Hubble diagram) (Explanation in p47 - p51). There is no dark energy to accelerate the space expansion.
The standard physics insists it as an experimentally proven fact that the light speed is not anisotropic and is invariant. Furthermore, the light speed is treated as an absolute invariant and not to change over time. The understanding on the anisotropy of the light speed is based on the Mickelson-Morley and similar experiments. These are interferometer experiments. If the apparatus is in linear motion to the medium, when the light divided to two beams in the parallel and perpendicular directions, reflected at each end mirror and returned to the same position, the phases differ depending on routing. It is correct so far. However, in order to detect a difference in the phase, the two beams are combined and guided to one direction toward the detector.
The existing understanding is that the wavelength of the interference wave should vary by the change in the velocity to the medium, and thus a change in the distance or position of the interference fringe should be detected. In the modern experiments using two-way resonators, it was expected that there should be a frequency change of the difference frequency (beat note). In both cases, however, the two beams are aligned in the same direction in order to detect the interference wave. Because they are in the same direction, two beams even with different phases show the same propagation velocity and the same frequency. In the combined beam wave, the amplitude (brightness) changes based on the variation of phases due to the change in the speed of the device, but the frequency and wavelength do not change. In the Mickelson-Morley experiment, the combined wave passes through both the two adjacent slits and creates a fringe. It is not that each of the parallel and vertical beams passes through a separate slit from the other, but the combined wave, that is, the both beams pass through the both slits. In the measurement of the difference frequency, the beams are completely overlapped.
If we measure a circadian variation of the brightness of the interference wave by a Michelson interferometer, we can obtain information on the anisotropy of the light speed. I wish any physicist would carry out this experiment someday.

(Refer to Michelson-Morley experiment)

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#13 (2022.03.26)

Beginning of wandering modern physics

In the Michelson-Morley experiment, there was detected no change over time in the distance or location of the interference fringe. The fringes were unstable, and sometimes disappeared or revived. It was said due to noise factors such as temperature changes and vibrations, but it should be possible that the brightness of the interference wave fluctuated over time. At an international workshop in 2010 or so, it was presented that they detected a circadian rhythm of the speed of information transmission. Information transmission between a satellite, Chile and the east coast of the US showed a clear circadian rhythm of variation in velocity. Unfortunately, it was not published in the proceedings or a journal after that. It is highly possible that the observation was a circadian variation showing the anisotropy of the light speed.
Following the above results of the Michelson-Morley experiment in late 19th century, physicists concluded, without discussing the detection principle, that the light speed is not anisotropic and that there is no medium for light. Lorentz proposed the Lorentz transformation, in which the passage of time depends on the velocity, in order to satisfy the light speed invariance. Einstein’s special theory of relativity is what the physical meanings are added to this transformation. It starts from the premises that the light speed is invariant and there is no special frame like a medium (principle of relativity). However, by the energy circulation theory, there exists the medium called the space energy for light and other apparent energies, and the light speed varies with the space expansion. The premises of the theory of relativity are wrong. Many experimental results that are said to support the theory of relativity are consistent with the interpretation that the light speed is anisotropic and the passage of time does not change with the velocity. Therefore, they are not support data. Later, the Lorentz invariance became to be considered to be essential for laws of physics. It made the mathematical representation to be more complex.

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#14 (2022.03.27)

Momentum in the hidden dimension

The motion of energy in the hidden dimension H of the 4D space shows a peculiar property as compared with that in the 3D space. First, the size of the hidden dimension is only one layer of spacia, and energy is possible only as a circulation with the radius μ₀. The energy circulation cannot move or expand in the H dimension (can move and prolong in space dimensions). Second, the hidden dimension is orthogonal to any directions in the 3D space. Therefore, we can treat the momentum in H as a scalar charge to the 3D space.
We define the "charge" as between which a force works. The charge for the gravitational force is a rest mass, which is a scalar. The charge for the fundamental force is a momentum and is a vector. Because its charges are vectors, the fundamental force is expressed by the equation including angles shown in p4. For momentums in the hidden dimension, θ₁ and θ₂ in the equation are limited to plus or minus π /2 to any space direction. Since H is one-dimensional, the space distance and the two momentums in H are always in a single plane, that is, θ_p = 0. The fundamental force is given by \[ F=K_f \frac{p_1 p_2}{d^2} . \] This means that we can treat a momentum in H as a scalar charge for interactions in the 3D space.
We can define the “electric charge” as the momentum in the hidden dimension H of an energy circulation in hidden(H)-space(X) dimensions, and the “magnetic charge” as its momentum in the space X direction. The electric charge is a scalar in the 3D space and a vector in the 4D space. The magnetic charge is a vector in either 3D or 4D space.

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#15 (2022.03.28)

Electric charge and electric force

At a local part on the circumference of a single circulation iS in hidden-space dimensions, the centripetal force shown at p5 works. In order to show the force component in the space direction X, we divide the total momentum to two half-circle momentums p_h. The component in X of the force between them is given by the following equation. \[ F_x=-\frac{ 8 }{ π^2 }K_f \frac{p_h ^2}{(2μ_0)^2} = -K_e \frac{e^2}{(2μ_0)^2} \] As mentioned in the previous page, the momentum in the hidden dimension H is the electric charge and the force is the electric force. Not all of p_h is the component in the H direction, but we define the "elementary charge" e as the half-circle momentum p_h for convenience and the electric force constant K_e as below. The single circulation iS has +e and −e charges with the distance 2μ₀ in the space dimension. \[ \text{Elementary charge :} \;\;\; e \equiv p_h = \frac{m_0 c}{2} = \frac{m_0}{2}μ_0 ω_0 \] \[ \text{Electric force constant :} \;\;\; K_e \equiv \frac{8}{\pi^2}K_f \]

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#16 (2022.03.29)

Prolongation of the hidden-space circulation iS

The energy distribution in the space dimension of an iS can be in any direction and even rotate in the 3D space. Furthermore, it can extend and disperse in plural spacias. However, energy is required for an iS to extend because the intra-circulation attractive force described in the previous page works.

Since an apparent energy is provided by an additional rotation of the spacia, an iS rotates the adjacent spacia, which spreads sequentially. The prolongation is limited to odd numbers of spacias. How is the possibility that the alignment of frequencies is not the plus-minus by turns as shown in the figure, but only the plus extension? From the origin of the apparent energy, it is inferred that the rotation spreads like between the connected gears, but not a rotation connected by a belt.
In the prolongation of iS to n spacias, only the potential energy in the space dimension increases, and the circular energy m₀μ₀²ω₀² with the hidden dimension H does not change and is divided to n circulations. The momentum is also divided. The intra-circulation force within a single circulation is given by the following equation. \[ F_x = K_e \frac{(+e/n)(-e/n)}{(2μ_0)^2} = -K_e \frac{e^2}{(2μ_0n)^2} = -K_e \frac{e^2}{d^2} \] At each junction of circulations, the forces are set off to zero, and the above force remains only at the two ends. This force is equal to the force between +e and −e charges with the distance d. This is the true feature of the electric charge. Electric charges always exist as a pair of plus and minus, and there is no isolated single sign charge. Most of what we observe as an electric force is the attractive intra-circulation force of a prolonged circulation, as shown above. While the two end charges of a prolonged circulation receive an electric force from an electric charge of another circulation, the charges are extremely small. In the case of an electron and proton in an atom, the number of circulations n by prolongation is about 10⁴, the charge is 10^-4 times of e. The force with an outer charge is 10^-8 times that of the intra-circulation force with the same distance. The electron charge −e does not exist as a point charge but is distributed evenly in the range up to the proton. The positive charge of the proton is also dispersed between the electron. Properties expressed by an electric charge in the standard electromagnetism such as the electric potential energy should be expressed by a polarization not an electric charge.

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#17 (2022.03.30)

Rotation of prolonged circulation n-iS

There are two kinds of rotations of a hidden-space dimensional circulation; one is around a space-dimensional axis, and the other is around a hidden-dimensional axis. If we rotate a circulation in H-X around a space dimensional axis Z, it rotates not only in X-Y but also in H-X. Since the energy in the H dimension is quantized with the frequency ω₀, the energy by the additional rotation transforms to propagate as vibrations in Y and H to X at the velocity c. This is the light, in which vibrations of the electric charge and the energy location in Y propagate. A mechanical rotation around a space axis of a hidden-space dimensional circulation causes a light radiation (bremsstrahlung), and loses an energy.
On the other hand, in a rotation around the hidden dimensional axis H, there is no rotation in H, that is, no vibration of an electric charge. Since any directions in the 3D space are orthogonal to H, the plane of rotation can be in any direction. With keeping the velocity of the intrinsic energy as the light speed c, it can be divided to individual components in X, Y and Z; v² = v_x²+v_y²+v_z² = c². There is no energy radiation in a rotation around the H axis.
Let us call the prolonged circulation n-iS (n is an odd integer ≥ 1) as the "elementary charge pair (eCP)". Examples of a rotation around H of an eCP are the magnetic charge rotation and the electron orbiting in an atom. The rotation around the hidden dimension H includes a rotation in space dimensions, and shows a rotating magnetic charge.
The composite of plural elementary circulations and the plus end of an elementary charge pair in a spacia is the proton. That of a neutrino and the minus end is the electron. They form a hydrogen atom. Because the energy of proton is high, the plus end is almost stationary, around which the minus end is orbiting. Since the axis of the rotation is the hidden dimension H, no light radiation occurs and no energy is attenuated. In the existing physics, “the electron orbiting is quantized and does not change continuously” or “the electron is indicated by a wave function as an exiting possibility and does not orbit” are raised as reasons for no emission of light. However, it is the real reason that the rotation is around the hidden dimensional axis. (We will see later the problems of the existing quantum mechanics and amendments by the energy circulation theory. Re: Quantum mechanics) (Explained from p22 to p32)

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#18 (2022.03.31)

About the light

As mentioned in the former page, light is radiated by a rotation of a hidden-space dimensional circulation around a space dimensional axis. Virtually consider a rotation of iS circulating in H-X around Z axis by ω. The energy by the rotation is ΔE = m₀μ₀²ω². This energy is not that of one rotation but the value per a unit time (second) for continuous rotation. By the rotation around the Z axis, only the plane X-Y rotates in the 3D space but the plane X-H also rotates in the 4D space. In the X direction, the energy is already quantized with vibrating at ω₀ by iS before rotation, and additional vibration is impossible. Therefore, the rotation breaks and the energy divides to two linear motions to +X and -X directions instead of vibration, and propagate to adjacent spacias. This energy is not quantized as a circulation and propagates at the circulating velocity of spacias c. The virtual rotation converts to two light beams to opposite directions. The energy of each light beam is a half that of the additional rotation. The energy of one cycle of light is defined as the "light quantum" or “photon”. The energies of a light and a light quantum are as follows. ν is the frequency ω = 2πν. The Planck constant is given by m₀ and μ₀. \[ \text{Light: }\;\;\; E_γ = \frac{m_0}{2}μ_0^2 ω^2 = hν^2 \;, \;\;\;\; \text{Light quantum / Photon: }\;\;\; E_q = \frac{E_γ}{ν} = hν \] \[ \text{Planck constant: }\;\;\;h = 2π^2 m_0 μ_0 ^2 \] The energy location moves at the light speed in X, but the displacement vibrates at sinωt in H and Y. The amplitude in H is μ₀, but that in Y expands to ω₀/ω times because the propagation speed is the light speed μ₀ω₀. \[ H = μ_0 \text{sin} ωt \;, \;\;\;\; Y = \frac{ω_0}{ω} μ_0 \text{sin} ωt \] The momentum in H is the electric charge and that in Y is the magnetic charge. Both of them vibrate with cosωt. Electric and magnetic charges show the maximum when the displacement in Y is zero and get zero when it is the maximum. To be exact, this magnetic charge is the component in the Y direction. The total value in the space dimensions is a vector consisting of X and Y components. \[ |\textbf{e}_\gamma |= |\textbf{b}_\gamma |= e_\gamma \cos{\omega t} \; , \;\;\; e_\gamma = \frac{\omega}{\omega_0}e \] Thus, the light is the propagation of fluctuations in the electric charge and the magnetic charge at the light speed, and can be called as an electromagnetic wave. The photon is the energy for one cycle, but not a particle. The location of the light is moving with vibrating in a vertical direction. (For details, refer to Light radiation)

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#19 (2022.04.01)

Elementary circulation and quantum particle

The spacia, a 4D sphere, has six planes, which are orthogonal to each other; three in space-space dimensions and three in hidden-space dimensions. In a spacia, it is possible to contain energy circulations in these planes. Such an energy circulation, which can enter on the planes, is called an elementary circulation. We define a composite of energy circulations in one spacia as the "quantum particle".
The elementary circulation of the lowest energy is the single circulations; S or iS. When an S and another S, or an iS and another iS, enter the two planes, they rotate and form a coupled pair of conjugate circulations as shown in the figure (a). We call it the "double circulation" and express it as D or iD. A double circulation can also occupy a plane in a spacia as an elementary circulation. Their excited forms D^# and iD^# (with the frequency 2ω₀) also can be an elementary circulation.

In the case of S and iS, they cannot rotate around the common axis X to a mixed direction of H and Y, so they attach each other as shown in the figure (b). The concrete compositions of elementary circulations for major mesons and baryons are described in Quantum particles.
In the standard model, 17 kinds of elementary particles are listed as particles that cannot be divided further. However, the grounds for their existence are weak, and related charges are given too conveniently. In the energy circulation theory, what corresponds to the elementary particles is a single circulation. The theory successfully demonstrates the compositions and interactions of quantum particles without a leap of logic. From the next page onward, we will see the beta decay of a neutron as an example.

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#20 (2022.04.02)

Structure and stability of neutron

The neutron is stable in a nucleus, but is unstable alone and decays to a proton with a lifetime of 15 minutes. What is the cause of this stability property? The energy circulation theory claims the composition of energy circulations for a neutron as follows. \[ \text{Neutron :} \;\;\; n^0 = (D^\text{#}, \;D, \;D, \;iS) \] Why is the composition? Scrutinized the relative energy (mass), electric charge, spin and decay reactions of the major particles, the compositions of all particles were determined so that all of them were as much closest to the measured values. D^# is an excited form (double the frequency) of D and is commonly included in baryons. iS is electrically polarized but is neutral as a whole. (Refer for details to Quantum particles)
The double circulation D is the coupled pair of conjugate circulations S:S. Once the two circulations are separated to the adjacent position by the flat separation, a repulsive force works from there and they move away irreversibly. This is the reason why the neutron is unstable by itself. S is the conjugate circulation of S, and has the frequency −ω₀. While we will explain the structure of proton later, there one D is replaced by S and iS is prolonged to form an elementary charge pair with an electron. S in neutron and another S in proton attract each other by the flat interaction and they are attached to each other. The remaining S of the D of neutron can move on two S. This means that a neutron and a proton interchange to the other by exchanging an S, and form a stable nucleus. Below are shown the graphs of the force and the potential energy versus the distance for the flat interaction between one S and two S. As the lower right graph shows, S takes the minimum energy when it is located on either S. When it is far out of them, it shows a crest of energy. Therefore, it stays in the nucleus stably.

The standard model of particles cannot explain the instability of the neutron by itself or its stability in a nucleus.

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#21 (2022.04.03) (revision 2024.09.24)

β decay of neutron: generation of proton and electron

A neutron converts to a free proton, a free electron and an antineutrino by the beta decay. It happens in two steps. \[ \text{(1)}\;\:\: n^0 (D^\text{#},D,D,iS)\;\: + \;\: \Delta E \;\: \longrightarrow \;\: p_f (D^\text{#},D,\overline{S},eCP ) \;\: + \;\: a (S,eCP) \] \[ \text{(2)}\;\:\: a (S,eCP) \;\: \longrightarrow \;\: e_f (H,eCP) \;\: + \;\: \overline{\nu}(\overline{H}) \] \[ eCP = iH_+ \cdots iH_- \] As explained in p16, an iS prolongs to become an elementary charge pair (eCP), the +e charge part of which is expressed as iH₊ and the -e part as iH_-. These are called as a hemi-circulation in the sense as a half-circle. The single circulation in space-space dimensions S is unstable alone, and divides to H and H. They are a neutrino and an antineutrino, which are linearly moving in the opposite directions. The intrinsic energy m₀/2 cannot be quantized, and are helically moving with the radius μ₀ at the light speed (the linear component is close to the light speed). As explained in p19, a hidden-space dimensional circulation attracts with a space-space dimensional circulation. p_f is the free proton, in which the plus end of eCP attaches to an S and the minus end is free. The free proton is so called the ionized proton. e_f is the free electron, in which the minus end of another eCP attaches to H and the plus end is free. The generated free proton and free electron recede each other. However, the free electron captures another free electron, and forms a hydrogen atom. \[ p_f (D^\text{#},D,\overline{S},eCP )\;\; + \;\; e_f (H,eCP) \;\ \longrightarrow \;\; p^+ (D^\text{#},D,\overline{S},iH_+) \cdots e^- (H,iH_-) \] The iH₊ end attaches with an S to form a proton. The iH_- end attaches with an H to form an electron. While each electric charge spreads between the proton and the electron, we regard the place of the neutrino and the minus charge end as the position of electron for convenience. The charge -e of electron is the sum of the all minus charges until the proton.
The first stage of the beta decay is that with addition of energy, the de-coupling of D and the prolongation of iS occur. Once a D separated to S and S attached to each other, a repulsive force works and the potential energy decreases with increase in the distance. Since the energy decrease is greater than the potential energy increase by the prolongation of the electric charge pair, the pieces continue to move away after the separation. This separation first releases a(S,eCP), which we call "anon". The second stage is that S in the anon orthogonally divides and separates to a neutrino and an antineutrino, which are moving at near the light speed to the opposite directions. The repulsive force that works here is so-called the weak nuclear force. The neutrino attaches to the minus charge end of eCP and form a free electron.
Let us summarize the forces. The force in the D separation is a flat interaction, which is first attractive with an overlap and then repulsive without an overlap. It is a strong interaction by the standard physics. The force in the iS prolongation is an electric force, which is an intra-circulation force. The force in the S division/separation is an orthogonal interaction, which is a weak interaction by the standard physics.
The existing standard model explains the essence part of this beta decay as that a d quark becomes a u quark, electron and antineutrino by the weak interaction mediated by W^- boson. It is as follows when compared with the essence part by the energy circulation theory.
\[ \text{Energy circulation theory: } \: (D,iS)\; \rightarrow \; (\overline{S},eCP) \; + \; a \:,\:\:\ \:\ \: a \rightarrow \; e_f \; + \; \overline{\nu} \] \[ \text{Standard model: } \:\: d \; \rightarrow \; u \; + \; W^- \:, \:\:\:\:\:\: W^- \rightarrow \; e^- \; + \; \overline{\nu} \] At first glance, there seem to be a similarity, but they are completely different. In the standard model, a quark is an elementary particle that cannot be further divided. The definition of what is the electric charge is shelved, and an electric charge is assigned to each quark. Furthermore, the charge of d is -e/3 and that of u is +2e/3. There is no basis at all but they request us to accept this as a starting point. They are looking for laws of physics based on this assumption. Furthermore, they request us to accept that W^- is a quantized particle of field mediating the weak interaction and is one of elementary particles. By the way, the rest energy of d (mass is divided by c²) is 4.1 – 5.7 MeV and that of u is 1.7 – 3.1 MeV, they claim. The force mediator W^- boson is said to have a charge of -e and a rest energy of such a huge value of 80 GeV. Based on the gauge field theory, a potential field is introduced. The force based on it and the gauge boson mediating the force by quantization of the field are further introduced. However, there is no rationale or ground for the quarks, which are the setting of the initial state. The gauge field theory, which seems to be mathematical at a first glance, cannot be said to be physically correct unless the definition of the initial state is clear. The current theory should be a virtual mathematics that ignores the reality and starts from an irrelevant and undefined premise.

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#22 (2022.04.04) (revision 2024.09.25)

Wave function showing a location in the real space

As already used in p10 and so on, let us use the notation that we express an energy distribution as Eψ using an energy quantity E and a function to show a position ψ. A stationary single circulation S in space-space dimensions is the circulation of the intrinsic energy m₀ with the radius μ₀ by the angular frequency ω₀. If we let Y-Z be the circulation plane, the energy distribution is shown as follows.
\[ E_{(S)} \; [\;Y \;\;\; Z\;]=E_{(S)}\psi_0=E_{(S)}\mu_0(\cos \omega_0 t + i \sin \omega_0 t) \] While the imaginary unit i is used, it shows the Z direction. When the particle is accelerated to move at the velocity v in the X direction, the energy distribution is expressed as follows, where j is the unit vector of X. \[ E\; [\;X \;\;\; Y \;\;\; Z\;]=E\psi \;, \;\;\; \psi = jvt + \mu_0(\cos \omega t + i \sin \omega t) \] This function ψ shows that vibrations in Y and Z by a frequency ω propagate in X at a velocity v, and is a wave function. Even if it is accelerated by receiving a force, the mass (intrinsic energy) does not change and remains as m₀. (For invariance of total energy by acceleration, please refier to "Dynamics by ECT-Summary" and the book "Novel dynamics by ECT" for full text.) The relation of helical motion is applied to not only elementary single circulations, but also to double circulations and any quantum particles. For any particle in general, if we express the mass by m, the intrinsic energy m is moving at the light speed, where its circular component is C_r=μ₀ω and linear component is v. \[ E=m c^2 = m(C_r^2 + v^2) = m(\mu_0^2 \omega^2 + v^2) \] The above ψ is a 3D wave function, but it can also be displayed as a sum of two plane waves in X-Y and X-Z planes. Although the plane X-Z is shown by an imaginary number, it simply means that the plane is orthogonal to the X-Y plane. The angular part kx - ωt = k(x - vt) shows the progress of the wave at the velocity v. Both the 3D display and the plane wave display show the same wave function. \[ \psi = \psi_1 + \psi_2 = \mu_0 \cos (kx - \omega t) + i \mu_0 \sin (kx - \omega t) \;,\;\;\; (k=2\pi/\lambda = \omega/v) \] This is a wave function of exactly the same form as a solution of the wave equation in the quantum mechanics. As explained above, the wave function ψ shows a distribution and helical motion of energy in the real space even if it contains an imaginary part.

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#23 (2022.04.05)

Orbiting of an energy circulation

When a high-energy circulation in space-space dimensions makes a linear motion, its radius μ gets smaller. However, the elementary single circulation S and the hemi-circulation H keep the constant and minimum radius μ₀ regardless of the linear velocity. Therefore, the aforementioned wave function has little utility value as far as it is in a linear motion. Since the radius is constant, it is enough to express that it is moving at a speed v. However, if the linear motion part makes a circle, a new restriction comes out. A wave function as an acceptable energy distribution shows a value of use. To avoid a confusion, we call the original circulation as the "internal circulation" and the circled motion of the linear part as the "orbiting".
When the linear part of the helical motion mentioned in the previous page becomes in circle, the internal circulation and the orbiting with a radius r and a frequency Ω are quantized and the following conditions are imposed. \[ \Omega = v/r \;, \;\;\;\;\; \omega = n \Omega \;\;(n: 1,2,3,\;\cdots \;) \] As the orbiting velocity v increases, the frequency ω of the internal circulation decreases and is uniquely determined by the velocity v. \[ c^2= \mu_0^2 \omega_0^2 =v^2 + \mu_0^2 \omega^2 \;, \;\;\; \omega = \omega_0 \sqrt{1-v^2/c^2} \] Furthermore, the orbiting velocity v is also limited. It is uniquely determined by the orbital radius and the above quantum number n as shown below, where R is the relative distance to μ₀. \[ v=\pm \frac{R}{\sqrt{n^2+R^2}}c \;, \;\;(R=r/\mu_0) \] In the case of an atomic electron, the relative radius R is about 10⁴ and the orbiting velocity v is very close to the light speed c. In addition, the centrifugal force and the centripetal electric force balance, so that only a radius of limited values is allowed.
In the case of iS in H-Y, the frequency in H remains ω₀ and does not change even if it makes a linear motion, but the frequency in Y becomes the same ω as S. Therefore, the wave function and its characteristics described above and in the previous page can be applied as they are by replacing the circulation in Y-Z with the vibration in Y. Since the frequency in H does not change, the electric charge does not change even if iS moves linearly.

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#24 (2022.04.06)

Characteristics of wave function and that for orbiting

The wave function ψ we mentioned so far shows a location in the 3D real space, but it also has an important feature. That is, ψ is determined only by the velocity v and is invariant to the energy value E. Therefore, ψ is common for all energy circulations with the radius μ₀, that is, elementary circulations. Since all quantum particles are a composite of elementary circulations, the wave function is common for any type of energy of any particle. In fact, the existence position is the same for all kinds of energy such as total energy, rest energy, kinetic energy, and intrinsic energy, and indicates that energy is at the position. We can write as Eψ, E_rψ, mψ, pψ etc. for energy location using the type of energy we target. Since this feature is based on the fact that a wave function shows an energy existence position, it also holds for orbiting of an energy circulation.
The information we want to know on an orbiting particle (energy circulation) is not about the internal circulation but about the orbiting; the radius r and the frequency Ω. The solution of the Schrödinger equation for electron in the existing quantum mechanics is also a wave function of an orbiting motion. Let us express the wave function of an orbiting in the X-Y plane using the following circular function φ.
\[ \psi_{xy} = r (\cos \Omega t + i\sin \Omega t) = r \varphi_{xy}(\Omega) \] If Ω and r are known, the frequency ω and the velocity v of the internal circulation are determined as shown in the previous page. If the orbiting is in a two-dimensional plane, Ω is a scalar. In the case of an atomic electron, the orbiting can further rotate in the Y-Z plane. A new quantization condition is imposed to this rotation. In such a three-dimensional orbiting, the frequency becomes a vector, and the motion can be expressed as follows as a general notation. This orbiting wave function is shown by a combination of the amplitude r_k and the vibration function φ_k (trigonometric function in which the circulation is read as a one-dimensional vibration) in each direction of X, Y and Z. \[ \psi_{xyz} = R(x,y,z) \varphi_{xyz}({\bf \Omega}) = [\;X \;\;\;Y \;\;\;Z\;] = [\;r_x \varphi_x(\Omega_x) \;\;\; r_y \varphi_y(\Omega_y) \;\;\; r_z \varphi_z(\Omega_z) \;] \]

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#25 (2022.04.07)

Energy of atomic electron

As mentioned in p21, the electron is what a neutrino, which is a hemi-circulation H, is attached to the minus end of an elementary charge pair. There are two types of the energy of the electron depending on the target direction. For a motion in the orbiting direction, the energy is limited to that in the spacia, where the minus charge end is located. It can be practically regarded as energy of only a neutrino. \[ \text{Orbiting direction: } \;\;\; E_{(e)} = \frac{m_0 c^2}{2} + \frac{E_{(n-iS)}}{2n} \simeq \frac{m_0 c^2}{2} \;,\;\;\;\;(n\simeq 10^4) \] \[ \text{Prolonged elementary charge pair: } \;\;\; E_{(n-iS)} = m_0 c^2 + \Delta E \] For the radial direction, the energy is the sum of a half the energy of the prolonged charge pair and that of the neutrino. \[ \text{Radial direction: } \;\;\; E_e(r) = \frac{m_0 c^2}{2} + \frac{E_{(n-iS)}}{2} = m_0 c^2 + \frac{\Delta E}{2} = m_0 c^2 + U(r) - U(2\mu_0) \] The energy ΔE/2 added to the electron is the difference in the electric potential energy.
The above is the total energy. On the other hand, the rest energy is an energy component orthogonal to a target direction. For the orbiting direction, the internal circulating velocity C_r of the neutrino, which is in the orthogonal direction, is extremely small whereas its orbiting velocity v is close to the light speed c. This is the reason why the electron mass is generally regarded so small as 0.5 MeV/c². For the radial direction, the total energy is the orthogonal component, that is, the rest energy. However, the radial velocity of an atomic electron is always zero. Therefore, there is no chance for the rest energy to be treated as an object for acceleration.
The important point in conclusion is as follows: For the orbiting direction, which is the target of a motion for the centrifugal force, it is enough to consider only the neutrino. In the radial direction, the electric force and the electric potential energy are determined only by the elementary charge pair as a function of the distance.

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#26 (2022.04.08)

Quantization of atomic orbital and its radius

An orbiting of an atomic electron in the X-Y plane can further rotate in the Y-Z plane. In one orbital circulation, there is a quantization condition of ω = nΩ for the frequencies of the internal circulation and the orbiting as explained in p23. The following quantization condition is required for a combination of the orbiting and the additional rotation. m is the number of circulations (orbiting + rotation). \[ \omega_{nm} = nm\Omega_{nm} \;\;\; (n=1,2,3 \cdots )(m=1,2 \cdots \leq n) \] The electron velocity v is close to the light speed c even if ω changes several times. We can treat the speed v as a constant for the centrifugal force. \[ \omega = \omega_0 \sqrt{1-v^2/c^2}\;, \;\;\;\; v=\pm \frac{R}{\sqrt{n^2+R^2}}c \approx \pm c \;, \;\;(R=r/\mu_0 \approx 10^4) \] The orbiting velocity is the electron velocity v divided by the number of circulations m. \[ v_{orb}=r_{nm}\Omega_{nm}=v/m \] Since the centrifugal force and the attractive electric force are balanced, we get the following equation, where m_e is the rest mass of the electron (for the orbiting direction). \[ \frac{m_e v_{orb}^2}{r_{nm}} = \frac{K_e e^2}{r_{nm}^2}\;, \;\;\; r_{nm} = \frac{K_e e^2}{m_e}\frac{1}{v_{orb}^2} \] Substituting the formula of the orbiting velocity to this, we obtain the following equation as the orbital radius. \[ r_{nm} = \frac{K_e e^2}{m_e}\frac{m^2}{v^2} \approx \frac{K_e e^2}{m_e c^2}m^2 \equiv K_r m^2 \] Here was obtained a very important relationship. The radius of an atomic orbital r_nm is independent of n, but is proportional to the square of the number m of circulations. Since the electric potential energy is kept constant in orbiting of an electron, the radius of an atomic orbital does not change with time.
In the existing quantum mechanics, the energy and radius of an atomic orbital are set to depend on the principal quantum number n (corresponding to n above). In addition, they do not regard the electron velocity as almost constant, but allow its variation. They request that the changes of the electric potential energy and the kinetic energy of an electron are offset. As explained above, the change in the electron velocity is extremely small and it is almost constant as the light speed. In addition, the neutrino, which bears the mechanical aspect of the electron, does not change in its energy even if its velocity varies because the speed change is offset by that of the internal circulating velocity.

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#27 (2022.04.09)

Wave functions of S and P orbitals

Next, let us see a specific wave function of an atomic orbital. In the case of the quantum number n = 1, m is limited to 1, and the orbital is 1S. n = 2, m = 1 is the 2S orbital. Its orbiting frequency is different from that of 1S, but the radius is the same in both 1S and 2S. \[ \text{1S orbital :}\;\;\;\; \psi_{1S}=[\;X \;\;\; Y \;\;\; Z\;]= r_s\;[\;\cos \Omega_{11} t \;\;\; \sin \Omega_{11}t \;\;\; 0\;] \;.\;\;\; \omega_{11}=\Omega_{11} \] \[ \text{ 2S orbital :}\;\;\;\; \psi_{2S}=[\;X \;\;\; Y \;\;\; Z\;]= r_s\;[\;\cos \Omega_{21} t \;\;\; \sin \Omega_{21}t \;\;\; 0\;] \;.\;\;\; \omega_{21}=2\Omega_{21} \] The orbital of n = 2 and m = 2, which is additionally rotated and quantized in the Y-Z plane, is 2P. Its wave function is as follows. \[ \text{2P orbital :}\;\;\;\; \psi_{2P}=[\;X \;\;\; Y \;\;\; Z\;]= r_p\;[\;\cos \Omega_{22}t \;\;\; \sin \Omega_{22}t\cos\Omega_{22}t \;\;\; \sin \Omega_{22}t\;] \] \[ = r_p\;[\;\cos \Omega_{22}t \;\;\; \frac{1}{2}\sin 2\Omega_{22}t \;\;\; \sin \Omega_{22}t\;] \] \[ r_p = m^2 r_s = 4 r_s \;,\;\;\; \omega_{22}=nm\Omega_{22}=4\Omega_{22} \] The formula for p orbital was wrong. I will explain in the future after publication. The corrected formula is below. \[ \psi_{2P}=[\;X \;\;\; Y \;\;\; Z\;]= r_p\;\frac{[\;\cos 2\Omega_{22}t \;\;\; \sin 2\Omega_{22}t \;\;\; \sin \Omega_{22}t\;]}{\sqrt{1 + \sin^2 \Omega_{22}t}} \]
The radius r is given from m by the formula in the previous page. The orbiting frequency Ω is also obtained from the relation of (ωμ₀)² + (Ωr)² = c² = (ω₀ μ₀)². Therefore, given n and m, the wave function of an orbital is uniquely obtained. The electric potential energy U(r) of an electron is proportional to -1/r, that is, -1/m². The shapes of the S orbital and the P orbital are shown below. (The figure is deleted. Corrected one will be in futre.)
In the existing quantum mechanics, a wave function is divided into a part that does not include time and a part including time. The time-independent part (corresponding to R(x,y,z) in p24) is obtained from the wave equation that does not include time. The lowest orbital, for instance, is basically the same as the above 1S orbital, but it is given a spherical symmetry. In the energy circulation theory, an orbital shows a stationary wave including time, but an orbital in the existing quantum mechanics shows only an amplitude. It is not possible to unconditionally give a spherical symmetry to the solution. The above-mentioned S orbital may rotate slowly, but its trajectory for a small number of orbiting is a plane. For P orbitals, the existing quantum mechanics treats the electron velocity v and its radial component as variable by time. However, as already mentioned, v is constant and its radical component is zero.

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#28 (2022.04.10)

Wave equation giving a wave function

As explained in p22 – p27, the wave function, which shows an energy location of a particle in a linear or orbiting motion, is uniquely determined if the linear component velocity v or the quantum numbers n and m is given. Therefore, it is not essential to solve a wave equation but various equations that give the wave function as a solution are possible. In order to compare with the existing quantum mechanics, let us obtain a wave equation corresponding to the Schrödinger equation for a linear motion.
The wave function is a function for location and time, and is shown by a wave number k = ω/v and a frequency in the plane-wave expression as in p22. According to the Euler’s formula, let us express it as an exponent of the base e of the natural logarithmd. This is because the differentiation of an exponential function is simple, and a sum of the power parts can be expressed as a product of exponentials. \[ \psi (x,t) = \psi_1 + \psi_2 = \mu_0 \cos (kx - \omega t) + i \mu_0 \sin (kx - \omega t) \] \[ = \mu_0 e^{(i(kx - \omega t))} = \mu_0 \exp (i(kx - \omega t)) = \mu_0 \exp (ikx) \exp (- i\omega t) \] The first half of the last formula shows an amplitude at each point of x, and the second half shows a vibration of the displacement over time. This is the most common expression for a propagating wave. In the energy circulation theory, the equation of the relation between the velocity v and the frequency ω is obtained. Therefore, we can convert the above equation to that of only a velocity instead of a wave number and a frequency. In the existing physics, however, since the relation was unknown, they tried to express the wave function by a momentum and an energy instead of a wave number and a frequency. Let us perform the same conversion here.
We use E = pv as a relation of a momentum and an energy. This relation holds only for the intrinsic energy m, which is moving at v. The intrinsic energy is not the mass. The two are equal only when the velocity is the light speed v = c. \[ E=mv^2=pv\;\;\;\;\; （m：\text{limited to an intrinsic energy}） \] Next, we use the relation E = hν. This relation holds only for an energy per one cycle, which we call the "energy quantum" E_q, as explained about the light in p18. \[ E_q=h\nu=\hbar \omega \;\;（E_q: \text{limited to an energy quantum}） \; \Rightarrow \;\; \omega = E_q / \hbar \] We can use these two energy relations only in the case to express an energy quantum by an intrinsic energy. The following relation of the momentum is obtained. p_q is the momentum of E_q. \[ p_q= E_q / v = \hbar \omega / v = \hbar k \;\; \Rightarrow \;\; k = p_q / \hbar \] Substituting these formulas of k and ω to the original expression, we get the following wave function. \[ \psi (x,t) = \mu_0 \exp (i(p_q x - E_q t)/\hbar) \] To obtain an equation, a solution of which is this function, take the partial differentials on t and x, and multiply the both sides by i. Then, we get the energy and momentum operators. \[ E_q \psi (x,t) = i\hbar \frac{\partial}{\partial t} \psi (x,t) \] \[ p_q \psi (x,t) = - i\hbar \frac{\partial}{\partial x} \psi (x,t) \] By substituting these operators into the equation for the linear motion component E_v of an energy quantum, we get the wave equation as follows. \[ E_q = m_q c^2 = m_q(v^2 + C_r^2) = \hbar \omega \] \[ E_v=m_qv^2=\frac{p_q^2}{m_q} \] \[ i\hbar \frac{\partial}{\partial t} \psi (x,t) = - \frac{\hbar^2}{m_q} \frac{\partial^2}{\partial x^2}\psi (x,t) \] This equation has a crucial difference compared to the Schrödinger equation. The point is that m_q in the right-side nominator is the intrinsic energy of an energy quantum. Since the frequency ω is determined by the velocity v, this intrinsic energy is determined only by the velocity. A wave function obtained as a solution indicates an energy location and applies to any type of energy not limited to an energy quantum.
In the Schrödinger equation, 2m is at the place of m_q, and m is the mass of individual particles. Therefore, the frequency ω of a solution differs depending on the quantity of an energy. As we will see in the next page, the Schrödinger equation has fatal contradictions.

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#29 (2022.04.11)

Contradictions of the Schrödinger equation

The Schrödinger equation of a particle in a one-dimensional motion is shown below using the energy and momentum operators that are shown in the previous page. \[ i\hbar \frac{\partial}{\partial t} \psi (x,t) = - \frac{\hbar^2}{2m_r} \frac{\partial^2}{\partial x^2}\psi (x,t) \] Following the De Broglie's hypothesis that a particle such as an electron also has the property of a wave like the light has, Schrödinger tried to find the wave (matter wave) associated with a particle. Since this is a wave, he used the following relation for the momentum and the energy. \[ (1)\;\;\; E=pv \;\;(=mv^2) \] By adding the relation of an energy quantum E = ℏω to this, he got the energy and momentum operators by the process described in the previous page. So far, it is a discussion on the matte wave as an energy quantum.
However, he substituted these operators to the below equation that shows the kinetic energy of a particle, and obtained the wave equation. \[ (2)\;\;\; E=\frac{1}{2}m_rv^2 = \frac{1}{2}pv = \frac{p^2}{2m_r} \] While trying to obtain a wave function of a matter wave, he applied the formula (2) for a particle to it. This is clearly a contradiction. He assigned m_r in the equation as a rest mass. Since the matter wave is associated with the matter, we may understand to align the position of the wave to that of the particle. However, it is completely wrong to equate the mass of the matter wave with the mass of the particle. In the derivation by the energy circulation theory described in the previous page, the operators are substituted to the linear motion component E_v = m_qv² = p_qv of an energy quantum.
Furthermore, in the case of an electron, the velocity v is close to the light speed, and the approximation of (2) cannot be used for its kinetic energy. In the energy circulation theory, the kinetic energy, by which a rest mass (mr) is accelerated to v, is given by the following formula. (Refer to Kinetics of an energy circulation) \[ E_k = - \frac{m_r c^2}{2} \log \left(1-\frac{v^2}{c^2} \right) = \frac{1}{2}m_r v^2 \left( 1 + \frac{v^2}{2c^2} + \frac{v^4}{3c^4} + \frac{v^6}{4c^6} \cdots \right) \] As mentioned above, the Schrodinger equation has crucial contradictions. The most serious point is that the mass in the equation is set to be the mass of a target particle.

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#30 (2022.04.12)

Summary of the new quantum mechanics

Up to here so far, we have discussed the new quantum mechanics based on the energy circulation theory. Now, let us summarize its key features.

(1) Stationary energy circulation (particle)

The energy circulation is a uniform and continuous energy, which spreads on a circumference. It is circulating, and can be treated as a particle. The centrifugal force and the centripetal force due to the intra-circulation interaction by the fundamental force are balanced. Its radius is proportional to the amount of the energy. The minimum radius, with which an energy circulation can be stationary, is μ₀; the radius of the spacia, and forms an elementary circulation. A single elementary circulation is what in which the intrinsic energy m₀ is circulating at the velocity μ₀ω₀. Its energy location can be expressed by the following circular function (wave function). The imaginary unit i indicates a direction in the real space, which is orthogonal to the real part.
\[ \psi = \mu_0 (\cos \omega_0 t + i\sin \omega_0 t) \;, \;\;\;\; E = m_0 \mu_0^2 \omega_0^2 \]

(2) Elementary circulation in a linear motion

When a particle of an elementary single circulation is accelerated to move at v linearly, the intrinsic energy m₀ helically moves at the light speed c = μ₀ω₀. The frequency ω is uniquely determined by the linear component velocity v. The wave function of this motion is shown by the 3D expression or as two plane waves. The plane waves can be also expressed by the energy quantum and its momentum instead of the wave number and frequency. \[ \psi = jvt + \mu_0(\cos \omega t + i \sin \omega t)\;. \;\;\; \omega = \omega_0 \sqrt{1-v^2/c^2} \] \[ \psi = \mu_0 \cos (kx - \omega t) + i \mu_0 \sin (kx - \omega t) \] \[ = \mu_0 \exp (i(p_q x - E_q t)/\hbar) \] \[ E=m_0 c^2 = m_0(C_r^2 + v^2)= m_0({\mu_0}^2 \omega^2 + v^2) \]

(3) Wave equation for a linear motion of a particle

The wave equation that gives the above wave function is as follows. m_q is the mass of the energy quantum. \[ i\hbar \frac{\partial}{\partial t} \psi (x,t) = - \frac{\hbar^2}{m_q} \frac{\partial^2}{\partial x^2}\psi (x,t) \;,\;\;\; m_q = E_q / c^2 = \hbar \omega / c^2 \] Solutions of this equation includes all values of the amplitude not limited to μ₀. However, the amplitude of the wave equation for all particles, which are a composite of elementary particles (circulations), is limited to be μ₀.

(4) Quantization of an orbiting motion

When there affects an attractive force, the linear motion part orbits, and the orbiting plane may further rotate. The quantization condition for the frequencies of the internal circulation and the orbiting is as follows. m is the number of circulations of the orbiting plus the rotation. \[ \omega_{nm} = nm\Omega_{nm} \;\;\; (n=1,2,3 \cdots )(m=1,2 \cdots \leq n) \] The velocity of an electron is almost the light speed, and can be treated as a constant for the centrifugal force. Due to the balance of the centrifugal and centripetal forces, the radius is proportional to the square of the quantum number m, which is the number of circulations in orbiting. The wave function is expressed by each amplitude and trigonometric function of frequency in respective 3D components.

(For details refier to Quantum mechanics )

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#31 (2022.04.13)

Problems of the existing quantum mechanics

At the beginning of the 20th century, the discovery of the photoelectric effect drew attention to the duality of light as a wave and a particle. According to the energy circulation theory, the linear motion component of the light is the light speed c and the internal circulation component is zero, which means that the light has no particle nature. The gravitational lens effect is due to the fact that the light energy functions as the rest energy for an orthogonal direction to the velocity. In 1924, de Broglie proposed the hypothesis that all particles including the electron have the wave-particle duality like the light has. He proposed that the de Broglie wave, later called a matter wave, accompanies any particle. The wave has the relations of E = pv and E = ℏω like light, and the two satisfy p = ℏk, he argued. In addition, the wavelength / frequency of the de Broglie wave is unique to each particle varying by its energy. The kinetic energy of a particle is E = pv/2, which does not satisfy this relation of de Broglie.
Following the de Broglie hypothesis, Heisenberg succeeded in formulating quantum mechanics as a matrix equation in 1925 and Schrödinger as a wave equation in 1926. The two were later proved to be mathematically equivalent, and both give a same wave function as a solution. The wave function shows a matter wave but it was unclear what the matter wave is in concrete. Schrödinger initially interpreted the wave function to indicate a charge distribution in the real space in the case of the electron. However, Bohr and Heisenberg proposed the probability interpretation that a wave function shows a probability of existence of a particle, and it became widely accepted. It is often explained that the wave function cannot be in the real space because it is a complex number including an imaginary part. However, the imaginary unit i is merely a unit vector for an orthogonal direction to the direction of the real number notation part. The imaginary part can be in the real space. The combination of the real space and the space showing the existing probability is described as one of Hilbert spaces, but this description does not affirm the existing probability.
As explained in p29, the mistake of the Schrödinger equation is that it confuses the mass of a matter wave with that of a particle. He substituted the operators for a matter wave into the kinetic energy E = p²/2m of a particle, and let m be the mass of the particle. This is an obvious mistake; m should be the mass of the matter wave, and the operators should be substituted to E = p²/m. However, it was urged that “this is the de Broglie hypothesis and accepting it is the quantum mechanics”, but this idea is exactly what made the quantum mechanics stray. In the energy circulation theory, the mass in the wave equation is that of an energy quantum, and its linear motion component satisfies E = pv and E = ℏω.
The existence-probability interpretation of the wave function generated further expanded interpretations one after another. A wave function of any amplitude is a solution of the wave equation, and a linear combination of the solutions is also a solution. Here, it evolved into the interpretation that “the wave equation is the essence of the laws of physics, and a specific wave function (eigen function) is selected by an observation”. This interpretation was also widely accepted as the essence of the quantum mechanics. They argue that a particle exists in a state of a linear combination of innumerable quantum states, one of which is selected by a concrete observation. The meaning of the amplitude of each function is ignored, and the absolute value ψψ* of the function is set to 1 by normalization. Why was such a reckless development accepted? They should say because it is based on the probability interpretation. Before that, however, we should scrutinize the de Broglie hypothesis and logically verify the wave equation. A stray similar to that of the anisotropy of the light speed described in p13 began also in the quantum mechanics.

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#32 (2022.04.14)

Fiction of the uncertainty principle

Heisenberg, who advocated the interpretation of the existence probability of the wave function, groped for a background to support it. He focused on the nature of waves, and reported the uncertainty principle in 1927. It claims; when a particle moves, the standard deviation of the position distribution and that of the momentum distribution have the following relation, and it is impossible to give the position and momentum accurately at the same time. \[ \Delta x \Delta p \geq \hbar / 2 \] There is a classical wave property called the uncertainty relation of a wave packet. A stationary wave packet can be formed by superimposing innumerable plane waves. When the wave number spread is increased (waves of various frequencies are combined), the position spread of the wave packet becomes smaller. When the wave number spread is decreased, the position spread becomes larger and approaches to a single plane wave. The two spreads have the following relation. \[ \Delta x \Delta k \cong 4 \] Substituting p = ℏk into this, we can see that it corresponds to the previous equation (meaning of Δ is different between the two equations).
The uncertainty relation is also applied to an energy circulation. When an intrinsic energy m is circulating at a frequency ω, it also can be expressed either as 4m is circulating at ω /2 or as m/4 is circulating at 2ω. Furthermore, it can be expressed as a wave packet, in which harmonic frequency components are combined. Therefore, it is not possible to determine both the position and the wave number (frequency) of local energies at the same time. For the same energy, the frequency (velocity) differs depending on what an intrinsic energy is taken. However, we treat an energy circulation as that its energy location in the circumference; which is the phase, is not specified, and the intrinsic energy evenly spreads throughout the circumference. The position that a wave function indicates is that the radius is constant as μ₀ for the internal circulation without considering positions in the circumference and the position in the linear motion component. Therefore, the uncertainty relation can be ignored for the internal circulation. The location of the internal circulation is fixed to the center while associated with a spread of μ₀. The linear motion position is given by vt, which is a single point at a given time. Therefore, the position of a particle and the wave number (velocity, frequency) can be determined at the same time, and the uncertainty relation is not established. The uncertainty principle does not hold for the position and motion of a particle shown by the wave function.
The uncertainty principle is also explained by the non-commutativeness of the operation in addition to the explanation by the wave packet described above. Consider the following case: When the operator A corresponding to a measurement is applied to an eigenfunction ψ, an eigenvalue a is given, and applying another operator B to the same eigenfunction ψ gives an eigenvalue b. The commutator, which is the difference of values between applying B first to ψ and then A is applied, and applying A first and then B is applied, is shown below. \[ A\psi = a\psi \;,\;\;\; B\psi = b\psi \] \[ AB\psi - BA\psi = (ab - ba)\psi = [A, B]\psi \] If ab - ba = 0, the operators A and B are commutative, and we can measure A and B at the same time for ψ. However, if it is not zero, the two operators are said to be non-commutative and cannot be measured at the same time.
The uncertainty principle claims that the operator X for expressing a position and the operator P for expressing a momentum are non-commutative. \[ X\psi = x\psi \;,\;\;\; P\psi = p\psi \] \[ XP\psi - PX\psi = [X, P]\psi = i\hbar \psi \] Here is used a mysterious thing called the position operator that gives a position. Not in relation to another operator such as the momentum one but to indicate a position alone, the position operator should be applied to an eigenfunction. This states that the position of a particle cannot be given at one point from the beginning. Therefore, the commutativeness does not provide a basis for the uncertainty principle, but merely describes it.
Then, why did they introduce such a position operator? This is symbolic to try to justify the probability interpretation of the wave function. They considered that the existence position of a particle is one point (mass point) and that the existence probability spreads to the wave function ψ. For that, they treated the position itself as an operator. In the energy circulation theory, however, the energy location of a particle itself is spread in the whole circumference. There is no need to introduce a position operator, and X = 1 always. The uncertainty principle for a particle does not hold.
Once the uncertainty principle was accepted, it escalated further. Despite using a selfish thing called the position operator, they expanded the range of uncertainty as that all operators cannot be measured at the same time if they are non-commutative to each other. One of them is the measurement of the energy and the time. Because of the uncertainty, they treated it possible to take a high-energy state for an extremely short duration. Accordingly, they allowed a virtual pair production and a high-energy boson mediating a force. The energy is a completely conserved quantity over time, and cannot take a higher value even temporally. When there are multiple energies, the quantity may be concentrated on some, which show a higher energy than the rest, but the total amount of energy is unchanged. The convenient uncertainty principle, combined with the gauge field theory, produced convenient charges, quantized field bosons etc., and ran away to the standard particle model. As mentioned in p21, the standard model is full of problems and has never been successful.
The probability interpretation of the wave function and the uncertainty principle have been believed in blindly for one century, and are treated absolute currently. However, they should be to be validated this timing that the energy circulation theory has been proposed.

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#33 (2022.04.30)

Separation and cyclic decomposition of early circulations of universe

As explained in p8, the distribution of the apparent energy in the 3D space just after the cosmic separation is shown as follows. \[ \textbf{x} = \; \mu_u (\omega t \textbf{e}_1 \cos \theta_2 + \sin \theta_2 (j\cos \omega t + k\sin \omega t) ) \] e₁ is the unit vector in the arc direction of the energy circulation in the 4D space, and forms a 3D Cartesian coordinate system with the other two space unit vectors j and k . With the expansion of the cosmic radius, the early circulations of the apparent energy make separations and cyclic decomposition as shown in the figure below.

The both ends of (a) are connected as a circulation in 4D. It separates to plural discs by the space expansion (b). Each disc separates to plural circulations (c). In this case, the radius of a circulation is proportional to sinθ₂, and the velocity in the e₁ direction is proportional to cosθ₂. θ₂ is a parameter showing a position and spreads in 0 ≤ θ₂ ≤ π . Then, the energy becomes insufficient as a continuous circulation due to the expansion. Each circulation makes the cyclic decomposition, in which orthogonal separations of local circulations occur all at once on the entire circumference (d).
Each circulation, which is resulted from the cyclic decomposition, further decomposes cyclically due to the space expansion. This process repeats in plural rounds, and a huge number of energy circulations are constellated in the vast expanded 3D space. We call these energy circulations as the “galactic seed”. The galactic seeds form galaxies later, and show the distribution of the vast number of galaxies we observe today.
In the above figure, (c) shows a separation of only one of the discs in (b), and (d) shows a decomposition only on one circulation in (c). The frequencies of the circulations in (c) are in the same direction. But their circulating directions facing their moving directions are left-handed in a half and right-handed in the rest half, depending on the value of θ₂. The image in the whole universe is as shown in the figure below.

Circles in the figure indicate superclusters or clusters of galaxies. A blue filled circle has the left-handed helicity, and a red open circle has the right-handed helicity. As shown here, the large-scale structure of the universe is not uniform but is biased, and the helicity distribution of its motion is also asymmetric. In recent years, a rotation of superclusters on a large scale of billions of light years has been reported. It has been also reported that constituent galaxies in a filament structure of a cluster are helically moving as a whole. Furthermore, it has been reported that the distribution of the helicity (spin) of galaxies in the entire universe is not uniform, and that there is a rotation on the scale of the entire universe. The existing standard cosmology cannot explain at all these large-scale motions of the universe, and leaves their causes unknown. However, the energy circulation theory gives these large-scale distributions and motions of the universe quite naturally as shown above.

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#34 (2022.05.01)

Energy expression of a galactic seed

The galactic seed is an energy circulation in space-space dimensions. Its energy is as follows if we express it as that the intrinsic energy M is circulating with the radius R and the frequency Ω. We call the circulation as the “main circulation”. \[ E=MV^2 = MR^2\Omega^2 \] The intrinsic energy M is the sum of local ones ΔM on the circumference. \[ M = \sum \Delta M \;, \;\;\; \Delta E = \Delta MV^2 \] If we take the next lower-level intrinsic energy, the local energy is expressed as follows, where the local intrinsic energy ΔM₁ is locally circulating with a radius μ and a frequency ω. We call this circulation as the "local circulation". \[ \Delta E = \Delta M_1 (V^2 + V_c^2) = \Delta M_1 (R^2 \Omega ^2 + \mu^2 \omega ^2 ) \] The energy of the whole galactic seed is expressed similarly. In the galactic seed, the intrinsic energy M₁ is helically moving. \[ E=M_1 (V^2 + V_c^2)=M_1 (R^2 \Omega ^2 + \mu^2 \omega ^2 )=M_1 V_G ^2 \] \[ E\psi \;,\;\;\; \psi = jR\Omega t + \mu (\cos \omega t + i\sin \omega t) \] Since the galactic seed is quantized as a continuous energy circulation, it has the following relation of the two frequencies. \[ \omega = n \Omega \;, \;\;\; ( n=1, 2, 3 \cdots ) \] Due to the balance of the centrifugal force and the intra-circulation force, the radius of the main circulation is proportional to the energy. \[ R \propto E \] By a cyclic decomposition, the ratio of the local circulation to the main circulation in the radius and that in the frequency vary as follows. \[ \mu / R \;\; \Rightarrow \;\; \text{decrease} \;, \;\;\; \omega / \Omega \;\; \Rightarrow \;\; \text{increase} \] After repeated the cyclic decomposition, the energy of a galactic seed reaches less than a certain threshold. The galactic seed is no longer capable to make a cyclic decomposition. Then, the separation to two galactic seeds starts.

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#35 (2022.05.02)

Separation of a galactic seed

Once the cyclic decomposition has got impossible for a galactic seed, it next divides to two seeds as shown in the figure below.

It is guessed there are two cases where a stable galactic seed (a) gets unstable. If the radius of the main circulation is increased a little by the space expansion, the energy becomes insufficient for the radius. The second case is that a galactic seed loses energy a little by radiation due to the orbiting of small circulations like iS, which are contained in the intrinsic energy. When the energy is insufficient for the radius of the main circulation in these ways, it shrinks to balance with the centrifugal force. It is associated with an increase of the radius of the local circulation. The radius of the main circulation and that of the local circulation should comply with the quantization condition, and can take only discrete values (b). Here, the galactic seed divides to two seeds (c). Between the two main circulations, there works an orthogonal interaction. At the same time, a flat interaction works between the local circulations. In total, the force is repulsive at (c) – (d), and attractive at (d) – (e). At (e), the attractive force of local circulations and the repulsive force of main circulations are set off to zero. At larger distances, the force becomes repulsive.
From (d), the flat separation, in which the two main circulations slide in the same plane, is also possible. It depends on the velocity in the orthogonal direction which separation will take place (to be discussed later).

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#36 (2022.05.03)

Flat interaction of galactic seeds

Let us see the forces and potential energies in the flat separation and in the orthogonal separation after a galactic seed has divided to two ones. Same as the case in p34, the intrinsic energy M₁ is helically moving at the velocity V_G (main circulation component is V) with the radius R for the main circulation and μ for the local circulation. We use the relative distance x to the diameter for the distance between the two galactic seeds. \[ x\equiv d/2R \;, \;\;\; x_0 \equiv \mu / R \;, \;\;\; P_h = \frac{1}{2}M_1 V \] The force by the flat interaction working between the galactic seeds is given by the following formulas. Here we use the approximation to treat one circular momentum as plus and minus two linear momentums, which are orthogonal to the distance direction. \[ F_{flat}(G-G) = Q_G f_{flat}(x) \] \[ Q_G \equiv K_f (V_G) \frac{P_h^2}{\pi^2 R^2} \] \[ f_{flat}(x)= \frac{2x}{\left(x^2 + x_0^2\right)^{3/2}} - \frac{x-1}{\left((x-1)^2 + x_0^2\right)^{3/2}} - \frac{x+1}{\left((x+1)^2 + x_0^2\right)^{3/2}} \] The constant part Q_G varies by the individual galactic seeds. The fundamental force constant depends on the velocity of intrinsic energies. The radius R and the momentum P_h also differ depending on the galactic seeds.
The potential energy is given by the following formula (set zero at the infinite distance). \[ U_{flat}(G-G) = Q_G\left( \frac{2}{\sqrt{x^2+x_0^2}} - \frac{1}{\sqrt{(x-1)^2+x_0^2}} - \frac{1}{\sqrt{(x+1)^2+x_0^2}} \right) \]
Various ratios for the radius and the frequency between the main and local circulations are possible. As an example, let us take the following case. \[ \mu/R = x_0 = 0.1 \;, \;\;\; \omega / \Omega = 4 \] The graphs of the force and the potential energy versus the distance are given below. At x = 1, where the two seeds are adjacent to each other, the potential energy takes a minimum value. The force is zero at x = 0, then becomes repulsive having them recede. It becomes zero again at x = 1, and then attractive at x > 1 having them attach.

By the way in the case of elementary single circulations, which construct quantum particles, the function part is exactly the same as that for galactic seeds. The constant part is given as follows. \[ F_{flat}(S-S) = F_{flat}(\overline{S}-\overline{S}) = Q_P f_{flat}(x) \] \[ Q_P \equiv K_f \frac{p_h^2}{\pi^2 \mu_0^2} \] Unlike the case of galactic seeds, the constant part is an invariant common to all elementary single circulations. The above graphs for the force and potential energy can be applied to nucleons as they are if Q_G is replaced by Q_P. In clustered nucleons of neutron and proton, plural S are attached to each other at x = 1.

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#37 (2022.05.04)

Orthogonal interaction of galactic seeds

For the flat separation in the previous page, the orthogonal distance is treated constant as the diameter 2μ of the local circulation. For the orthogonal separation, we have to consider also the flat interaction of the local circulations (see the figure in p35).

Orthogonal separation of galactic seeds:
Orthogonal interaction of main circulations + Flat interaction of local circulations

The force between two galactic seeds by the orthogonal interaction of the main circulations is as follows. \[ F_{ort}^{main}=Q_G f_{ort}(x) \] \[ f_{ort}(x)= \pi \left( \frac{1}{x^2} - \frac{x}{(x^2 +1)^{3/2}} \right) \] The force by the flat interaction of the local circulations is as below. \[ F_{flat}^{local} = Q_{flat}^{local}f_{flat}^{local}(x) \] \[ Q_{flat}^{local} = Q_G \left(\frac{\omega}{\Omega} \right)^{2} \] \[ f_{flat}^{local}(x) = \frac{2x/x_0}{\left( (x/x_0)^2 + X_0^2 \right)^{3/2}} - \frac{x/x_0-1}{\left((x/x_0-1)^2 + X_0^2 \right)^{3/2}} - \frac{x/x_0+1}{\left((x/x_0+1)^2 + X_0^2 \right)^{3/2}} \] As an example, we take the following values same as the case of the flat separation. \[ x_0 = 0.1 \;, \;\; X_0 = 0.1 \;, \;\; \omega/\Omega = 0.4 \] The total force in the orthogonal separation is the sum of the above two forces. \[ F_{ort}(G-G) = Q_G \left(f_{ort}(x) + 16f_{flat}^{local}(x) \right) \] The potential energy is shown as below. \[ U_{ort}(G-G)= -Q_G \pi \left( \frac{1}{\sqrt{x^2+1}}-\frac{1}{x} \right) + \] \[ 1.6Q_G \left( \frac{2}{\sqrt{(10x)^2 +0.1^2}} - \frac{1}{\sqrt{(10x-1)^2 +0.1^2}} - \frac{1}{\sqrt{(10x+1)^2 +0.1^2}} \right) \] The graphs of the force and the potential energy in the orthogonal separation are shown in the figure below.

The potential energy takes a minimum around x = 0.1, then once increases and reaches a maximum, after that decreases. Once crossed over the energy crest, the two galactic seeds continue to recede. In the case they cannot pass the crest, they go back to the energy trough, from where happens the flat separation described in the previous page.

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#38 (2022.05.05)

Energy radiation from a galactic seed separation

As explained in the previous page, there are two cases for the divided two galactic seeds; to continue to separate orthogonally or to start the flat separation. In the below figure, the graphs of the both separations are shown together so that we can see how the potential energy to vary.

The change of the potential energy is set off by that in the intrinsic energy and that in the linear receding velocity v as well as the energy radiation. If the potential energy decreases without radiation, it results in a decrease of the intrinsic energy and an increase of the separating velocity. In the case that a potential energy decreases only by radiation, there is no change in the velocity, and the intrinsic energy decreases. \[ E = MV^2 - \Delta E_p + \Delta E_p = (M-\Delta M)(V^2 + v^2) + \Delta E \] The intrinsic energy M can be decomposed into various levels of local energy circulations; M₁, M₂, … m. The lowest level is m (mass), which is moving at the light speed in total. Depending on what an intrinsic energy we use, its moving speed for the same energy varies with the following relation. \[ E = MV^2 = M_1 (V^2 + V_1^2) = M_2 (V^2 + V_1^2 + V_2^2) = M_n (V^2 + V_1^2 + V_2^2 \cdots + V_n^2) = mc^2 \] Since the change of the potential energy occurs almost all at once at the same time in all the component circulations, the energy radiation becomes a pulse one.
In the case of space-space dimensional circulations, the ratio of the radiation to the increase in velocity is flexible. The released radiation from them is the gravitational wave. It does not mediate the gravitational force, and the name "gravitational wave" is not adequate. Anyway, what is observed and called as a gravitational wave is a radiation of a vibration in space-space dimensions. Various levels of energy exist for them, and the lowest one is the neutrino.
The radiation from a hidden-space dimensional circulation is the light. Because the hidden dimension is quantized with the radius μ₀ and cannot be extended, a variation of the potential energy is done by its shrink / prolongation in a space direction with a release / absorption of a light. \[ prolonged\;iS(x + \Delta x) \rightleftharpoons prolonged\;iS(x) + \Delta E_\gamma \] Even if the receding velocity v increases, the helically moving velocity of the intrinsic energy m₀ in the space dimensions is invariant as the light speed c. The decrease of the potential energy is released only by a light radiation. This radiation is the "gamma-ray burst".

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#39 (2022.05.06)

Gamma-ray burst

The gamma-ray burst (GRB) is a luminescence phenomenon, in which an enormous energy comparable to a galaxy is emitted from a narrow area in a short time of 10 milliseconds to 100 seconds. Although candidates for light emitting sources have been proposed, the GRB including its light emitting mechanism is said to be the most mysterious cosmic phenomenon. GRBs with 2 seconds or less are called short GRBs, and those with more than 2 seconds are called long GRBs. In the later case, they are often accompanied by so called the afterglow, in which lights of a wide range of frequencies from X-ray to lower are emitted.
As mentioned in the previous page, the GRB is what a part of the decrease in the potential energy is emitted as an energy radiation in a galactic seed separation. In addition to gamma-rays, space-space dimensional radiations (gravitational waves) are also emitted. After the galactic seed separations terminated, the BRG became to no longer occur. The GRB is no longer emitted now, and we observe past radiations arriving in order at the earth. In the vibration around the trough of the potential energy, other radiations than gamma-rays are also emitted by bremsstrahlung from hidden-space dimensional circulations, which are a part of the intrinsic energy. This vibration is particularly remarkable around the energy trough by a flat separation, the emission from which is the afterglow. Before starting release of stellar seeds later, a galactic seed is releasing quantum particles and atoms so on from component small circulations. They are observed as a very faint background galaxy. Thus, the radiations from a galactic seed separation based on the energy circulation theory match the characteristics of GRBs very well.
The magnitude of the conversion of the energy to the velocity determines which one orthogonal or flat separation proceeds, and also the time duration of the vibration around an energy trough. GRBs can be roughly classified to the following three types.

The patterns of GRBs are just an image of the possibility, and sometimes one pulse is split to plural ones or broaden. In addition, bremsstrahlung due to a vibration around an energy trough is added to the radiation of gamma-rays. Type 3 GRBs, which are long bursts with afterglow, are the most common. Attached two or more galactic seeds later develop to one barred spiral galaxy.
In the current cosmology, the following two are considered as the most promising origins of GRBs. The short GRB is originated from a merger of binary neutron stars or a neutron star with a black hole. The collapsar model is proposed for long GRBs: “A massive star collapses to a black hole with a supernova explosion at its end. The fall of materials into a black hole derives relativistic jets, which hit the stellar envelop and radiate gamma-rays.“ However, these models have the following contradictions. (1) GRB has been no longer emitted since 130 million years ago. GRB should happen in the milky way and near galaxies according to the models. (2) Only a little portion of long GRBs are associated with a supernova. Furthermore, it is a hyper-luminous one. Is it really a supernova derived from a star? (3) The accompanying supernova is delayed about one day from the first gamma-ray emission. By the current model, supernovae should be at the same time or ahead. (4) The energy is too large and corresponding to a galaxy. A star cannot be the origin.
According to the energy circulation theory, the black hole does not exist. What is said to be a black hole existing at the center of a galaxy is a galactic seed. What is said to be a small black hole located in a galactic disc is a stellar seed, which will be explained later. Before a complete gravitational collapse to a black hole, any energy forms a continuous energy circulation.

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#40 (2022.05.07)

Release of stellar seeds from a galactic seed

By a galactic seed separation to two seeds, the ratio of frequencies ω/Ω of the local circulation to the main circulation becomes to a half. Once the ratio has got ω/Ω = 1, a further separation to two seeds is no longer possible. This is the reason why no gamma-ray burst has been emitted since 130 million years ago.
After the ratio got ω/Ω = 1, the next process of simultaneous release of stellar seeds starts. It happens at the same time at individual local circumferences in the whole main circulation that a local circulation divides to a major circulation and a minor one by an inclined flat separation. The major circulation remains as a part of the galactic seed. The minor circulations have relatively a very small radius, and are called as "stellar seed". They are orthogonally separated to each other and form a cluster in a ring, which we call the "ring of stellar seeds". We can regard this simultaneous release of stellar seeds as a partial cyclic decomposition of a galactic seed. The ratio ω/Ω of stellar seeds cyclically decomposed from a galactic seed has increased to a much larger number. Since the ring of stellar seeds is not a continuous energy circulation, its radius can seamlessly increase by the space expansion. While the ring is not a continuous circulation, it can maintain its circulation by the intra-circulation force eve if it expands.

When a ring of stellar seeds is released, it is circulating at the same velocity as that of the galactic seed. Releasing a ring of stellar seeds is repeated intermittently by the space expansion, and results in a disc of a spiral galaxy, in which a huge number of stellar seed rings are distributed radially.
The above-mentioned release of a stellar seed ring is limited in the plane of the galactic seed. A stellar seed release is also possible to an orthogonal or mixed direction. However, a seed is released not simultaneously on the whole circumference but one by one. Between these plural isolated stellar seeds, the intra-circulation force does not work. As shown in the below figure, a stellar seed receives a repulsive force from the near part of the galactic seed and an attractive force from the opposite part. A stellar seed, which is released to a vertical direction, moves spirally to the center, and then gets stationary. The distribution of these seeds is like an ellipse by its side view, and forms the central structure of a galaxy called the "bulge". Such a stellar seed, which is released to a mixed direction of radial and vertical, recedes linearly from the galactic seed. Such seeds, which are mutually aggregated by the gravitational force, form a globular cluster. Completely isolated seeds form a halo.

Thus, these releases of stellar seeds from a galactic seed form the structure of a typical spiral galaxy, which consists of the bulge at center, spiral disc surrounding it, and plural globular clusters above and under the disc. There remains a galactic seed in a galaxy, in which star formations are active around the center.
A galactic seed, which exhausted energy and disappeared early, is now observed as a ring galaxy. A galactic seed with a slow circulating velocity hardly releases rings of stellar seeds in the plane. Instead, it releases stellar seeds individually to various directions, and results in an elliptic galaxy.

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#41 (2022.05.08)

Circulating velocity of stars in a spiral galactic disc

The orbiting speed of stars composing a disc of a spiral galaxy is almost same at any radial distances. According to the standard cosmology, it is regarded that a star is orbiting with the balance of the centrifugal force and the gravitational attraction, and that the square of the velocity is inversely proportional to the radius. \[ m\omega^2 r - G\frac{Mm}{r^2} = 0 \;, \;\;\; v^2 r = GM \] The rotation velocity of a galactic disc is one of the most important mysteries, and it is expected that unknown dark matter exists in the halo surrounding the disc.
By the energy circulation theory, however, the initial speed of a stellar seed when it is released is equal to the circulating velocity of the galactic seed as shown in the previous page. If the release is alone and within the plane, the seed moves linearly to the tangential direction. In the case that the releases happen simultaneously on the circumference and form a ring of stellar seeds, the intra-circulation force works and the seeds continue to circulate. Once the ring of stellar seeds has separated from the galactic seed, the intra-circulation force is not balanced with the centrifugal force. However, the radial extending speed is very small compared with the tangential velocity in a spiral galaxy. We can regard the ring as near in a uniform circulation. Later, the radius of the ring is enlarged by the space expansion.
During the space expansion, the changes of the potential energy and the kinetic energy in the radial direction e₀ of the 4D space are set off each other. An energy moving in the 3D space can be expressed as a motion of an intrinsic energy derived from a vibration in e₀. This intrinsic energy is invariant by the space expansion. Since the total energy is also invariant, the moving speed in the 3D space does not change by the space expansion. Therefore, the circulating velocity of a ring of stellar seeds does not change with the initial speed by the space expansion, while the radius of the ring is expanded.
The release of a stellar seed ring from a galactic seed is a division of the intrinsic energy as shown below. So, the circulating velocity does not change before and after the release. \[ E = M_0 V_G^2 \;\; \rightarrow \;\; E = (M_1 + M_2)V_G^2 \] By repeating a release of a stellar seed ring, the radius of the galactic seed gets smaller due to the decrease of energy, but its circulating velocity does not change. Therefore, whenever a ring of stellar seeds is released, the circulating velocity is the same for any rings. It results in the fact that the orbiting speed of stars (matters) in a galactic disc is almost constant at any radial distances from the galactic center.
As explained above, the constant orbiting speed of stars in a galactic seed can be explained by the energy circulation theory without a contradiction. Therefore, we do not have to suppose dark matter, and it does not exist.
Here is shown below a simulation of the path of a stellar seed since released from a galactic seed 4 billion years after the start of the universe to the present 13.7 billion years after the start. v is the circulating velocity. r₀ is the radius of the galactic seed when the stellar seed was released..

The driving force of a release of a stellar seed ring from a galactic seed is the space expansion. The above figure shows what a track a circulating star (matter) shows by the space expansion. (a) is a case that the circulating speed per 100 million years is 0.5 time of the radius of the galactic seed. A circular motion gradually turns to a spiral one. The increase of the distance from the galactic center (radius) is due to the space expansion, so there is no change in the circulating speed even after the expansion. The figure shows a spiral motion of a star with a right-handed turn. Let us consider a linear alignment of stellar seeds over plural rings at a certain time. After the seeds have been circulating at the same speed by a right turn, they give a left-handed spiral alignment. In the case that not uniform stellar seed rings are released, a galactic seed of right-handed circulation gives a galaxy having left-handed turning arms.
Later, a stellar seed repeats to release a smaller energy circulation by an inclined flat separation. Each released energy circulation decomposes to elementary circulations of the smallest radius μ₀ (quantum particles) by a cyclic decomposition. Since the release of an energy circulation from the stellar seed happens intermittently one by one, but not simultaneously on the entire circumference, the intra-circulation force does not work between the released pieces, which recede from the stellar seed. After released, they are controlled by the gravitational force. Clusters of energy pieces, which show an elliptic motion at first, repeat collisions each other by the gravity and the fundamental force, then many of them become to show a circular motion. Thus, protoplanetary discs are formed. Finally, a cyclic decomposition takes place on the stellar seed, which has lost energy, and gives a protostar at the center. (Refer to galactic evolution)

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#42 (2022.05.09)

Cosmic microwave background

The Cosmic Microwave Radiation (CMR) is observed almost isotropically from all directions in the universe. It has a frequency distribution almost same as that of a black body radiation at an absolute temperature of 2.7 K. This is regarded as the evidence of the Big Bang theory that the universe started from an extremely high temperature and density state then has become a low temperature and density state due to the space expansion. Let us look at the generation of the CMR from the energy circulation theory.
The initial separations and cyclic decomposition just after the cosmic separation, which are shown in the figure of p33, are orthogonal separations of energy circulations. Like the gamma-ray bursts, they emitted enormous energy due to the decrease in the potential energy. The radiated energies generated various elementary circulations such as iS, iD, S, D and their excited forms by mutually interacting and exciting spacias. These elementary circulations made quantum particles such as protons and neutrons. It is likely that lights by bremsstrahlung were also emitted from component circulations iS and prolonged iS, which were orbiting as a part of the intrinsic energy. The elementary circulation iS in hidden-space dimensions prolongs by light absorption and the prolonged one contracts by light emission as explained before. \[ iS(x=1) + \Delta E_\gamma \rightleftharpoons n\text{-}iS(x) \;\; (\text{prolonged}\;iS) \] \[ n\text{-}iS(x) + \Delta E_\gamma \rightleftharpoons n\text{-}iS(x + \Delta x) \] We call a prolonged iS as the “elementary charge pair”. An absorption of high-energy light causes a division of an elementary charge pair to two ones. The state, where an elementary charge pair between a proton and an electron in an atom is divided, is an ionized pair and is in a plasma state. We can call a free elementary charge pair without an adduct at its two ends also as in a plasma state.
The lights, which were emitted as mentioned above in the early-stage universe, repeated absorption and radiation by the plasma, and reached an equilibrium state. This is in the same manner as the thermal equilibrium. After that, as is said in the standard cosmology, due to the decrease in energy density by the space expansion, electrons were captured by protons to form atoms, and the space became transparent to light, which started to go straight. The wavelength has been expanded by the space expansion, and is currently observed as a microwave distribution equivalent to 2.7 K.

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#43 (2022.05.10)

Energy circulation theory and the standard cosmology

From p33 to this point, we have seen the galactic evolution since the cosmic separation. As shown there, we have successfully derived it by the energy circulation theory so that we feel it like a miracle. At the same time, this galactic evolution model denies the existing standard model from the ground. Although the standard model has been established over a long period of time, it leaves fundamental matters as unknown and makes assumptions without grounds. In response to this imperfection, they believe in the existence of unknown energy and matter, and are pursuing to discover them. It is often added in word that there may be a new unknown theory, but they are looking for an extension of existing physics or something more fundamental embracing it. However, this does not mean looking for a truly brand new one. It is necessary to take off all preconceived ideas once and start from scratch. The energy circulation theory, which is explained here, starts from the premise that an energy is a vibration in multiple dimensions. With added the prerequisite that there exists a force working based on energy movements (momentums), it has succeeded in constructing a completely new physical system.
The standard cosmology argues as follows: Immediately after the Big Bang there were no matter but only hot energy. From there, pairs of elementary particles were generated by pair production. Since matters were a little excess to antimatters, remained only matters while antimatters disappeared by pair annihilation. After that, the temperature dropped to form protons and neutrons. By the space expansion, the temperature further dropped to form nuclei, which got in plasma with electrons. The temperature dropped further, and a nucleus captured the electron to form an atom. The quantum fluctuations of the initial state spread to the expanded universe, which appeared as deviations in the energy density and the material distribution. By gravity, matters aggregated and stars and galaxies were formed in sequence.
By the standard cosmology, the space is expanding but matters aggregate to form large-scale structures. This is a galaxy formation by an accretion process. On the other hand, the energy circulation theory argues that high-energy circulations separate and decompose to smaller circulations, and finally give the elementary circulations of the smallest energy. That is, it is a galaxy formation by an excretion process. These two are completely opposite ideas.
In recent years, it was broadcasted to succeed in filming a black hole. The obtained image is said to be an accretion disk, in which materials are orbiting at high speed around a black hole. However, this is plural rings of stellar seeds released from a galactic seed, which are at stages before starting star formation. If named, it would be an excretion disk. From now, instead of falling into the blackhole, it will spread out by the space expansion.
In the standard model, it is unknown how the structure of a galaxy is formed and how it is maintained. It is said that there is a big black hole in the center of a galaxy, into which energy falls. It means that the energy to make stars decreases. Then, there arises an interpretation that the energy existing in the halo accretes on and is supplied to the galactic disc. How does the energy accrete? What a convenient phenomenon the accretion is. Does the energy transfer from the black hole to the halo occur in fact? By all accounts, the explanation is unfounded and seems driven by pain. The standard model once again leaves details on the generation of galactic structures as unknown. What exists in the center of a galaxy is not a black hole but is a galactic seed.
In order to solve many unresolved problems, it is necessary to first remove the ghost that the current modern physics are correct. Once accepted that there is a force working based on energy movements, the electric, magnetic and nuclear forces have been derived from it, and further have been successfully given the features of the cosmic evolution, which meet the observed results well.

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#44 (2022.05.24)

Division to space energy and apparent energy

This page was deleted.

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#45 (2022.06.08)

Light speed variation over time 1: Time

In p11, we described the change over time in the light speed associated with the space expansion, but for details, we only mentioned to refer to Light speed. We also omitted an explanation on the space expansion derived from it in p12, but only mentioned to refer to Hubble diagram for details. From here, I will extract the main points from the references, and introduce the formula to show the light speed and the observation result that the space expansion is not accelerating.
Let us think about time first. In facts, the time dimension does not exist independently of the space but is one of the space dimensions, in which the energy exists. We have already mentioned that an energy is a vibration in multiple dimensions. The frequency ω of an energy in the dimension A is a value traced by another dimension B. If it is traced by a dimension other than B, it shows a different value of frequency. There is no absolute time that we unconsciously feel, but exist only relative positions in respective dimensions for an energy. How the value in the A dimension changes with respect to the value change in B is the movement in A when it is traced by B. Such a tracing dimension can work as a time. Not only a dimension that directly traces movements in other dimensions, but a common energy movement, which has a one-to-one correspondence to a tracing dimension, can indirectly trace them. This is the clock.
We define the time t that can express the circular motion of an energy circulation as ωt with an invariant ω as the “original time”. The dimension that has the longest cycle among the multiple dimensions, in which an energy is vibrating, can relatively express movements in all other dimensions and work as the original time. The most important feature of the original time is that it expresses an energy circulation by a constant speed. A clock, which is proportional to the original time, is essentially equivalent to it. Only the unit is different due to the difference in the proportionality constant.
Direct tracing is limited to the location where an energy exists. It is not possible to directly trace plural energies by a single movement. It is necessary to indirectly trace them by a clock, which shows a common movement for all of them. The radius of the universe in the 4D space shows such a common movement. We define it as the “Observed Time”. On the time scale we observe, we can treat the Observed Time as proportional to the original time. However, on the time scale of the space expansion, the passage of the Observed Time slows down in the expression by the original time. In the current standard physics, the definition of time interval is defined using an atomic clock. However, even if the same atom is placed, the potential energy differs depending on where it is placed, and the total energy also changes. In the general relativity, the difference in clock display is said to be due to a fluctuation of time interval by the gravity. However, the time interval does not change by the gravity, but the energy of the clock alters by locations.
Details on what is mentioned above are given in Features of time. Until now in this corner, we have used the original time, which treats an energy circulation as of a constant circulating speed. However, when we deal with the space expansion, light speed and redshift, the notation becomes extremely simple if we use the Observed Time, which is the radius of the universe. If you feel uncomfortable to use the Observed Time, you may treat it just as the radius instead of time. In the following pages, I will introduce the expressions of the light speed and the space expansion, respectively, by the variable of the cosmic radius.

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#46 (2022.06.09)

Light speed variation over time 2: Formula of the light speed

The light speed is the internal circulating velocity of the spacia, which is a unit energy of the space energy, as we mentioned many times in this corner. \[ c = \mu_0 \omega_0 \] This shows the current speed of light. With the space expansion over time, the radius μ₀ does not change, but the frequency ω₀ varies. The light speed as well as the frequency is a function of the radius of the universe. In facts, before I proposed the energy circulation theory, I had claimed that the light is a wave propagating in the medium; space energy, whose density should decrease with the space expansion, and raised a formula of the light speed as a function of the cosmic radius. It was derived from the rule of thumb that the propagation velocity of a wave in general like the sound is proportional to the square root of the density of the medium. The formula of the light speed was exactly of the same form as that derived later from the energy circulation theory. Here, I will explain the formula showing the change with time from the above equation of the light speed based on the energy circulation theory.
The number of spacias increases due to the space expansion, but the total energy does not change. So, the energy of a single spacia decreases. This is a decrease of the density of the medium; space energy, and named as the "energy density factor" f_D. Another factor, which affects the light speed, is that a light interacts with matters and causes scattering. It results in lengthening the effective path and slowing the apparent speed of light. This is why the light speed in matters slows down. We named it as the "electromagnetic interaction factor" f_EM. As the radius of the universe, take the relative ratio x to the maximum radius. The light speed can be expressed as follows. \[ c(x) = K\cdot f_D\cdot f_{EM} \;\;\;\;\; (x_0 \leq x \leq 1) \] In the vacuum space, f_EM = 1. Let us see first f_D. The number of spacias at the radius x is (x/x_p)³ times the current number (x_p is the current radius). Since the energy is proportional to the square of the velocity, the light speed is given as follows, which is inversely proportional to the 3/2 power of the radius. \[ c(x) = \mu_0 \omega_0(x) = \mu_0 \omega_0 \sqrt{\frac{x_p^3}{x^3}} \equiv K_1\frac{1}{\sqrt{x^3}} \] The expansion of the cosmic radius is decelerated by the intra-circulation force (fundamental force) acting on the circulation of the cosmic energy for the entire universe. While we skip explaining details, the expansion speed of the radius by the original time is given by the following equation. The maximum value of the radius is x=1, where the velocity is zero. So, the constant is K₂=1. \[ \frac{dx}{dt}=\pm\sqrt{\frac{K_f E_U}{\pi}\left(\frac{1}{x}-K_2\right)} \;\;, \;\;\; K_2 = \frac{1}{x_0} - \frac{\pi v_0^2}{K_f E_U} \] \[ \frac{dx}{dt}=\pm\sqrt{\frac{K_f E_U}{\pi}\left(\frac{1}{x}-1\right)} \] Take the cosmic radius x as the Observed Time T, then there is the following relation between the light speed by the Observed Time and that by the original time. \[ C(x) = \frac{dL}{dT}=\frac{dL}{dt}\frac{dt}{dT} \;\;, \;\;\; c(x)=\frac{dL}{dt} \;\;, \;\;\; \frac{dt}{dT} = \frac{dt}{dx} \] \[ C(x)=c(x)\frac{dt}{dx} \] By substituting the former two equations into this, we get the following equation as the light speed by the Observed Time. \[ C(x) = K_1 \bigg/ \sqrt{\frac{K_f E_U}{\pi}x^3\left(\frac{1}{x}-1\right)} = K \frac{1}{x\sqrt{1-x}} = K\cdot f_D \] Thus, we obtained the energy density factor f_D by the Observed Time (cosmic radius x).
Next, let us see the electromagnetic interaction factor. The sound wave propagates faster in the water than in the air. This is because both water and air work as a medium and water has a higher density. On the other hand, the light speed is faster in air than in water. Neither air or water is a medium of the light, but the medium is just the space energy. Light interacts with water molecules and scatters. The light speed of propagating in the medium is the same, but the apparent velocity gets slower by the scattering. For a while after the cosmic separation, the universe contained a lot of energies in the plasma state, and the light could not go straight in the space. According to the standard cosmology, about 370,000 years after the opening of the universe, electrons were captured by protons to form atoms, and the space became transparent to the light. By the energy circulation theory, we also regard that the light could not go straight due to the interaction with plasma, and received scattering for a while after the space clearing due to the high concentration of hydrogen atoms. It is unclear when by the Observed Time the space got transparent, but we quote it as T_c. I proposed the electromagnetic interaction factor to be shown as below. \[ f_{EM} = 1 - \frac{T_c^3}{x^3} \;\;, \;\;\; (T_c \leq x < 1) \] Here we have got the formula of the light speed based on the Observed Time as below. \[ C(x) = K \frac{1}{x\sqrt{1-x}} \left(1 - \frac{T_c^3}{x^3} \right) \] The graph of this formula is given below. Graphs for some values of T_c are shown. Except for the very small x region, we can neglect the electromagnetic interaction factor. The light speed is zero for the radius less than T_c , and increases rapidly after x=T_c , and then varies in accordance with the energy density factor.

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#47 (2022.06.10)

Redshift

The wavelength of a light emitted from a star is enlarged by the space expansion when it reaches the earth. When the wavelength is multiplied by n, the redshift z is defined as follows. \[ z+1=n \] In the standard physics, since the light speed is treated as invariant over time, the same value of redshift is obtained regardless of whether the wavelength or the frequency is measured. However, the light speed varies with the space expansion in fact, and it differs depending on whether compared by the wavelength or the frequency. Furthermore, conceptually the measured value is compared with that at the emission, but it is in fact compared with the current value of the same element.
We use the Observed Time T= x, which is the cosmic radius x, as the time. Let T_E be the time of emission, and T_P be the preset time. There is the following relation since the light speed is the product of the frequency and the wavelength. \[ C(T_E) = \nu_0(T_E)\cdot \lambda_0(T_E)\;\;\; \longrightarrow \;\;\; C(T_P) = \nu(T_P)\cdot \lambda(T_P) \] \[ \text{Present atom:}\;\;\; C(T_P) = \nu_0(T_P)\cdot \lambda_0(T_P) \] Firstly, let us see the redshift from the value at the time of light emission. If the wavelength is enlarged by n times, it indicates the multiple of the current radius of the universe from that at the emission. We refer the time of emission T_E divided by the present time T_P to as the relative time of emission T_ER. \[ n= \frac{T_P}{T_E}=\frac{1}{T_{ER}} \] The wavelength-based redshift is given by \[ z_{\lambda}^e + 1 = \frac{\lambda(T_P)}{\lambda_0(T_E)} = n = \frac{1}{T_{ER}}\;. \] However, the frequency-based redshift is different form it and given as follows. \[ z_{\nu}^e + 1 = \frac{\nu_0(T_E)}{\nu(T_P)} = \frac{C(T_E)}{\lambda_0(T_E)}\frac{\lambda(T_P)}{C(T_P)}= n\frac{C(T_E)}{C(T_P)} = \frac{1}{T_{ER}}\frac{C(T_E)}{C(T_P)} \] In actual observations, the measured value is compared with the current value of the same element. Initially, I thought that the energy of an atom would not change by the space expansion. However, based on the energy circulation theory, the energy of the elementary energy circulation, which constitutes a particle, changes with the variation of ω₀ like the light speed alters. The number of particles increases, and the energy of the particle decreases. Therefore, the frequency at the emission of the same element alters by the space expansion, and is proportional to the light speed as shown below. \[ E_\gamma = h \nu^2 \propto m_0 c^2 \;\;\;\;(m_0,\;h\;\text{are invariant}) \] \[ \frac{\nu_0(T_P)}{\nu_0(T_E)} = \frac{C(T_P)}{C(T_E)} \] The wavelength-based redshift and the frequency-based redshift, which are compared with current atomic values of the same element, become as shown below and are the same. Hereinafter, we express the redshift simply as z. \[ z_\lambda + 1 = \frac{\lambda(T_P)}{\lambda_0(T_P)} = \frac{\lambda(T_P)}{\lambda_0(T_E)}\frac{\lambda_0(T_E)}{\lambda_0(T_P)}= n\frac{C(T_E)}{\nu_0(T_E)}\frac{\nu_0(T_P)}{C(T_P)} = n = \frac{1}{T_{ER}} \] \[ z_\nu + 1 = \frac{\nu_0(T_P)}{\nu(T_P)} = \frac{\nu_0(T_E)}{\nu(T_P)}\frac{\nu_0(T_P)}{\nu_0(T_E)}= \frac{C(T_E)}{\lambda_0(T_E)}\frac{\lambda(T_P)}{C(T_P)}\frac{C(T_P)}{C(T_E)} = n = \frac{1}{T_{ER}} \]

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#48 (2022.06.11)

Light propagated distance and present distance

In the observation of a star, what is measured are the brightness and the redshift. The redshift correlates to the time from the emission to the measurement. The brightness responds to the luminosity and the distance. There are, however, plural types of distances for a star due to the space expansion. Take a case that a light is emitted at the location A at the time T_E, and reaches the position B at the time T_P.

The figure above shows how the light propagates including the passage of the time. The radial direction is the cosmic radius equal to the Observed Time, and the arc direction is the 3D space. The light propagates from A_E to B_P, but the part in the time is not included in the propagated distance. So, C-B_P is the distance in the 3D space where the light has actually propagated. We named it as the "light propagated distance" LD (it is called the luminosity distance in general). Each brightness of stars with the same luminosity is inversely proportional to the square of LD. The current distance of the star is A_P-B_P, which we call as the "present distance" PD (equal to the proper distance at present). In the Hubble diagram to be explained later, it is attempted to express the relation of PD and the redshift. Let D₀ be the distance of A_E-B_E at the emission, then PD and LD are given as below. \[ PD = nD_0 \;, \;\;\; LD = \frac{D_0}{2} (n+1) \] Therefore, the factor to convert LD to PD is as follows. \[ \frac{PD}{LD} = \frac{2n}{n+1} = \frac{2(z+1)}{z+2} = \frac{2}{1+T_{ER}} = \frac{2}{1+T_E/T_P} \] The LD-PD conversion factor is very important. The length l between two light emissions expands to nl at the observation. However, in the case of a light emission from a single point, not only the remaining distance from the light to the observation point B but also the propagated distance from the emission point A to the light will enlarge. In the increased part of the distance between A and B, only a half of it is the increased path where the light has propagated. The light propagated distance LD in total is C-B_P. There seems to be some confusion in this regard in the standard cosmology. I will explain it in the next page on the Hubble diagram.
The light propagated distance LD is obtained by integrating the light speed per the Observed Time from T_E to T_P by the time (radius). We can ignore f_EM when z<12.8. \[ LD(T_E) = \int_{T_E}^{T_P}C(x)dx = \int_{T_E}^{T_P}\frac{K}{x\sqrt{1-x}}dx = K\left( \log \frac{1-\sqrt{1-T_P}}{1+\sqrt{1-T_P}} - \log \frac{1-\sqrt{1-T_E}}{1+\sqrt{1-T_E}} \right) \] Thus, we have obtained the formulas of the light propagated distance LD of a stat and its present distance PD, respectively, with T_E, which is the Observed Time (cosmic radius) when the light was emitted.

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#49 (2022.06.12)

Hubble diagram 1: Distance modulus

Hubble found that the speed of a star to move away from us is proportional to the distance of the star. This Hubble’s law is the basis of the expanding universe as well as the cosmic microwave background. The receding speed from the earth is measured by the redshift. The rotation speed in a galaxy is observed as the Doppler effect associated with the motion of the light source. However, in a large cosmic level including many galaxies, the redshift of a radiated light is caused mostly by the wavelength enlargement as the space expands. A plot of distances on the vertical axis and redshifts on the horizontal axis is called as a Hubble diagram.
Type Ia supernovae have the common peak absolute magnitude (light intensity) and act as a standard light source, a measured brightness of which reveals the distance. First, let us see the case that we assume the light speed would have been constant. The light propagated distance is as below. \[ LD_c = c(T_P - T_E) = cT_P(1 - T_{ER}) = cT_P\frac{z}{z+1} \] This shows the simple relation that the light speed times by the time from the emission to the present gives the propagation distance. Since the light speed is set as constant, the distance is proportional to the time. Multiplying the distance by (z+1) gets proportional to the redshift. \[ (z+1)LD_c = cT_P\cdot z \] Multiplying LD_c, obtained from the brightness, by (z+1) and putting it on the vertical axis gives a linear relation to the redshift z on the horizontal axis. This multiplication by (1+z) is called the time dilation. This is equal to the expansion rate n of the cosmic space, and the rate from D₀ at the emission to the present distance PD. In the standard model, they seem to regard this time dilation as the conversion of the light propagated distance LD to PD. However, as mentioned in the previous page, the LD-PD conversion factor is not at this magnification. This multiplying by (z+1) is to make the resulted distance index be proportional to the redshift for the original distance proportional to the time. Anyway, in actual data processing of astronomical observation, they multiply the distance by (z+1) as the time dilation.
From here, let us return to the actual situation where the light speed varies by the cosmic radius, and obtain a distance index from a brightness. Take a case that a light of a luminosity L is emitted at T_E and reaches us at T_P. The luminous flux (brightness per unit area) is \[ F(T_E) = \frac{L}{4\pi LD(T_E)^2}\;. \] Since we handle a wide range of distances, let us use the common logarithm with the base of 10, and define the magnitude of the flux as follows. \[ m(T_E) \equiv -2.5 \lg F(T_E) \] An absolute brightness of a star such as the absolute magnitude is expressed as a relative brightness at a certain distance to the standard brightness. Here, let us take the magnitude of the relative brightness to the case that a star of the same luminosity is located at the distance showing z=0.05. z=0.05 corresponds to T_ER=1/1.05. This relative value is a distance modulus since the luminosity is the same as that of the standard. Let us express it using T_ER instead of T_E as a variable as follows. \[ DM_{0.05}(T_{ER})\equiv m(T_{ER}) - m(1/1.05) = 5\lg LD(T_{ER}) - 5\lg LD(1/1.05) \] \[ (T_E = T_{ER} T_P) \] Substitute the equation for the light propagated distance LD shown in the previous page to the above distance modulus, then we get the following equation and its graph.

Since we do not know yet the present time T_P, graphs for 0.6, 0.7 and 0.8 of it are shown. The dotted line in black is the case where the light speed has been constant (independent of T_P). Since the logarithm is used in the distance modulus, the horizontal axis is also in a logarithmic scale. The horizontal axis in the left graph is the redshift z. The horizontal axis in the right graph is z/(z+1), which is the time from the emission to the present relative to the present time (relative back in time T_BR=1-T_ER). As shown by the dotted line, the distance modulus becomes a straight line to the time in the case of the constant light speed. The right graph is essentially the same as the one, where z is on the horizontal axis and the distance multiplied by the time dilation (z+1) on the vertical axis.

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#50 (2022.06.13)

Hubble diagram 2: K-correction

In obtaining a Hubble diagram from observed data of stars, so called the K-correction is done in addition to the time dilation that multiples the distance by (1+z) as described in the previous page. The K-correction is to convert the measured data of a star with a redshift z to data in the rest frame at z=0 without the space expansion. To measure the emission energy of a star, it is observed in a frequency band where it radiates a lot. The frequency band used differs between the light largely redshifted and the light at the emission.
Consider virtually a non-expanding universe, that is, a rest frame, by which the measured magnitude in the band X can be expressed as follows. \[ m_x^0 = M_x + DM^0 \] M_x is the absolute magnitude measured in the band x and is the magnitude when the distance is 10pc (parsec). The reference target differs depending on a frequency band used, and there is sometimes a little difference in the absolute magnitude by bands. DM is the distance modulus versus the standard 10pc, and the above formula shows the change in brightness with distances. Since these elements are logarithmic, a sum shows a product of elements displayed on the normal scale.
If this star shows a redshift z and a magnitude m_y by the band y in the actual observation in the expanding universe, the difference from the above value in the rest frame is defined as the K-correction. \[ K_{xy} \equiv m_y - m_x^0 \] There is the following relation. \[ m_y = M_x + DM^0 + K_{xy} \] On the other hand, in the actual observation showing the redshift z, m_y is given by the following formula. \[ m_y = M_y + DM(z) \] Therefore, the K-correction is shown as follows. \[ K_{xy} = M_y - M_x + DM(z) - DM^0 \;\;, \;\;\;\; K_{xy}^D = DM(z) - DM^0 \] The difference in the absolute magnitude by a band to use is zero or very small, which falls in an observational adjustment. The distance part of the K-correction is exactly the difference between the light propagated distance LD and the present distance PD in the logarithmic display, and corresponds to the LD-PD conversion. The K-correction is a negative value because it takes the conversion from PD to LD by definition.
Doing the K-correction is synonymous with converting the measured light propagated distance LD to the present distance PD as shown below. \[ PD = \frac{2(z+1)}{z+2}LD = \frac{2}{1+T_{ER}}LD \]

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#51 (2022.06.15)

Hubble diagram of supernovae and expected values

Once a redshift is obtained by observing a star, the light propagated distance and the present distance of the star are uniquely determined. In the discussion so far, we regarded the object star is stationary to the space energy. However, in fact, galaxies and galactic clusters are rotating. Therefore, plots in the Hubble diagram of observed data are not on a line, but are distributed with a dispersion. However, the mean values should be on the theoretical line. Let us verify whether the cosmic evolution model based on the energy circulation theory, which have been discussed here so far, meats the observed data or not.
In a typical Hubble diagram covering a wide range of the universe, both the time dilation described in p49 and the K-correction described in p50 are made to the light propagated distance LD obtained from the brightness. In order to express the present time, the time dilation is not necessary. For expressing the distance as proportional to the redshift z in the case of the constant light speed, the K-correction is not necessary. However, since the both are done in most of reported papers, we take the present distance PD multiplied by (1+ z), which is referred to as the adjusted present time, for the purpose of comparison. We express the distance and the redshift z by the common variable T_ER. (The formula of LD is given in p48).) \[ (1+z)PD =(1+z) \frac{2(z+1)}{z+2}LD \] \[ \frac{1}{T_{ER}}PD = \frac{1}{T_{ER}}\frac{2}{1+T_{ER}}LD \;\;, \;\;\;\; z = \frac{1}{T_{ER}} - 1 \] Take the distance modulus of the adjusted present time to the standard distance of z=0.05 on the vertical axis, then its graph with the redshift z on the horizontal axis is shown as follows.

The left graph has a logarithmic scale of z on the horizontal axis, and the right graph has a normal scale of it. Since the present time T_p is unknown, lines of some values for it are shown. The dotted line is for the case where we virtually assume that the light speed has been constant. The both axes of the left graph are on a logarithmic scale, but the line is not straight even if the light speed has been constant.
It is the Supernova Cosmology Project (SCP) that created a stir on the speed of the space expansion. It observed type Ia supernovae, which have the same peak luminosity, and the distance can be determined only from the brightness. The below is the Hubble diagram in the historical SCP’s paper in 1999, which claimed that the speed of the space expansion is accelerating. In this report as well, the multiplication by (1+ z) and the K-correction were made to the observed values. z is on a logarithmic scale. They argued that the expansion speed of the universe is accelerating because in the large z area, observed plots are upward from the straight line, subject to the invariant light speed. They regarded the distance divided by the constant light speed on the vertical axis as a propagation time of light, and the redshift on the horizontal axis as an index of the space expansion speed. In the standard model, it is believed that the dark energy to accelerate the expansion should exist. In the below figure, we superimposed the above theoretical lines from our proposed model to the observed data of supernovae. Our model with the varying light speed fits well with the measured values.

After that, data by space telescopes were added more and more. The report in 2013 is shown in the next figure. This uses a normal scale for z, and is a semi-logarithmic graph. The authors concluded that the cold dark matter model with 73% by dark energy and 27% by matter including dark matter is the best fit to the measured values.

In the above figure, the theoretical values from our proposed model are superimposed on the reported plots. The curved line for T_p = 0.7 (in pink) almost completely overlapped with the line of their best fit model (in black). It is hard to see, but the black line lies under the pink line with overlap. The difference in numbers on scale of the vertical axis is due to the difference of the standard to give the relative distance.
As we have seen here, our proposed model, in which the light speed varies by the cosmic radius, is very well in agreement with observed supernovae in the Hubble diagram. These observation results strongly support our model. The speed of the space expansion is decelerating by the original time, and is constant by the Observed Time, which is the cosmic radius. The space expansion does not accelerate by no means, and dark energy that accelerates the expansion does not exist. But there is the space energy in the space of the universe as the medium. From the observation results of supernovae, it has been revealed that the current radius of the universe (Observed Time) is about 0.7 of the maximum value.

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#52 (2023.07.12)

Isolated electric charge or electrostatic force does not exist

In the standard electromagnetism (EM), an electron and a proton exhibit the elementary charge of ±e, which is the smallest charge and integer multiples of which are possible as an isolated charge. The electrostatic force works between isolated charges. Although this is accepted as a basic concept of the standard EM, it is in fact wrong; there exist no isolated charges nor electrostatic forces between them.
We explained the definition of the electric charge and the electric force in p14 and p15. The electric charge is the momentum in the hidden dimension H of the 4D space. The elementary charge e is the momentum in the plus or minus direction in H of the elementary single circulation iS, and does not change even if an iS prolongs to plural spacias. As explained in p16, an iS prolongs and shows an intra-circulation attractive force as shown below.

\[ F_x = K_e \frac{(+e/n)(-e/n)}{(2μ_0)^2} = -K_e \frac{e^2}{(2μ_0n)^2} = -K_e \frac{e^2}{d^2} \] We call such a prolonged iS as the elementary charge pair (eCP). At junctions inside, forces are set off, and the attractive force remains only at the two ends. We named such a force within an eCP as the connected electric force. The proton and electron in an atom are an eCP attached with a neutrino at the minus end and S at the plus end. The force between the electron and proton is a connected electric force, which shows a strong attraction.
The electric charge at the two ends of eCP is e/n and extremely small as about 10^-4e in an atom. The elementary charge e is not the minimum but is the maximum value as an electric charge. A non-connected electric force, that is, electrostatic force of an ECP with another eCP is possible, but the effective distance for it is very short as some times of the size of a nucleon. Therefore, except for a force between protons in a nucleus, the electrostatic force does not exist practically.
In the current EM, an electric charge consisting of plural elementary charges is possible, and the electrostatic force works between such charges. However, is there any observed example of this force? What is generally called an electrified body is not a collection of plus or minus electric charges, but a collection of prolonged eCPs, in which the polarization energy is increased. The total electric charge of an eCP is zero. Furthermore, the distance of individual polarizations is extremely short as the distance of a spacia.
Let us give an example to show that there is no electrostatic force. It is said that in a battery, positive charges are gathered on the positive electrode and negative charges on the negative electrode. If this were true, there should have been detected a strong attractive or repulsive force between the electrodes of the two batteries. However, in fact, no force is detected when two battery cells are put close to each other.

Between electrodes of a capacitor, where plus and minus electric charges are said to be stored, no force works, either. A high-capacity charged body can discharge to an outside body, but no force can be observed between them. In textbooks etc., diagrams of the electric field between multiple electric charges are drawn plausibly, but such charges themselves do not exit, and the electrostatic force does not work. As an example of an electrostatic force, standing hairs due to static electricity is often mentioned. It is not by an electric repulsive force among hairs, but is due to a connected electric force in each hair. eCPs align in series in a hair, and try to straighten out due to the attractive force inside.

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#53 (2023.07.13)

What is the electric current?

In the existing EM, it is said that the electric current is the flow of electric charges and is made by the movement of electrons. However, as pointed out in the previous page, such electric charges do not exist. What kind of phenomenon is what is generally called as the electric current? Currently in general, the electric current is defined as the charge passing through the cross-section of the conductor per unit time (one second) I = Q/t. However, the electric charge is not actually measured. The energy passing during a unit time, that is, the power P = U/t is measured. Electrical appliances commonly display the power with the unit of watt (W). The electric current I (unit: ampere A) is obtained by dividing this power by the electromotive force E (unit: volt V) P = IE. The power is often displayed by the unit of ampere volt (AV) instead of watt. The power is an actual measurement and is correct, but the current understanding of the electric current and the electromotive force is wrong, and needs to be redefined.
From the ECT, we can say that the electric current is the transmission of the electric polarization energy. Electrons never transmit in it. To define the electric current, let us define the polarization energy instead of the electric charge.
As explained in the previous page, an elementary charge pair eCP prolongs by absorbing an energy (light). Take x as the length of an eCP, the eCP with x=2μ₀ means iS itself. The electric polarization energy of an eCP is obtained by integrating the attractive force at the two ends by their distance from 2μ₀ to x, and is shown by the following formula with setting the standard as the energy m₀c² of iS. \[ U(2\mu_0) \equiv E_{(iS)} = m_0 c^2 \\ U(x) = \Delta E + U(2\mu_0) = K_e e^2 \left( \frac{1}{2\mu_0} - \frac{1}{x} \right) \quad (x \geq 2\mu_0) \] We call this electric potential energy as the polarization energy. The polarization has eCP as a unit structure. Let us define the electric current quantitively from the next page onwards.

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#54 (2023.07.14)

Propagation model of polarization energy

How does the polarization energy transmit in a conductor? I propose the following model, an image of which is shown below. In a conductor, two oppositely directed eCPs form a coupled conjugate pair, which aligns in series. The polarization moment of the conjugate pair is zero since those of individual ones are set off. If a single eCP enters there, it rotates in an orthogonal plain and gets static to the conductor. It shows a rotating magnetic charge, which will be explained later. The intrinsic energy (mass) of a hidden-space dimensional circulation moves at the light speed, but its components in 3D space directions can change flexibly. The direction in X of prolongation of an eCP changes to in Y, and forms internal circulations in X-Y, which rotate to the direction of Z. \[ v_x^2 + v_y^2 + v_z^2 = c^2 \\ V_{major}^2 + V_{local}^2 = c^2 \] This rotating eCP release an energy (light) and gets smaller in the radius. Then it causes a rearrangement of pairing with the adjacent conjugate pair of eCPs, and gives a new conjugate pair and a single eCP. The single eCP absorbs the released energy, and becomes a rotating eCP with an increased radius. The process repeats, and a rotating eCP moves in the conductor. This is the phenomenon of the electric current.

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#55 (2023.07.15)

Polar potential

In the current EM, what is obtained by dividing the electric potential energy by the electric charge is the electrostatic potential; also called as the electric potential (unit: volt). However, such an electric charge does not exist. Let us define the polar potential as a new index that adequately shows the electric potential energy (= polarization energy).
We define a series connection of the conjugate pairs of eCPs in a conductor, which is explained in the previous page, as the unit line. The polar potential is defined as the sum of polarization energies in one unit line, in more strictly by the formula in the figure below. In an uncharged conductor, polarized eCPs form conjugate pairs and cancel the polarization moment, which results in zero polar potential.

If we add an eCP to a non-connected conductor, its energy spreads to the whole length as shown in the above figure. The polarization energy does not depend on the length of a conductor. When plural unit lines are connected in parallel, all of them show the same polarization energy. If one unit line temporally shows a higher energy, the excess is transferred to the others, resulting in the same value in all. A conducting wire is a bundle of plural unit lines in a parallel connection. The polarization energy (electric potential energy) of the whole conductor is the product of the polar potential and the number m of the unit lines. \[ U = mV_p \] This shows a similar relation to U=QV of the existing EM, but m is dimensionless and V_p has the dimension of energy.

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#56 (2023.07.16)

Definition of the electric current

Let us define the electric current quantitively based on the polarization energy. As mentioned in p53, the real significance of using the electric current is to indicate how much energy passes through per unit time, that is, the power (unit: W). If we use a unit of energy that makes us image the origin of this passing energy, it is easy to have an image that a polarization energy is passing through. It is considerable to show how many eCPs pass through per unit time instead of electric charge. However, the energy of an eCP is not constant but varies by its length. Therefore, using the energy of iS, which is the smallest eCP, as a unit, we define the polarization energy divided by the energy U₀ of iS as the "polar charge C_p". \[ \text{Polar charge:} \quad C_p \equiv U/U_0 \:, \quad U_0 = E_{(iS)} = m_0 c^2 \\ \textbf{C}_{\textbf{p}} = C_p \textbf{e}_{\textbf{p}} = +C_p \:, \: -C_p \] The polarization has a direction; plus or minus. We define the direction from the minus charge to the plus one inside an eCP as plus. The poplar charge also has a direction, plus or minus.
We define the "electric charge" as the polar charge that passes through a cross section of a conductor during a unit time (second). \[ \text{Electric current:} \quad \textbf{I}_{\textbf{p}} \equiv \textbf{C}_{\textbf{p}} / t \] The electric current has a direction whether the energy moves to the plus or minus direction of the polar charge.

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#57 (2023.07.17)

Current potential

In the current EM, the power by the electric current is expressed by the product of the electric current and the electromotive force P=IE. Volt is usually used as a unit of the electromotive force E. As a unit for the electrostatic potential V=U/Q, volt is also used. The two are different but use the same named units.
We defined the polar potential V_p in p55. Here we define the “current potential V_c”, which corresponds to the electromotive force when an electric current flows, as the power (energy/time) in a unit line. \[ \text{Current potential:} \quad V_c \equiv P / m = I_p U_0 / m \] The power is the product of the current potential and the number m of unit lines. \[ P = U/t = mV_c \\ \left( U = mV_p \right) \] The dimension of V_p is energy, but that of V_c is energy/time.

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#58 (2023.07.18)

Comparison with standard EM

Let us compare the items related to the electric current by the ECT, that have been discussed so far, with the existing EM. The existing relational formulas ⇒ the new ones are shown below.

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#59 (2023.07.19)

Magnetic charge

The current EM does not suppose a magnetic charge, but assumes that a magnetic force acts through the interaction of magnetic fields. The magnetic field is supposed to be generated by fluctuations in the electric fields. However, the electric charge does not exist in fact, and the electric field does not, either. In the ECT, the magnetic charge is defined as a momentum in 3D space dimensions of a hidden-space energy circulation. The magnetic charge has a direction, and is a vector charge, showing the fundamental force shown in p4 with another one. The force between two magnetic charges b₁ and b₂ is expressed as below (for angular factors, please refer to the figure in p4). \[ F = K_f \frac{b_1 b_2}{d^2} \cos{\theta_p} \sin{\theta_1} \sin{\theta_2} \] The magnetic charge of a static eCP is zero in total since reverse ones are set off. An eCP can rotate around the axis of the hidden dimension H, and the velocity component in each space dimension can be changed flexibly. As mentioned in p54, an eCP rotates in space dimensions as shown below. We call it as the “magnetic rotation”.

The magnetic rotation rotates also in space dimensions around the center of the eCP. As shown in the figure, it shows each magnetic charge at each radius r_k from the center to the end. Each value of radius has two phases; 0 and pi (180 degrees), but we treat them as one rotating magnetic charge. The energy and the rotating magnetic charge at each radius are given as follows.

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#60 (2023.07.20)

Magnetic charge density

For one cycle of a magnetic rotation, a magnetic charge circulates one round on the circumference. Here, we call the magnetic charge per minute line segment on each circumference as the “linear density of magnetic charge”, which is defined as below. \[ \textbf{b}_{\textbf{L}}(r_k) \equiv \frac{\textbf{b}_{\textbf{c}}(r_k)} {2\pi r_k} \] The radius in the denominator cancels the radius in the formula of rotating magnetic charge, which was shown in the previous page, then the linear density does not depend on the radius. We define the sum of linear densities of all radiuses as the “linear density of gross magnetic charge”. Here is a question how we should treat the radius of the gross magnetic charge. Since the size of a magnetic rotation is at the atomic size level, there is no problem even if we regard the gross magnetic charge exists on the surface of the magnetic rotation in an actual conductor with many unit lines. \[ \boldsymbol\beta_{\textbf{L}} = \frac{m}{2\pi} \omega \textbf{e}_{\textbf{c}} = \frac{E}{2\pi c^2} \omega \textbf{e}_{\textbf{c}} \] From here, let us examine the magnetic charge that is associated with an electric current I_p in a unit line. Take a minute length Δx of a unit line. The value of the electric current is the energy passing per second, and the energy passing through the region Δx under a constant current is the product of the power P and the time for which the energy passes the region. Since the electric current transmits at almost the light speed, the energy in Δx is given as below. \[ E(\Delta x) = Pt = P \frac{\Delta x}{c} = I_p U_0 \frac{\Delta x}{c} \] The linear density of gross magnetic charge on the length Δx of a unit line becomes as follows. \[ \boldsymbol\beta_{\textbf{L}} (\Delta x) = \frac{E(\Delta x)}{2\pi c^2} \omega \textbf{e}_{\textbf{c}} = \frac{I_p U_0 \Delta x}{2\pi c^3} \omega \textbf{e}_{\textbf{c}} \] Dividing this by Δ x gives the magnetic charge density per unit area of the surface, which we named as the “surface density of gross magnetic charge”. \[ \boldsymbol\beta_{\textbf{s}} \equiv \frac{\boldsymbol\beta_{\textbf{L}} (\Delta x)}{\Delta x} = \frac{U_0}{2\pi c^3} I_p \omega \textbf{e}_{\textbf{c}} = \frac{m_0}{2\pi c} I_p \omega \textbf{e}_{\textbf{c}} \] This is the formula to show the surface density of gross magnetic charge that is generated when an electric current flows in a unit line. Multiplying it by the area Δ s = Δ x Δ l gives the exact gross magnetic charge. The above equation is expressed using the unit vector e_c that circulates around the unit line, but if we use the notation of rotation toward the electric current direction, it is rewritten as follows. \[ \nabla \times \boldsymbol\beta_{\textbf{s}} = \frac{m_0}{2\pi c} \omega \textbf{I}_{\textbf{p}} \]

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#61 (2023.07.21)

Rotating magnetic charge associated with an electric current

As explained in the previous page, the surface density of gross magnetic charge associated with an electric current in a unit line is given as follows. \[ \boldsymbol\beta_{\textbf{s}} = \frac{m_0}{2\pi c} I_p \omega \textbf{e}_{\textbf{c}} \quad \text{or} \quad \nabla \times \boldsymbol\beta_{\textbf{s}} = \frac{m_0}{2\pi c} \omega \textbf{I}_{\textbf{p}} \] In fact, a conductor consists of a very large number of unit lines connected in parallel. A unit line on the surface shows the surface density of magnetic charge shown above. Inside the conductor, however, magnetic charges are set off as zero since all unit lines show the same magnitude and same directional rotating magnetic charges. Since the electric current is the sum of individual ones of all unit lines, the electric current in one unit line is I_p/m , where m is the number of unit lines. Therefore, on the surface of the conductor, the surface density of gross magnetic charge is given by the formula below. \[ \nabla \times \boldsymbol\beta_{\textbf{s}} = \frac{m_0}{2\pi c} \omega \frac{\textbf{I}_{\textbf{p}}}{m} \quad (m:\: \text{number of unit lines}) \] I_p/m is an electric current per unit line, but is also an electric current density in multiple unit lines. The above equation shows that an electric current produces a rotating magnetic charge and that the surface density of it is proportional to the rotating frequency and the electric current density. This corresponds to the Ampere’s low expressed by the following equation in the standard EM. \[ \nabla \times \textbf{H} = \textbf{j} \quad (\textbf{H}: \text{Magnetic field}, \quad \textbf{j}: \text{Current density}) \] The magnetic rotation is to right toward the direction of a plus electric current. It is called as the Ampere’s right-hand screw law, but was an empirical rule and why it was in only one direction was unknown. In the ECT, asymmetric energy circulations were generated by the cosmic separation as explained in p7. The energy circulations repeated the cyclic decomposition many times, and changed into smaller and smaller ones. In the process, the rotating direction to the travelling one, that is, the helicity has been inherited. This is the reason why the magnetic rotation is asymmetric, we guess.

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#62 (2023.07.22)

Magnet

Take a circular closed circuit of a conductor connected at the both ends. If there exist unpaired eCPs, that is, a polarization energy, an electric current flows in the circuit, and many magnetic rotations appear. As shown in the figure in p54, a rotating eCP releases an energy (light) and gets shorter, then causes a rearrangement of pairing with the adjacent pair of eCPs. The resulted new lone eCP absorbs the light, which was released from the former one, and becomes a new magnetic rotation. In this way, such energy release and absorption occur continuously, and the circuit conductor shows a stable surface density of magnetic charge if there is hardly an energy emission to the outside. It shows a magnetism without external supplement, which is the paramagnetism. We named this circuit of the minimum structure of the magnet as the “unit magnet”. We define the unit magnet as a closed unit line (circuit) in which an electric current is flowing.

A cluster of concentrical unit magnets with increasing values of radiuses shows a large plane of radial magnetic charges as shown in the figure (b) above, which we named as the “unit layer of magnet”. Between adjacent unit magnets, a magnetic force works and they attract each other, but the magnetic charge at the junction of them is set off and gets zero. In total, magnetic charges remain only on the surface of a unit layer of magnet. The directions of magnetic charges radiate from the center, and if they are outward on one side, they are inward on the other side. Each red circle in the figure shows a gross magnetic charge of a magnetic rotation, and blue arrows indicate a direction of a gross magnetic charge.
Numerous magnetic layers assemble in series and form the “brock magnet” shown in the figure (c). The directions of the internal electric currents of the constituent unit layers of magnet are the same, and the directions of magnetic charges on the connected surfaces are opposite. A magnetic force acts between the adjacent layers to attract each other, but the magnetic charges on the adjacent plane are set off. A brock magnet, in total, shows zero magnetic charge inside since the neighboring magnetic charges are set off, and the magnetic charges with directions shown in the figure (c) remain only on the surface. This is the basic structure of magnets that we commonly see.

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#63 (2023.11.05)

Formation of shapes of galaxies: Types of galactic seeds

There are various types of galaxy shapes such as elliptical, disc, spiral and barred spiral ones. However, the current standard cosmology has no idea how these shapes were formed. The standard model states that the gravity gathers matters to form stars, and that their gravitational interactions form galaxies. It argues that complex shapes such as spiral galaxies were formed by the collision of galaxies. This theory cannot explain the very early formation of galaxies. Furthermore, although it should take some time for secondary shapes to be formed through galaxy collisions, many spiral galaxies in the early times of cosmic evolution have been actually observed. It cannot explain even why a single disc galaxy aggregates into such a thin disc. Unless they set too convenient initial conditions, it cannot explain the formation of any types of galaxies.
I explained the formation of galaxies by the ECT on pages p40 and p41. Later, simulations by the ECT gave many of the observed galaxy shapes (press release). From onward on some pages, I will introduce the formation of various galaxy shapes. First, let us sort out the types of galactic seeds that release stellar seeds.
After repeated galactic seed separations, a seed becomes no longer capable to separate, then starts to release stellar seeds. Depending on the form of the last galactic seed separation, the shape of the galaxy resulting from stellar seed releases differs. We use the same classification as that for gamma-ray bursts explained on p39 as sources of stellar seed releases.

Type-1 shows a sufficient receding speed in the orthogonal separation, and the two galactic seeds continue to move away from each other. Each can be treated as an isolated single galactic seed.
In Type-2, a flat separation takes place just after orthogonally divided. The distance of the two seeds does not shrink again, but keeps almost constant. The two galactic seeds rotate like binary stars. Let us call them as the binary galactic seeds.
Type-3 shows a large release of energy by radiation, and the two seeds vibrate around the energy trough then come to rest, resulted in two attached galactic seeds. This type of attached galactic seeds may or may not rotate by cases.

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#64 (2023.11.06)

Types of stellar seed releases

There are two types of stellar seed releases from a galactic seed; the linear release and the ring release.

In the linear releases, stellar seeds are released individually, randomly, and continuously from the circumference of a galactic seed, then make a linear motion. On the other hand, in the ring release, stellar seeds are released horizontally all at once on the circumference of a galactic seed, resulting in a ring-shape distribution of stellar seeds. The important feature is that the released stellar seed ring is not a continuum but exhibits an intra-circulation force and continues to circulate. Furthermore, the ring release does not occur continuously, but a ring of stellar seeds is released intermittently.
When the circulating velocity is high, majority of stellar seeds are released in the plane of the galactic seed, which we call as the flat release. They are also released in the vertical directions (called as the orthogonal release) and in intermittent directions. In the case of the orthogonal release, as explained in p40, a stellar seed receives a force from the galactic seed, moves spirally, and finally comes to rest above or below it. These stellar seeds accumulate to form a bulge.

If only linear releases occur from an isolated galactic seed (Type-1), it will give an elliptical galaxy (Type 1-1). The major feature is that the component stars (stellar seeds) do not circulate, and exhibit an elliptical (rugby ball-shaped) distribution.

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#65 (2023.11.07)

Single galactic seed – Ring releases

If a ring release from a single galactic seed occurs intermittently, it will show a disc-like distribution with many concentric circles spread out. It is accompanied by a bulge in the center and a halo structure around the periphery. We call this type of galaxies as the disc galaxy (Type 1-2). A typical example is NGC 3923. This galaxy is generally called an elliptical galaxy, but detailed observations have shown that it has a disc structure consisting of many concentric circles, and that the ratio of the radius of adjacent circles is about 1.1 times.
In simulating galaxy formation, we use the exponential time, during the value one of which the space expands by 1.1 times, as the time interval for ring releases. During T_1.1=m, the space expands by 1.1^m times. If the radius of a stellar seed ring was r_m at T_1.1 = - m, the current radius r₀ has expanded to become: \[ r_0 = 1.1^m r_m \:\: \:\:\: (r_m : \text{radius at } T_{1.1}=-m) \] The ring releases for m=24 - 0 give the disc galaxy shown by the below figure (b). Its example is NGC 3923. If the galactic seed is exhausted on the way, the annulus galaxy shown by the figure (c) is formed. This type is usually called a ring galaxy, but we use the term annulus because the ring is used for a different form. The figure (c) is the results of ring releases for m = 26 - 22. An example of this type is Hoag's Object.

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#66 (2023.11.08)

Rotating binary galactic seeds – Formation of bar-bulge

Type-2 binary galactic seeds, which were resulted by a flat separation, lie on the same plane and are rotating. The radius of this binary rotation is almost constant in the short term, but expands in the long term due to the space expansion. In contrast to that a ring release from a galactic seed occurs intermittently, linear releases happen randomly on the circumference, but in the long term it can be treated as occurring continuously throughout the circumference.
Flat releases of stellar seeds from a galactic seed occur in all directions. But, in directions facing each other as shown in the below figure (c), when stellar seeds pass each other in opposite directions, attraction by the fundamental force works between them to form a circulation of stellar seeds. This accumulates over a long period of time, and form a new type of a bulge-like structure. As time progresses, increases the distance of the rotating binary galactic seeds. In the case of right rotation, as shown in the figure (d), is formed an elliptical bulge-like structure that is shifted to the left from the current positions of the galactic seeds. I named it as the bar-bulge. The bar of generally called a barred galaxy is this bar-bulge.

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#67 (2023.11.09)

Rotating binary galactic seeds – Ring releases

Let us consider the intermittent ring releases with an interval of T_1.1=1 from rotating binary galactic seeds. The below figure (a) shows the positions of the galactic seeds from T_1.1=-18 to the present T_1.1=0 and the current forms of the released stellar seed rings. Since the stellar seed ring does not interact with the galactic seed, stellar seeds remain in place whereas the galactic seeds rotate. For both of stellar seeds and galactic seeds, the distance from the center of the galaxy increases due to the space expansion. The angular velocity of the binary rotation decreases as the radius increases. The radius of the galactic seeds is almost constant, but the radius of the stellar seed rings increases as the space expands. The released stellar seed rings currently show a ring-shape distribution as shown in the figure (a). The binary galactic seeds are located at the two ends.
The stationary part of a bulge at the center remains on the stellar seed ring, while the peripheral part disperses. As a result, as shown in the figure (b), a continuous ring distribution of the bulge appears on the same position as the ring distribution of the stellar seed rings. Furthermore, as mentioned in the previous page, a bar-bulge is formed in the center, giving the overall shape as shown in the figure (b). I named this type as the barred ring galaxy. An example of it is NGC 5728.

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#68 (2023.11.10)

Rotating binary galactic seeds – Binary-end linear releases

When the rotational angular velocity of binary galactic seeds is large, linear releases from the binary end of each one become prominent, and the ring release becomes hard to occur. If this state continues to the present, the distribution of stellar seeds shown in the figure (a) is formed. The figure shows the positions of galactic seeds every T_1.1=1 and the current positions of stellar seeds released from them. In fact, they are released continuously. The release direction is tangential to the binary rotation, and the released stellar seeds move linearly at a constant speed. However, the distance of each one from the center expands due to the space expansion. The figure (b) shows the overall shape including a bar-bulge. This type is named as the barred arm galaxy. An example of it is NGC 1300.
The rotational angular velocity of binary galactic seeds decreases as the distance between the two seeds expands. If it decreases to the threshold, the binary-end release becomes impossible on the way and changes to the intermittent ring releases, forming the distribution as shown in the figure (c). We call this type as the barred ring-arm galaxy. An example of it is NGC 2217.

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#69 (2023.11.11)

Attached galactic seeds - Ring releases

Intermittent ring releases of stellar seeds from the Type-3 galactic seeds, which are attached each other after a flat separation, form a double-disc galaxy. There are a variety of attached galactic seeds different in the rotation speed; non-rotating or various values. When the rotation speed is zero, the distribution shown in the figure (a) is given.

In the case of non-rotating attached galactic seeds, the bulge remains over and under the galactic seeds. An example of this type of a non-rotating double-disc galaxy is Andromeda Galaxy. Two galactic cores have been confirmed at the center of the Andromeda Galaxy, and observations at various wavelengths have revealed a double-disc structure.
If attached galactic seeds rotate, spiral structures emerge splendidly. The below figures (b)(c)(d)(e) are results of simulations for respective angular velocities. I named them as the spiral double-disc galaxy. NGC 5861, NGC 6384, NGC 3147 are examples of the spiral type.

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#70 (2023.11.12)

Bulges of a spiral double-disc galaxy

Let us consider the distribution of bulges of the spiral double-disc galaxy shown in the figure (c) on the previous page. The attached galactic seeds rotate, and their distance does not change with kept as attached. However, each bulge formed by orthogonal releases remains stationary, and departs from each galactic seed. Each bulge, which was stationary at the center of each galactic seed in the early stage of its formation, increases in the radius of its distribution and the distance from the center of the galaxy as the space expands. The simulation results of distribution of bulges are shown in the figure (a) below. The bulges in the figure are shown as intermittent circles, but in reality, the bulge formation occurs continuously.

The bulges are located in the disc exactly between the spirals of stellar seeds, and expands above and below the disc due to the space expansion. The overall shape including stellar seeds and bulges is shown in the figure (b) below. Bulges are shown in green. The concentration of bulges is high in the center, and becomes lower towards the periphery.

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#71 (2023.11.13)

Attached-then-binary rotating galactic seeds – Ring releases

The radius of an energy circulation is proportional to the amount of its energy. When a galactic seed repeats the ring release of stellar seeds, the radius gradually decreases. In previous simulations so far, the radius of galactic seeds was dealt as constant over time. In the case of attached galactic seeds, if they are kept as attached, we can ignore the decrease in the radius even if the radius decreases to some extent. However, if the rotation speed of attached galactic seeds is high, they become incapable to keep attached when the radius of galactic seeds gets small, and they separate on the way and convert to rotating binary galactic seeds. As an example, in the below figure are shown simulated results of the following case of ring releases: The galactic seeds were firstly attached each other from T_1.1=-24 to T_1.1=-13, then became binary ones from T_1.1=-12 to T_1.1=0 with the radius reduced to a half.
In the figure (a), is shown the distribution in the disc of stellar seeds by ring releases, and two red circles show the current locations of galactic seeds. The figure (b) shows the projection of the bulges onto the disc plane (spreading upward and downward). The figure (c) shows the overall structure of this galaxy including the bar-bulge. There bulges are shown in green. I named this type as the barred ring & double-disc galaxy. An example of it is NGC 105.

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#72 (2024.10.08)

Two ways to express a particle energy

From here, let us discuss the novel dynamics by the ECT. The following Newtonian equation of motion, which shows the acceleration by a force, is correct when the initial speed is zero, but does not hold true when the velocity becomes large. Any particle cannot be accelerated to the light speed or greater. Let us examine a new equation of motion as well as relations of some kinds of energy. \[ F=m\alpha=m\frac{dv}{dt} \;\; \;\; \left( v_0 =0 \right) \] There are two ways to express the energy of a particle: (1) expression by the rest energy and the kinetic energy of the entire particle, (2) expression by the helical motion of the intrinsic energy.
(1) Expression by rest energy and kinetic energy:
We define the rest energy as the total energy minus the kinetic energy. As we will explain on the next page onward, the potential energy is incorporated in the rest energy. \[ E_r \equiv E - E_k \\ E = E_r + E_k = mc^2 + E_p + E_k \] (2) Helical expression:
The intrinsic energy of a static elementary single circulation is circulating by the radius μ₀ and the frequency ω₀. If it receives a force and is accelerated to a velocity v, the intrinsic energy shows a helical motion. The velocity is the vector sum of the circular component C_r and the linear component v, and its magnitude is equal to the original circulating velocity = light speed. \[ {\mu_0}^2 {\omega_0}^2 ={C_r}^2 + v^2 = {\mu_0}^2 {\omega}^2 + v^2 = c^2 \] The elementary double circulation, which is a coupled pair of conjugate circulations, has its internal motion of the frequency ±ω₀ when stationary and of ±ω after acceleration. Therefore, in term of energy, it can be treated exactly the same as the elementary single circulation. The same is true for all quantum particles consisting of elementary circulations. In all types of particles, their mass (intrinsic energy) m is helically moving, and shows the following circular energy E_c and linear energy E_L. \[ E = mc^2=E_c + E_L =m{C_r}^2 +m v^2 =m \left( {\mu_0}^2 {\omega}^2 + v^2 \right) \] In either of (1) or (2), the total energy does not change due to an acceleration caused by a force. This will be explained on the next page onward.

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#73 (2024.10.09)

Potential energy

If a force acts between two objects, there exists a potential energy of the force. When a force F works on an object, the potential energy can be defined as follows, with distance x as a variable. \[ U(x) \equiv \int^{x}_{x_0} \left( -F(x) \right) dx + U(x_0) \] We specify the value U(x₀) at a reference point x₀ as the reference value. In general, such as for the gravitational force and the inter-circulation force between energy circulations, the value at infinity is set to be zero, and the potential energy is defined as below. \[ U(x) \equiv \int^{x}_{\infty} \left( -F(x) \right) dx \;\; \;\; \;\; \left( U(\infty) := 0 \right) \] The elementary charge pair eCP, which was explained in p52, is the building block that makes up the electric potential energy. These are connected in series or parallel, and the vector sum of individual eCP values becomes the total polarization energy (= electric potential energy). In an eCP, which is a prolonged iS, the force shown in p52 remains only at the two ends, and the forces are cancelled out inside. The force is equal to the virtual case that the elementary charges +e and -e are located at the ends. We define the "electric potential energy" as follows. This is a vector, having the direction between electric charges at ends (negative charge to positive charge is taken as plus direction). \[ U_e(x) \equiv \int^{x}_{2 \mu_0} \left( -F_e (x) \right) dx + m_0 c^2 \;\; \;\; \;\; \left( U_e(2\mu_0) := m_0 c^2 \; , \; \;\; x \ge 2\mu_0 \right) \] By absorbing or emitting a light (energy), the length and the electric potential energy of an eCP change. We set the electric potential energy at the smallest length 2μ₀ of eCP, which is that of iS, to be the total energy m₀c² of iS. With this setting, the electric potential energy of an eCP becomes equal to the total energy of the eCP.

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#74 (2024.10.10)

Various energies in a free motion

The term "free motion" here means a motion that shows a free acceleration by a force without hindered by others. It includes the free fall, but is a wider concept. When a static object receives a force and get accelerated, how does its energy change?
Consider the case where a ball of mass m is hit by another object (counterpart) at the position x = 0, then departs from it at x = Δx and linearly moves at velocity v. According to the standard physics, it is perceived that the kinetic energy of this ball increases due to the work done by the force it receives, and the total energy also increases by the same amount. There, the rest energy is considered to be invariant. However, this is actually incorrect; the total energy does not change even if it receives a force and gets accelerated. Let us see the details.
There is a very important point to note here. The potential energy exists only in the region where a force acts. The ball receives a force only in the region 0 ≤ x ≤ Δx where it is in contact with the counterpart, and a potential energy exists only there. Taking the value at x = 0 as zero as the reference value, the potential energy is given by the following equation. \[ U(x) \equiv \int^{x}_0 \left( -F(x) \right) dx \;\; \;\; \;\; \left( U(0) := 0 , \;\;\;\; 0\le x \le \Delta x\right) \] In a free motion, the kinetic energy is given by the below formula. \[ E_k (x) = - E_p (x) \] Therefore, the total energy of the ball is shown as follows, and remains unchanged from before acceleration. \[ E = mc^2 + E_p (x) + E_k (x) = mc^2 + E_p (x) - E_p (x) = mc^2 \] The rest energy is defined as the total energy minus the kinetic energy. \[ E_r (x) \equiv E - E_k (x) \] Therefore, the potential energy is incorporated in the rest energy, as shown below. \[ E = mc^2 + E_p (x) + E_k (x) = E_r (x) + E_k (x) \\ E_r (x) = mc^2 + E_p (x) \] In the case of this ball before the collision, a potential energy does not exist, and the velocity is zero, and the total energy is equal to the rest energy. In 0 ≤ x ≤ Δx , it receives the force F from the counterpart, and accelerates. In x > Δ x it shows a uniform motion at speed v, and no potential energy exists but there is a kinetic energy, by the amount of which the rest energy is reduced. In 0 ≤ x ≤ Δx where it is in contact, it exerts the force -F to the counterpart. Therefore, while the ball receives a force and its kinetic energy increases, in the same time it exerts a force of the opposite direction to the counterpart, and its potential energy decreases. Thus, the total energy does not change. By the collision, the counterpart shows a decrease in kinetic energy and an increase in potential energy. The standard physics considers only the change in kinetic energy for the two objects, and fails to see the change in potential energy, which is reflected in the rest energy.

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#75 (2014.10.11)

Novel equation of motion

Next, let us derive a novel equation of motion. First, let us see the acceleration of the single circulation S in space-space dimensions.
At the initial speed is v = 0, the Newtonian equation of motion holds true. \[ F = m_0 \alpha = m_0 \frac {dv}{dt} \;\;\;\; (\text{for } v_0 = 0) \] This equation is valid only for the range 0 ≤ v ≤ 0 + dv.
Next, let us consider the acceleration of the particle at the speed v = v₁. Take a moving frame at v₁ in the same direction of the particle’s motion. The helical expression of the energy in this frame becomes
\[ E = M \left({C_r}^2 + V^2 \right) = m_o c^2 . \] V is a linear velocity, having the following relation. \[ V = v - v_1 \] The circular velocity C_r is the same either in the rest frame or the moving frame. \[ {C_r }^2= c^2 - v^2 \] At v = v₁, that is, V = 0, the particle shows only the circular energy. \[ E = M{C_r}^2 = m_0 c^2 \] At this point, since the initial speed is V = 0, the Newtonian equation of motion holds true in this moving frame. \[ F = M \frac{dV}{dt} \;\;\;\;\; (\text{at }V=0) \] The moving speed v₁ of the moving frame is a constant, so the acceleration in the moving frame is equal to that in the static frame, as shown below. \[ \frac{dV}{dt} = \frac{v-v_1}{dt} = \frac{dv}{dt} = \alpha \] Therefore, from these relations shown above, the equation of motion at V = 0 is transformed to as below. \[ F = M \frac{dV}{dt} = m_0 \frac{c^2}{{C_r}^2} \frac{dv}{dt} = \frac{m_0 c^2}{c^2 - {v_1}^2}\alpha = \frac{m_0}{1 - {v_1}^2 / c^2}\alpha \] This equation holds true for any value of v₁ as long as 0 ≤ v₁ < c. As the equation of motion for the particle S, we get the following formula. \[ F = \frac{m_0}{1 - v^2 / c^2}\alpha \] Next, let us see the acceleration of the elementary single circulation iS in hidden-space dimensions. iS shows the same intrinsic energy m₀ and circulating velocity v_c = c as those of S. The velocity in the hidden dimension H is invariant with c. The velocity in space dimensions is c in total, but each of components in 3D can be flexibly changed by rotating around the H axis. \[ {v_x}^2 + {v_y}^2 + {v_z}^2 = c^2 \] Let in Y-Z plane be the circulation at rest. Then, the circular velocity and the linear velocity become as follows, which are exactly the same as in the case of S. \[ {C_r}^2 = {v_y}^2 + {v_z}^2 \;, \;\;\; v^2 = {v_x}^2 \] \[ m_0 \left( {C_r}^2 + v^2 \right) = m_0 c^2 \] Therefore, the equation of motion for S applies as it is to iS.
The above discussions apply not only to the elementary single circulations, but also to the elementary double circulations, and further to quantum particles that consist of elementary circulations. By replacing the intrinsic energy (mass) m₀ with the value m of each particle, we obtain the following general equation of motion. \[ \textbf{Equation of motion} : \;\;\; F = \frac{m}{1 - v^2 / c^2}\alpha \] This equation can be interpreted in two different ways depending on the frame.
(1) In the static frame to the space energy, the intrinsic energy is m, and its acceleration varies by velocity. \[ F = m \alpha_v \;, \;\;\; \alpha_v = \frac{1}{1 - v^2 / c^2}\alpha_0 \] (2) In the co-moving frame with the particle, the intrinsic energy M varies by velocity. \[ F = M \alpha \;, \;\;\; M = \frac{m}{1 - v^2 / c^2} \]

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#76 (2024.10.12)

Kinetic energy

Based on the equation of motion, which was obtained in the previous page, let us derive an equation that shows the kinetic energy in a free motion.
Take the case that a particle of mass m receives a force F. Let v = 0 be the initial speed at the location x = 0, and we will express the kinetic energy by the velocity v at any x. At v = 0 , the total energy is the rest energy, in which the potential energy is incorporated. \[ E = E_r (0) = mc^2 + E_p (0) \] When it is accelerated to a velocity v, its potential energy decreases and a kinetic energy is added. \[ E = E_r (v) + E_k (v)= mc^2 + E_p (v) + E_k (v) \] Since it is a free motion, the total energy does not change by the acceleration. So, the kinetic energy is as below. \[ E_k (v) = E_p (0) - E_p (v) \] If we express the potential energy with the variable x, we obtain the following relation from the definition of the potential energy. \[ E_k = - \int^{x}_{0}\left( -F(x) \right) dx = \int^{x}_{0} F(x) dx \] From the equation of motion in the previous page, the force is expressed by the velocity as a variable as follows. \[ E_k = \int^{x}_{0} \frac{m}{1 - v^2 / c^2} \frac{dv}{dt} dx = m \int^{v}_{0} \left( 1 - \frac{v^2}{c^2} \right)^{-1} vdv \] Here, we perform the following integration by substitution. \[ T \equiv 1 - \frac{v^2}{c^2} \; , \;\;\;\;\; \frac{dT}{dv} = -\frac{2v}{c^2} \] \[ m \int T^{-1} v \frac{c^2}{-2v} dT = - \frac{mc^2}{2} \int T^{-1} dT = - \frac{mc^2}{2} \log T + C \] Taking the definite integral from v = 0 to v = v, we obtain the following equation of the kinetic energy. \[ \textbf{Kinetic energy}: \;\;\;\; E_k = - \frac{mc^2}{2} \log \left( 1 - \frac{v^2}{c^2} \right) \] By the Taylor expansion, it becomes as follows. \[ E_k = \frac{1}{2} mv^2 \left( 1 + \frac{v^2}{2c^2} + \frac{v^4}{3c^4} + \frac{v^6}{4c^6} \; \cdots \right) = \frac{1}{2} mv^2 \sum_{n=1}^{\infty} \frac{1}{n} \left( \frac{v^2}{c^2} \right)^{n-1} \] This is the novel equation of the kinetic energy by the ECT. It differs from both the equation in the Newtonian mechanics and that in the theory of relativity. As v approaches to c, the kinetic energy diverges to the plus infinity, and the potential energy diverges to the minus infinity.
The helical expression by the circular and linear energies covers v = c. Even if a particle is accelerated near to the light speed, the total energy never increases. The linear energy increases near to the total energy in the case.

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#77 (2024.10.13)

Energy of a static particle under receiving a force

So far, we have been talking about the free motion. There is another type of motion that is not a free motion. It is that an object is receiving a continuous force but keeps stationary even if the distance with the counterpart changes. A typical example is the change in the altitude of an object on the earth.
Under receiving a continuous force F(x), if a static particle moves by a distance Δx and keeps stationary, its total energy is increased or decreased by the change in the potential energy. The initial energy at x = x₁ is as shown below, where the potential energy is incorporated in the rest energy. (The rest energy is equal to the total energy as the particle is static.) \[ E(x_1) = m_1 c^2 = mc^2 + E_p (x_1) \] The energy at x = x₁ + Δx becomes as follows. \[ E(x_1 + \Delta x) = E(x_1) + \int^{x_1 + \Delta x}_{x_1} \left( -F(x) \right) dx = m_1 c^2 + \Delta E_p \] By the helical expression, it is shown as below, where we can confirm that the mass (intrinsic energy) has changed. \[ E(x_1 + \Delta x) = m_1 c^2 + \Delta E_p = E_c (x_1 + \Delta x) = (m_1 + \Delta m)c^2 \] In the standard physics, it is said that the rest energy (mass) remains constant even if the potential energy changes. However, in reality, as shown above, the rest energy (total energy) increases or decreases with a change in the potential energy.

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#78 (2024.10.14)

Change of mass of a static particle with altitude above ground

As explained in the previous page, the gravitational potential energy of a particle at rest on the ground changes with altitude. So, the total energy and the mass (intrinsic energy moving at the light speed) also change with altitude. The mass m₀ of an elementary single circulation, which appeared time to time in this book, is the value in the outer space where the gravity can be ignored. Consider a particle, which shows a mass m outside the earth’s gravity.
The energy and mass of a particle at a distance r from the center of the earth are reduced by the amount of the potential energy, as shown below. \[ E(r) = m(r) c^2 = E_r (\infty) + U(r) = mc^2 + U (r) \] Let M be the mass of the earth, then the potential energy is given by the below equation, which is negative (zero at infinity). \[ U(r) = \int^r_{\infty} \left( -F(x) \right) dr = \int^r_{\infty} G \frac{Mm(r)}{r^2} dr \] Let r₀ be the reference point for r such as the sea level. The energy of the particle can be expressed as follows. \[ E(r) = m c^2 + U(r_0) + U(r) - U(r_0) = m(r_0)c^2 + \Delta U(r - r_0) \] Here, we approximate m(r) as constant at m(r₀). \[ \Delta U(r - r_0) = \int^r_{r_0} G \frac{Mm(r)}{r^2} dr \approx GMm(r_0) \left( \frac{1}{r_0} - \frac{1}{r} \right) \] \[ E(r) \approx m(r_0)c^2 + GMm(r_0) \left( \frac{1}{r_0} - \frac{1}{r} \right) \] Here, take the see level as the base, and let h be the altitude above it. \[ r = r_0 + h \] If h is extremely smaller than r₀, we can further approximate it as below, where g is the gravitational acceleration at zero in the altitude. \[ E(r) \approx m(r_0)c^2 + \frac{GMm(r_0)}{r_0} h = m(r_0)c^2 + m(r_0)gh \;, \;\;\;\; g \equiv \frac{GM}{r_0} \] Thus, the higher the altitude is, the greater the rest energy and mass of a particle are. \[ E(r) = m(r) c^2 = \left( m(r_0) + \Delta m \right) c^2 \] For this case, the standard physics claims that the potential energy increases, but the rest energy and rest mass remain constant. However, as we have explained so far, it is incorrect.
The change in altitude causes the change in mass for all types of particles. It also makes the energy levels of atomic orbitals change. Therefore, the radiation frequency of an atom also increases at a high altitude. There is a historical experiment that measured this change. Pound and Rebka reported in 1960 a difference of the gravitational potential energy over a height of 22.5 meters as a shift in frequency of the electromagnetic radiation of ⁵⁷Fe. They detected a frequency difference of Δν / ν = 2.5×10⁻¹⁵, which was equal to the theoretical energy difference of ΔE / E = gh / c².
The clock frequency of an atomic clock also alters with the altitude. Therefore, an atomic clock needs the adjustment of its clock frequency for one second by the altitude of its location. In the standard physics, they insist that the change of clock frequency comes from the difference of the gravitational redshift by the height from the general relativity. They claim that time passes faster at a higher altitude than at a lower altitude. However, as explained in this book, their claims are wrong since they are subjected that the rest mas remains constant regardless of altitude differences, the assumption of which is incorrect. There is no change in the passage of time, but the increase in potential energy causes the atom to have a larger mass and a higher radiation frequency.

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#79 (2024.10.15)

Charge for the gravitational force - Orthogonal energy

Let us think about the mass in the Newtonian equation of gravity. This is a charge to render a force. The charge for the fundamental force is a momentum, but the equation in p4 shows that the orthogonal component momentum _rp is the charge if precisely speaking. This is the momentum of the component energy derived from the motion of the intrinsic energy in orthogonal directions.
For the gravitational force, the charge is not the total energy but the component energy, the motion of whose intrinsic energy is orthogonal to the force direction. Let us define the "orthogonal energy" as the energy component of the motion of the intrinsic energy (mass) in orthogonal directions to the force, and express it as E_ort.
Any energy circulation, which is a particle, can be treated as orthogonal to any directions, regardless of the direction of its plane. In the case of a static particle, all of the total energy, rest energy, circular energy, and orthogonal energy are equal to each other. \[ E = E_r = E_c = E_{ort} \] The circular energy is in the direction orthogonal to the motion of the particle. On the other hand, the orthogonal energy is in the direction orthogonal to the force.
The gravitational force acting on a particle of a mass m moving at a speed v from a static object of a big mass M is given by the following equation. \[ \textbf{Gravitational force}: \;\;\; F = - G\frac{Mm_{ort}}{d^2} \;, \;\;\;\; m_{ort} \equiv \frac{E_{ort}}{ c^2} \] (1) Gravitational force is in the same direction as its motion:
The circular energy acts as the orthogonal energy. \[ E_{ort} = E_c = m{Cr}^2 = m (c^2 - v^2) \;, \;\;\; m_{ort} = m \left( 1 - \frac{v^2}{c^2} \right) \] (2) Gravitational force is in an orthogonal direction to its motion:
The total energy acts as the orthogonal energy. \[ E_{ort} = E = mc^2 \;, \;\;\; m_{ort} = m \] In the case of (2), the linear velocity v is also orthogonal to the force, so the total energy acts as the orthogonal energy. If a particle is accelerated from at rest, the moving direction will be the same as that of the force. However, if it has an initial velocity, the direction of motion will bend when a force acts in an orthogonal direction. Typical examples are orbiting planets around the sun, and satellites around the earth.
In the caser of light, its circular energy is zero. Therefore, the light does not receive any gravitational force in the moving direction. However, in an orthogonal direction to the motion, the orthogonal energy is the total energy, and the light receives a gravitational force, which bends its propagation direction. This is the phenomenon of gravitational lensing. By a gravitational force, the light cannot be accelerated in magnitude of its speed, but can be bent in its direction. \[ E_{\gamma} = m_{\gamma} c^2 \;, \;\;\; C_r = 0 \;, \;\;\; v = c \] \[ E_c = m_{\gamma} {C_r}^2 =0 \;, \;\;\; E_L = m_{\gamma} v^2 = m_{\gamma} c^2 \]