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Canadian Journal of Pure and Applied Sciences

Vol. 15, No. 3, pp. 0000-0000, Oct 2021

Online ISSN: 1920-3853; Print ISSN: 1715-9997

Available online at www.cjpas.net

AN ALTERNATIVE TO UNDERSTAND THE ORIGIN OF UNIVERSAL

GRAVITATION AND THE COSMIC BACKGROUND MICROWAVE RADIATION

FROM A SUPER PHOTON THOERY

Wenzhong David Zhang

Address: Hembury Avenue, Manchester, M19 1FH, UK.

ABSTRACT

Through analysing the interactions between the immersed matter particles and the thermal bath of a vast Super photon

ocean, the Super photon theory is developed quantitatively. The correlation between the Gravitational constant and the

Hubble constant is deduced. The generalised law of Universal Gravitation, the Tully-Fisher law, and the Modified

Newtonian Dynamics relation are derived theoretically. The dynamic equilibrium and circulation of mass and energy of

the Universe are discussed. Flavour oscillation observed in neutrinos is taken as an evidence of immersed matter particles

that undergo two-way energy exchange with the thermal bath of the vast Super photon ocean having local fluctuations.

Gravitational waves are viewed as periodic density and pressure oscillations of the Super photon particles propagating

through the vast Super photon ocean. The temperature and the spectrum of the Cosmic Microwave Background Radiation

are explained theoretically and determined accurately using the Super photon theory together with the fluctuation-

dissipation theorem. The capability of a photon particle travelling at the constant speed of light in the free space with a

friction force is verified theoretically. Further supporting evidences to the Super photon theory are provided. An experiment

is proposed for the further proof of the Super photon theory.

Keywords: Super photon, Universal Gravitation, dynamic equilibrium and circulation, Tully-Fisher law, Modified

Newtonian Dynamics, Cosmic Background Microwave Radiation, fluctuation-dissipation theorem.

INTRODUCTION

It is interesting to know that Hubble remained cautiously

against the Big-Bang hypothesis until the end of his life. In

order to account for cosmic redshifts in a nonexpanding

Universe, Hubble called for a new principle of nature, like

the kind of Tired-Light mechanism (Hubble, 1937; Assis,

1992). On the other hand, he was aware of the theoretical

difficulties of such a radical assumption that was in conflict

with Einstein’s General Relativity. The differential

geometry used in Einstein’s General Relativity is

technically useful and predictive, however, it has

limitations. Einstein’s General Relativity spring out of

Maxwell’s equations, hence, the ideal approximations of

massless photon and frictionless free space are inherited, it

also does not include the self-rotational effect (Zhang,

2021a, 2021b, 2021c). The dynamic absorption and

dissipation of energy are not handled by the geometric

theory of gravitation (the General Relativity.)

Photon particles propagate at constant velocities

(in the free space and other spaces of transparent

media (Pound and Rebka, 1960; Broberg, 1993; Kardar and

Golestanian, 1999; Manjavacas and García, 2010). They

interact with each other, although the interactions are

extremely weak. Photon particles experience an extremely

weak force () resembling friction in the spaces they

travelling through (Zhang, 2021a, 2021b), i.e.

(1)

where is the viscous resistance coefficient of the space,

is the constant velocity of the photon particle travelling

through the space. From a mechanical perspective, a lightly

damped oscillator model was applied to elucidate the

properties and propagations of the photon particles in the

free space. Based on the analysis of the lightly damped

oscillator model for the photon particles, an alternative for

the understanding of the physical origin of the Cosmic

Redshift and the Hubble constant were elucidated. An

equation was deduced displaying the exponential

relationship between the Cosmic Redshift and the Hubble

constant with clearly defined physical meaning of every

parameter involved (Zhang, 2021a). The Hubble constant

was derived as an extremely low frequency with its origin

from the time constant, the ratio between the viscous

resistance of the free space and the inertial mass of

the photon particle travelling through, i.e.

(2)

_____________________________________________________________________

Corresponding author e-mail: WenzhongZhang2008@gmail.com

Canadian Journal of Pure and Applied Sciences

2

The energy dissipated by a photon particle during one cycle

was deduced as the product of the Planck constant and the

Hubble constant, which was defined as a Super photon

(Zhang, 2021a, 2021b). A Super photon is a fundamental

unit of energy and mass in dynamic circulation. There is an

unnoticeable and vast Super photon ocean in the Universe.

The normal photons and the Super photons in gigantic

number in the Universe interact with each other and create

a thermal bath, a vast photon ocean, or more fundamentally

a vast Super photon ocean. Through the analysing of the

interactions between the Super photons and the normal

photons, the foundation of the Super photon theory was

developed quantitatively (Zhang, 2021a, 2021b). A normal

photon particle is a dynamic packet of a number (N) of the

Super photon particles in a local agglomeration. The

interacting strength between a normal photon (having

energy ) and a Super photon (having energy ) as

an effective cross-section area was introduced,

where is the interacting strength thus effective cross-

section area between two Super photons. The average

numerical density of the Super photons (including the

Super photons in the dynamic packets of the normal

photons) in a unit of the free space was defined as .

During the time interval , a normal photon sweeps

through an effective volume of space as

, where is the speed of light in the free space.

Therefore, the normal photon particle meets a number

() of the Super photons during the time interval

. The number of Super photons interacts

with the normal photon particle during the time interval .

Hence, the normal photon particle exchanging energy with

the Super photon ocean during the time interval (Zhang,

2021a) is

(3)

The Super photons are spread out in the observable

Universe and they have a giant number. Hence, the average

mass density of the Super photons () must be a constant

on a cosmological scale. Two other Universal constants

( and ) were proposed together with (Broberg,

1993; Zhang, 2021a), where is the ratio between the

effective cross-section area and the inertial mass of a

photon particle, is the volume of the free space, which

is swept through by the effective cross-section area of a

photon particle during one cycle. These constants are

applicable to both the normal photons and the Super

photons. Some defined or derived relations (Zhang, 2021a)

useful for this article, are listed as follows:

(4)

(5)

(6)

where is the Planck constant, is the Hubble constant,

is the speed of the photons in the free space,

and are

subsequently the wavelength and the inertial mass of the

Super photon.

In this article, the correlation between the Universal

Gravitational constant and the Hubble constant is deduced.

A generalised law of Universal Gravitation is derived. The

Virial relation within the Solar system, the Tully-Fisher

law, and the Modified Newtonian Dynamics relation and

acceleration in Galaxies are derived theoretically. The

capability of a photon particle travelling at the constant

speed of light in the free space with a friction force is

theoretically verified. The temperature and the spectrum of

the Cosmic Microwave Background Radiation (CMBR)

are explained theoretically and determined accurately

using the Super photon theory and the fluctuation-

dissipation theorem. Further supporting evidences to the

Super photon theory are provided. An experiment is

proposed for the further proof of the Super photon theory.

The interactions between Super photon particles and

concrete matter particles, the origin of the Universal

Gravitation

Imagining a relatively stationary concrete matter particle

(Zhang, 2021b) immersed in the ocean of Super photon

particles as shown schematically in Figure 1, the matter

particle with the inertial mass and the equivalent

effective interacting cross-section area would

receive an inflow of the Super photon particles and

neutrinos at light speed from its surrounding space. This

article focuses on the Super photon particles (including the

normal photon particles that are dynamic packets of the

Super photon particles locally) because neutrinos are

fermions that are supposed to make negligible contribution

to the long-distance force of the Universal Gravitation.

A Super photon is a photon with the smallest unit of energy

and mass, a photon is a dynamic packet of Super photons

locally. All photons including the normal photons and the

Super photons have wave and particle dualities. The

average numerical density of the Super photon particles in

a unit of the free space was defined as (Zhang, 2021a),

assuming a percentage ( of the

Super photon particles from the free space flowing into

the matter particle with the momentum of every Super

photon particle as follows:

(7)

where ,

, , and are subsequently the momentum,

the wavelength, the energy, and the inertial mass of the

Super photon particle.

Wenzhong David Zhang

3

It is interesting to point out that the Super photon particle

has a momentum, so there must be pressure in the Super

photon ocean. Gravitational waves may be viewed as

periodic Super photon density and pressure oscillations

propagating through the vast ocean of the Super photons

with relatively long wavelengths. The number of Super

photon particles flowing into the matter particle during the

time is

(8)

Fig. 1. The schematic diagram showing the inward flow of

the Super photon particles with momentum per Super

photon towards a relatively stationary matter particle with

the mass .

If , it means that the matter particle absorbs all the

Super photons from its surrounding space. The 100%

absorbing without emitting cannot last forever from a

dynamic equilibrium point of view, eventually it will emit

to achieve a dynamic equilibrium with its surrounding

space. At this extreme, the matter particle behaves similar

to some Black Hole but without the problem of singularity.

Another extreme, if , it means that the matter

particle emits its mass and energy out, the mass and energy

of the matter particle will eventually be spread out into the

vast space of the Super photon ocean if keeping

all the time. The restricted occasion of a net number of the

Super photon particles flowing into the matter particle will

be investigated first, which means . The

corresponding mass and energy flowing into the matter

particle are

(9)

(10)

where and are subsequently the mass and energy of

the matter particle.

Inserting and from equations (4)

and (5) into equations (9) and (10) leads to

(11)

Because from equation (4), hence,

(12)

The mass and energy of the matter particle as the function

of time can be derived through the integration of equations

(11) and (12) as follows:

(13)

(14)

where and are the mass and energy of the

matter particle at its state of the lowest mass and energy at

.

Remembering is approximately

(Zhang, 2021a) and . Therefore, during a

relatively short period of time, for instance, days or years,

the mass and energy increasing are extremely tiny.

However, the tiny change of mass and energy accompanies

an inward force, the force leads to contracting, vibrating

and spinning of the matter particle around its equilibrium

position because the interacting with photons with linear

and circular polarizations. It may be explained further as

following. It is verified that the effect of the two kinds of

polarization of photons (linear and circular) at a certain

range of frequencies on silica nano-particles is quite

different (Ahn et al., 2018). Linear polarization causes the

silica particles to vibrate along the line of polarization

while circular polarization causes the silica particles to

spin. This may help to explain the spinning and vibrating

of the galaxies, the stars, the planets, and elementary

particles. The contracting, vibrating, and spinning of the

compositions of the matter particle induce internal friction

forces, which cause the increase of the internal temperature

and pressure. This increase of temperature and pressure

inside the matter particle trigger off expanding and

radiation, therefore, photons are released into surrounding

space. Part of the energy and mass absorbed is emitted out.

It can be predicted that the total energy radiated will be at

the maximum while the radius of the matter particle is at

its minimum and the total energy radiated will be at the

minimum while its radius is at the maximum.

While the author searched literature for supporting

evidence, it was found that the above prediction has been

Canadian Journal of Pure and Applied Sciences

4

confirmed by the quantitative measurement of the relation

between the total irradiance and the radius variations of the

Sun (Pap et al., 2001) and the amplitude of the fluctuation

is approximately 0.015%. It shall be viewed as a supporting

evidence of the dynamic circulation and equilibrium of the

immersed matter particle with the thermal bath of the Super

photon ocean. To maintain a relatively stable state of

temperature and movement (including the spinning and the

orbital velocity) the matter particle needs absorbing mass

and energy through interacting with the thermal bath of the

Super photon ocean at its surrounding, which means

. The matter particle also emits photons

because of compressing, frictions, and radiations. The mass

and energy radiated can be slightly more or less than the

mass and energy absorbed, which causes a mass and energy

oscillation of the matter particle. A dynamic circulation

and equilibrium state with fluctuation will be achieved.

Flavour oscillation observed in neutrinos (Cai et al., 2017)

may be taken as an evidence of immersed matter particles

that undergo two-way energy exchange with the thermal

bath of the Super photon ocean having local fluctuations.

The secret of the dynamic circulation and equilibrium of

mass and energy of the Universe is uncovered. Quantitative

details of the mechanism need further research. For a

normal photon, it releases a Super photon every cycle, its

wavelength continually increases slowly. It is the normal

photons that are expanding, it is not the space itself. The

matter particles absorb mass and energy through

interacting with the thermal bath of the Super photon ocean

to maintain their characterized temperatures and

movements. And the matter particles release mass and

energy by radiations, the released mass and energy mainly

as photons, which eventually return the mass and energy to

the free space by releasing Super photons every cycle while

travelling at light speed to achieve mass and energy

balance with the thermal bath of the vast Super photon

ocean. The nuclear reactions and element generations

inside the centre of galaxies and inside stars are probably

merely by-processes because of the impinging of photons,

neutrinos, and cosmic rays from all directions, and the high

temperature and high pressure induced by impinging and

frictions, which worth further research.

For a general illustration in a parable, all the galaxies, stars

and planets are music instruments with different keys and

strings, meanwhile, the Super photons, the normal photons,

neutrinos and cosmic rays flowing towards the music

instruments are the fingers of a glorious musician. All sorts

of emitted matters, visible and invisible lights are like

melodies spew out from the music instruments. It is

interesting that the melodies can eventually turn back to the

wonderful fingers of the glorious musician. Matter

particles with different size and mass absorb and release

different range of frequency and wavelength of photons to

sustain their characterized movements and temperatures,

and achieve dynamic equilibriums with their surrounding

spaces such as the thermal bath of the vast Super photon

ocean. Dynamic equilibriums are achieved, which is

manifested by the relatively stationary spectrums of

radiations from the galaxies, the stars, the planets, the

fundamental particles and elements, with their

characteristic range of temperatures, colours, brightness,

and movements.

Although we are still lacking of technologies to detect a

Super photon particle directly, we are capable to figure out

the mass and energy balance of galaxies, stars, and planets.

The Super photon particles are mainly single Super photon

particles and packets of the Super photon particles as the

normal photon particles in the free space. However, when

they are approaching the mass centre of the galaxies, stars,

and planets, a large percentage of them would pack

together in superposition and change appearance to

detectable normal photons and matter particles. For

instance, we are able to prove the energy balance of the

Earth through measuring and calculating the energy

absorbed by the Earth and the energy emitted by the Earth.

Certainly, through measuring and calculating the energy

and mass flowing towards the Sun and the energy and mass

the Sun radiated, we will be able to prove approximately

the energy and mass balance of the Sun in average,

although there are small fluctuations as observed on the

total irradiance variations of the Sun (Pap et al., 2001).

Another exciting point is that Newton’s law of gravitation

in the Solar System, the Tully-Fisher law, and the Modified

Newtonian Dynamics relation and acceleration in Galaxies

can be derived from the Super photon theory

quantitatively, which can help us to gain deeper insight into

the origin of the Universal gravitation.

As shown schematically in Figure 1, we define to

represent the radius of the effective interacting cross-

section area () of the matter particle

with a mass , hence,

(15)

Outside the ball of the effective radius , there will be a

random distribution of the Super photon particles. From

equation (8) written above, the number of the Super photon

particles flowing through the effective interacting cross-

section area () towards the matter particle during the

period is

(16)

Because the matter particle is in a dynamic equilibrium

with its surrounding, around the effective interacting

radius, the number of Super photon particles flowing

towards the matter particle should be approximately 50%

of the total number of Super photon particles to maintain a

random distribution of the Super photon particles in

Wenzhong David Zhang

5

average, hence, (fluctuating around 0.5 with an

average at 0.5). At a distance from the matter centre,

the fluid towards the matter particle must carry the same

number of Super photon particles, but flow through a

smaller area, if we define the local numerical density of

Super photon particles as , i.e.

(17)

The local numerical density with a local gradient of the

Super photon particles around the matter particle as a

function of is therefore,

(18)

Similar to equation (16) but applied at the radius , the

inward flowing rate of the Super photon particles is

(19)

This represents a directed rate of momentum or a force

transferred to the matter particle corresponding to

(20)

The force in equation (20) represents the Universal

Gravitation force between the centre mass and an

equivalent effective mass (), which represents the

average counter interactions from the rest of the Universe

through the vast Super photon ocean to achieve an energy

and force balance. The negative sign in front of simply

means when the centre of the matter particle is

absorbing the Super photons and contracting, the

equivalent effective mass of the rest of the Universe ()

is releasing the Super photons and expanding. While the

centre of the matter particle is releasing the Super

photons and expanding, the equivalent effective mass

() is absorbing the Super photons and contracting.

There is a mass and energy balance across the Universe. If

locally two matter particles with different masses interact

with each other, like the Sun and the Earth, a net

gravitational attracting force is induced between them

because they shield each other in the ocean of roaming

Super photon particles. Hence, they tend to become closer

to each other. If the Sun and the Earth are viewed together

as a whole, this net is contracting and local increasing of

the density of mass and energy happens, thus a counter

force emerged to cancel out the attracting force. These

reactions are for achieving a dynamic equilibrium of mass

and energy and to maintain relatively stable distribution of

mass and energy on a cosmological scale. Detailed analysis

and calculation will be done in next section.

Now let us compare equation (20) with Newton’s law of

gravitation, they are the same if we assign that

(21)

By using equation (5), we get

(22)

The Universal Gravitational Constant may be interpreted

as the interacting and coupling constant of a matter particle

with the rest of the Universe through its interacting with

the vast ocean of Super photons. Physical science is mainly

about the correlation of physical quantities. The correlation

between the Universal Gravitational constant and the

Hubble constant is disclosed quantitatively from equation

(22). For fully understanding its implications, further

research is worthwhile. By inserting

, [m3/kg s2] and

into equation (22), the average mass density of Super

photons on a cosmology scale as a Universal constant can

be derived as follows:

[kg/m3]

(23)

The value of the Universal constant R0 , the ratio between

the effective cross-section area and the inertial mass of a

photon particle (applicable to the Super photon as well) can

be estimated as follows:

2.44 [m2/kg]

(24)

Then we can derive that

(25)

The accuracy of the numbers in equations (23), (24), and

(25) depends on the accuracy of the values of and .

Having and at hand, we can do some interesting

calculations. As an example, let us start from using

equation (15) to calculate the effective radius of the Solar

System and the Milky Way Galaxy based on their known

total masses. In the Solar System, 99.86% of the system's

known mass concentrates in the Sun (Woolfson, 2000), the

total mass in the Solar System is approximately

. Inserting this value and into equation (15), we get

[m]. The border where the Solar System

terminates is not precisely defined because its outer

boundaries are shaped by two separate forces: the solar

wind and the Sun's gravity. The limit of the solar wind's

influence is roughly four times Pluto's distance from the

Sun, the heliopause, the outer boundary of the heliosphere,

is considered the beginning of the interstellar media, which

is approximately [m]. The Sun's Hill sphere, the

effective range of its gravitational dominance, is thought to

extend up to a thousand times further, which approximately

reaches [m] (Littmann, 2004). Our calculation of

[m] sits approximately in the middle of these

estimated radius based on the observations and

calculations.

Canadian Journal of Pure and Applied Sciences

6

Regarding the Milky Way Galaxy, recent studies (Phelps

et al., 2013; Kafle et al., 2014) indicate a range in mass, as

large as M☉ and as small as M☉,

where M☉ is the standard mass of the Sun. If we take both

the values, which are approximately from to

[kg], and insert them into equation (15), we

have from to [m]. The Milky

Way is the second-largest galaxy in the Local Group, with

its stellar disk approximately 30 kpc in the diameter. If we

believe that the ring-like filament of stars wrapping around

the Milky Way belongs to the Milky Way itself, which are

rippling above and below the relatively flat galactic plane,

its stellar disk can reach a diameter of 46 to 55 kpc (Xu et

al., 2015). The radius based on a diameter from 30 kpc to

55 kpc are between approximately and

[m], which are in good agreement with our

calculated values from equation (15), which is between

and [m].

Vice versa, the total mass based on the observed effective

radius may be estimated. For instance, if we use the

observed approximately [m] and

[m] as the effective radius, the estimated mass of the Milky

Way from equation (15) would be between

M☉ and M☉. The dimensions and masses of

other galaxies and stars may be estimated in the same way.

The gravitational force between two bodies, the

generalised law of Universal Gravitation, the Tully-

Fisher law and the Modified Newtonian Dynamics

The total momentum rate carried by the Super photon

particles from background space to the body of a matter

particle corresponds to a limited force from equations (4),

(5), (8), and (16) as follows:

(26)

Specifically, for the Sun (with at dynamic

equilibrium state) there is:

(27)

The value obtained with formula (27) can be compared

with the following gravitational force on the Earth from the

Sun according to Newton’s Law:

(28)

This would imply that the Earth-Sun system receives a

larger total momentum per second than the limited

momentum flow rate towards the Sun from the Sun’s back-

ground space. How can this and the Newtonian

gravitational force be explained? The solution is hidden in

the difference between the flows of the Super photon

particles absorbed by the matter particles in each of the two

participating bodies and the number of interactions that

takes place between the Super photons and the two

participating bodies. Each matter particle absorbs the Super

photon particles corresponding to the following rate of:

(29)

where is the mass of the Super photon particle, is

the mass of the matter particle.

Specifically, the would be the mass of the Earth if we

aim to calculate the gravitational force between the Earth

and the Sun. Let us imagine a Super photon in the Sun-

Earth two-body system while it interacts with the Earth.

The Earth absorbs

Super photon particles from

its surrounding space during the time interval of ,

meanwhile the Earth interacts with a total of

Super photons directed towards the

Sun. From equation (18), for the Sun-Earth system

. There must be a small percentage

( of the Super photon particles absorbed by the

Earth but not of the Super photon particles flowing towards

the Sun. Hence, the probability for absorption by the Earth

is defined by

(30)

The item containing the percentage in the denominator

of equation (30) is for avoiding double counting. As a

result, equation (30) can be simplified to:

(31)

The probability for interaction without absorption is

. Inserting the numerical values of (the mass

of the Sun) and (the distance between the Sun and the

Earth), it can be calculated that

. As

we know , the small percentage can be

neglected in comparison with , for the Sun-Earth

system, and .

Therefore, as an average, the Super photon particles in the

flow towards the Sun would interact with the Earth-Sun

system approximately times, and each

interaction would supply the momentum of to

the Earth-Sun system directed towards the Sun from the

Earth. It may be noted here that the wavelength of the

Super photon is comparable with the one in the observable

Universe. Therefore, the discussed interactions may take

place simultaneously over long distances. Our Universe is

entangled together with a gigantic number of the Super

photons with super long wavelengths. For wider

applications, represents the centre mass inside the

system, like the for the Solar System. So, equation

(31) can be generalised as follows:

Wenzhong David Zhang

7

(32)

In accordance with equations (22), (26), (29), and (31)

written above, the total force acting in between the Earth

and the Sun can be derived as follows:

(33)

where is the mass of the Earth. Therefore, for a two-

body system interacting via the gravitation, the equation of

Newton’s law of gravitation is an ideal approximation

while

, which is the case in the

Solar System. For wider applications, represents the

mass of the centre body, represents the mass of the

obiter, and represents the distance between them. So,

equation (33) becomes

(34)

Equation (34) may be called the generalised law of

Universal Gravitation of a two-body system. The

generalised acceleration of the two-body system can be

derived from equation (34) by dividing the mass of the

obiter, i.e.

(35)

The Newtonian acceleration is

(36)

The Universal acceleration is

(37)

and

(38)

The minus sign in equations (33)-(37) simply means that

the direction of the force is towards the centre. Because

and , from equation (37), the

absolute value of the Universal acceleration

[m/s2]. Inserting , and

(approximately

of the Super photons absorbed by the

orbiter is not from the Super photons flowing towards the

centre of the system, which is a reasonable assumption,

considering one of six faces in a cubic), the calculated

is approximately [m/s2]. For stars rotating

with the velocity around its rotational axis located in the

galaxy centre, the centripetal acceleration (

) must be

equal to the acceleration from equation (35), hence,

(39)

Therefore,

(40)

If

, which is the case of the Solar System, it

can be derived from equation (39) that

(the Virial

relation, which has been proved in the Solar system), then

we are in the Newtonian regime. For galaxies with much

larger and distributed masses, when becomes distant

enough,

becomes negligible, a regime is entered

with approximately constant density of the Super

photons,

, which leads to:

(41)

Combining equations (37), (40), and (41), we have

(42)

Equation (42) reveals the Tully-Fisher law (Binney et al.,

2008) and the modified Newtonian dynamics (MoND)

proposed in 1983 (Milgrom, 1983a, 1983b). is the

acceleration of the MoND,

according to Milgrom if taking the Hubble constant as

approximately 70.8 , which is in good

agreement with the theoretical calculation from the Super

photon theory with equations (37) and (42).

Astronomical observations show that for disk galaxies, the

fourth power of the orbital speed (

) of stars moving

around the core of the galaxy at the flat end of the rotation

curve is proportional to the total luminosity of the

galaxy. Since is proportional to the observable inertial

mass M of the galaxy, it is obtained that

M. This is

well-known as the Tully-Fisher law, which is a widely

applicable relation and it is originated from the empirical

fitting of astronomical observations and calculations. This

type of rotation curve differs drastically from that of the

planets rotating around the Sun, whose orbital speed,

according to the Newtonian mechanics and the General

Relativity in the weak field and small velocity

approximations, is

(the Virial relation). The

physical basis of the Tully-Fisher law is the relation

between a galaxy's total observable inertial mass and the

velocity at the flat end of the rotation curve .

In 1983, Milgrom interpreted the Tully-Fisher law as an

indication of a deviation from the Newtonian gravitation,

Canadian Journal of Pure and Applied Sciences

8

claiming the MoND (Milgrom, 1983a, 1983b; Binney et

al., 2008). Milgrom hypothesized that this relation should

hold exactly, thus interpreting it as an inductive law of

nature instead of an empirical relation. According to

Milgrom, the deeper significance of this relation between

this special galactic acceleration and the Hubble constant

should be revealed by future cosmological insights. Now

the Super photon theory has revealed the cosmological

insights into the physical origin of both the MoND and the

Tully-Fisher relations, which have been sought after for

over thirty years by McGaugh (2011) and (Hass, EPJ de.

2018. The 'constant Lagrangian' fit of galaxy rotation

curves as caused by cosmic space expansion under energy

conservation conditions. Pre-print.

https://vixra.org/pdf/1805.0342v1.pdf). Taking into

account the distribution of the observable inertial masses,

the rotation curve of Galaxies will be able to be fully

determined accurately without the assumption of dark

matter. If the universe is neither expanding continuously

nor expanding in accelerating, the adoption of the

assumption of dark energy becomes unnecessary as well.

Further supporting evidences of the Super photon

theory, the origin of the CMBR and the theoretic

determination of the temperature and the spectrum of

the CMBR

There may be a doubt that how a photon particle can travel

at a constant speed inside the free space with a viscous

friction force. The explanation is that the photon particle

behaves like a tiny spin rocket that releases an extremely

tiny fragment of mass and energy every cycle to combat

the viscous friction force and maintain the constant speed

of propagation. Let us do a simple calculation, first

assuming that is the speed of the photon particle with an

inertial mass of travelling through the free space with a

viscous friction force . According to equations (1) and

(2), for keeping a constant speed of , the average energy

dissipation of the photon particle within one

second of time to combat the friction force must be equal

to

(43)

Within the short period of one second, the frequency of the

photon () can be viewed as a constant value. Hence, the

photon totally spins as many as -cycles within the period

of one second. According to the Super photon theory, the

photon releases a Super photon every cycle with the energy

of . Employing the Planck-Einstein equation

, it can be derived that the energy releasing of the

photon particle within the period of one second of time

must be

(44)

The energy releasing of the photon particle within the

period of one second must be the average energy

dissipation of the photon within one second,

hence equalling equations (43) and (44), we can derive

: the photon particle in the free space can indeed

propagate at a constant speed . From an electromagnetic

point of view, the speed of photons in the free space is a

constant

because is the electric constant of the free

space, and is the magnetic constant of the free space.

These two constants imply that there is substance inside the

free space. The speed of light is determined by the intrinsic

properties of the substance inside the free space.

Interestingly, Maxwell derived the expressions for the

dielectric constant and the magnetic permeability of the

free space in terms of transverse elasticity and density of a

subtle substance inside the free space, i.e. the aether

(Maxwell, 1865; Rubik and Jabs, 2018). It is not well-

known that Einstein called for a relativistic aether in his

1920 speech given at the University of Leiden (Rubik and

Jabs, 2018), namely he proclaimed in German that

"According to the General Theory of Relativity, space

without aether is unthinkable."

Now it is theoretically derived that the subtle substance in

the free space is an interactive thermal bath of the vast

Super photon ocean spreading all over the observable

Universe. The subtle substance in the vast space of a

vacuum such as the interactive thermal bath of the vast

Super photon ocean is worth for further research. As far as

we already know, the subtle substance inside the vast Super

photon ocean has an elastic modulus, a stress tensor, a

shear tensor, a dielectric constant, a magnetic permeability

coefficient, a gravitic constant, a cogravitic (torsionic)

constant, a gravitoelectric constant, a cogravitoelectric

(torsionoelectric) constant, a gravitomagnetic constant, a

cogravitomagnetic (torsionomagnetic) constant

(Zakharenko, 2020), a magnetic susceptibility and a

characteristic electromagnetic wave impedance of 376.73

Ohms.

From an electromagnetic perspective, electromagnetic

waves propagate through a medium containing the

substance with an impedance must experience energy

dissipation. From a mechanical perspective, for the photon

particles roaming at light speed together with cosmic rays

and neutrinos through the interactive thermal bath of the

vast Super photon ocean there must be frictions and, as a

result, energy dissipations. Therefore, there must be energy

fluctuations according to the Fluctuation-dissipation

theorem (Kubo, 1966; Kardar and Golestanian, 1999).

While cosmic rays, neutrinos, and high-energy photons are

travelling through the thermal bath of the vast Super

photon ocean locally, the weak interactions will lead to a

linear increase of the energy of the thermal bath of the vast

Super photon ocean locally above its dynamic equilibrium

Wenzhong David Zhang

9

of energy level transiently. Consequently, a tendency of

relaxing to its original energy level builds up. While the

process of relaxing to the dynamic equilibrium of energy

level happens, the CMBR is emitted (Zhang, 2021b). The

energy fluctuations of the thermal bath of the vast Super

photon ocean caused by cosmic rays, neutrinos, and high-

energy photons locally travelling through must be the

origin of the spectrum of the CMBR. Hence, the origin of

the CMBR must be local and nonredshifted, thus it can

preserve its black-body radiation spectrum.

There is an excellent large-scale homogeneity because of

the dynamic equilibrium between the immersed travelling

particles and the vast thermal bath of the giant Super

photon ocean across the observable Universe. A piece of

supporting evidence is as follows: the Pierre Auger

Collaboration discovered that the anisotropy signal of

cosmic rays appears to be consistent with the sources of

cosmic rays in a cosmic-ray frame coincident with the

reference frame of the CMBR (Aab et al., 2017). The

author believes that the CMBR is the manifestation of the

energy fluctuations of the thermal bath of the vast Super

photon ocean, the weak afterglow of the free space where

cosmic rays, neutrinos, and high-energy photons are

locally travelling through. The weak anisotropy of the

CMBR must be linked with the anisotropy local

distribution of cosmic rays, neutrinos, and high-energy

photons, which must be a promising direction for further

research to validate.

Now let us determine the temperature and the spectrum of

the CMBR theoretically. The amplitude of the energy

fluctuation

of a unit volume of the free space

can be estimated based on information from (Assis and

Neves, 1995; Pap et al., 2001; Bradt, 2008; Huang et al.,

2012; Leff, 2015; Cai et al., 2017; Hill et al., 2018; Batista

et al., 2019), which must be approximately 0.015%. The

average mass density of Super photons in the free space is

known from equation (23) as [kg/m3].

Employing the Stephan-Boltzmann law for the cavity

black-body radiation (Bradt, 2008) and the Mass-Energy

equation, it infers that

(45)

where is the Stephan-Boltzmann constant, is the speed

of light in the free space.

Substituting all these values into equation (45), the

temperature of the CMBR can be determined as

theoretically, which is a nice match to the

measured value by COBE’s instruments (Bradt, 2008). The

theoretic modelling of the fluctuation-dissipation theorem

may be traced back to the Rayleigh-Jeans law, Wien

radiation formula, and Planck radiation formula for the

interpretation of the blackbody radiation spectrum (Boya,

2003). The thermal bath of the vast Super photon ocean is

a perfect cavity blackbody because it fulfils two conditions:

(*) The bath is in a thermodynamic equilibrium at a

relatively stable temperature, (**) The external

perturbation from the week interactions between the

thermal bath of the vast Super photon ocean and the cosmic

rays, neutrinos, and high-energy photons travelling through

locally is in the linear response regime because the

viscosity coefficient of the free space is extremely low.

Hence, it can be asserted from the fluctuation-dissipation

theorem that the spectrum of the CMBR obeys the Planck

radiation formula and have an excellent match with the

radiation spectrum of an ideal blackbody at the CMBR

temperature of approximately 2.73 [K]. The normal

photons of starlight can be treated approximately as an

ideal gas, the amplitude of the energy fluctuation of the free

space because of the normal photons can be theoretically

calculated (Leff, 2015) as follows:

(46)

According to the work by Assis and Neves (1995), the

energy density of the flux of cosmic rays is comparable

with the energy density of the starlight (the normal

photons). So, the amplitude of the fluctuation of the free

space must be doubled to 0.011% approximately by

including the influence of the cosmic rays. If adding further

the estimated small amount of energy fluctuation caused by

high energy neutrinos (Cai et al., 2017; Batista et al.,

2019), the total amplitude of the fluctuation of the free

space must be approximately 0.015%. The fluctuation-

dissipation theorem is a powerful tool in interrelating the

interactions between the thermal bath of the vast Super

photon ocean and the immersed travellers such as cosmic

rays, neutrinos, fundamental particles, elements,

molecules, planets, stars, and galaxies.

An experiment is proposed which may distinguish the

Super photon theory from the theories of expanding

Universe and Big-Bang cosmology. First, suppose that we

have a well-shielded vacuum chamber, inner surface

coated with graphite, with two well-aligned and transparent

windows at two opposite sides, locating in a laboratory at

a constant low temperature. If we shine different

electromagnetic waves through the chamber with well-

controlled vacuum environment and measure the

temperature fluctuations, and associate secondary

radiations inside the chamber, what can we expect to get?

If we shine intense -rays or

-rays through it, there will

be a detectable temperature fluctuation and associate

secondary radiations, according to the Super photon theory

because the energy dissipation must be able to reach a

measurable level. If we shine intense radio waves with

wavelength of tens of centimetres through it, there must

have no detectable temperature change because the energy

Canadian Journal of Pure and Applied Sciences

10

dissipation is at a negligible low level. However, according

to the theories based on massless photons travelling

through frictionless vacuum with no energy dissipation,

like the theory of General Relativity, Expanding Universe,

and Big-Bang cosmology, there will be no measurable

difference no matter what kind of photons shinning though

it. The author is confident that the proposed experiment

will be able to demonstrate clearly the limitations of

General Relativity, Expanding Universe, and Big-Bang

cosmology that are based on massless photons travelling

through frictionless vacuum with no energy dissipation.

Concerning many assumptions dependent on the

cosmological models, these assumptions employed during

the analyses of astronomical observational data create

confusions. For instance, the cosmology models based on

the General Relativity take into account the effect of time

dilation (Melia and Maier, 2013). However, the time

dilation effect is not generally applicable, no time dilation

effect was observed in the light curves of quasars and in

duration measures of gamma-ray bursts (Hawkins, 2010;

Kocevski and Petrosian, 2013; Littlejohns and Butler,

2014). The time dilation effect of Supernova Ia light curves

can be explained as clock retardation because of the local

increase of viscosity, or being the signature of some special

evolutionary process (Drell et al., 2000), or cosmology-

dependent assumptions made during the analyses of the

light curves (Crawford, 2017). Big-Bang cosmological

model claims that the CMBR is composed by photons that

is a remnant from an early stage of the Universe, known as

relic radiation dating back to the epoch of recombination

(photon decoupling) with a redshift value of approximately

1100. It is a questionable hypothesis that those photons can

travel in space containing a variety of matter particles for

such a long time through such a long distance without

being absorbed and without being scattered.

It is well-known that matter particles of a variety of size

and temperature spread all over the Universe from the very

distant past, up to current; they absorb and scatter photons,

and re-emit photons in a spectrum of their own characters.

Hence, photons must have mean and maximum free travel

path lengths, also mean and maximum free travel times.

The free path length and the free travel time of a certain

spectrum of photons must fall in a statistic distribution

around a mean value. This is the reason why the most

distant astronomical object observed in the Universe such

as the galaxy GN-z11 has a redshift value of just below

11.1, which is the largest confirmed observable redshift

value of any astronomical object (Oesch et al., 2016).

There is the redshift value of no larger than 12 that was

reported for any observable astronomical object. The

Universe becomes opaque to observers beyond a distance

with a maximum value of redshift below 12. If the photons

that existed at the time of photon decoupling and

afterwards have been propagating unimpeded ever since

and stretched by the space expanding as assumed in the

Big-Bang model, we must be able to observe a range of

redshift values much higher than 12 but less than 1100. It

is a seriously flawed argument to disprove the Tired-Light

models based on the wrong assumption of an infinitely

large redshift value for a nonexpanding Universe. The

nonexpanding Universe Tired-Light model making a

superior fit on observational data of eight cosmology tests

was reported by LaViolette (2021).

CONCLUSION

The Super photon is treated as a fundamental unit of mass

and energy in dynamic circulation. Through the analysing

of the interactions among the Super photons, normal

photons, immersed concrete matter particles, and the

thermal bath of the vast Super photon ocean, the Super

photon theory is developed quantitatively. Gravitational

waves are proposed as periodic density and pressure

oscillations of the Super photon particles propagating

through the vast Super photon ocean. The equation of a

mass and its effective interacting radiusis derived from the

Super photon theory and it is employed to calculate the

effective radius of the Solar System and the Milky Way

Galaxy based on their known masses, or vice visa. The

calculated results are in good agreement with the estimated

values based on the astronomical observations and

calculations. The Universal Gravitational Constant is

derived from the Super photon theory and it is interpreted

as the interacting and coupling constant of an immersed

matter particle with the rest of the Universe through the

thermal bath of the vast Super photon ocean. The

correlation between the Universal Gravitational constant

and the Hubble constant is deduced theoretically.

The mysteries behind the dynamic circulation and

equilibrium of energy and mass of the Universe are

discussed, supporting evidences, demonstrating signs and

validation methods are presented. Flavour oscillation

observed in neutrinos is taken as an evidence of immersed

matter particles that undergo two-way energy exchange

with the thermal bath of the Super photon ocean with local

fluctuations. Immersed matter particles can absorb the

roaming Super photons, normal photons, neutrinos, and

cosmic rays thus mass and energy from the thermal bath of

the vast Super photon ocean because they locate at places

with low potential energies. They convert the absorbed

energy to kinetic energy and higher-grade thermal energy

through internal interactions to sustain their characteristic

movements and temperatures. Immersed matter particles

emit mass and energy to their surrounding spaces to

achieve dynamic circulation and equilibrium. Immersed

matter particles with different size and mass absorb and

emit photons of different ranges of frequencies,

demonstrating relatively stable characteristic masses,

temperatures, colours, brightness, and movements, which

manifests the state of dynamic equilibrium achieved.

Wenzhong David Zhang

11

The generalised law of Universal Gravitation is derived

while applying the Super photon theory to the two-body

system interacting via gravity. Thereafter, the Virial

relation within the Solar System, the Tully-Fisher law, and

the Modified Newtonian Dynamics relation and

acceleration within galaxies are derived theoretically. The

cosmological insights into the origins of both the Modified

Newtonian Dynamics and the Tully-Fisher laws, which

have been sought after for over thirty years, are revealed

quantitatively. The temperature and the spectrum of the

CMBR are explained theoretically and determined

accurately using the Super photon theory together with the

fluctuation-dissipation theorem. The capability of a photon

particle with an inertial mass travelling at a constant speed

inside the free space with a viscous friction force is

theoretically verified. The speed of light is determined by

the intrinsic properties of the substance inside the free

space. An experiment is proposed, which may further

distinguish the Super photon theory from the theories of

Expanding Universe and Big-Bang cosmology in a simple

way. Time dilation effect is not generally applicable, it may

be alternatively explained as clock retardation because of

the local increase of viscosity.

The Super photon theory is still in its stage of infancy.

However, the author believes that the theory has a huge

potential to be further developed to explain phenomena that

have plagued the physical world for many years. Wider

research directions and frontiers may be further developed.

For instance, it is necessary to better understand the

interacting and recirculating of photons, neutrinos, cosmic

rays, and all sorts of immersed matter particles in the

thermal bath of the vast Super photon ocean quantitatively.

It may help in the understanding of the mechanisms of the

production and the stability of fundamental particles and

elements, predicting the relative abundance of the elements

in the Universe. Further development of the Super photon

theory together with the fluctuation-dissipation theorem

may help to develop a unified theory of physics, which

would be applicable in both the microcosm and the

macrocosm.

ACKNOWLEDGEMENT

The author gratefully acknowledges the encouragements

and supports from my family, friends, and colleagues to

these theoretical investigations.

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