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# AN ALTERNATIVE TO UNDERSTAND THE ORIGIN OF UNIVERSAL GRAVITATION AND THE COSMIC BACKGROUND MICROWAVE RADIATION FROM A SUPER PHOTON THOERY

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## Abstract

I am grateful that after nearly six years independent research, this paper has been accepted for publishing in Canadian Journal of Pure and Applied Sciences. Vol. 15, No. 3, Oct 2021. 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.
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
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)

(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.
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
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
confirmed by the quantitative measurement of the relation
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
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
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
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


(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 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,



(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
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
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
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
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
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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