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A TRANSLUMINAL ENERGY QUANTUM MODEL OF THE COSMIC QUANTUM
Richard Gauthier
Santa Rosa Junior College, 1501 Mendocino Ave., Santa Rosa CA 95401, U.S.A.
E-mail: richgauthier@gmail.com
www.superluminalquantum.org
An internally transluminal model of the hypothesized unique cosmic quantum of the very early universe is proposed. It consists of a
closed-loop photon model, which has the total mass-energy
of the atomic matter and dark matter of our observable universe that will
develop from it. The closed-loop photon model is composed of a rapidly circulating point-like transluminal energy quantum (TEQ).
This TEQ circulates in a closed helical path with a maximum speed of c and a minimum speed of around the photon model’s
one-wavelength closed circular axis. The transluminal energy quantum model of the cosmic quantum is a boson. The cosmic quantum
model may help shed some light on several fundamental issues in cosmology, such as the nature of the cosmic quantum, the
predominance of matter over antimatter in our universe, the possible particles of dark matter, the quantum interconnectedness of the
universe, and the very low entropy of the very early universe. The cosmic quantum may be the first particle of dark matter, from
which all other particles are derived.
Keywords: Cosmogony; Big Bang; Quantum; Dark Matter; Superluminal
1. Introduction
In 1931 Lemaître
1
hypothesized that a single quantum
particle (primeval atom) composed the universe at the
beginning stage: “If we go back in the course of time
we must find fewer and fewer quanta, until we find all
the energy of the universe packed in a few or even in a
unique quantum.” (p. 706)
According to this hypothesis the primeval atom
transformed into many other particles. The system of
particles and the volume of space expanded according
to Einstein’s general theory of relativity to produce our
current universe. This hypothesis later came to be
known as the Big Bang theory of the universe.
In 1956 Goldhaber
2
built on Lemaître’s hypothesis
in an attempt to explain why anti-matter is much less
abundant in our universe than matter. He proposed that
a single particle, a “universon”, existed before the Big
Bang. The universon decayed into a “cosmon” and
“anti-cosmon”. The cosmon then decayed to produce
our universe whose atomic matter is ordinary matter (as
opposed to anti-matter).
In 1975, Tryon
3
proposed that the universe could
have resulted from a quantum fluctuation (in the sense
of quantum field theory) from the vacuum state of
space. This could have happened without violating the
conventional laws of physics, such as conservation of
energy and conservation of electron and baryon
number. The universe formed would have to be on the
border of being open or closed (because the quantity of
negative gravitational potential energy would exactly
balance the quantity of positive mass energy) and also
contain an equal amount of matter and anti-matter.
Tryon does not give a model of the quantum fluctuation
that produced the universe.
In 1989 Dehmelt
4
built on Lemaître’s hypothesis.
He suggested that a “cosmon, an immensely heavy
lower layer subquark, is the elementary particle. The
world-atom, a tightly bound cosmon/anticosmon pair of
zero relativistic total mass, arose from the nothing state
in a quantum jump. Rapid decay of the pair launched
the big bang and created the universe.”
The recent Wilkinson Microwave Anisotropy
Probe’s (WMAP)
5
detailed measurements of the very
nearly uniform (to about 1 part in 100,000) cosmic
microwave background radiation (CMBR) coming from
all directions in space, with a black body radiation
temperature of 2.725 Kelvin, have yielded strong
support for what has become the Standard Model of
cosmology, the Lambda Cold Dark Matter (
!
CDM)
with Inflation model. To briefly summarize this model,
the very early universe was a rapidly expanding hot,
dense physical state (the Big Bang). This was followed
very quickly by a period of extremely rapid inflationary
expansion, followed by normal expansion. This
inflationary period is supposed to have wiped out all
physical evidence of particles that existed before it.
There are however physical models for the pre-
inflationary era that try to describe this era and explain
the cause of inflation.
After the inflationary period there were small
variations in mass/energy densities in the universe
produced by quantum fluctuations of energy during the
5
c
inflationary period. The post-inflationary matter and
energy evolved into an extremely hot concentration of
elementary particles, which later formed atomic nuclei
of hydrogen, helium and lithium. Later hydrogen,
helium and lithium atoms formed, and still later stars
and galaxies formed in the regions of greater mass
densities caused by the quantum fluctuations of the
inflationary period. The universe continued to evolve
into our current universe. According to the WMAP
data, our universe now consists of about 4.6% atomic
matter, 22.7% dark matter composed of relatively slow
(cold) unknown particles, and 72.8% dark energy also
of an unknown nature. Currently our universe appears
to be geometrically flat and has an accelerated spatial
expansion (related to Lambda or the cosmological
constant of Einstein’s equations of general relativity)
that may be caused by the dark energy.
There is an active search for a theory of quantum
gravity to describe the very early universe, where the
micro-scale realm of quantum physics and macro-scale
realm of general relativity converge. A leading
approach to the development of quantum gravity is
Hawking’s
6
“no boundary condition” of the very early
universe. The expansion of the universe would have
begun from a state that was very smooth and ordered.
“There had to be small fluctuations in the density and
velocity of particles. The no boundary condition,
however, implied that these fluctuations were as small
as they could be, consistent with the uncertainty
principle.” (p.148)
In 2010 Wayte
7
proposed that a single particle,
with its internal material circulating coherently at speed
c, formed the primeval particle of our universe. That
first particle transformed into the energy configuration
known as the hot big bang of cosmological theory.
The present article, based on the author’s
8
work on
internally transluminal models of the photon and the
electron, proposes that the hypothetical first particle of
our universe may have been an internally transluminal
single quantum particle—a closed-looped photon. This
article also proposes two varieties of the internally
transluminal closed photon model as candidates for
particles of dark matter.
2. Previous Work on Transluminal Energy
Quantum Particle Models
The proposed transluminal energy quantum (TEQ)
model for the cosmic quantum, or first quantum particle
of our universe, grew out of an attempt to model the
photon and the electron physically and geometrically in
a way that would contain the main physical properties
of these particles (8). The TEQ photon model contains
an uncharged TEQ moving helically with a constant
speed of c, with a forward angle of 45-degrees and
with a helical radius equal to the photon’s wavelength
(the pitch of the photon model’s helical trajectory)
divided by . (See Appendix.)
For the TEQ electron model, one Compton-
wavelength (
!
C
= h / mc
where m is the electron’s
mass) of the TEQ photon model’s helical axis is formed
into a double circular loop and then closed on itself so
that the axis of the closed double-looping helix forms a
double-looping circle with a radius
R
o
= ! / 2mc
. The
electron TEQ’s trajectory closes after its helical axis
makes this one-Compton-wavelength double loop. The
circulating TEQ photon model’s forward momentum is
p = h /
!
C
= mc
. The helically moving point-like TEQ
has the charge of the electron. The closed double-
looping of the TEQ photon model gives the TEQ
electron model the electron’s spin
.
The helical radius of the TEQ electron’s closed
helical trajectory is chosen to be
2R
o
so that the TEQ
electron model has the pre-quantum-electrodynamics
magnetic moment of the electron--one Bohr magneton (
M
B
= e! / 2m
). Increasing this helical radius slightly in
the TEQ electron model would give the current
experimental value of the electron’s magnetic moment.
With these size parameters, the TEQ moves in a closed
trajectory along the surface of a spindle torus. The
maximum speed of the electron model’s TEQ is
and the minimum speed is or
.
3. The Proposed TEQ Closed Photon Model for
the Cosmic Quantum
Several other close-looped TEQ particles with different
spins and different helical radii were analyzed
mathematically to compare their physical and
geometrical properties. One model for a particle with
rest mass stood out for its simplicity—the single-looped
closed photon model. In this model, a one-wavelength
open-helix TEQ photon model is formed into a closed-
helix photon model by turning the one-wavelength axis
into a circle and turning the open-helix trajectory of the
2
2
!
s = R
o
! p = (! / 2mc) ! mc = ! / 2
1.516... c
0.5c
0.707... c
uncharged TEQ into a closed helix. The TEQ in this
closed photon model now follows a closed helical
trajectory along the surface of a horn torus, with a
maximum speed calculated from the model to be
5c
and a minimum speed of
c
, independent of the energy
of the photon being modeled.
The TEQ closed photon model is a boson, with
spin
1!
due to its single-closed-loop structure. The
TEQ photon’s closed helical axis length is a circle of
one wavelength circumference. Based on the
parameters of the TEQ open helix photon, the radius of
the circular axis of the closed helix and the radius of the
closed helix itself are both equal to the TEQ photon’s
wavelength divided by
2
!
, creating the
mathematically simple horn torus surface on which the
TEQ moves.
4. Mathematically Generating the TEQ Closed
Photon Model of the Cosmic Quantum
The TEQ closed-helical photon model is generated
geometrically and mathematically in the following way.
A mathematical generating point moves at the speed of
light c around a closed horizontal circular path of radius
R =
!
/ 2
"
. The TEQ is on a vertical mathematical
circle, also of radius R, whose center is the moving
generating point and whose plane is perpendicular to
the direction of movement of the generating point
around the horizontal circle. The speed of the TEQ
along the vertical circle is also the speed of light c. The
combined motion of the generating point around the
horizontal circle and the TEQ around the vertical circle
creates a 3-dimensional TEQ trajectory that closes after
the generating point completes one circuit around the
horizontal circle. The coordinates of the TEQ’s
trajectory can be given parametrically as follows:
x(t) = R(1+ cos(
!
t ))cos(
!
t )
y(t) = R(1 + cos(
!
t))sin(
!
t)
z(t ) = Rsin(
!
t )
where
R = !c / E
is the radius of both generating
circles, and
!
= E / !
(where
!
is the angular
frequency of a circulating photon with energy E and
wavelength
!
= hc / E
). The radius R of the horizontal
circle is the radius of the circle whose circumference is
the wavelength of the circulating photon, so
.
The radius of the vertical circle used to generate
the TEQ trajectory is equal to the radius of the closed
helical path of the TEQ photon. This radius in the TEQ
open-helix photon model is equal to the photon’s
wavelength of the photon
!
= hc / E
divided by , so
again .
It will be noticed that the equations for the closed
TEQ photon correspond to the parametric equations
used to generate a horn torus. Based on the above three
coordinate equations, the TEQ is found to move along
the surface of this mathematical horn torus with a
maximum speed of
5c
and a minimum speed c,
independent of the energy of the photon. The TEQ
closed photon model of the cosmic quantum looks like
Figure 1.
Fig. 1. The transluminal energy quantum closed photon model of the
cosmic quantum. The mathematical horn torus surface on which the
transluminal energy quantum travels is cut away to show the interior.
The black closed curve on the surface of the horn torus is the
trajectory of the transluminal energy quantum (indicated by the black
dot.)
The TEQ’s maximum speed occurs when the TEQ
is farthest from the center of the torus, while the
minimum speed occurs when the TEQ passes down
through the center of the torus.
5. Parameters of the TEQ Closed Photon as a
Model of the First Quantum in the Very
Early Universe
The closed photon model permits estimates of various
physical parameters of the initial cosmic quantum,
based on the estimated positive mass-energy of the very
early universe. (An equal amount of negative mass-
energy is associated with the gravitational potential
energy of the very early universe.)
5.1 Mass
The geometry and velocities of the closed photon TEQ
model are independent of the energy of the photon in
the model. The radius R of the model varies inversely
with the closed photon’s energy E. The TEQ closed
R = (1 / 2
!
)(hc / E) = !c / E
R
2
!
R = (1 / 2
!
)(hc / E) = !c / E
photon model, with the appropriate energy E and radius
R given above, is proposed to be a model of the cosmic
quantum, the hypothesized first quantum particle of the
very early universe.
First, estimate the mass
M = E / c
2
of the closed
photon by estimating the mass-energy of the very early
universe. According to the 7-year WMAP
5
results,
about 4.56% of today’s universe is considered to be
atomic matter, the rest being dark matter at 22.7% and
dark energy at 72.8%. WMAP found that the universe
is very nearly “flat” or Euclidian (to within 0.6%) and
so its density for all mass-energy would be the critical
density of . The spherical volume of
the observable universe is
(4 / 3)
!
R
o
3
= 3.55 " 10
80
m
3
,
where = 14,238 Mpc (Megaparsecs) = 46.4 billion
light years =
4.39 ! 10
26
m
is the radius of the
observable universe. The total mass-energy is thus
found to be
9.30 ! 10
"27
kg/m
3
! 3.55 ! 10
80
m
3
= 3.30 ! 10
54
kg.
But
according to the current cosmological standard model
(the Lambda cold dark matter (
!CDM
) with inflation
model), the dark energy portion of this total mass-
energy was mostly produced as the volume of the
universe expanded from its volume at the time of light
decoupling at 379,000 years after the Big Bang to its
volume at the present time. The positive mass
(excluding dark energy) of the present universe is the
current atomic mass plus the current mass of dark
matter, or (4.56% + 22.7%)
!3.30 ! 10
54
kg=9.00 ! 10
53
kg
. But according to the 5-
year WMAP
9
data, the mass energy density of the
universe at the time of light decoupling consisted of
25% photons and neutrinos (both of which today
contribute a negligible percentage to the total mass
energy density) and 75% atomic matter and dark
matter). The mass energy M at the time of decoupling is
therefore larger than mass calculated above by a factor
of 4/3. So a better estimate M of the total positive mass-
energy of the universe at the time of decoupling or
recombination, including atomic matter, dark matter,
photons and neutrinos is
M = (4 / 3) ! 9.00 ! 10
53
kg=1.2 ! 10
54
kg
. This is the
value used to estimate the mass energy M of the cosmic
quantum.
5.2 Radius
This leads to a radius estimate of the first TEQ closed
photon to be
R = !c / E = !c / Mc
2
= ! / Mc = 1.05 ! 10
"34
/ (1.2 ! 10
54
! 3 ! 10
8
)
= 2.9 ! 10
"97
m
5.3 Frequency
The corresponding frequency of the closed photon is
!
= E / h
= Mc
2
/ h
= 1.2 " 10
54
" (3.00 " 10
8
)
2
/ 6.63 " 10
#34
= 1.6 " 10
104
Hz
5.4 Period
The period of the TEQ closed photon would be
T = 1 /
!
= 1 / (1.6 " 10
104
) = 6 " 10
#105
sec.
5.5 Mass Density
The TEQ closed photon model allows an estimate for
the initial mass density of the very early universe. This
would be approximately the mass density of the first
closed photon. The mass of the first closed photon was
estimated above to be
M = 1.2 ! 10
54
kg
while the
estimated radius of the photon model is
R = ! / Mc = 2.9 ! 10
"97
m.
If the volume of the closed
photon is estimated as
R
3
, the mass density of the
closed photon would be
!
mass
= M / R
3
= M / (! / Mc)
3
= M
4
c
3
/ !
3
= (1.2 ! 10
54
)
4
! (3.00 ! 10
8
)
3
/ (1.05 ! 10
"34
)
3
= 1.6 ! 10
344
kg/m
3
5.6 Energy Density
The corresponding energy density would be
!
energy
= M
4
c
5
/ !
3
=
!
mass
c
2
= (1.6 "10
344
) " (3.00 " 10
8
)
2
= 1.4 "10
361
Joules/m
3
6. Why is the TEQ Closed Photon Model
Proposed as the Cosmic Quantum?
First of all, a photon is a basic constituent quantum
particle of the universe. Second, a photon might be able
to travel in a short closed path, even of a single
wavelength. At the earliest stage of the universe, a first
photon has nowhere to go, since the space-time
9.30 ! 10
"27
kg / m
3
R
O
!
T
structure of the universe has presumably has not yet
begun to expand as long as only the first particle exists.
Third, a closed photon has a rest mass corresponding to
its energy content, which an open photon does not have
a rest mass.
The primeval atom proposed by Lemaitre was
described as a super-large radioactive atom that upon
decomposing could have become all of the other
particles of the universe and formed the expanding hot
mass-energy system that has come to be called the Big
Bang. But the question of course would remain: from
where did the primeval atom come? If there were a first
cosmic quantum particle for our universe, it would
likely have been very simple. It could possibly have
emerged as a quantum fluctuation from a cosmic
quantum field.
7. A Cosmic Field Theory for the Cosmic
Quantum Boson?
The primordial closed photon’s properties are at a
convergence of a radius
R = 2.9 ! 10
"97
m quantum-
sized particle (so quantum theory should apply) with an
estimated mass
M = 1.2 ! 10
54
kg (so general relativity
theory should apply). It is well known that quantum
theory and general relativity theory are mathematically
inconsistent under combined conditions of extremely
small sizes and extremely large masses. A synthesis of
quantum theory and general relativity theory into a
quantum gravity field theory is much needed and much
sought. Such a theoretical synthesis would be expected
to lead to new and surprising predictions. Quantum
gravity field theory could describe a cosmic field that
produces cosmic quanta such as the first quantum
particle of our universe. Quantum gravity field theory
could reasonably be called cosmic field theory.
The TEQ closed photon model is a boson, because
its spin is one quantum unit of angular momentum:
s = ! = h / 2
!
. This spin around the particle’s vertical
axis is calculated in the TEQ model from the formula
for calculating the angular momentum of a circularly
moving object (the photon):
Spin = (radius of photon model) (momentum of the
photon model)
s = R ! p
s = R ! (Mc)
where Mc is the momentum of a photon
carrying energy corresponding to a mass M.
s = (! / Mc) ! Mc
since
R = ! / Mc
is the radius of a
one-wavelength closed photon model corresponding to
a mass M.
s = ! = h / 2
!
8. A Second Very Early Universe Particle—
a Closed-Photon Fermion?
At some very early time (perhaps at the beginning of
time itself) the original TEQ closed photon is proposed
to start generating other particles in the process of the
Big Bang. The TEQ closed photon might sometime
during this process generate a new particle—a TEQ
closed photon fermion—that could lead to the
production of other TEQ fermions such as electrons,
positrons, quarks, antiquarks and neutrinos. These are
all particles with spin
! / 2
. The way to generate a TEQ
closed-photon fermion from a TEQ photon is for the
straight one-wavelength
!
axis of a TEQ open photon
to wrap itself around into a double circular loop before
closing on itself. The associated helical TEQ trajectory
also closes on itself to form a closed, double-looping
helical trajectory. If this TEQ single-wavelength
double-looping closed helical photon keeps the same
helical radius
R =
!
/ 2
"
as that of the TEQ open
helical photon, the TEQ closed trajectory that is formed
is a path along the surface of a self-intersecting torus
(technically a spindle torus) whose central spindle’s
width is the radius R. In this double-looping closed
TEQ photon, the TEQ’s maximum speed is calculated
from the TEQ coordinate equations for this model to be
3.162 c, which is larger than the maximum speed for
the TEQ single-loop closed photon of
5c
or 2.236 c ,
while its minimum speed is still c, the same as for the
TEQ single-loop closed photon. The double-looped
TEQ photon’s trajectory and associated torus surface
are shown in Figure 2.
Fig. 2. The transluminal energy quantum model of the double-looped
closed-photon fermion. Some of the outer part of the mathematical
spindle torus on which the TEQ moves is cut away to show the
spindle inside. The black closed curve on the surface of the spindle
torus is the trajectory of the TEQ (indicated by the black dot).
!
The coordinates for this second TEQ particle are:
x(t) = 0.5R(1+ 2 cos(
!
t ))cos(2
!
t )
y(t) = 0.5R(1+ 2 cos(
!
t))sin(2
!
t)
z(t ) = 0.5R sin(
!
t )
where
R =
!
/ 2
"
is the radius of the photon helix for
the TEQ’s double-looped helical trajectory of
wavelength
!
,
0.5R = 0.5
!
/ 2
"
is the radius of the
circular axis of the double-looped helical trajectory, and
!
= 2
"
c /
#
is the angular frequency of the photon. This
particle is a fermion with spin
s = 0.5!
. The
calculation of its spin around its vertical axis follows:
Spin = (radius of circular axis of double-looped photon
model) (momentum of the photon model)
where
h /
!
is the momentum of a
photon of wavelength
!
.
9. The production of further particles from the
original TEQ closed photon
Once the Big Bang gets started from the original closed
photon, there is hypothesized to be a rapid increase in
the number and types of TEQ elementary particles such
as TEQ electrons and TEQ photons produced from the
original closed photon, as well as a rapid expansion of
the space in which the particles are formed.
TEQ models for the electron and the photon have
already been developed (8). The TEQ electron model is
a fermion and so is based on a double-looped TEQ
photon model. In the TEQ electron model the
circulating TEQ is charged with the negative electric
charge of the electron. A TEQ positron would have a
positively charged TEQ and an oppositely turning
closed double-looping helical trajectory compared to
that of the TEQ electron. The circulating of the
negatively charged TEQ in the electron model gives the
TEQ electron model its magnetic moment so that the
TEQ electron acts like a tiny magnet. The parameters of
the TEQ electron were selected so that the TEQ
electron has the main parameters of an actual
electron—its mass, charge, spin and magnetic moment.
The TEQ model of the electron is shown in Figure 3.
The TEQ model of the electron differs somewhat in
shape from the double-looped closed photon model.
The helical radius of the TEQ electron model is smaller
than the helical radius of the corresponding closed
double-looped TEQ photon model. This shortening of
the electron model’s helical radius is done to give the
TEQ electron model a magnetic moment equal to the
double-looped TEQ photon model. This shortening of
the electron model’s helical radius is done to give the
Fig. 3. The transluminal energy quantum model of the electron. Some
of the outer part of the mathematical spindle torus on which the TEQ
moves is cut away to show the spindle inside. The black closed curve
on the surface of the spindle torus is the trajectory of the TEQ
(indicated by the black dot).
TEQ electron model a magnetic moment equal to the
magnetic moment of the actual electron (which in pre-
quantum-electrodynamics is found from the Dirac
equation for the relativistic electron to be one Bohr
magneton or
e! / 2m
. A slightly larger helical radius
will give to the TEQ electron model the slightly larger
experimental value of the electron’s magnetic moment.)
The result is that the maximum speed of the TEQ in the
electron model is 2.516 c , smaller than the maximum
TEQ speed of 3.162 c for the double-looped closed
photon model but larger than
5c
or 2.236 c for the
single-looped closed photon model. The electron TEQ’s
minimum speed is less than the speed of light, at
0.5c
or 0.707 c, compared to the minimum speeds of exactly
c for both the double-looped and single-looped closed
photon models. The electron model’s TEQ passes
through the speed of light twice during each closed
trajectory. Since the TEQ is not a particle with rest
mass like the electron as a whole, the TEQ can pass
through the speed of light as it internally circulates to
form the electron, while the TEQ electron moving as a
whole cannot reach the speed of light, due the limitation
on its external speed prescribed by Einstein’s special
theory of relativity.
The coordinates for the TEQ in the TEQ electron
model are:
x(t) = R
o
(1+ 2 cos(
!
t ))cos(2
!
t )
y(t) = R
o
(1+ 2 cos(
!
t))sin(2
!
t)
z(t ) = R
o
2 sin(
!
t )
!
s = (0.5R) ! p
= (0.5R) ! h /
"
= (0.5
!
/ 2
"
) # h /
!
= 0.5h / 2
!
= 0.5!
where m is the
radius of the double-looped circular axis of the TEQ’s
closed helical trajectory,
2R
o
is the radius of the
helix of the TEQ’s closed double-looped helical
trajectory, and m is the mass of the electron.
radians/sec is the
angular velocity of the TEQ in its internal trajectory in
the TEQ electron model. Like the closed double-looped
TEQ photon model, the TEQ electron model is a
fermion.
10. Possible Relevance of the TEQ Closed
Photon Model to Cosmology
The proposed TEQ closed photon model is closely
related to earlier TEQ models of the photon and
electron
8
(also see Appendix of the present article).
Cosmological considerations were not included in the
development of these models. But when the TEQ
closed photon model was later considered as a model
for the first quantum entity in the very early universe,
the model was seen to be possibly relevant to several
currently unanswered major cosmological questions.
10.1 Could a Single Quantum Particle Produce
Our Universe?
If this is possible, then the question becomes, what
could that first quantum have been? The proposed TEQ
closed photon model of this hypothesized cosmic
quantum is postulated to contain in its circulating TEQ
the entire mass of ordinary matter and dark matter of
the very early universe (where there was apparently
relatively little dark energy due to the small volume of
the very early universe).
The universe is currently understood to have an
associated negative gravitational potential energy that
could mathematically cancel out the total positive
physical energy of the universe to give a net energy of
the universe to be exactly zero. This seems to be the
currently scientifically accepted view of the total
energy content of the universe. Both these positive and
negative energies of the universe could be built into a
theory of quantum gravity that would describe the first
TEQ closed photon or other initial quantum particle or
particles of the universe leading to the Big Bang.
Current quantum theory and general relativity theory
cannot make meaningful predictions for lengths and
durations that are less that the Planck length
and Planck time
s. Clearly the radius
R = 2.9 ! 10
"97
m and period
T = 6 ! 10
"105
s of the
proposed closed photon model for the very early
universe are well below these limits. Since quantum
theory and general relativity theory are acknowledged
to be inconsistent, a new quantum gravity theory could
lead to physical descriptions that go well beneath the
current Planck length and time values.
What initial hypothesized state of the universe
would have the smallest quantum fluctuations,
consistent with the Heisenberg uncertainty principle?
The position and momentum parameters of the
circulating TEQ composing the closed photon model
are near the minimum limit set by the uncertainty
principle, as seen below.
The uncertainty of the x coordinate is defined as
the root mean square (rms) value for the x
component of a particle. For the TEQ in the closed
photon model, the rms value for x, calculated from the
TEQ position coordinate equations presented above, is
where
!
is the wavelength of the
closed photon.
The uncertainty of the x component of momentum
is defined as the rms value of the x component of the
momentum. For the circulating TEQ, the momentum
p = h /
!
rotates in a horizontal circle (for the x-y
dimensions) and in a vertical circle (for the z
dimension) for the closed photon model. So is
found to be
.
And so
.
A similar calculation of for the y
components of the position and momentum of the
closed photon model gives
.
A similar calculation of for the z
components of the position and momentum of the TEQ
closed photon model gives
.
Compare the three results for the x, y and z
components of position and momentum of the TEQ
closed photon model with the Heisenberg uncertainty
relation for the position and momentum coordinates of
a particle:
R
o
=
!
compton
/ 4
"
= ! / 2mc = 1.931 # 10
$13
!
= 2
"
c /
#
compton
= 7.77 $ 10
20
l
P
= 1.616199 ! 10
"35
m
t
P
= 5.39106 ! 10
"44
!x
!x = 1.87
"
/ 4
#
!p
x
!p
x
!p
x
= p / 2 = 0.5h /
"
!x " !p
x
= (1.87
#
/ 4
$
) " 0.5 h /
#
= 1.32(! / 2)
!y " !p
y
!y " !p
y
= (1.58
#
/ 4
$
) " ( 0.5h /
#
) = 1.12(! / 2)
!z " !p
z
!z " !p
z
= ( 2
#
/ 4
$
) " ( 0.5h /
#
) = 1(! / 2)
The variability of the position and momentum of
the TEQ in the closed photon model of the cosmic
quantum are nearly equal to the conditions for
minimum uncertainty in the Heisenberg uncertainty
relations for a single elementary particle.
A single quantum particle such as the proposed
TEQ closed photon, formed by a circulating sub-
quantum particle (the TEQ) with the calculated
variation in its position and momentum, may be a
candidate for the most highly ordered (and therefore
lowest entropy) state of the very early universe,
consistent with the Heisenberg uncertainty principle
and the total positive energy content of the early
universe. Evolution of that single quantum entity could
lead to a “hot Big Bang” of many particles and the
associated extremely high temperature of the early
universe. This “hot Big Bang” evolving from the single
closed photon could then evolve to the very smooth and
ordered state that is apparent in the universe today, as
seen in the extremely but not completely smooth, low
temperature cosmic microwave background radiation
(CMBR)
5
observed coming from all directions in the
sky today. This CMBR is some of the best current
scientific evidence for the Big Bang.
10.2 Why Does Matter and not Antimatter
Dominate in the Atomic Matter in Our
Universe?
The proposed TEQ closed photon model has a closed
helical form. A helix has the property that it turns either
clockwise or counterclockwise along its axis, as seen
from behind. Clockwise in the TEQ closed photon
model of the cosmic quantum might correspond to the
TEQ closed helical structure of ordinary matter
particles such as the TEQ electron model, and
counterclockwise might correspond to the opposite
helicity, that of antimatter particles such as the TEQ
positron model. If the helicity of the original cosmic
quantum closed-photon model’s TEQ corresponded to
that of TEQ-composed ordinary matter (as opposed to
antimatter), this would provide an initial bias in our
closed-photon-evolved universe towards ordinary
matter. This bias towards ordinary matter in our
universe’s cosmic quantum might then help explain
why almost all of the observed atomic and subatomic
matter in our present universe, which would have
evolved in stages from the original closed photon’s
TEQ, appears to be ordinary matter.
If the proposed TEQ closed photon model, a boson
having spin
!
and determined by its helicity to be
matter (as opposed to antimatter), emerged from a
cosmic field to become our very early universe, an
equally massive TEQ closed photon model with spin
!!
, and described as antimatter due to its opposite
helicity, could have also emerged from this cosmic field
at the same time. This assumes that the laws of
conservation of total angular momentum and matter-
antimatter pair production are valid for the cosmic field.
If so, what happened to the original TEQ antimatter
spin
!!
closed photon that was paired with our cosmic
quantum? Could it have formed a mainly antimatter
universe, perhaps in a different space-time dimension?
10.3 Could Dark Matter Be Composed of Closed
Single or Double-Looped TEQ Photons?
According to the WMAP
5
results, about 22.7% of the
matter-energy content of the universe appears to consist
of cold (relatively slow moving) dark matter, whose
main presumed feature is that its particles have a
relatively large mass and are mainly affected by
gravity, but so far have shown no other identifying
physical features. The second proposed very early
universe TEQ particle, the closed double-looping
photon model, is a fermion, composed of one
wavelength of a photon, wrapped around twice before it
joins itself. This gives the uncharged TEQ particle !
unit of quantum spin as well as a mass that depends on
its internal wavelength according to
E = hc /
!
.
The fundamental particles of matter are all
fermions—the electron, muon, and tau particles, the
neutrinos and the quarks, and all their antiparticles—
while the fundamental particles of force for
electromagnetism, the strong and the weak nuclear
interactions are bosons—photons, gluons, W and Z
particles and the Higgs boson and their antiparticles.
(Gravity is not included here since a gravity force
particle or graviton has not been observed.)
Perhaps dark matter consists of uncharged closed,
double-looped TEQ photon fermions. Such particles
could qualify as cold dark matter particles if they would
interact with other particles mainly through the
gravitational force. Uncharged single-looped closed
TEQ photon bosons could also be possible candidates
!x " !p
x
# ! / 2
!y " !p
y
# ! / 2
!z " !p
z
# ! / 2
for cold dark matter, or for force particles associated
with cold dark matter particles.
If an uncharged closed double-looping TEQ
photon, with the helicity of a TEQ electron, has a mass
slightly less than the mass of an electron, it could be a
very stable particle. It would mainly interact with other
matter-energy particles through gravitation. It could
only be annihilated to produce photons by its
corresponding dark matter anti-particle, an uncharged
closed double-looped TEQ photon of opposite helicity
to this proposed dark matter particle. For the same
(currently unknown) reason that there seems to be very
little anti-matter in our observable universe, there
would also presumably be in our universe very little
dark anti-matter consisting of closed double-looped
TEQ photons of opposite helicity to this proposed dark
matter particle.
If this proposed neutral double-looped photon dark
matter particle has the lowest mass of a possible family
of related double-looped photon fermions, it might only
be able to decay into one or more low mass neutrinos,
that are also hard to observe. Since this proposed dark
matter particle could also only annihilate with its dark
matter anti-particle, which is very scarce, it would like
the electron be a very long-lived particle. Further, since
this proposed dark matter particle is a fermion, it would
not clump closely together with other like dark matter
fermions due to the Pauli exclusion principle and the
related Fermi-Dirac statistics for fermions. Single-
looped closed TEQ photons bosons however could
clump close together, according to Bose-Einstein
statistics.
Fermions and bosons have already been proposed
as candidates for dark matter particles. Boehm and
Fayat
10
found two theoretical possibilities: “Either dark
matter is coupled to heavy fermions … or dark
matter is coupled to a new light gauge boson U.”
Astrophysical research is ongoing in search of
gamma ray photons that could result from the
annihilation of dark matter particles with their
corresponding antiparticles. One proposed type of
dark matter particle is the Weakly Interactive
Massive Particle (WIMP) that is proposed to be able
to annihilate with its antiparticle, producing pairs of
gamma ray photons. A tentative positive result has
been found by Weniger
11
using data from the Fermi
Large Area Telescope. The proposed TEQ dark
matter particles could also be sought using this
approach. TEQ matter-antimatter annihilations
would be rare though, due to the relatively low
presence of TEQ antimatter in our universe, as
explained above.
10.4 Does the Universe Have Quantum
Non-Local Interconnectivity Due to an
Original Quantum Particle?
With the TEQ closed-photon model of the cosmic
quantum, all the hypothesized TEQ-based atomic (or
baryonic) matter and dark matter expressions of the
universe would evolve from the cosmic quantum during
and after the Big Bang. According to quantum theory,
confirmed by many recent experiments, objects that are
quantum-entangled when they separate can retain this
quantum interconnectivity even when separated over
vast distances. This implies that all of the particles
derived from the hypothesized cosmic quantum, i.e. all
the atomic matter and dark matter in our universe, could
retain quantum non-local interconnectedness to some
degree. This would be the case despite even
intergalactic distances separating many elementary
particles and energetic structures today. In a quantum-
theoretic as well as experimental sense the atomic and
dark matter portions of our universe could still remain a
single vast quantum entity.
10.5 Did Time Begin with the Original Quantum
Particle?
One of the unsolved problems about our universe is
why our early universe, consisting of a nearly uniform
dense, hot state of matter and energy, had such a low
entropy compared to its entropy today, and how this
relates to the origin and nature of time. Carroll
12
estimates the entropy of our early, post inflationary
universe (the part that developed into our observable
universe—our “comoving patch”) to be
S
early
! 10
88
.
This is based on there being an estimated
10
88
freely
moving particles in our comoving patch in our young
and smooth universe. He estimates the entropy of our
comoving patch of universe today to be
S
today
= 10
101
.
This is based on an estimate of
10
11
supermassive
black holes (estimated at one per galaxy in our
observable universe) and an amount of entropy of
10
90
per supermassive black hole, calculated according to
the Bekenstein-Hawking formula for the entropy of a
black hole.
The entropy of our universe, consisting of a single
TEQ cosmic quantum before it subdivided into other
energy particles, would have been
S
cosmic quantum
! 1
according to this particle-count method. Since the
entropy of a closed system generally increases with
time, in our observable universe time could have begun
when the TEQ cosmic quantum particle started to
subdivide into other quantum particles and the entropy
of this system began to increase. Time has apparently
been flowing in a positive direction (towards increasing
entropy) in our observable universe from then until
now.
11. Can Quantum Mechanics and General
Relativity Be Unified through
Transluminality?
Transluminal energy quanta move superluminally and
sometimes through luminal to subluminal speeds as
they hypothetically form different force and matter
particles such as TEQ photons and TEQ electrons.
Although particles with mass such as electrons always
travel through space at less than the speed of light,
according to the special theory of relativity and with
much experimental confirmation, the hypothetical TEQ
that composes the TEQ electron model is not so limited.
An electron’s TEQ travels from superluminality
through the speed of light to subluminality and back
with a frequency
!
= mc
2
/ h = 1.24 " 10
20
Hz.
According to the TEQ hypothesis, an electron is the
average motion of a rapidly circulating TEQ.
Gravitational waves are proposed in the general theory
of relativity to travel at the speed of light. But if the
proposed graviton also has a TEQ structure, these
graviton TEQs may also travel superluminally like the
TEQ composing a photon.
The hypothesis that fundamental particles are
composed of transluminal energy quanta could provide
a different approach to the evolution of the very early
universe. At earlier and earlier cosmological times, the
four interactions of physics (the strong nuclear
interaction, the weak nuclear interaction, the
electromagnetic interaction and the gravitational
interaction) are projected to lose their distinguishing
features and merge or nearly merge into a single force
at or near the end of the “Planck era” around
10
!43
s
after the Big Bang, according to the traditional (non-
inflationary) cosmological standard model.
According to the TEQ approach, during this era of
unified interactions, which would also occur in
inflationary cosmology, all positive energies could have
been carried by TEQs moving at transluminal speeds.
The original cosmic quantum, a TEQ single-looped
closed-photon, would have transformed into an
expanding volume of superluminal TEQs collectively
carrying the total energy of the original cosmic
quantum. This would have been a volume of purely
TEQ-carried energy, whose total energy content was
proportional to the sum of the frequencies of vibration
of all the TEQs carrying this energy. This would be the
original “hot big bang”. As this volume of TEQs
expanded with the expanding very early universe, the
number and types of TEQs would multiply as the
gravitational interaction separated from the electro-
nuclear interaction. The types of TEQs would further
multiply as the electro-nuclear interaction separated
into the strong nuclear interaction and the electro-weak
interaction. More types of TEQs would evolve as the
electro-weak interaction separated into the
electromagnetic interaction and the weak interaction.
Finally all types of TEQs would exist and would form
the fundamental particles such as photons, quarks,
gluons, electrons and neutrinos.
Perhaps the cosmic field theory for the origin and
evolution of the cosmic quantum, that combines
quantum theory and general relativistic theory, will be
based partly on the proposed internal transluminality of
the cosmic quantum and other transluminal energy
quanta derived from it.
12. Conclusions
The transluminal energy quantum (TEQ) model of a
closed photon is a new approach to answering the
question “Could the universe have been formed from a
single quantum?” The TEQ model of the cosmic
quantum exists well below the Planck length and
Planck time values that currently restrict models of the
very early universe to greater than about
10
!43
s
.
The TEQ model of the cosmic quantum suggests a
value of the positive energy density of the cosmic
quantum of about
10
361
Joules/m
3
, based on the
baryonic matter and dark matter content of the observed
universe and the radius of the proposed TEQ closed
photon model of the cosmic quantum.
The TEQ closed photon model of the cosmic
quantum is a boson, whose helical geometry creates a
bias in favor of matter over antimatter in our universe.
Conservation of angular momentum suggests that
another closed photon model of opposite spin would
have been formed at the same time as our cosmic
quantum, if the first closed photon was formed as a
quantum fluctuation in a cosmic field obeying physical
conservation laws.
The TEQ single-looping (boson) and double-
looping (fermion) closed photon models provide two
possible candidates for particles of dark matter having
masses perhaps similar to the mass of an electron. Since
both of these proposed dark matter particles have their
corresponding anti-particles, they could possibly be
detected by observing photons produced from particle-
antiparticle annihilation. Finding such TEQ dark matter
particles could provide indirect support for the TEQ
cosmic quantum hypothesis as well. An experimental
approach for detecting TEQ dark matter particles was
suggested, which is in line with a current approach to
detecting dark matter particles through trying to detect
pairs of photons created from dark matter – anti-dark
matter particle annihilation. Testing of the TEQ cosmic
quantum hypothesis may have to await the development
of a theory of quantum gravity. In the meantime,
possible cosmic evolutionary scenarios leading from the
proposed cosmic quantum to the current Big Bang
standard model can be explored.
Appendix
The parameters of the transluminal energy quantum
model of the photon
From “Superluminal quantum models of the photon and
electron”,
http://superluminalquantum.org/superluminal17Oct200
5
A photon is modeled as a superluminal pointlike
quantum traveling along an open helical trajectory
having a straight axis. The radius of the helix is R and
the pitch (wavelength) of the helix is
!
. The helical
trajectory makes an angle
!
with the forward direction.
The circumference of the helix is
2
!
R
. Using the
superluminal quantum model, the result is:
1) The forward helical angle is found to be ,
for any photon wavelength.
2) The photon helix’s radius is found to always be
R =
!
/ 2
"
.
3) The speed of the superluminal quantum is
2c = 1.414.. c
along its helical trajectory.
These results are derived below.
The superluminal quantum, with total momentum
directed along its helical trajectory, has a forward
component of momentum
P cos(
!
)
determined by the
wavelength
!
of the helix, and a transverse component
of momentum
P sin(
!
)
that is used to calculate the spin
of the photon. The superluminal quantum’s longitudinal
component of momentum is
P cos(
!
) = h /
"
, (1)
the experimental longitudinal or linear momentum of a
photon. The total momentum
!
P
’s transverse
component of momentum is
P sin(
!
)
. This transverse
component is perpendicular to the helical radius vector
!
R
to the superluminal quantum from the helical axis.
The magnitude S of the angular momentum or spin of
the superluminal quantum model is then
(2)
the experimental spin or angular momentum of the
photon. Combining equations (1) and (2) gives
(3)
Now look at the helical geometry. As the
superluminal quantum advances along the helix a
distance
!
(one wavelength) in the longitudinal
direction, the superluminal quantum travels a transverse
distance , i.e. once around the circle of radius R of
the helix. From the way the helix’s angle is defined,
(4)
We now have two equations (3) and (4) for
tan(
!
)
.
Setting them equal gives
This will only be true if
that is,
R =
!
/ 2
"
and
tan(
!
) = 1
and since
tan(
!
) = 1
we have
!
= 45
o
These results are for any photon in this
superluminal quantum model of the photon. Since
!
= 45
o
and the forward speed of the superluminal
quantum along its straight helical axis is postulated to
be c, then the forward speed of the photon model is also
c, and the speed v of the superluminal quantum along
its helical trajectory is
v = c / cos(45
o
) = 2c
.
References
1. Lemaître, G., Letters to Nature, Nature 127, p. 706 (9
May 1931), reprinted in The Primeval Atom: An Essay
on Cosmogony, New York: D. Van Nostrand Company,
1950, p. 3.
2. Goldhaber, M., “Speculations on cosmogony”, Science
Vol. 124 no. 3214, 3 August 1956, pp. 218-219.
3. Tryon, E. P., “Is the universe a vacuum fluctuation?”,
Nature Vol. 246 no. 5433, 14 Dec. 1973, pp. 396-397.
4. Dehmelt, H., “Triton,…electron,…cosmon,..: an infinite
regression?”, Proc. Nati. Acad. Sci. USA Vol. 86, pp.
8618-8619, November 1989 Physics.
!
45
o
!
P
S = RPsin(
!
) = h / 2
"
sin(
!
) / cos(
!
) = tan(
!
) =
"
/ 2
#
R
2
!
R
!
tan(
!
) = 2
"
R /
#
tan(
!
)=2
"
R/
#
=
#
/2
"
R
!
= 2
"
R
5. Jaroski, N. et al., “Seven-Year Wilkinson
Microwave Anisotropy Probe (WMAP)
Observations: Sky Maps, Systematic Errors, and
Basic Results”,
http://lambda.gsfc.nasa.gov/product/map/dr4/pub_papers
/sevenyear/basic_results/wmap_7yr_basic_results.pdf ,
basic results p. 39. (accessed 10/07/2012) .
6. Hawking, S., A Brief History of Time: From the Big
Bang to Black Holes, Bantam Books, New York, 1988.
7. Wayte, R., “On the accelerating universal expansion”,
viXra:1011.0066, 26 Nov 2010, p.15. (accessed
11/18/2012).
8. Gauthier, R., “FTL quantum models of the photon and
the electron”, CP880, Space Technology and
Applications International Forum--STAIF-2007,
pp.1099-1108, edited by M.S. El-Genk, available at
http://www.superluminalquantum.org/STAIF-2007article
9. WMAP 5-year data: “Content of the universe” page,
wmap.gsfc.nasa.gov/media/080998/index.html, (ac-
cessed 24 Dec 2012).
10. Boehm, C. and Fayat, P., “Scalar dark matter
candidates”, arXiv:hep-ph/0305261v2, 25 Oct. 2003, p. 1
(accessed 22 Nov 2012).
11. Weniger, C., “A tentative gamma-ray line from dark
matter annihilation at the Fermi Large Area Telescope”,
arXiv:1204.2797v2 , (accessed 23 Nov 2012).
12. Carroll, S., “From Eternity to Here: The Quest for the
Ultimate Theory of Time”, Dutton, New York, 2010, p.
299.
Gauthier, R. (2013) ”A transluminal energy quantum model of the cosmic quantum", in R.L. Amoroso, P. Rowlands & L.H.
Kauffman (eds.) The Physics of Reality: Space, Time, Matter, Cosmos, 8th Symposium in Honor of Mathematical Physicist Jean-
Pierre Vigier, Hackensack: World Scientific.
