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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

.

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!

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S = RPsin(

!

) = h / 2

"

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!

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!

) = tan(

!

) =

"

/ 2

#

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R

!

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!

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"

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#

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!

)=2

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#

=

#

/2

"

R

!

= 2

"

R

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