H. Javadia and
F. Forouzbakhshb
a Invited
professor of Faculty of Science at Azad Islamic University in
Tehran campuses.,
Tehran, Iran
Javadi_hossein@hotmail.com
b Academic
Researcher, Office of the Vice Chancellor for Research and
Technology
University of
Tehran., Tehran, Iran
fforouz@ut.ac.ir
Abstract
Zero Point Energy (ZPE)
describes the random electromagnetic oscillations that are left
in a vacuum after all other energy has been removed.
One way to explain
this is from the uncertainty principle from quantum physics that
implies that it is impossible to have an absolutely zero energy
condition.
In this article, ZPE
explained by using the Dirac equation.
Keywords: Zero
point energy, Dirac equation, Hawking radiation, graviton,
photon, pair production, renormalization, color-charge,
magnetic-color, photon, spin.
Contents;
1 Introduction
2 Photon and
gravitational field
3 Color-charges and color-magnet
4 Gravitons
5 Definition
of a CPH
6 Principle of the CPH theory
7 CPH and Cyclic group
8 Zero Point Energy
9 Hawking Radiation
10 Graviton Spin
References;
1 Introduction
Zero Point Energy (ZPE),
or Vacuum Fluctuation energy are terms used to describe the
random electromagnetic oscillations that are left in a vacuum
after all other energy has been removed.
The concept of
zero-point energy was proposed by Albert Einstein and Otto Stern
in 1913, which they originally called "residual energy" or
Nullpunktsenergie. All quantum mechanical systems have a zero
point energy. The term arises commonly in reference to the
ground state of the quantum harmonic oscillator and its null
oscillations. In cosmology, the vacuum energy is taken to be the
origin of the cosmological constant. Experimentally, the
zero-point energy of the vacuum leads directly to the Casimir
effect[1],
and is directly observable in nanoscale devices.
One way to explain
this is from the uncertainty principle from quantum physics that
implies that it is impossible to have an absolutely zero energy
condition.
In this article,
according to gravitational blue-shift it has been tried to put
into consideration the Mössbauer effect and Pound-Rebka
experiments and interaction between gravity and photon from
Higgs field point of view[2].
Blue-shift and Mössbauer effect indicates clearly that three
different Higgs bosons cause increasing photon mass while they
have the electromagnetic specifications. These Higgs bosons are
called positive and negative color-charges and color-magnet
which will be explained by using the Dirac equation.
2 Photon and
gravitational field
Let's take a new
look at the behavior of a photon in gravitational field; it can
help us in resolving the vacuum energy.
The electromagnetic fields around
a "ray of light" are electromagnetic waves not static fields.
Relativistically, the electromagnetic field generated by a
photon is much stronger than the associated gravitational field.
When a photon falls in
gravitational field, energy (mass) of it increases. According to ,
the gravity force works on photon, so the mass (energy) of
photon increases. But energy of photon depends on its electric
field and magnetic field. So, a part of gravity work converts to
electric energy and the other part of gravity work converts to
magnetic energy. How can it be explained by Higgs boson which it
shows how particles acquire mass? And also, according to Higgs
boson what happens to blue-shift?
2 Photon and
gravitational field
Let's take a new
look at the behavior of a photon in gravitational field; it can
help us in resolving the vacuum energy.
The electromagnetic fields around
a "ray of light" are electromagnetic waves not static fields.
Relativistically, the electromagnetic field generated by a
photon is much stronger than the associated gravitational field.
When a photon falls in
gravitational field, energy (mass) of it increases. According to
W=Dmc2,
the gravity force works on photon, so the mass (energy) of
photon increases. But energy of photon depends on its electric
field and magnetic field. So, a part of gravity work converts to
electric energy and the other part of gravity work converts to
magnetic energy. How can it be explained by Higgs boson which it
shows how particles acquire mass? And also, according to Higgs
boson what happens to blue-shift?
3 Color-charges and
color-magnet
The frequency of photons changes
in a gravitational field that given by;
The minus sign is for red-shift
(photon leaves gravitational field), and plus sign is for
blue-shift (photon falls in gravitational field).
Where: is
the 2nd
and is
the 1st frequency of photon, G is the constant gravitational
law, M is the body mass. r is distance between body and photon,
c is the speed of light, E is the photon energy, h is Planck
constant.
During a photon is
falling in gravitational field, it acquires energy equal as that separates
into three parts; a part behaves like positive electrical field
and another part that behaves like negative field, which they
annihilate each other in structure of photon (photon is neutral)
and the third part that behaves like magnetic field.
In quantum mechanics
theory, every field is quantized. Also,
force is described as energy per distance that shown by:
If we consider this equation from
point of quantum mechanics, the graviton enters to the structure
of photon where graviton carries gravitational force. As a
result, a graviton disappears and the energy of photon
increases. Similarly, red-shift has opposite effect. As photon
escapes from gravitational field, its frequency shifts to red
and its entire energy converts to gravitons. How we can describe
interaction between photon and gravitons in sub-quantum scale
such as in structure of photon?
Another considerable item is virtual
particles, that the uncertainty principle in the form:
implies that in the
vacuum one or more particles with energy above
the vacuum may be created for a short time .
So, any analysis of ZPE should be able to explain particles
production even Hawking radiation in a strong gravitational
field such as black hole. To do this best way is using the Dirac
equation that of the first time showed the pair particle and
anti-particle.
The Dirac equation can
be written as:
where i=1, 2, 3, m is
the rest mass of the electron, c is
the speed of light, p is
the momentum operator, x andt are
the space and time coordinates
respectively, and is
a four-component wave
function.
A convenient (but not
unique) choice of α�s
is:
The Dirac equation
describes the probability amplitudes for a single electron. This
is a single-particle theory; in other words, it does not account
for the creation and destruction of the particles.
In modern physics for
massless particles, in the (4) equation m =
0, then recover the relationship between energy and momentum
for massless particles given by:
Now let�s do change our
definition about rest mass of particles. As we know some
particle such as photon never seem at rest condition in all
reference frame.
According relativity,
they have mass that come of their energy. For example a photon
has a mass that given by:
So, there are two kinds
particles in physics;
-
Some particles like
photon move with the speed of light c, in all inertial
reference frame, only. Let�s call these kind the N. R. or
Never at Rest condition Particles.
-
Other particles like
electron move with speed v that always v<c in all inertial
reference frame.
According above
definition photon and graviton are NR particles, electron and
proton are particles.
Suppose a photon with NR
mass m and energy at
high h falls toward the earth relative an inertial reference
frame on the surface of earth. Its frequency increases of to , lot
gravitons enter to structure of photon that. The
problem is that how many gravitons enter into photon to change
the least photon energy (minimum of )?
Thus, according to this expression, for
calculate the number of gravitons of and
explain them properties, suppose photon with frequency is
formed of n1 elements
and with frequencycontains
n2 elements.
These elements are not same, because they behave with deferent
properties. Let�s propose a 4x1 matrix
as following;
This matrix must satisfy in
following relation;
Now we should calculate A, B, C
and D that they satisfy with properties of photon. When gravity
works on a photon, gravitons enter into photon and intensity of
electric field increases. Photon has no electrical effect;
therefore A and B must carry electric effect around the photon
with opposite effect. So, according relative between intensity
of electric and magnetic fields E=cB we can write;
There H+is
positive color-charge and H- is negative
color-charge. Also, In above relation c is a pure number that is
relative E and B in electromagnetic. So, let�s show ,
then the above relation becomes to:
When
lots H+ enter
into photon, intensity of positive electric field increases.
According to Maxwell equations, intensity of magnetic field
increases, too. Also, element C must carries magnetic effect
around positive color-charges and same reason is for D element.
Therefore C and D are same with opposite direction. So,
according relationship between intensity of electric and
magnetic field we can write;
Then the matrix (7) becomes to
following form the named CPH matrix;
According to above expression,
we are able define the least magnitude of a photon. A tiny
energy photon contains some positive color-charge H+, negative
color-charge H-, right rotation color-magnet Hm and
left rotation color-magnet -Hm that
showed in CPH matrix (relation 9). This tiny energy comes of
following limit;
Energy of a CPH (ECPH) defines
in relation (12).
Now we are on a place
that guesses some provable conceptions about photon and a new
definition of graviton.
4 Gravitons
Many physicists
believe the graviton does not exist, at least in the simplistic
manner in which it is envisioned. Superficially speaking,
quantum gravity using the gauge interaction of a spin-2 field
(graviton) fails to work like the photon and other gauge bosons
do.
Maxwell's equations
always admit a spin-1, linear wave, but Einstein's equations
rarely admit a spin-2, linear wave, and when they do it is only
perturb active and not exact. But string theory showed graviton
is a 3/2 spin particle.
However, if photon is made of gravitons, then graviton does not
obey of 2-spin. So, let�s continue with definition of CPH and
Principe of CPH and then return to properties of graviton.
5 Definition
of a CPH
What is a CPH? Creative
Particles of Higgs or CPH
is an existence unit of nature. Another words, everything is
made of CPH. Therefore, a CPH is appropriately referred to as
the unit of nature. Although, this is not meant to be the
particle as it has been referred to in physics.
A CPH is a particle with constant
NR mass, that
moves with a constant magnitude speed of in
any inertial reference frame, that c is speed of light.
According to the relation mass-energy (relation 11), the NR mass
of a CPH is defined relative to photon's NR mass;
The relationship between
energy and momentum for NR mass CPH given by;
Relation (12) shows in any
interaction between two (or more) CPH, energy of ever CPH is
constant. So, when does
decrease, it takes spin. Other word, in any inertial reference
frame and Cartesian components;
When;
there is no different between
boson and fermions, in this case CPH carries gravity force and
behaves like fermion. So, there are color-charges, only.
When;
For particles like electron or
quarks;
other bosons do occurrence. For
example reconsider to pair production, before pair production
there is a photon, only, but after pair production there are an
electron (fermion), a positron (anti-fermion) and virtual photon
(boson) that carries electric force. So, we can write:
According a CPH with spin, calls
graviton, so space is full of CPH. When density of CPH increases
in space, their distance decreases, then they feel and absorb
each other. Suppose two CPH are moving on x axis direction and
absorb each other, their path change without decreasing the
magnitude of . According
relation (12), we are able to construct an operator which
rotates CPH by angle about
the x-axis (toward z-axis or y-axis) in position space. Also, we
can construct which
rotates the CPH by about the x-axis in spin space. We would
expect such an operator to take the form;
Thus, according to this expression, two CPH rotated each other,
they can not have same direction spin. They spin with opposite
direction, if positive color-charge has up spin, then negative
color-charge must takes down spin. In general their spin must
satisfy of Pauli matrix. A great result is this fact that spin
of graviton is one-half.
6 Principle of the CPH theory
CPH is a unit tiny energy with constant NR mass ()
that moves with a constant magnitude of speed equal ,
in all inertial reference frames. Any interaction between CPH
and the other existing particles presents a momentum of inertia I where
the magnitude of is
constant and never changes. Therefore,
Based on principal of CPH, a CPH has two types energy generated
by its movement within its inertial frame. One is transfer and
the other spin. In physics, we present energy summation (both
kinetic and potential) by Hamiltonian equation and energy
difference by LaGrange. Therefore, in case of CPH, we use
Hamiltonian to describe the summation of energy generated by
transfer and spin as following:
Where T is transferring and S is spinning energy of a CPH
respectively. Since speed and mass of CPH is constant, then .
CPH produces energy and energy produces Matter and Anti-Matter.
In fact everything has been formed of CPH.
7 CPH and Cyclic group
As we explained in section 3, gravitons in interaction with each
other convert to color-charges and color-magnetic. Also, when
CPH has spin, it calls graviton. Now we can define a cyclic
group for electric field that generates by graviton.
So, given
by;
Suppose 2k color-charges
combined and move in space. So, there are two electric fields
with opposite sign in space. About each field does form a
magnetic field that produces by graviton. According sign of
these fields, direction of magnetic is different, so their
elements are same. Therefore a cyclic group given by:
According above groups and CPH matrix (relation 9) we can
explain zero point energy.
8 Zero Point Energy
Space is full of gravitons. Gravitons interact with each other
and convert to color-charges. Interaction between gravitons
depends to their density of graviton in
volume. Energy production given by:
If we combine relations (4) and (9), then we are able explain
the mechanism of ZPE. Some gravitons with same NR mass convert
to color-charges, two electric fields do form. These fields
neuter each other. But positive color-charges repel each other,
same action happens for negative color-charges. So, when
intensity of color-charges grows, about each fields (negative
and positive fields) a magnetic field do form. Magnetic field
keeps electric field. This mechanism is explainable by Larmor
radius (gyro-radius
or cyclotron radius) that
given by;
Where is
the gyro-radius, m is the mass of the charged particle, is
the velocity component perpendicular to the direction of the
magnetic field, q is
the charge of the particle, and B is
the constant magnetic field.
Defines the radius of
the circular motion of a charged particle in the presence of a
uniform magnetic field. when color-charges change in structure
of photon, then magnetic-color changes too. Therefore charge
particles don�t decay.
However, we should
change m with in
relation (4), then we can write;
Consider to n depends to
density of graviton in space
(relation 20). In
general depends
to CPH matrix and it given by:
Dirac equation for space given as;
In quantum
mechanics of plane waves of specific spin shows that a general
field can always be written in terms of photons with a simple
spin state and a general spatial wave function. Thus the
fundamental entity, the photon can be considered quite generally
to be a plane wave with a circularly polarized spin piece (Any
field can be built from this basic ingredient). For simplicity
consider a photon traveling in the x direction or consider the
direction of the photon as choosing the coordinate axis so that
x point along the photons momentum. Every element in photon
(relation 24), moves with momentum same as photon.
9 Hawking Radiation
In a
simplified version of the explanation, Hawking predicted that
energy fluctuations from the vacuum causes the generation of
particle-antiparticle pairs near the event horizon of the black
hole. One of the particles falls into the black hole while the
other escapes, before they have an opportunity to annihilate
each other. The net result is that, to someone viewing the black
hole, it would appear that a particle had been emitted.
How Hawking radiation is explainable by equation ZPE (relation
24)? For resolving this problem, there are three considerable
items in black hole;
-
Intensity of graviton is so high around a black hole.
-
Gravitons convert to photons speedy.
-
Dirac
equation shows how photon produces matter and anti-matter.
According relations (20) and (24), space around black hole
produces high energy photon that its energy is enough for pair
production. Dirac equation results for total
energy given by;
Compare relation (25) with equation (24), energy equation can be
written as;
In black hole n growth
speedy, so is
comparable with total mass of particle and anti-particle. The
problem is conversation of momentum that it is resolvable by
interaction between photon and existence of heavy particles
around black hole, especially in photon sphere. This looking not
need to time that the
uncertainty shows in relation (3). So, pair production is a
common projection around a black hole.
10 Graviton Spin
Relations (26) and pair production is considerable to thinking
of graviton spin. Root of relation (26) given by;
Pair production shows a
photon with spin one, produces two particles (electron and
positron). Relation (27) results an electron with spin � (and a
positron with spin �) is formed of gravitons. Compare this
expression with quarks and proton. A one-half spin (proton) made
of three quarks with � spin. In high speed (c or greater than c)
graviton (color-charges) behaves like fermions (electron). So,
we should reconsider our ideas about spin of graviton. Relation
(27) shows graviton has a one-half spin.
The quantum loop calculation comes with a very big problem. In
order to properly account for all virtual processes in the
loops, one must integrate over all possible values of momentum,
from zero momentum to infinite momentum. But these loop
integrals for a particle of spin J in D dimensions take the
approximate form;
If the quantity 4J+ D - 8 is negative, then the integral behaves
fine for infinite momentum (or zero wavelength, by the de
Broglie relation.). If this quantity is zero or positive, then
the integral takes an infinite value, and the whole theory
threatens to make no sense because the calculations just give
infinite answers.
The world that we see has D=4, and the photon has spin J=1. So
for the case of electron-electron scattering, these loop
integrals can still take infinite values. But the integrals go
to infinity very slowly, like the logarithm of momentum and it
turns out that in this case, the theory can be renormalized so
that the infinities can be absorbed into a redefinition of a
small number of parameters in the theory, such as the mass and
charge of the electron.
Quantum electrodynamics was a renormalize able theory; this was
regarded as a solved relativistic quantum theory.
One big problem was that classical gravitational waves carry
spin J=2, so one should assume that a graviton, the quantum
particle that carries the gravitational force, has spin J=2. But
for J=2, 4J -8+D=D, and so for D=4, the loop integral for the
gravitational force would become infinite like the fourth power
of momentum, as the momentum in the loop became infinite. And
that was just hard cheese for particle physicists, and for many
years the best people worked on quantum gravity to no avail*.
According graviton converts to color-charge in interaction with
other particles and it has a J=1/2, so, in 4J-8+D,
J=1/2, we have, then for our universe D=4, so;
and relation (28) is renormalize able simply.
References;
1- Richard Cushman. and. Wilberd van der Kallen. .(2005) �A
new interpretation for the mass of
a classical relativistic particle�, Elsevier Journal,
Physics Letters Volume 24, Issue 3, May 2006, Pages 230-234
2- Ravindran V. (2006) �Higher-order
threshold effects to inclusive processes in QCD�, Elsevier
Journal, Physics Letters B, Available online 11 July 2006
Perelstein M. (2006) �Little
Higgs models and their phenomenology�, Elsevier
3- Journal, Progress in Particle and Nuclear Physics, Available
online June 2006
4- Gupta G. P. and. Lal K. C.(1971) �On
the equivalence of gravitational red shift and temperature shift
in the M�ssbauer effect�,
Elsevier Journal, Physics Letters A Volume 36, Issue 5,
September 1971, Pages 421-422
5 - Peter S. Riseborough , E-book , Advanced Quantum Mechanics
March 14, 2007
6- Stefan Waner, E-book, Introduction to Differential Geometry &
General Relativity
4th Printing January 2005
7- http://www.daviddarling.info/encyclopedia/C/Casimir.html
8- * advanced
string theory http://superstringtheory.com/basics/basic3a.html
9- F.
Smarandache, V. Christianto, Fu Yuhua, R. Khrapko, J. Hutchison,
E-book, Unfolding
the Labyrinth: Open Problems in Physics, (University
of Microfilm International)
[1] -
Casimir, H. G. B. "On the attraction between two
perfectly conducting plates." Proc.
Con. Ned. Akad. van Wetensch B51
(7): 793-796 (1948).
[2] -
General relativity forces Masataka Mizushima Department
of Physics, University of Colorado, Boulder, CO 80309,
USA November 2004. 30 November 2005-15 December 2005,
Pages e369-e378