International Journal of Physics and Research (IJPR) ISSN(P): 2250-0030; ISSN(E): 2319-4499 Vol. 4, Issue 3, Jun 2014, 23-30 © TJPRC Pvt. Ltd.
PHOTON’S MASS: THE QUESTION OF UNIVERSE? ARKA DEV ROY & ABHISHEK DAS Guest Lecturer, Department of Physics, Rampurhat College, Buardwan University, Rampurhat, West Bengal, India
ABSTRACT The following approach is concerned with the development of an intuition regarding the massive nature of photon, From Einstein’s SRT we know that every particle that travels at the speed of light must accordingly be massless. We have assumed that the frequency ( ) of the radiation is a function of the wavelength ( ), i.e. (
= (
. At first, we expand
as a Laurent series and strive to search for an expression for the mass of a photon. Our non-conventional approach
may succour to the understanding of the nature of the universe, during the hot epoch or Planck epoch and its infancy. And in the second fold we consider the three massive photon states to consistent with the frequency dependence dispersive relation.
KEYWORDS: Photon Mass, Glinka Model, Planck Epoch, Frequency Dependence. Graviton, Higgs Boson INTRODUCTION The history of the photon in the 20th century started in 1901 when the eminent physicist Planck [(1)] put forward the formula for radiation of a black body and introduction of what was called later the quantum of action ‘h’ (Planck’s constant). In the year 1905 Einstein [(2, 3)] demonstrates that energy of light is distributed in space not uniformly, but in a form of localized light quanta. Einstein’s light quanta behave as particles; it’s carrying both the energy as well as momentum. The term ‘photon’ for particles of light was given by Lewis [(4)] in 1926 in an article “The Conservation of Photons” considering photons to be “atoms” of interaction. Now, neutrinos appear to travel at the speed of light and on account of the ‘Special Theory of Relativity’, they must be massless. Massless neutrinos have a problem to describe the phenomenon of Neutrino oscillations [(5)] because this requires massive Neutrinos as described by Fermi and his Research Scholar Ettore Majorana. This intuition could be consistently helpful to conceive the phenomenon of the photon mass being zero and it can also show that the photon mass has a non-conventionally finite and non-zero value.
THEORY In the beginning of our theory we assume the photon mass to be non-zero and assign to it the value m. Thus, for the photon the mass-energy relation due to Einstein ([3]) is given by: =
+
(1)
Where, the symbols have their usual meanings. =
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/
—
(2)
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Arka Dev Roy & Abhishek Das
Where we have used De Broglie's relation: - p = Hence, for non-zero photon mass we must have ]
[
0
(3)
Now, from this equation we can clearly assume that the frequency i.e.
=(
. From this we are using L.A GLINKA’S MODEL [(6)]
Where he considered: The ([6]). So
of the photon is a function of the wavelength
(
=
(
can be expanded in terms of the wavelength
resorting to the Laurent series
.
Latter he consider the simple situation when +
(4)
Where he neglected all other terms to simplify the problem and have put =
and
= c, being the velocity of light.
Squaring this equation and balancing he got =
+
=
[
+
]
(5)
=
Where
=
,
is termed as the zero-point photon mass and
=
, where
is
termed as the additional photon mass. Now we want to take different view. Here, we resort to the Planckian system of units ([7]). Now, instead of many types of elementary point like particles, it is postulated that in nature there is a single variety of one dimensional fundamental object known as strings exists. strings have a characteristic scale which comprises of the following three fundamental units:- the velocity of light 'c' governing the laws of relativity, the reduced Planck constant h related to quantum physics and 'G' being Newton's gravitational constant. In terms of these three we have Planck length (
)=
Planck mass (
)=
Impact Factor (JCC): 1.9845
= 1.602 ×
=2.176 ×
cm
gm.
(6. a)
(6.b)
Index Copernicus Value (ICV): 3.0
25
Photon’s Mass: The Question of Universe?
Planck time (
)=
/C =
=5.4×
Sec
(6.c)
Here, we take the risk to assume that the zero-point photon mass (
)=
. Let us investigate whether our
assumption provides some justification regarding the concept of the Planck epoch right after the Big Bang ([8]) and that of the infancy of our universe. According to our assumption =
=4.75×
(7)
Putting the values of h and c we obtain
So we may write
So we get:
=
=3
=
/S
(8)
.
(9)
=
=
=
Therefore we may write
Putting the value of
=
we get
=
×
=4π
Therefore from equation (9) and (10) we have
(10)
=
.
(11)
its resemblance to L.A GLINKA [(6)]. Now, since =
=3
/S so we can say:
3.3
Where the time period ( Hence, our assumption that (
S
(12)
) is very nearly equal to duration of the first few moments of the Planck epoch ([7)]. )=
is quite justified if from the viewpoint of our work it is interpreted that
corresponds to the initial or zero-point mass of the photon during the first few seconds of the Planck epoch, right after the Big-Bang. Therefore, in light of this new theory, we can adopt the notion that the photon mass (m o
) was non-zero
during the birth of our universe! Now, if
corresponds to the zero-point frequency ( eV
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) then (13)
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Arka Dev Roy & Abhishek Das
Which is of the order of the same energy in the Planck epoch? Thus, our theory provides an intuition regarding the state of the universe, during its birth in accordance with the Big Bang. But, the question that remains is: - what happened to the photon mass? If it exists then why does it remain undetected? Now come to another issue: We have from our calculation:
Then
=
+
=
(14)
The equation (14) comes into existence in a strictly non-conventional manner, which implies that the photon has a negative mass-value .Nonetheless, in analogy with Schwinger ([9]) we introduce three massive combination states comprised of the massive states •
[+
•
[
•
[+
) ;( [+
. So may consider the three combined massive states of the photon is given by
)
) ;( [) ;( [-
) or [
) ;( [+
Where, in case of the third combination are obviously equivalent. The three massive combination states mentioned previously yield two mass- square values. Now the most direct consequence of a non-zero photon mass is frequency dependence in the velocity of electromagnetic waves [(10)] Propagating in the free space. The Phase velocity and the group- velocity (the velocity of energy flow). A free massive wave would then take the form
Thus, it is obvious that conventionally a finite photon mass
will culminate in frequency dependence, and the
group velocity will differ from the phase velocity. Now, we take into account the three massive states of the photon so that the original dispersion relation ( •
=
=
-[(
Which yields:
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|)( =
| -
) may be [(10)} written as following: |)] and
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27
Photon’s Mass: The Question of Universe?
•
=
- [(
Yielding
|) (
|
|]
+
These two relations combine to give the general dispersion formula independent of the photon mass as: = Where: And
=
+
=
Consequently, the concept of the three massive states elegantly annuls the dilemma regarding the frequency dependence of the velocity of the massive photon. Now we may consider from eqn (9):
=
Again, Newton's Law of Gravitation is given as F=
(15)
Where the symbols have their usual meaning. So we have:
=
(16)
Then we have F =
(17)
If the photons with velocity c take time t to traverse the distance r, then we can rewrite the above equation as:
F=
Now, since
(18)
corresponds to the zero-point photon mass of the photon during the Planck epoch, from the above
equation it can be said that Newton's Law of Gravitation is fundamentally a law depending on the two ratios
, where M and m are the masses of the concerned bodies in the gravitational field. From this dependence, we may boldly venture to conclude that the photon is the quanta of radiation. The explanation that follows for such a bold conclusion is that:- the two mass-to-mass ratios M, m and the photon with mass
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, may signify the interactions between the two masses
, necessary for the gravitational attraction. It might have been such that during the
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Arka Dev Roy & Abhishek Das
first few moments of the Planck epoch the zero-point photon mass (
) along with the quantity
contributed to the
distribution of matter and arrangement of the framework of gravitational field and are the precise reasons for the existence of the said field. In the process, it might have been possible that
became undetectable, for the sole reason of its
indefatigable and constant interaction with matter throughout the universe, to retain the gravitational field. Now, we know that the photon is a spin-1 particle and the predicted graviton ([8]) if exists must be a spin-2 particle. The term
in equation (37) might be interpreted as two photons with the zero-point photon mass and parallel
spin constituting a single spin-2 particle, which acts as the quanta of the gravitational field. Again, the question that arises primarily for this kind of conclusion is: - we know that the photon is the quanta of the electromagnetic field, then how can it be the quanta, namely graviton ([11]), of the gravitational field? This is quite an interesting contradiction, but we have to admit that scientists have been trying to unify the forces of nature. So, it may obviously be possible that the photon is responsible for two forces of nature. Now the graviton is predicted to be massless, but what if it is actually a particle comprised of two photons whose mass is undetected because of the fact that the zero-point photon mass is never revealed. The Higgs-Boson particle has two main characteristics, i.e. its parity is '+' and spin is '0'. It is the particle which creates the Higgs field and imparts mass to all known particles. Again, we know that the photon has parity '' and spin '1'. In equation (18) we have shown that the force (F) of attraction depends on the zero-point photon mass with the multiplicity of 2. We have also put forward a rather speculative and yet interesting notion that two photons if unite with parallel spin then they may be considered as a single spin-2 particle, namely graviton. In a similar manner, if we consider two photons to unite with anti-parallel spin then they may be viewed as a single spin-0 particle. Also, since parity is multiplicative, the resultant parity for two photons with parity (+, +) or (-, -) will be '+'. But, this is exactly the same criteria of a Higgs-Boson. Now, it might have been so that the photons, during the creation of the universe had given life to the Higgs-Boson and the graviton. Like before this is also a speculative notion, since we are considering the photons as the source of all energy and mass distributed throughout the universe. Yet, this hypothesis might aid in the understanding of the formation of the Higgs-Boson, whose existence has been recently verified and the reason why it has the ability to impart mass to all particles. Therefore, our theory and the aforementioned conclusions invoke the question whether the photon is responsible for both the graviton and the Higgs-Boson??
CONCLUSIONS It is great Louis de brogley [(12)] who is the first person of the globe to talk about the none zero Value of photon mass. So it contradicts the scientist as if it is not violate the fundamental second postulate of Relativity? Till now we are totally blind to know about the universe of astrophysics and cosmology where many doubts and suspicious view wait for a mind-blowing resolution as well as for determination of a nonzero value for the mass of the photon, encouraged for work on the formation and early evolution of stars and stellar systems.Other than that, with the advent of string theory as an ultimate theory towards the understanding of our universe may account for the non zero photon mass in the Hidden dimensions.
Impact Factor (JCC): 1.9845
Index Copernicus Value (ICV): 3.0
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Photon’s Mass: The Question of Universe?
ACKNOWLEDGEMENTS We are Very much thankful to Dr. S. sahoo, Department of Physics, NIT DURGAPUR, India for stretching his kind and supportive hands to build our thesis. We are also thankful to Ujjwal Das, Department of physics, Krishnanagar Govt. College, Kalyani University, India for his support.
REFERENCES 1.
Planck, M. Ann. Phys 4,561 (1901)
2.
A. Einstein, Ann. Phys. 17, 132 (1905) “Monochromaticity and Massive Photon Introduction”: A.D Roy, A Das International Journal of Physics and Research (In Press).
3.
“On the Heuristic point of view Concerning the production and Transmission of light”- Albert Einstein
4.
G.N Lewis, Nature, No. 2981. Volume. 118 (December 18, 1928) 874
5.
Are Photons Massless or Massive? G.G NYAMBUYA vixra: 1301.oo61
6.
Glinka, Lukasz Andrzej. Vixra: 1110.0014v1, on nonzero photon mass within wave-particle duality, October 5, 2011.
7.
Zwieback, Barton. A First Course in String Theory, second ed., Cambridge University Press, New York, p-55
8.
Drees, W.B. (1990), beyond the big bang: quantum cosmologies and God, Open Court Publishing. pp. 223224. ISBN 978-0-8126-9118-4.
9.
Schwinger, J. Phys. Rev. 128, 2425, (1962)
10. Tu, Liang-Cheng., Luo, Jun. and Gillies, George T. The Mass of the photon, Rep. Prog. Phys. 68 (2005) 77130. 11. Zee, A. (2003), Quantum Field Theory in a Nutshell, Princeton University Press, ISBN0-691-01019-6. 12. On
the
massive
nature
of
Photon.
Arka
Dev
Roy,
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