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ABSTRACT

There is an incoherence in the Einstein’s general relativity, because he has started his mathematical formalism by considering a particle with unit mass, but later the formalism applied to the photon led him to the conclusion that the particle is massless.

Here we show that such incoherence can be eliminated by considering the model of no massless photon composed by two corpuscles: a particle and its anti-particle, as proposed in the author’s Quantum Ring Theory.

A) THE EINSTEIN’S POINT OF DEPARTURE

Let us analyse the equation of photon according to the relativity. First of all, let us note that Einstein has considered, in the equation

a free particle of unit mass so that L= m.v2/2 reduces to v2/2, according to Lindsay and Margenau[1].

Consider the equation

which suffices to determine the geodesic corresponding to the path of the particle, where “m” is a constant of integration.

COMMENTARY ONE: The eq. (10) differs from the Newtonian one only in the addition of the term 3mu2. And since “m” in the classical theory is the mass of the body, we conclude that in the relativity “m” also refers to mass (“m” in the eq. [10] is the quantity GM, where G is the constant of gravitation, and M is the mass of a body - as the Sun - that produces the gravitational field).

The fact that “m” in the eq. (10) is the quantity GM shows us that, when Einstein has introduced the velocity of light in eq. (9), without to know he was introducing in his equations the interaction of the gravitational aether with the magnetic aether when a body moves.

COMMENTARY TWO: Other evidence that suggest that “m” is related to the mass of the particle comes from the equation:

If m=0, we have and the resulting arc element is that of a field-free region (Euclidean space).B) WHY THE PHOTON IS NO MASSLESS

After the introduction above, let us analyse the equation of a photon according to the relativity:

where u= 1/r, and “r” is the radius of a sphere in which ds2 is the arc element.

The equation (12) shows clearly that the photon is not massless, since “m” is related to the mass of particle under consideration, as we have seen in the “commentary one” and “commentary two” above.

But the eq. (12) also help us to understand other paradoxes of the Modern Physics, as we show ahead:

1- First of all, we now can understand why the photon is considered massless in the Modern Physics:

1.1- Firstly because “m” in the eq. (12) does not represent the classic Newtonian mass.

1.2- To arrive to his equation Compton has started up from the equation E2 = (h?)2 + (mc2)2 , where he has considered m=0.1.3- As in the relativity “m” is not the mass in the Newtonian sense, and since Compton has considered m=0, we realize why in the Modern Physics the photon is considered massless. However we already have seen that Compton’s starting point (that is, m=0) can be applied to the aspect of the photon energy only, and not to the question of momentum. In other words, the mass of the photon has a duality:

a) regarding to energy, the photon behaves as massless.

b) and with regard to the momentum it behaves as no massless.

And such a duality of the photon is explained through

the model of photon constituted by matter-antimatter,

as proposed in Quantum Ring Theory.

2- Of course that there is an incoherence in the relativity formalism, because in the beginning Einstein has considered in eq. (9) a particle with unit mass, but in the end he arrived to the result that the photon is massless, and such a conclusion is incompatible with the starting point.

By considering the mass of photon as unit in eq. (12) of photon, what would be the meaning of “m” in that equation?

Let us respond this question by remembering the quoting the new “second premise” of Lorentz, as it has been proposed in the page 37 of the book Quantum Ring Theory:

Lorentz’s premise: the energy interaction between the magnetic and the gravitational

ethers grows according to the relation E = mc2/(1 – v2/c2 )-1/2 – mc2,

where “m” is the mass of the body that drags with velocity “v” the magnetic ether.

Well, through this new premise we get to understand why the mass of photon disapears in the Einsteinian formalism: it’s because “m” actually represents the interaction (which unity is J.m/kg) between the magnetic aether and the gravitationa aether when the photon moves, and such interaction is provoked by the unit mass of photon.

There are three theoretical restrictions against a no massless model of photon:

1- The Compton mathematical formalism, from which he obtained his equation by considering as a point of departure a massless photon (from the viewpoint of the photon’s energy). We already have eliminated such theoretical restriction in a former paper[2]2- The photon is massless in the relativity, or, in another words, a no massless photon would be incompatible with the relativity. However we have seen in the present paper that such a conclusion is not true. Actually there is an incoherence in the relativity, since Einstein developed the general relativity from the point of departure of considering a particle with unit mass. And we have seen in the present paper that such incoherence of the relativity can be eliminated by considering a model of photon with a new sort of duality:

the “massless/no-massless” duality of the photon ,

according to which the photon is massless regarding to its energy, but it is no massless regarding to its momentum.

3- A no massless photon would be incompatible with the gauge invariance. However such a restriction is valid only if we consider a no massless photon constituted by ordinary matter, because there is no way to find a symmetrical model of photon constituted by matter only. But a massless model of photon constituted by matter-antimatter has a symmetrical structure, and so we can find a Lie Group for such a model, and thereby a model of photon constituted by matter-antimatter does not violate the gauge invariance.

Besides, it is shown in another author’s paper[3] that a photon composed by matter-antimatter generates the Maxwell’s Equations, and therefore such model does not violate the gauge invariance.

Einstein started the development of General Relativity by considering a particle with unitary mass, and later he applied it to a photon.

Actually the mathematical formalism to be applied to a photon must be different of that applied to a particle with mass, since the photon is massless.

Let us see what is the correct starting point for a photon.

Consider the Hamilton’s principle for a particle with mass “m”:

which can be placed into the form

where T is the kinetic energy and V the potential energy, and the eq. (14) can be written:

Now instead of considering a particle with mass “m”, consider a photon constituted by a particle and its antiparticle. The eq. (15) becomes:

and by considering a unitariy mass m=1, we have

Pat attention that although the particle has a mass m=1 and the antiparticle has a mass m=1, however the photon with struture “particle-antiparticle” has rest mass zero, as shown in another author’s paper[2].

The half potential energy V of the photon in eq. (18) can be equivalent to a kinetic energy of a particle with mass m=1 moving with speed “v”, in order that V can be written:

and because m=1:

The eq. (18) then can be written:

Writting

v2 = (dx/dt)2 + (dy/dt)2 +(dz/dt)2 ,

we can see that eq. (22) can be put into the form

if we choose

which is the arc element in the four-dimensional manifold in the absense of a field, obtained by Einstein in the beginning of the formalism concerning the motion of a particle in a gravitational field. But Einstein obtained eq. (24) by considering a particle with unitary mass, and herein we have obtained it by considering a null rest mass photon. The incoherence of Eisntein’s formalism has been eliminated, because we see that eq. (22) can be applied to a no massless particle, but it can be applied to a massless photon too, if we consider a photon with structure matter-antimatter.

An experiment ( published in 2003 by the American Institute of Physics , made by Jun Luo[4] ) has imposed a new limit for the mass of the photon. But the experiment did not show that photon's mass is null. And so the controvery continues.

Is it possible to detect the mass of a photon, by making an experiment in the way made by Jun Luo?

And suppose that it is not possible to detect the photon mass from an experiment similar of that made by Jun Luo, but it is possible to make it in another way. Does such experiment imply that the rest mass of photon is not null?

No, it doesn’t.

It is important to have in mind the following:

1. Consider a particle and its antiparticle, they both with mass “m”. Each one have such mass “m” when they are not within the structure of a photon. Therefore each one is no massless.

2. But when the particle and the antiparticle are packed together performing the structure of a photon, the photon behaves as massless, as shown in the author’s paper[3]. Although the particle and the antiparticle have each one a mass “m”, however together (performing a photon) they have a behavior characteristic of a massless particle.

3. When the light hits a surface and the photon is absorbed, the structure of the photon is broken.

4. When the structure of the photon is broken, the two particles are absorbed by the aether. And so there is no way to perform an experiment capable to detect the mass of the photon, as tried by Jun Luo.

Actually there is no way to measure the mass of a photon in that way tried by Jun Luo, because when the struture of the photon is broken the particle and the antiparticle are absorbed by the aether. So, it’s impossible to detect the mass of a photon with that sort of experiment, because the indidual masses of the particle and antiparticle are absorbed by the aether, and so no mass is deposited in the surface where the photon had fallen down.

1- In Modern Physics the photon is considered to have wave-particle duality. But we realize that the photon has actually a new sort of duality: the photon is massless regarding to the aspect of its energy, but it is no massless regarding to its momentum, as we have seen in the author’s paper[2].

The duality “massless/no-massless” is not known in the current theories, and one of the reasons is because Einstein’s relativity has been published earlier the Dirac’s discovery on the existence of antiparticles.

2- It seems to be impossible to measure the mass of photon by experiments

1- R. Lindsay, H. Margenau, Foundations of Physics, Ox Bow Press, 1988, pg. 365

2- W. Guglinski, Why the Photon is Not Massless, submitted to Infinite Energy

3- W. Guglinsi, A Model of the Photon, Quantum Ring Theory, Bauu Institute Press, 2006, pg. 20

4. Jun Luo , American Institute of Phyhsis, http://www.aip.org/pnu/2003/split/625-2.html

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