The law of the inertia of energy and the speed of gravity

### By Alfonso León Guillén Gómez

Bogotá, Colombia, October 23 of 2004

This work the author sends to Elsevier, Science Publishers, in Amsterdam, Netherlands, and submitted for review and publication to Professor Doctor Charles R. Doering, of the Department of Mathematics, University of Michigan, USA, and Editor, of “Physics Letters A”. He in his referee report said “This manuscript is not appropriate for publication in Physics Letters A. Besides being much too long for a letters journal, it is more an essay on the author’s theory that apparently has not garnered much attention (not as much as the author would like, apparently). Perhaps this paper would be appropriate for a “foundations” journal.”.

The professor doctor Gerard't Hooft, Nobel Prize in Physics of 1999, said “you can use general relativity to derive that gravitational waves move with exactly the same speed as light: c”

Barry Setterfield, Australian astronomer, said “At first glance I do have some reservations about the speed of the photon at the time of emission and its energy, but that may be because I have not given myself enough time to read your paper more thoroughly”.

Serguei Krasnikov, of the Central Astronomical Observatory at Pulkovo, St. Petersburg, Russia, said “I agree that the subject (the speed of gravity) is very interesting and deserves all possible attention”.

"The divine thing must be ONE, must have an existence that differs from which we called appearance"

Fedérico Hegel

Abstract

All the existing particles in the nature have inertia, this is, according four moment both massive and massless particles. And the inverse dependency of the speed of particles of the magnitude of its inertia is a law of the nature.

The massive particles of the substance have inertia and the substance comes from the energy then massless particles of the energy have inertia and the energy is the source of inertia in the nature. But, the inertia of the energy is not just like the inertia of the substance. Whereas inertia in the substance is caused by the law of action-reaction between the mass of the particles of the substance and the vacuum, the inertia of the energy is caused by the law of absorption-emission between the energy of massless particles of the waves and the vacuum. The particles interact with the vacuum because vacuum is full of free fields of their sources.

The electromagnetic and the gravitational waves, that is the electromagnetic and gravitational dynamic fields, are transported through their respective electromagnetic (electric and magnetic fields uncoupled) and gravitational static fields of the vacuum. The interaction between these dynamic and static fields provides the mechanism with the absorption-emission processes that happen in the interaction between the waves and the vacuum. This mechanism consists of the real particle of the waves passage to virtual particles of the vacuum and the virtual particle of the vacuum return to real particles of the waves.

The energy of particles is direct dependent of the frequency of the waves. And the law of absorption-emission, that governs the interaction of the energy with the vacuum, presents that their magnitudes are direct dependents of the magnitudes of the energy of particles of the waves and the density of the energy of the vacuum.

The frequency of the absorption-emission of the vacuum is increased with the greater energy of particles of the waves that increases its frequency of interaction with the vacuum, and with the greater density of the energy of the vacuum that increases its interaction with the waves. Consequently, the speed of the gravity waves is greater than the speed of the electromagnetic waves because the energy of particles of gravity waves is much smaller than the energy of particles of the electromagnetic waves.

For the vacuum, with refractive index ≈ 1, the speed of gravity is maximum 2,2222 × 1010 × c, in agreement with the equation of Cramer-Collins, fit by the author with the considerations of Schaefer for the speed of the photon and the measurement of Tom Van Flandern for the speed of the gravity.

After 2009, in project GLAST, the NASA will establish if the gamma rays, which are the highest energy, this is, the highest inertia of spectrum electromagnetic when interacting with the quantum gravitational field, travels in the vacuum under c. Contrary also must be truth, then NASA indirectly will test my theory, that I exposed in 1969, about graviton more higher speed that photon because graviton has the lowest energy, this is, the lowest inertia in front of spectrum electromagnetic and graviton also interacting with the quantum gravitational field.

1 Greater speed to smaller inertia

2 Mass is concentrated energy and energy is scattered mass

3 The energy has mass

4 The energy has inertia

7 Reflections on the interaction between the waves and the vacuum

8 ¿What is the speed of gravity

9 Conclusions

10 Bibliography

11 Works of the author

Este trabajo también el lector puede verlo en español (This work also the reader can see it in Spanish).

### Introduction

In 1969, for particles of the fields, the author discovered and formulated the law that it establishes that when a particle is less inertial than another then particle has a greater speed This law that comes from the phenomena of the substance, this is, with nuclear and electronic composition or, in general, from particles with mass according to the four-vector moment, the author extended it to the phenomena of the energy, that is to say, with devoid particles of mass according to the four-vector moment, in the electromagnetic and gravitational fields.

In the newspaper the "Siglo", Dominical Weekly magazine, between the 14 of December of 1969 and the 8 of February of 1970, in four articles, the author published its theory on the existence in the nature of speeds greater than the speed of light, one of which would be the speed of gravity . This theory has like foundations the quantum theory on the gravity formulated by Andrei Saharov, M Vasiliev, and K Staniukovich, that explains the gravitational effect on particles like the action of the interaction force that transports the virtual graviton and the law of the author who, in agreement with its initial formulation, says: "As the matter is disintegrated, its movement acquires rapidity. Thus, while the speed of molecules, in the gaseous state, is of about 0,5 km by second the elementary particles and mesons move at speeds superior to 24000 km by second and photons 299999 km by second. Therefore, the graviton must have a speed greater than the speed of light. Or is it perhaps that the mass of the graviton is greater in relation to the mass of the photon? Or the law of the greater speed for the smallest particle is not been worth for the graviton? Or this law does not exist? ".

As the graviton is less inertial, that is to say, it offers a smaller resistance moves it, that the photon the graviton must have a speed greater than the speed of the photon. In agreement with this law, the particle that more tends toward vanished will have the greater speed in the nature. This particle can be the graviton very smaller than the photon. But, if a particle exists with inertia almost zero, this particle will have an almost infinite speed.

Since 1998, the astronomer and scientist doctor Tom Van Flandern, made several theoretical experiments and esteem that the speed of gravity is minimum 20 billion times the speed of light. Tom says: “if gravity is once again taken to be a propagating force of nature in flat spacetime with the propagation speed indicated by observational evidence and experiments: not less than 2 x 1010 c” .

### 1 Greater speed to smaller inertia

In the substance this law about the greater speed to smaller inertia was well-known by Albert Einstein that said: "if a same force acts on two different bodies that leave from the rest, their resulting speeds will not be equal. This is expressed saying that the speed depends on the mass of the body, and is smaller when greater is mass." .

In the 2001, in the electromagnetic field, this is, for the phenomenon of the electromagnetic energy, the physicists Dimitri Nanopoulos of the Theoretical Physics Division of the Academy of Athens, Nikolaos Mavromatos of King's Collage, in London, and John Ellis of the European for Center Particle Physics (CERN), in Genoa, discovered a new expression for the speed of the light, the one that depends on its frequency, that is to say, of their energy in agreement with the relation to greater energy smaller speed. Nanopoulos says: "Through our calculations, we found that the speed of light is frequency-dependent. But a change in the usual speed of light value of 186,282 miles per second is noticeable only for light coming from astronomical objects situated very far from Earth, which is why this frequency dependence has not been noticed so far.". "One way to experimentally test our hypothesis is to consider galaxies or other objects in the sky that are very far from us". "Then we collect the photons (particles of light) simultaneously emitted by these sources, and we look at differences of arrival times in a detector on earth between photons of different frequencies. The photons of higher frequencies should come later." .

### 2 Mass is concentrated energy and energy is scattered mass

In agreement with Einstein the "mass is concentrated energy and the energy is scattered mass" . In “The physical adventure of the thought” Einstein says: "The energy has mass and the mass represents energy. Instead of two principles of conservation of mass and energy we have one single principle the principle of the conservation of the mass-energy" . In “The Meaning of Relativity” Einstein says: "Mass and energy are essentially analogous then are only expressions of same thing". "The law of conservation of the mass of a system is equivalent to the law of conservation of energy" . Equivalence exists between mass and energy that is expressed in the equation:

E = mc2

In Nature 438, of 22 December 2005, is reporting that Einstein's relationship E=mc2, is separately confirmed in two direct tests the which yield a combined result of 1-mc2/E=(-1.44.4)10-7, indicating that it holds to a level of at least 0.00004%. Also it is commenting “If this equation were found to be even slightly incorrect, the impact would be enormous given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems.” .

This equivalence this verified in the following transformations:

- Energy to mass.

“a travelling photon may briefly be transformed into a virtual electron-positron pair, which moves forward less than one photon wavelength before annihilating to create a new photon indistinguishable from the old one.” .

“an electron–positron pair is created from the photon as it passes close to an atomic nucleus. A minimum energy (1,020,000 electron volts [eV]) is required for this process

Pair production is a process in which a gamma ray of sufficient energy is converted into an electron and a positron.” .

- Mass to energy

“The collision of a positron and an electron results in the intermediate production of a short-lived atomlike system called positronium, which decays in about 10-7 second into two gamma rays.”. In general, all the existing particles have their corresponding antiparticle that when hitting is transformed into radiation.

### 3 The energy has mass

In the present version of relativity, denominated modern relativity, some physicists have discarded that the energy constitutes mass, in the sense that the energy variation can cause the variation in mass. This conclusion obtains from the examination of the unit mass-energy only of the side of equivalence between mass and energy without considering the other side, that is to say, equivalence between energy and mass.

These scientists remain in the examination of the equation of mass equal to energy more moment. This equation they have evolved it towards new conceptual expressions, constructed from the new terms of relativist energy, energy center of masses, mass "shell", moments four-vectors of first and second class etc. that formulated in the mathematical context of special relativity, of one part, they look to save relativist orthodoxy in front of the opening, of some physicists, at the superluminales speeds and, of the other part, the integration of relativity with the quantum mechanics. This way, equivalence between mass and energy in both directions of the original conception of Einstein appear castrated

The author presents the problem created by the denominated modern relativity that deliberately is against to consider the equivalence of the energy in mass with physical effect in the mass. Like consequence, modern relativity considers mass in rest and relativist mass like not valid terms that replaces by energy in rest and relativist energy. With this one is returning to the classic thought on the energy, like devoid of mass, but despite modern relativity it maintains the energy like foundation of the mass and this one like foundation of the energy. The tangle created is in the consideration that the mass is a phenomenon of the four-vector moment, p, whereas the energy a phenomenon of the one-vector moment, p0. Exiling the mass of the energy leads to deny the inertia of the energy, and, consequently, to block that it is possible at least logically to be defended that the forms of energy in agreement with its inertia, they can vary in speed, this is, that the speed of the electromagnetic energy is frequency-dependent and, for example, that the speed of gravity can have a speed greater than c, since gravity, conceived from the quantum theory, is less inertial than electromagnetism.

The version of modern relativity distinguishes the mass according to three levels:

- Mass of a system of photons, “a photon does not have mass. It is also inappropriate to say that light waves have mass. Instead of saying light has mass, in special relativity it is better to talk about light having a mass-shell because it is a system of particles. In that case plane waves of light moving in one dimension have zero mass-shell, whereas light moving spherically away from a source would have a nonzero mass-shell” . However, the author indicates that the laser beam have clearly inertial properties, soon it is not clear that a unidirectional wave lacks mass, another thing is that it lacks mass in rest as it happens with the photon and the graviton.

- Mass of a particle that they define from the slight knowledge of energy in rest, E0, relativist energy, Er, and moment, p when the speed of the particle is zero. “The special relativist definition for the mass of a particle given those relations is:

m = [(ER/c2)2 - (p/c)2]1/2<

“The above definition of mass, that a mass is rest energy m = E0/c2 , E0 = ER|v=0” .

Of the previous equation follows that a photon does not have mass but if energy

and moment, since:

ER=pc ← m=0

- Mass of a particle system that defines from the slight knowledge of the energy center of masses, Ecm, the element time center of masses of the four-vector moment, p0cm , and the speed center of masses, vcm, when the speed center of masses is zero “that its is center of momentum frame relativist energy m = Ecm/c2, Ecm = p0cmc|vcm=0, in the case of a system of particles” .

In agreement with these three levels of definition of the mass “This mass is an invariant. It does not change with speed!” “is called the mass-shell condition, because they are of isomorphic form to the equation of a spherical shell. ” . Under the previous considerations modern relativity introduces a new object in the reality different from particles and the waves. This new object is the multidimensional photon system that would explain the transit of devoid particles of "mass in rest" to particle systems with "mass in rest" since, although, it affirms that no, really this mass is equivalent to the mass in rest. And, also, it would solve the existing problem in the quantum physics to find the mechanism that from the field produces the substance, to backs of the hypothetical Higgs boson that would give "mass in rest" to the devoid packages of energy of her, to produce subquarks constituent of quarks ".

The dilation of the time, γ, tie to the relation between the coordinated time and the proper time, dt/d, that it is consequence of the relativity of the simultaneity, on which special relativity is based, in agreement with modern relativity it is only associate with the speed, that is to say, with the kinetic energy, but not with the mass, due to which modern relativity rejects the terms mass in rest and relativist mass. The dilation of the time makes vary the kinetic energy but not the mass because the energy does not constitute mass. This interpretation that makes denominated relativity modern does not correspond to the conception of Einstein that however mentioned physicists declares to rescue. For Einstein, the dilation of the time associated with the speed represents an energy variation that causes the variation of the mass. In "On the special theory and the general theory of relativity", page 34, Einstein textually say "the inertial mass of a body is not a constant, but that varies in agreement with the changes of energy of body" . And in "The meaning of Relativity", Page 102, Einstein says "La mass of a body is not constant; it varies with the variations of energy" . Then, how to call the mass of a non subject body to energy variations? And how to call the mass of a body when energy variations exist? One is the mass in rest and the other the relativist mass.

“The γ term is physically associated to the velocity term through time dilation. In the past a few physicists starting with Planck, Lewis, and Tolman, not Einstein, have miss-associated the γ term with the mass defining a new kind of mass

This M is then inappropriately called "relativist mass". In the absence of a potential, the zeroth element of the momentum four-vector is defined as the energy divided by c, resulting in

p0 = Mu0

E/c=Mc

“The m in this method is then inappropriately qualified and called the "rest mass". It is wrong to do this for the following reason. Calling m the "rest mass" infers to the listener that m is not the mass according to other frames for which it is not at rest. We have already noted that m is an invariant as it is the same value as calculated according to any frame. It is not just the value for the rest frame. The relativist mass method also leads to many erroneous conclusions. By that method light has zero "rest mass". For one of many examples, it has been argued that since light is not at rest in any frame, that the question of whether it has mass at rest or "rest mass" is unanswerable. No. m = 0 is observed as the contraction of a photon's four-momentum according to any frame, not just the "rest frame".

In short the terms "relativist mass" and "rest mass" need to be done away and the real mass m which is actually observed is an invariant. It does not change with speed. Also, by this, the physically correct definition a photon, or anything that travels at the Lorentz invariant speed c, has zero mass.” .

The previous arguments against the mass in rest also can be used against the energy in rest, used by modern relativity to explain the mass. Really, the term of mass in rest is valid in the same sense of the proper time or the energy in rest, that is to say, by mediums of referring the movement of the other frames of reference to a frame "in rest", that can be all frame, with the only exception of the frame of the electromagnetic field in the vacuum, due to the principle of relativity of the movement. The question is that the "relativist mass" of when a frame is referenced in movement is "mass in rest" for when the frame is taken in rest. Therefore, in special relativity no-covariance for the increase of the mass with the speed exists. This is direct consequence of the equivalent relation, of special relativity, between a frame of reference considered in rest and the same frame of reference considered in rectilinear movement uniform. Nevertheless, in special relativity, it is indeed of this lack of covariance from where equivalence between kinetic energy and mass arises directly: The kinetic energy attributed to a body in a frame of reference in rectilinear movement uniforms is part of the "mass in rest" of the body when this frame of reference is taken in "rest".

“we have

ER = (dt/dτ)mc2

ER = γmc2 ← Good

This is the mass - relativist energy relationship for a massive particle. Now this energy does not go to zero as v goes to zero so we see that a massive particle still has energy even when it is at rest. This tells us that mass is equivalent to rest energy meaning relativist energy at zero velocity

E0 = ER|v=0 = mc2 ← Good

The kinetic energy of a particle is the amount of energy that is associated with its motion only. Therefore

EK = ER - E0

This result in

EK = (g - 1)mc2 “ .

The previous mathematical development is based on that Einstein carried out, which privileges the definition of the variation of the energy based on the effect of the dilation of the time in exchange of the variation of the mass in function to this dilation. Einstein used the previous method due to the restriction imposed by the objective to explain the physical mechanism that it prevents to reach speed c. This mechanism is which the necessary energy becomes divergent for that a body with mass according to the four-vector moment reaches c. But, this is not caused because the mass cannot be distinguished between mass in rest and relativist mass.

Of another part, the definition of mass for a particle system that does modern relativity presents a double problem. First, it is the uncertainty that exists in the measurement of the mass, as a result of the principle of relativity of the simultaneity, on which special relativity is based. And the second, the deficiency of mass of the energy, in the direction of the wave, that considers relativity modern. The first problem if it is real, although this uncertainty is different from the one from the principle of uncertainty of Heisenberg of the quantum mechanics. But, the second problem is the product that creates modern relativity, already before discussed of energy without mass.

“We have seen that for a single particle mass is equivalent to rest energy.

E0 = mc2.

For a system of particles the best concept for system mass m is defined as center of momentum frame energy Ecm.

Ecm = mc2.

The system mass does not turn out to be equal to the total or sum of masses mtot of the constituent parts. Instead it is the total energy summed for all of the constituent parts according to the center of momentum frame” .

“Due to relative simultaneity psys is not always equal to the "simultaneous" sum of the four-momentum of the constituent parts when there are external forces acting at various locations on the system. The system mass is defined as the following invariant.

m = Ecm/c2

“the system net four-momentum is indeed a four-vector itself and yields

ERsys = γcmmc2

where m is the system's mass and is its center of momentum frame energy as well as

p = γcmmucm

and

m2c2 = Ecm2/c2

The reason that the mass, m = Ecm/c2, is not the same as the "total" of constituent masses, mtot , is that the sum of masses of the constituent parts does not always equal the center of momentum frame energy. For example, a system of massless particles have a zero mass shell condition when they all move the same direction while the system has a nonzero mass shell condition when they move in different directions. One advantage the definition of center of momentum frame energy for mass has over "total mass" is that by this definition, not only is mass an invariant, but this mass of a system is also conserved.” .

The author notices that the existing confusion with relation to the mass concept really is in which this concept becomes equal to the concept of mass in agreement with "massive" particles like the electron, proton, neutron, quarks and subquarks etc. Thus, the mass exists in the spacetime, that is to say, the mass has four-dimension and, consequently, the mass exiles of "non massive" particles like the photon and the graviton whenever they exist in an only dimension, since according to modern relativity a photon system that moves in different directions if it has mass, which also would be applicable to gravitons. With which mass-energy is broken with the unit, and it is arrived has to consider energy without it constitutes mass and the mass without it can undergo changes due to energy variations. Why mass must to be of four-dimension? Why mass cannot also be of one-dimension? Modern relativity seems to not know the strongly inertial properties of laser beam.

The author observes that if really is followed Einstein the energy structured in the four-vector moment is concentrated energy, therefore, which commonly we called mass, whereas the structured mass as one-vector moment is scattered mass, that is, which exactly we denominated energy.

### 4 The energy has inertia

In relativity the inertia of the energy has two definitions.. In the theory of special relativity inertia would be an attribute of the mass that has the energy and in the general relativity inertia is associated with the properties of spacetime.

#### 4.1 The energy has inertia according to special relativity

In the theory of the relativity of Einstein, the concept of inertia of the substance and the field comes from the special relativity, which discovers the support of inertia, in the universal law of the physics of equivalence between mass-energy “the fact that mass-energy equivalence emerges so naturally from Einstein's kinematics, applicable to all kinds of mass and energy, was mainly responsible for the recognition of this equivalence as a general and fundamental aspect of nature.” .

The scientists understand by inertia fundamentally inertia of the mass, which extend to the energy whenever energy is equivalent to mass and the mass is equivalent to energy. In relation to this equivalence special relativity presents a double problem. First, it is respect to the conservation of the moment that due to the relativity of the simultaneity is only worth in approximate form. And the second problem is the partial validity of equivalence between energy and mass, in agreement with its definition at the relativist moment, because this breaks the principle of correspondence of the energy in the Newtonian limit. For these two reasons properly special relativity does not reach to explain the unit and equivalence mass-energy, that is to start off of philosophical conception of Einstein and of the observation it is intuited, like a total equivalence “The equivalence of mass and inertia seems to hold true according to all empirical evidence. In theory at least they are sometimes regarded as being separate qualities” . In addition, special relativity does not differentiate the inertia of mass of the inertia of the energy. Therefore, the relativity of Einstein comes near but it does not solve absolutely as it operates inertia in the nature.

Other physicists conscientious of both problems also, have reviewed the reach of equivalence between mass and energy although in relation to inertia. They use the terms of relativist mass and mass in rest. With respect to the relativist mass they say: “the two small atoms have slightly less total rest mass than the original large atom, but at the instant of the split the overall "mass-like" quality is conserved, because those two smaller atoms have enormous velocities, precisely such that the total relativist mass is conserved. (This physical conservation is the main reason the old concept of relativist mass has never been completely discarded.)”. “In either case (fission or fusion), a net reduction in rest mass occurs, accompanied by the appearance of an equivalent amount of kinetic energy and radiation. (The actual detailed mechanism by which binding energy, originally a "rest property" with isotropic inertia, becomes a kinetic property representing what we may call relativist mass with anisotropic inertia, is not well understood.) .

These physicists demonstrate, of a part, that the mathematics of special relativity only explains the conservation of the moment for interaction forces, on a body, in contact in a point and in the direction of its movement and, of another part that only explains the extra inertia that acquires a body due to its movement.

They examine the equation of equivalence between mass and energy, in agreement with their definition within the conceptual frame of special relativity, and find that the inertia concept is doubly restricted. First, quantitatively, since of the principle of the relativity of the simultaneity, basic foundation of special relativity, it derives that in the variations of the moment of a body uncertainty exists about its conservation, then the measurement of the variation of inertia, in units of mass, lacks of exactitude. And second qualitatively, since the absence of correspondence between the definition of energy of relativity according to the four-vector moment, and the definition of kinetic energy in agreement with the classic mechanics, causes that this concept of energy loses representativeness, and equivalence between energy and mass lets apply for the total inertia of a body.

Nevertheless, in spite of these faults, basically of mathematical order, the experience indicates that this equivalence is general and that the conception of Einstein on the unit and equivalence mass-energy is a law of the nature. In addition, other reasonings by outside relativity lead to the same result. But, in these physicists, ideological certain reservation is observed that it aims at an irreducible basic mass to energy, that is to say, mass without energy. Is paradoxical that such thought is originated in the purely mathematical interpretation of relativity, behind the back of the philosophical conception of Einstein, about the mass like concentrated energy and to the energy like scattered mass and, however, finally, as it is seen, this thought rests in a reflection to backs of the mathematical Manichaeism, to that at the present time the truth has been reduced, in the science of the physics. That is to say, that this thought finally is based on an ideological prevention that can have its roots in a physical crass materialism.

The author, next, includes some parts from the article "The inertia of Energy" that creates the double problem that affects inertia, from equivalence between mass and energy, in agreement with mathematical of special relativity, which leads by part of these physicists to the thesis of an irreducible mass to energy.

The inertia notion is come off the action-reaction law, and consequently it appears like an attribute of the energy that is measured by the resistance of the mass to modify its state.

“The basic principle of Einstein's special relativity is that inertial measures of spatial and temporal intervals are such that the velocity of light with respect to those measures is invariant. It follows that relative velocities are not transitively additive from one reference frame to another, and, as a result, the acceleration of an object with respect to one inertial frame must differ from its acceleration with respect to another inertial frame. However, by symmetry, an impact force exerted by two objects (in one spatial dimension) upon each another is equal and opposite, regardless of their relative velocity. These simple considerations lead directly to the idea that inertia (as quantified by mass) is an attribute of energy” .

The inertia of a particle varies with the changes of energy that the reaction to a force of interaction, applied on the particle, cause in its speed and it is measured in mass units. In individual, inertia in the direction of movement of a particle increases like result of its acceleration. This increase is due to the energy used in the acceleration.

“Given an object O of mass m, initially at rest, we apply a force F to the object, giving it an acceleration of F/m. After a while the object has achieved some velocity v, and we continue to apply the constant force F. But now imagine another inertial observer, this one momentarily co-moving with the object at this instant with a velocity v. This other observer sees a stationary object O of mass m subject to a force F, so, on the assumption that the laws of physics are the same in all inertial frames, we know that he will see the object respond with an acceleration of F/m (just as we did). However, due to non-additivity of velocities, the acceleration with respect to our measures of time and space must now be different. Thus, even though we're still applying a force F to the object, its acceleration (relative to our frame) is no longer equal to F/m. In fact, it must be less, and this acceleration must go to zero as v approaches the speed of light. Thus the effective inertia of the object in the direction of its motion increases. During this experiment we can also integrate the force we exerted over the distance travelled by the object, and determine the amount of work (energy) that we imparted to the object in bringing it to the velocity v. With a little algebra we can show that the ratio of the amount of energy we put into the object to the amount by which the object's inertia (units of mass) increased is exactly c2” .

The measurement of the change in the inertia of a particle requires the division of the mass in mass in rest, m0, and relativist mass, m. The difference between m - m0 is exactly proportional to the change in the kinetic energy of the particle.

“If the force F were equal to m0a (as in Newtonian mechanics) these two quantities would equal m0 and (1/2)m0v2 respectively. However, we’ve seen that consistency with relativist kinematics requires the force to be given by equation

F = m0a / (1- v2 / c2)3/2

As a result, the inertial mass is given by m = m0 / (1- v2 / c2)1/2

, so it exceeds the rest mass whenever the particle has non-zero velocity. This increase in inertial mass is exactly proportional to the kinetic energy of the particle, as shown by

E / (m-m0) = c2

The exact proportionality between the extra inertia and the extra energy of a moving particle naturally suggests that it is the energy itself which has contributed the inertia and this in turn suggests that all of the particle’s inertia (including its rest inertia m0) corresponds to some form of energy. This leads us to hypothesize a very general and important relation, E = mc2, which signifies a fundamental equivalence between energy and inertial mass. From this we might imagine that all inertia is potentially convertible to energy, although it's worth noting that this does not follow rigorously from the principles of special relativity. It is just a hypothesis suggested by special relativity (as it is also suggested by Maxwell's equations)“ .

The theory of special relativity fault not in its philosophical conception but if in its mathematical consistency for the conservation of the moment, in agreement with equivalence between mass and energy, within the frame of the relativity of the simultaneity. The same happens to the quantum theory with the conservation of the moment, although in front of the principle of uncertainty. That is to say, the two great theories on the physics, that prominence dispute, present problem with the conservation of the moment.

The relativity of the simultaneity is global and even local. According to special relativity true simultaneity between events only exists when they happen mathematically in the same point, this is, with the same spacetime coordinates. This fundamental limitation of the simultaneity introduces uncertainty in the conservation of the moment, since solely the interaction between events, with true simultaneity, that is, in mutual contact and with parallel operating forces to the direction of movement, it does not have problem with the law of action-reaction of Newton. Like consequence, in special relativity the law of conservation of the moment, in its mathematical representation, is due to take like an approach, strictly valid for the case of when the true simultaneity exists

“Incidentally, the above derivation followed Newton in adopting the Third Law (at least for impulse interactions along the line of motion) as a fundamental postulate, on the basis of symmetry. From this the conservation of momentum can be deduced. However, most modern treatments of relativity proceed in the opposite direction, postulating the conservation of momentum and then deducing something like the Third Law. (There are complications when applying the Third Law to extended interactions, and to interactions in which the forces are not parallel to the direction of motion, due to the ambiguity of simultaneity relations, but the preceding derivation was based solely on interactions that can be modelled as mutual contact events at single points, with the forces parallel to the direction of motion, in which case the Third Law is unproblematic.)” .

“The typical modern approach to relativist mechanics is to begin by defining momentum as the product of rest mass and velocity.” “this definition is motivated by the fact that it agrees with non-relativist momentum in the limit of low velocities” .

“Based on this definition, the modern approach then simply postulates that momentum is conserved. Then we define relativist force as the rate of change of momentum. This is Newton's Second Law, and it's motivated largely by the fact that this "force", together with conservation of momentum, implies Newton's Third Law (at least in the case of contact forces) .

On the other hand, the formulism of the relativity, constructed by mediums of tensors, requires that the three-vector moment, that is perfectly consistent with the no-relativist moment in limits of low speeds, meets with the energy in order to return it the tensor relativist moment. This transformation presents the problem that violates the principle of correspondence for the element p0 of the relativist moment of a particle. This p0, that represents the energy of the particle, must have the property that the energy in the Newtonian limit of low speed, would have to be reduced to the classic quantitative expression of the kinetic energy, which does not happen. This does that the quantitative relativist expression of the energy, in agreement with p0, is conventional and loses its physical meaning that is nothing minus the equivalence between mass and energy. By this lack of correspondence, the validity of equivalence between mass and energy it is limited the extra inertia strictly, that acquires a particle due to its speed, but does not apply for total the inertial mass of the particle.

“from a purely relativist standpoint, the definition of momentum as a 3-vector seems incomplete. It's three components are proportional to the derivatives of the three spatial coordinates x,y,z of the object with respect to the proper time γ of the object, but what about the coordinate time t? If we let xj, j = 0, 1, 2, 3 denote the coordinates t,x,y,z, then it seems natural to consider the 4-vector

pj = m / √1-v2 dxj / dt

where m is the rest mass. Then define the relativist force 4-vector as the proper rate of change of momentum” .

“correspondence principle easily enables us to identify the three components p1, p2, p3 as just our original momentum 3-vector, but now we have an additional component, p0, equal to m(dt/dγ). Let's call this component the "energy" E of the object. In full four-dimensional spacetime coordinate time t is related to the object's proper time t according to dγ2 = √dt2 - dx2- dy2 - dz2 “. Consequently:

E = m / √1-v2

“The first term is simply m (or mc2 in normal units), so we interpret this as the rest energy of the mass. This is sometimes presented as a derivation of mass-energy equivalence, but at best it's really just a suggestive heuristic device. The key step in this "derivation" was when we blithely decided to call p0 the "energy" of the object. Strictly speaking, we violated our "correspondence principle" by making this definition, because by correspondence with the low-velocity limit, the energy E of a particle should be something like ½mv2, and clearly p0 does not reduce to this in the low-speed limit. Nevertheless, we defined p0 as the "energy" E, and since that component equals m when v = 0, we essentially just defined our result E = m (or E = mc2 in ordinary units) for a mass at rest. From this reasoning it isn't clear that this is anything more than a bookkeeping convention, one that could just as well be applied in classical mechanics using some arbitrary squared velocity to convert from units of mass to units of energy. The assertion of physical equivalence between inertial mass and energy has significance only if it is actually possible for the entire mass of an object, including its rest mass, to manifestly exhibit the qualities of energy. Lacking this, the only equivalence between inertial mass and energy that special relativity strictly entails is the "extra" inertia that bodies exhibit when they acquire kinetic energy” .

However, it is possible by other mean mathematicians, who were developed by the authors of "The Inertia of Energy", to be induced like probable total equivalence between mass and energy.

“Returning to the question of how mass and energy can be regarded as different expressions of the same thing, recall that the energy of a particle with rest mass m0 and speed V is m0/(1-V2)1/2. We can also determine the energy of a particle whose motion is defined as the composition of two orthogonal speeds. Let t,x,y,z denote the inertial coordinates of system S, and let T,X,Y,Z denote the (aligned) inertial coordinates of system S'. In S the particle is moving with speed vy in the positive y direction so its coordinates are t=t x=0 y=vyt z=0

It follows that the total energy (neglecting stress and other forms of potential energy) of a ring of matter with a rest mass m0 spinning with an intrinsic circumferential speed u and translating with a speed v in the axial direction is

E = m0 /(1-V2)1/2 = m0 /(1-u2)1/2(1-v2)1/2

A similar argument applies to translatory motions of the ring in any direction, not just the axial direction. For example, consider motions in the plane of the ring, and focus on the contributions of two diametrically opposed particles (each of rest mass m0/2) on the ring” . “If the circumferential motion of the two particles happens to be perpendicular to the translatory motion of the ring, then the preceding formula for E is applicable, and represents the total energy of the two particles. If, on the other hand, the circumferential motion of the two particles is parallel to the motion of the ring's center then the two particles have the speeds (v+u) / (1+vu) and (v-u) / (1-vu) respectively, so the combined total energy (i.e., the relativist mass) of the two particles is given by the sum:

E = m0 / (1-u2)1/2 (1-v2)1/2

Thus each pair of diametrically opposed particles with equal and opposite intrinsic motions parallel to the extrinsic translatory motion contribute the same total amount of energy as if their intrinsic motions were both perpendicular to the extrinsic motion. Every bound system of particles can be decomposed into pairs of particles with equal and opposite intrinsic motions, and these motions are either parallel or perpendicular or some combination relative to the extrinsic motion of the system, so the preceding analysis shows that the relativist mass of the bound system of particles is isotropic, and the system behaves just like an object whose rest mass equals the sum of the intrinsic relativist masses of the constituent particles. (Note again that we are not considering internal stresses and other kinds of potential energy.)

This nicely illustrates how, if the spinning ring was mounted inside a box, we would simply regard the angular kinetic energy of the ring as part of the rest mass M0 of the box with speed v, i.e.,

E = m0 / (1-u2)1/2 / (1-v2)1/2 = M0 / (1-v2)1/2

where the "rest mass" of the box is now explicitly dependent on its energy content. This naturally leads to the idea that each original particle might also be regarded as a "box" whose contents are in an excited energy state via some kinetic mode (possibly rotational), and so the "rest mass" m0 of the particle is actually just the relativist mass of a lesser amount of "true" rest mass, leading to an infinite regress, and the idea that perhaps all matter is really some form of energy” .

Nevertheless, paradoxically nowadays between some physicists exists the tendency to reject the original conception of Einstein of total equivalence between mass-energy, still without a mathematical cause, but in last ideological cause, with which it is blocked that this way the idea of the inertia of the energy passes, that leads to accept like probable the existence in the nature of speeds, in the information transmission, greater than c, since at the present time the existence of "speeds greater is recognized than the one of light, for example, connected with the phase velocity of the solid electromagnetic waves" [ 10 ].

“But does it really make sense to imagine that all the mass (i.e., inertial resistance) is really just energy, and that there is no irreducible rest mass at all? If there is no original kernel of irreducible matter, then what ultimately possesses the energy?” .

It seems that these physicists are not aware that when rejecting total equivalence between mass and energy ¡they end with the principle of equivalence between inertial mass and gravitational mass, in which is based general relativity¡. The author asks ¿is false the prediction done by the general relativity of the bending that undergoes a beam of light by the action of gravity? Which Einstein explains as a result of which the light has mass. These physicists say that they have solved this problem as it follows:

“a star's gravitational field can bend the path of a massless photon. This takes us into the realm of Einstein's general theory of relativity. The mass of the photon isn't attracted to the star's mass under Einstein's theory. Rather, the star's mass distorts space and the photon's path changes because the space is curved, says Paul Hewitt in his book Conceptual Physics” .

Really, general relativity explains the gravity like the inertia of the bodies in a curved spacetime of Riemann. That is to say, of the inertial movement of inertial bodies in absence of forces. Then, the light follows a curved trajectory because irremediably it has mass, although non mass in rest, that is, mass in agreement with the four-vector of the relativístico moment. But, if mass by the indestructible unit between mass and energy, in this case, mass according to the one-vector moment.

The author differs of the reserves of these scientists about the unit and equivalence between mass and energy that limit it is an irreducible mass in energy or minim amount of mass without equivalence in energy.

The author, in the first place, take refuges in the cosmological thesis of which in Big-Bang, during the quantum era, down of the period of Planck, only there was energy. Then, all the substance is reducible to energy and the source of inertia is the energy.

#### 4.2 The energy has inertia according to general relativity

The author notices that if well special relativity introduces inertia only can really be understood it, in the terms of equivalence between mass and energy in agreement with the general relativity, whose base is the principle of equivalence between inertial mass and gravitational mass and not the relativity principle of the simultaneity. Additionally, general relativity was not the continuation of special relativity.

Although, Einstein non origin the general relativity (GRT) of special relativity (STR) if he construct general relativity from the main product of special relativity. This product is equivalence between mass and energy that in special relativity is the physical base of the local invariancia of c, in front of the transformation of Lorentz, within the frame of spacetime of Minkowski.

Einstein before developing general relativity chose the more obvious methodological alternative. Einstein treats to give an explanation of gravity, by mediums of constructing it from the theory of the special relativity, which called the relativist theory of gravity (TRG), as before it Poincare and Minkowski, had tried. But, Einstein found in the invariancia of the mass in rest of special relativity, the unsolvable obstacle that made him leave the relativist theory of gravity, within the process of its formation. This is due to “the non-covariant representation of mass increase with velocity led in particular to the conclusion of impossibility of describing the gravity potential by a 4-vector. What is more, this representation was served as the basis of the so-called law (principle) of mass and energy equivalence or the law of energy inertia.(LEI)”. “LEI is considered as one of the main results of STR.” “it has become one of the bases of GRT. Just on basis of LEI the gravitational potential has been ascribed the properties of a 4-tensore of rank 2. This makes it possible to identify the gravitational potential with the metric tensor, and GTR has come simultaneously a theory of non-Euclidean spacetime” .

“LEI in fact conditioned the GTR origin and became the basis of its construction. Specially, it was expressed in that tensor characteristics were ascribed to the gravitational potential. This allowed one to identify it with the metric tensor reflecting the geometrical structure of spacetime. Thus, GTR, along with theory of gravity, became the theory of spacetime as well” .

The unit and equivalence mass-energy constitutes the proper essence of the relativity and the law of the inertia of the energy, that includes all form of energy. The law of the inertia of the energy is applied to the forms of the kinetic energy and the binding energy of the particles and, also, to the potential energy, that in its manifestation of energy of the gravitational potential, is one of the foundations of the construction of general relativity.

“The very distinctive peculiarity of GTR is undoubtedly a direct relation between the potential of gravity and metric tensor. In its turn, this is a consequence of the fundamental statement that the gravitational characteristic of any system should be its energetic properties. The statement in itself, as kwon, leans directly upon LEI. As a result, the mass density in the Poisson equation is substituted for the energy density – a component of the energy momentum tensor. And as Einstein notes: “If there is an equation analogous to the Poisson equation in GTR, then it mist be a tensor equation for the tensor of gravitational potential gik” .

The relativist mass that some physicists deny or restrict, as soon as has a vision of relativity very closed to special relativity, really constitutes the base of which in the GTR the gravitational potential is described with the four-tensor of rank 2.

“As far as one can judge, the representation of mass increase with velocity; m = γm0 has served as decisive factor in favour of describing the gravitational potential with the help of a 4-tensor. Let us give some reasoning conceivable here. Let us begin that Coulomb’s and Newton’s potentials have a similar form. In so doing, the electric potential is transformed as a 4-vector component. If one takes into account that the “gravitational charge” (mass), unlike the electric field, increase with velocity, then the gravitational potential has to behave as a tensor of rank 2 at expense of an additional Lorentz factor. The other reasoning that is in essence similar to the previous ones are based on that energy becomes a source of gravitational field in accordance with LEI. Since energy is a 4-vector component the “gravitational charge“ also acquires the same quality and son on” .

In general relativity the mass is “the length of the momentum four-vector”; in according to the function that describes the metric relations of spacetime, this is, of the gravity field. This “mass will be local rest frame relativist energy “ . The equation of the equivalence mass-energy is:

m2c2 º |gmnpmpn|

“Under this definition, mass is an invariant. It does not change with speed, or with location in a gravity field!” .

In general relativity the inertia of the mass is defined as the resistance that exerts the mass of particles to that the particles move by outside geodesies. Therefore, “mass is the resistance of a particle to deviation from geodesic motion” y la “inertia as the resistance to deviation from geodesic motion” . Then the inertia is linked to the structure of spacetime. Thus, “according to general relativity, inertial and gravitational forces arise directly out of the structure of spacetime. This implies that an adequate description of inertia cannot be obtained solely on the basis of inertial mass; the role played by spacetime must also be considered” .

The general relativity combined with the quantum theory leads to explain inertia like the result of the action-reaction between the mass of particles and the structure of spacetime, that is to say, like an interaction, that B. Haisch, A Rueda, and H. E Puthoff consider “between the quarks and electrons constituting matter and the vacuum electromagnetic .

The spacetime is considered like “sea of electromagnetic zero-point energy that is traditionally called the electromagnetic quantum vacuum“ .

“Quantum physics predicts the existence of an underlying sea of zero-point energy at very point in the universe. This is different from the cosmic microwave background and is also referred to as the electromagnetic quantum vacuum since it is the lowest state of otherwise empty space. This sea of energy fills all of space and is absolutely the same everywhere as perceived from a constant velocity reference frame. But viewed from an accelerating reference frame, the radiation pattern of the energy becomes minutely distorted: a tiny directional own is experienced by an accelerating object or observer, the Rindler flux. Importantly, the force resulting from that energy-momentum own turns out to be proportional to the acceleration. When this energy-momentum own that arises automatically when any object accelerates interacts with the fundamental particles constituting matter (quarks and electrons) a force arises in the direction opposite to the acceleration. This process can be interpreted as the origin of inertia” .

Newton's third law states that if an agent applies a force to a point on an object, at that point there arises an equal and opposite reaction force back upon the agent. In the case of a fixed object the equal and opposite reaction force can be traced to interatomic forces in the neighbourhood of the point of contact which act to resist compression, and these in turn can be traced to electromagnetic interactions involving orbital electrons of adjacent atoms or molecules, etc.” .

“Now a similar experience of an equal and opposite reaction force arises when a non- fixed object is forced to accelerate. Why acceleration create such a reaction force? We suggest that this equal and opposite reaction force also has an underlying cause which is at least partially electromagnetic, and specifically may be due to the scattering of electromagnetic quantum vacuum radiation” .

Haisch and Rueda have “demonstrated that from the point of view of the pushing agent there exists a net flux (Poynting vector) of quantum vacuum radiation transiting the accelerating object in a direction opposite to the acceleration: the Rindler flux. Interaction of this flux with the quarks and electrons constituting a material object would create a back reaction force that can be interpreted as inertia” “deviations of an object from its proper geodesic motion results in an inertial reaction force” .

Nevertheless, Haisch, and Puthoff are criticized because “the quarks and electrons constituting matter must themselves be endowed with an inertial mass of their own. As is well known, subatomic particles can be each associated with a rest-energy, which is each particle's internal energy content in the absence of motion. According to E = mc2, called the "law of inertia of energy" in earlier times, the rest energy of subatomic particles must give rise to inertial effects in addition to those induced by the ZPF. In this sense, if the inertial properties of ordinary matter are shown to arise out of an interaction between subatomic particles and the ZPF; but then inertial properties must also be ascribed to the particles themselves, then the problem of inertia has been merely shifted to a smaller quantity of matter rather than truly solved” .

Of such way, the meaning of inertia is complex and difficult exactly understand it. From the most general expression of the quantum theory, that considers electromagnetism and the gravitation phenomenons of the physical field, the author understands inertia like the phenomenon of interaction between particles and the vacuum, through which the particles move. Inertia would be the reaction of the vacuum on particles to the action exerted by particles on vacuum, during the process of movement of particles within the vacuum. Since the vacuum in agreement with the quantum theory this full "of non null free fields, that is to say, moved away fields of its sources" .

The author understands the inertia of phenomenons of the substance qualitatively different of the inertia of the phenomenons of the field. This is the inertia of the mass, four-vector moment, qualitatively different of the inertia of the energy, one-vector moment. Thus inertia is not only of the mass, of the substantial phenomenons, but also of the energy, of the phenomenons of the field.

For the author, the inertia of a substantial particle is the result of the reaction of the fields that compose the vacuum on the substantial particle. And the inertia of the energy of the fields is the result of the reaction of the fields that compose the vacuum on non substantial particles of the waves that interact with these.

### 5 In the electromagnetic field the law of greater speed to smaller inertia will be tested

Because the fields have inertia the law that I discovered for fields about the greater speed to smaller inertia is a universal law that governs the substance and the field.

In the case of the phenomenons of the field the inertia is directly proportional to the amount of energy of the packages that constitute particles in the field. Consequently, the inertia of electromagnetism is directly proportional to the amount of energy of photons and the inertia of the gravity is directly proportional to the amount of energy of gravitons.

For the electromagnetic field experimental and theoretical bases exist that aim at the inverse dependency of the speed of group of the electromagnetic waves of their energy, or what is the same of the inertia of component photons of these waves.

Although, for relativity the photons have an only speed that is c, according to EM theory, of recent formulation, the photons can have any speed depending on their apparent mass, environment temperature and is present at of other forms of matter

“The energy of the photon is described via the mediate electromagnetic (EM) self-field model” “[Fleming 2003],” “Thus the photon is currently considered a messenger particle for EM forces representing the fundamental quantum unit of EM energy”. “According to relativity theory, photons can move only at the speed of light, 300,000 km/sec or ~ 186,000 miles/sec. The EM self-field theory is much more flexible in regard the velocity of the photon; photons can have any speed depending on their mass, the ambient temperature, and the presence or otherwise of matter. The edict of relativity as to the constancy of light is really a statement as to the total reaction upon a single photon of the entire matter within the universe when considered isotropic and homogeneous.” .

#### 5.1 The experiments with evanescent waves

A fort indication exists about the validity of velocity inverse dependent frequency wave law for the electromagnetic field in the experiments made by Professor Doctor Günter Nimtz that has produced very weak waves that propagate superluminally. With respect to the nature of these very weak waves Habich says that they are the refraction with maximum limit of .001 of the energy of the electromagnetic signal used like source to produce them  whereas Nimtz explains these waves like virtual photons .

“A signal is thought to cause a corresponding effect”. “A signal may be a single photon with a distinct energy, more general a signal is characterized by a carrier frequency and its modulation and it is bound to be independent of magnitude” .

“signals have usually a frequency band width much less than 1 % of the carrier frequency thus dispersion effects as a result of an interaction between the electromagnetic wave and any potential don’t necessarily cause significant signal reshaping.” “For example a digital signal is defined by the envelope which contains the total information. The amplitude doesn’t carry information only the half width represents the number of digits. Here the carrier frequency is 2×1014 Hz and the relative frequency band modulation is 10−4. For long distance signal transmission signals were modulated on a high frequency carrier.” .

The production techniques of very weak waves from singular microwaves, photons and infrared light  that has been used, are based on the induction of evanescent waves by the passage of the signal source by the narrow section of the guided waves, by the photon passage by heteroestructuras or by the failure of total the internal reflection in double prisms. The very weak waves that take place are evanescent waves, because its number of wave is an imaginary value.

The very weak waves, this is, of VLF take place by the passage of the signal source through barriers dielectric photons that are of two types. The first type of barrier, is constituted by the central part of the guided waves, who is a sufficiently narrow section, less than half of the wavelength in both directions, perpendicular to the propagation, through which they only pass the frequencies of wave lower of the frequencies of the signal source. The other type of barrier is the air hollows of the heteroestructuras and double prisms in which the signal source passes inside air hollows. In this case the production of the waves of VLF is due to the mechanism of change of the transit of the signal between a refractive index greater than 1 of the dielectric and the refractive index ≈ 1 of the air hollow.

“A couple of months after the discovery of superluminal tunnelling of microwave signals a study on superluminal group velocity and transmission of single optical photons tunnelling a photonic barrier was published. Yes certainly, as the authors claimed they did not measure a signal velocity as the photons were emitted in a spontaneous process. However, the group velocity of the investigated black box (i.e. the tunnelling barrier) has been determined and the data are also valid for the transmission of signals. Sending signals containing millions of optical photons analogous to the microwave experiment, the black box would result in the same superluminal group velocity as in the single photon experiment. In fact the same experimental set-up and procedure has been proven with a sample of bulk glass instead of the tunnelling barrier this black box analogy to be correct. Actually in this case the single photon experiment yielded the sub-luminal group velocity known from bulk glass as measured in standard spectroscopy. In both in the microwave and in the single photon experiments the group velocity has been measured with a detector located in free space far away from the investigated black box. In such asymptotic measurements the relation holds, i.e. the group velocity equals the signal velocity.” .

The evanescent waves in their passage by the barrier do not spend time, since they do not present change of phase, and is the cause of the superluminal speeds of the evanescent waves.

The maximums superluminal speeds have been obtained with the double prism. In these experiments two dielectric prisms of perspex are used, of equal refractive index, and separated up to 5 cm. by an air hollow. The used signal is microwaves of 3 cm. in length, with which it has been reached to 30c, for the speed of group of the evanescent waves .

The superluminal waves are refracted waves of VLF, therefore of very low energy, closed to 001% of the energy of the primitive microwaves. These waves produce like remainder of energy of order smaller or just as 001%, that reaches to refract when the internal reflection of the microwaves failed, that have entered the prism with an angle of incidence greater than the angle of total reflection, when the microwaves hit the "limit" of the first prism. This it is the phenomenon of tunnel, in agreement with the quantum mechanics, since the refraction of so weak energy surpasses the high potential of energy of the barrier, which theoretically is not possible in the classic mechanics of waves. These superluminal waves do not travel to the past but that when not spending time when crossing the air barrier arrives at the receiving antenna before which they would make photons at speed c .

#### 5.2 Project GLAST

In the 2006, in project GLAST, of the NASA, it will be proven for the gamma rays that are the greatest energy of the electromagnetic spectrum, the law of greater speed to smaller inertia. The gamma-ray radiation, the most energetic form of radiation, billions of times more energetic than the type of light visible to our eyes. Due to the inverse speed dependency of the energy the gamma rays must have a speed smaller than c. On the matter Christopher Wanjek wrote in Astronomy Today:

“Not yet observed in nature, quantum gravity is the long-sought missing link between Einstein's General Relativity and Quantum Mechanics, the two incongruous pillars of modern physics. NASA's Gamma-Ray Large Area Space Telescope (GLAST), planned for a 2005 launch (postponed to august of 2007 and advanced to 2006), may be able to detect for the first time the effects of quantum gravity in the speed of gamma-ray burst photons, according to two NASA scientists.

The gist of this is that the gamma-ray bursts that GLAST detects will be powerful enough and distant enough to see the highest of the high-energy photons travelling slightly more slowly than lower-energy photons, weighed down by the effect of quantum gravity.

Drs. Jay Norris and Jerry Bonnell of NASA Goddard Space Flight Center did the math. The two observational astronomers said that only time will tell if GLAST will see this lag time, for the quantum gravity theory (and the numbers that go along with it) are still rather speculative” .

“Last year, Dr. Bradley Schaefer of the University of Texas tested the consistency of the speed of light to great accuracy, with both high- and low-energy photons, and found no variation in time. The photons at issue in Norris and Bonnell's analysis, though, are of higher-energy than anything studied before.

When it comes to burst photons, GLAST will detect the highest of the high. The instrument would be able to detect photons from gamma ray bursts with energies thousands of times higher than those detected on burst missions that will come before GLAST, such as HETE-2 and Swift. So, with the source of the gamma ray burst likely billions of light years away, GLAST might see a lag in photon arrival times as they travel through the endless soup of gravitons” .

### 6 The interaction between the fields and the vacuum and the law of greater speed to smaller inertia in the fields

The first result that the author obtained, of the law greater speed to smaller inertia, was the prediction, done in 1969, of which the speed in the vacuum of the graviton will be greater than the speed of the photon, because the equivalent mass of the energy of the real photon is minor who 10-51 grams, in agreement with its more recent calculation of the 2003, made by Jun Luo and its colleagues in the Huazhong University of science and technology in Wuhan, China, whereas the value superior limit of the equivalent mass of the energy of the real graviton would be less than 4.5 × 10−66 grams, who estimated by S S Gershtein, A A Logunov and M A Mestvirishvili, in 1997, with base in the observed parameters of the expansion of the Universe, and that is consistent with the value smaller than 0,5 × 10−65 grams estimated by K Staniukovich and M Vasiliev towards 1968. In addition, because as the photon as the graviton move in the "vacuum", that in agreement with the quantum physics is filled "with non null free fields, that is to say, fields propagate away of their sources that fluctuate"  and still in the zero absolute of temperature the vacuum has energy called "zero-point energy (ZPE)". This "vacuum" interacts as with the photon as with the graviton, since the graviton also is under the effect of other fields and even of the own gravity.

The interaction of the "vacuum" with the fields is made through several mechanisms. These are: ZPE, background radiation and static gravitational field.

#### 6.1 ZPE

The interaction of the ZPE with the electromagnetic field has been studied by several groups of scientists.

the ZPE, which is inherent in the vacuum, gives free space its various properties. For example, the magnetic property of free space is called the permeability while the corresponding electric property is called the permittivity. Both of these are affected uniformly by the ZPE” .

”Since the vacuum permeability and permittivity are also energy-related quantities, they are directly proportional to the energy per unit volume (the energy density) of the ZPE. It follows that if the energy density of the ZPE ever increased, and then there would be a proportional increase in the value of both the permeability and permittivity.

Because light waves are an electro-magnetic phenomenon, their motion through space is affected by the electric and magnetic properties of the vacuum, namely the permittivity and permeability. To examine this in more detail we closely follow a statement by Lehrman and Swartz. They pointed out that light waves consist of changing electric fields and magnetic fields. Generally, any magnetic field resulting from a change in an electric field must be such as to oppose the change in the electric field, according to Lenz's Law. These mediums that the magnetic property of space has a kind of inertial property inhibiting the rapid change of the fields. The magnitude of this property is the magnetic constant of free space 'U' which is usually called the magnetic permeability of the vacuum.” .

“The quantity Q is usually called the electric permittivity of the vacuum. It is established physics that the velocity of a wave motion squared is proportional to the ratio of the elasticity over the inertia of the medium in which it is travelling. In the case of the vacuum and the speed of light, c, this standard equation becomes

c2 = 1 / (U Q)

As noted above, both U and Q are directly proportional to the energy density of the ZPE. It therefore follows that any increase in the energy density of the ZPF will not only result in a proportional increase in U and Q, but will also cause a decrease in the speed of light, c” .

“It has already been mentioned that an increase in vacuum energy density will result in an increase in the electrical permittivity and the magnetic permeability of space, since they are energy related. Since light-speed is inversely linked to both these properties, if the energy density of the vacuum increases, light-speed will decrease uniformly throughout the cosmos. Indeed, in 1990 Scharnhorst and Barton demonstrated that a lessening of the energy density of a vacuum would produce a higher velocity for light.” .

“The question then arises as to whether or not any other observational evidence exists that the speed of light has diminished with time. Surprisingly, some 40 articles about this very matter appeared in the scientific literature from 1926 to 1944. Some important points emerge from this literature. In 1944, despite a strong preference for the constancy of atomic quantities, N. E. Dorsey was reluctantly forced to admit: "As is well known to those acquainted with the several determinations of the velocity of light, the definitive values successively reported have, in general, decreased monotonously from Cornu's 300.4 megametres per second in 1874 to Anderson's 299.776 in 1940 " Even Dorsey's own re-working of the data could not avoid that conclusion.

However, the decline in the measured value of 'c' was noticed much earlier. In 1886, Simon Newcomb reluctantly concluded that the older results obtained around 1740 were in agreement with each other, but they indicated 'c' was about 1% higher than in his own time, the early 1880's. In 1941 history repeated itself when Birge made a parallel statement while writing about the 'c' values obtained by Newcomb, Michelson, and others around 1880. Birge was forced to concede that " these older results are entirely consistent among themselves, but their average is nearly 100 km/s greater than that given by the eight more recent results". Each of these three eminent scientists held to a belief in the absolute constancy of 'c'. This makes their careful admissions about the experimentally declining values of measured light speed more significant.” .

How interactions occur of the photon with the ZPE? A cycle of absorption-reemission of photons by part of present virtual particles in the vacuum exists. This cycle takes certain time. When the photons travel within a region of the vacuum of smaller density of energy than another region the photons travel more quickly. The opposite also happens. Therefore, the speed of the photon is inverse-dependent of the density of the energy of the vacuum. The same, it is due to hope happens with the speed of the graviton.

“The virtual particles that make up the "seething vacuum" can absorb a photon of light and then re-emit it when they annihilate. This process, while fast, takes a finite time. The lower the energy density of the vacuum, the fewer virtual particles will be in the path of light photons in transit. As a consequence, the fewer absorptions, and re-emissions which take place over a given distance, the faster light travels over that distance.

However, the converse is also true. The higher the energy density of the vacuum, the more virtual particles will interact with the light photons in a given distance, and so the slower light will travel. Similarly, when light enters a transparent medium such as glass, similar absorptions and re-emissions occur, but this time it is the atoms in the glass that absorb and re-emit the light photons. This is why light slows as it travels through a denser medium. Indeed, the more closely packed the atoms, the slower light will travel as a greater number of interactions occur in a given distance. In a recent illustration of this light-speed was reduced to 17 metres/second as it passed through extremely closely packed sodium atoms near absolute zero. All this is now known from experimental physics. This agrees with Barnett's comments in Nature that "The vacuum is certainly a most mysterious and elusive object...The suggestion that the value of the speed of light is determined by its structure is worthy of serious investigation by theoretical physicists." .

Also, in the vacuum occurs the interaction between the background radiation, originating of Big-Bang, and the radiation of gamma rays of stars that cause the appearance of electron-positron pair.

“physicists detected very energetic photons emitted by the galaxy Markarian. The most energetic of these photons were expected to interact with other very low-energy photons from the infrared background radiation, which is a radiation present since the early universe".

"When a very energetic photon interacts with a low-energy photon, they have just the right quantity of energy to create an electron-positron pair. But physicists at HEGRA did not see any of the expected electron-positron pairs, but did observe very energetic photons instead.”

"By using the frequency-dependent expression of the speed of light, Kifune, Protheroe and Meyer found that the combined energy of each type of photon was not enough to create an electron-positron pair" .

#### 6.3 Static gravitational field

Another mechanism of interaction of the vacuum is due to the static gravitational field that acts on the photon and the same graviton, giving rise also to a cycle of absorption-emission of these particles. This cycle spends certain time.

“In quantum mechanics, the vacuum of space is not a vacuum; rather, it is field with virtual particles, such as the graviton. Light passing through this field of virtual particles is refracted, just as it is when passing through water or any medium.

The graviton, being the essence of gravitational force, would interact with (or slow down) those particles with greater gravitational potential. With mass directly proportional to energy, as expressed in e=mc2, photons of higher energy have greater gravitational potential than lower-energy photons -- as if they "weigh" more.

The highest-energy photons would therefore travel through space more slowly than lower-energy photons. (This does not violate the constancy of the speed of light, for light travels at the same speed only in an absolute vacuum.) To detect the very slight difference in photon speed, one needs an extremely distant source emitting extremely high-energy photons: that is, the gamma ray burst.”.

gravity slows light speed from “c” to v=c/(1+GM/c2r). This assumes conservation of momentum, moc=mv, when a photon enters a gravitational field and gains energy GM/r. This increases the apparent mass “m” to mo[1+GM/c2r], and is equivalent to an increase of the index of refraction in a vacuum to n=c/v=1+GM/c2r. A numerical ray tracing calculation, without any adjustable parameters, finds the missing deflection. These mediums that the speed of light at sea level on earth is less than that in gravity free space, by 21 cm/sec. It is important that this be confirmed by direct experiment, since a positive finding would invalidate the principle of equivalence underlying GR..” .

“a photon, upon entering a gravitational field, or well, acquires excess energy, compared with the energy of the surrounding gravitational field, much the way a ball dropped from a tower gains energy as it heads toward the ground.” .

The author makes the distinction between inertia of the substance and the inertia of the field. The substantial particles have mass in agreement with the four-vector moment, they are subject at the principle of exclusion of Pauli, and obey to the statistic of Fermat-Dirac. And the particles of the field, only have the coordinate t=E/c2, they are subject at the principle of superposition and to the statistic of Bose-Einstein. This fundamental difference in the nature of the substance in front of the nature of the field causes that the inertia of the field it is manifested like the cycle of absorption-emission of component particles of the fields during its interaction with the vacuum. This cycle spends time that makes the speeds of the photon and of the graviton are frequency-dependents of occurrence of his interaction with virtual particles of the vacuum. This frequency of interaction is inverse-dependent of the frequency of the wave or energy of the particle that is to say, of its inertia. Therefore, the speed of the photon and the graviton depends on the vacuum properties and like the graviton has very less inertia than inertia of the photon then the speed of graviton will surpass the speed of the photon various times.

### 7 Reflections on the interaction between the waves and the vacuum

The waves are radiated and they are transported in the vacuum that presents variations in the density of its energy, in agreement with the variations of the mass-energy distribution of local regions. These variations, give rise to different finite regions in the vacuum. Some regions are density of low energy, for example, a region of the intergalactic, interstellar or interplanetary vacuum. Others regions are of density of high energy, for example, a region in the proximity of a star, of a binary star neutron system, of a supernova or of a black hollow etc. A region of the vacuum is defined with base in an energy density more or less constant. The interphase between two regions of the vacuum is the limit among them. The behavior of these waves in the limit is similar to the behavior of a mechanical wave in the limit. But, while these waves travel in the vacuum the mechanical waves are the own disturbance of mediums, within that propagate. Therefore, it is due to distinguish in the propagation of the waves in the field its energy of the density of the energy of the vacuum.

The mediums constituted by fields are formed by virtual and real particles. The virtual particles are the transmitters of the forces exerted by the fields and the real particles are the components of the waves that are generated and are transmitted in the fields.

The laws that govern the mechanism of the interaction of a mechanical wave, that propagates between substantial mediums, of different materials, are the laws of the Newtonian mechanics, applied to the collision between particles. However, the interaction between the waves and the vacuum are regulated by the laws of the quantum mechanics, of the processes of interaction between radiations. In this case, the law of action-reaction of the interaction between particles in the substance is replaced by the law of absorption-emission that prevails in the interaction between particles in the field. Even, this law of absorption-emission prevails for when the interaction is made between the electromagnetic field and atoms of substantial bodies. Although, then the absorption-emission of electromagnetic energy is produced by electrons when they change of orbital. For the case of the interaction of the waves with the vacuum the absorption-emission energy is produced by virtual particles of the vacuum when absorbing energy of the waves and they change to real particles that when returning to virtual particles re-emit to the waves the energy that absorbed of these.

When a wave passes of a vacuum region to another the wave can be that it goes:

- Of a region of the vacuum from smaller energy density to another region of greater energy density. The speed of the wave must change to a smaller speed, because the frequency of the interaction of the wave with the vacuum is increased. This greater frequency of interaction slows down the propagation of the wave, as a result of the diminution of the lapse of interaction between the wave and the vacuum.

- Of a region of the vacuum from greater energy to another region of smaller energy density. The speed of the wave must change to a greater speed, because the frequency of interaction of the wave with the vacuum diminishes. This class of interaction accelerates the propagation of the waves as a result of the increase of the lapse of interaction between the waves and the vacuum.

In these events the phenomenons of reflection and refraction that are caused by the interaction of the wave and the vacuum in the limit between regions, must be similar to these phenomenons when the interaction takes place with a mechanical wave that propagates between different substantial mediums. And, still, more similar with the interaction of an electromagnetic wave with substantial mediums.

The mechanisms of the interaction of the mechanical waves and electromagnetic and gravity waves, although, are essentially different also, are similar mechanisms. In the propagation of a mechanical wave, between different mediums, the interaction always happens by the passage of the disturbance between atomic structures with different density. And in the propagation of the electromagnetic and gravity waves inside of different regions of the vacuum, the interaction of the waves occurs with structures of the vacuum of different density of energy. Consequently, the waves, when they reach the limit, on the one hand, a part of their energy are given back, this is the reflection effect, and the rest of their energy is transmitted to the new region, this is the refraction effect.

The primitive waves are divided in the reflected energy, that remains in the original region and the energy that transmit to the new region. The wave that returns is the reflected pulse. While, the wave that happens to the new region is the transmitted pulse. But, the reflection and refraction occur due to two processes. The first process is the energy absorption from wave by virtual particles of the vacuum, in that they become real particles. The second process is the wave-energy reemission from real particles of vacuum when become back virtual particles.

In the reflection, the waves of the reflected pulse conserve the frequency, speed and length, invests to the phase and the sense of the direction and reduces their amplitude with respect to the primitive waves. When the primitive waves affect the new region not perpendicularly, that is to say, they form an angle with respect to the normal line, the reflected pulse maintains the same angle of the front of incident wave, although, invested.

In the refraction, the waves of the transmitted pulse experience the changes of amplitude, rapidity and depending on the angle, whereupon they do it, can that, also, they change of direction. The waves conserve their direction when the front of wave penetrates perpendicularly to the new region that is with angle zero. When the front of wave penetrates with an angle greater to zero, the waves, that came rectilinear, exactly change to their direction when crossing the limit, and continue propagating straight in line, in ahead, in the new direction. The change in the direction obeys to the law of Snell. In all the cases, the refracted waves maintain the phases and the frequencies of the primitive waves.

When the waves happen to a region of greater energy than the energy of the primitive region, the length and the speed of the waves diminish. If, on the contrary, the energy of the new region is minor who the energy of the primitive region the length and the speed increase.

The speed of a wave in the vacuum is inverse dependent as of its energy as of the density of the energy of the vacuum.

The effect of the variations of the vacuum in the speed of the waves can be measured by means of a refractive index of each region in which the vacuum can be segmented. Then, the speed of a wave of a field in agreement with its inverse dependency of the density of the vacuum will be: v/n(v), where n(v) is the refractive index of the vacuum according to a given region.

The energy of the waves is direct frequency-dependent. Of such way, that frequencies remarkably different from the waves of a same field as well as waves of fields different in a same region of the vacuum have different speeds.

The speed of the waves is inverse frequency-dependent, and then the waves of smaller frequency are quicker than the waves of greater frequency. Or what is the same the waves of greater energy have a speed smaller than the waves of smaller energy. Therefore, the magnitude of energy of the waves constitutes its inertia.

### 8 ¿Which is the speed of gravity?

In order to measure the speed of the photon when its energy is increased and braking by action of gravity Cramer  uses the equation:

c"=c / α

mv = moc

where the left side refers to a gravity environment and the right hand side refers to gravity −free space”  .

Of the equation of Collins it is had α = mo / m

Nevertheless, “Dr. Bradley Schaefer of the University of Texas tested the consistency of the speed of light to great accuracy, with both high- and low-energy photons, and found no variation in time” . Then, necessary is to introduce a constant, k, in α in order to gather the absence of variation of the speed between high and low energies of the electromagnetic spectrum. Consequently, α = k mo / m

But, the result of Schaefer is contradictory, with the calculations and measurements of Dimitri Nanopoulos, Nikolaos Mavromatos and John Ellis , Setterfield , Crammer , Collins , and with EM theory , although is due to consider a rank within as the variations of energy of photons do not cause a sensible variation in their speed.

The author with base in Schaefer considers that the speed of the photon is c at least within the lapse between 10 KeV and 1000 KeV, because the maximum limit of low energy is < 10 KeV and minimum limit of high energy is > 1000 KeV . This rank corresponds to reason 102. If considers that reason between energy of rays gamma, which they are those of more high energy, and the radio waves, that are those of more low energy, is 1013 , also, that most of this dispersion must to the high energies of the gamma rays and, additionally, includes in the analysis the highest speed of gravity of minimum 2 x 1010 c, found by Tom Van Flandern, then can be done k 10-4

The author applies the equation of Cramer-Collins, modified with factor k, to calculate the speed of the graviton that like the photon, lacks mass according to the four-vector moment, but that has much smaller energy.

The supposed mass of the photon, mo, is maximum 10 x 10-51 grams, in agreement with Jun Luo  and the supposed mass of the graviton, m, is maximum 4.5 × 10−66 grams, in agreement with S.S. Gershtein, A.A. Logunov, and M.A. Mestvirishvili . Therefore, the author finds that α can be done equal to: k 10-51 / 4.5 × 10−66 that is the relation between the supposed mass of the photon, mo and the supposed mass of the graviton, m. Then, the speed of the graviton, C ", is maximum:

2,2222 × 1010 × c

A better value of k will be obtained with base in the speed of the gamma rays in project GLAST.

### 9 Conclusions

The quantum theory in its considerations on electromagnetism and the gravity, with the support of the theory of the inertia of the energy of relativity, leads to that the speed of photons is not unique in the vacuum, but inverse dependent of its energy, this is, that the photons of greater energy are slower and the photons of smaller energy are faster. Also, it leads to that the speed of the graviton is several times greater than the speed of the photon, because the higher energy estimated for the graviton is a great number of times smaller than the lower energy of the photon.

Actually, measurements exist, that come from sources very authorized, within world-wide the scientific community, to favour and against the inverse dependency of the energy of the speed of photons. In addition, speeds over c are admitted, although it does not for information transports and the speed of gravity supposed greater than c is defended at least by the top scientific Tom Van Flandern.

It is evident that the conflict that comes near to a century of duration, between the relativity and quantum theories have been transferred to the scenery of the inertia of the energy and the speed of particles of electromagnetic and gravitational fields. Many of the experiments that are to favour, in this scenery, of the theory of relativity about its postulates of the unique speed c for photons and of this speed like the maximum limit for all speed, are supported in point technologies and none of the experiments that are to favour opposing party, in the quantum theory, has such support. This has been consequence of the favouritism by relativity.

Nevertheless, the results of the experiments, within the reference scenery, even the most advanced as the experiment of doctor Sergei Kopeikin, that supposedly measured in 2002 speed c of gravity and confirmed relativity, do not have the acceptance of the scientific community, not even to provisional title. These reserves, about the validity of the result that throw the experiments, that are favour relativity, never before had arisen, although the measures of the deflection of the by the Sun during the eclipse of 1919, like recent scientist Paul Marmet has demonstrated were technological impossible but this passed like true history.

At the moment, a remarkable progress of the new ideas, that exists within the mentioned scenery, are those that catch the creation of the renovator scientific thought. And there is a greater root, in the scientific conscience, of which one or both theories are bad. Like consequence, of this change of leadership, for the first time, in the project GLAST, that if it is product of the point technology, will prove the new ideas, about the speed dependency of the energy, as a result of the quantum gravitational effect on the gamma rays, and can that constitutes the foundation for a final verdict, of the scientists, about this controversy, within the referred scenery.

It can happen that this new spring of the scientific thought in the physics, succumbs in front of the genius of Einstein that yet not would permit, one century after of the apparition of Special Relativity, new developments. However, which this to resurge of the creative thought one is based on the true rescue of the original conception of this wise person, who lies dead and quo is disturbed in the cabinet of the museums of orthodoxy of the ideology of status quo, where are going all the scientific ideas, once that they revolutionized the world.

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## 11 Works of the author:

ANTECEDENTS

Between 1969-1970, the author formulates the existence in the nature of speeds greater than c, in four articles, published in the newspaper "El Siglo". The originals are here.

Introduction

10 Bibliography

11 Works of the author