Quantum Theory of Gravity - "QTG"

11. The paradox of the mass of two gravitational systems. 

                The best definition of mass, in contemporary physics, is that it is equal to a certain amount of energy (which I suppose to be potential) divided by the square of the speed of light. Interesting? Now all we need to know is what is energy.

                In the QTG, the mass of an object or particle is intimately linked to time. The mass of an object or particle is relative, and depends on its velocity in relation to the OS. When we measure of a mass, it is always in relation to something, the most common reference being the Earth itself. This mass is a force or weight where the action of gravity is discounted.

                We should not forget that it is the relativity of the mass of the electron in the atom that gives the atom the ability to generate gravity. We have seen that this gravity is a force without mass, and that it modulates time. The passage of time depends on the intensity of gravity: the more intense the gravity, the slower the rate of progression of time.

                We have seen that the same atom will generate different gravities in different locations in the solar system. The further it is from a gravitationally active concentration of mass, the greater will be the intensity of the gravity generated, because there will be less temporal definition. It is this time that gives greater or lesser consistency to the mass. The greater the velocity of an object or particle, the greater the relative mass and, consequently, the greater the definition of the present of the LTR.

                In an accelerator, when we increase the velocity of the particles, we increase the definition of their time, bringing them towards the present. This requires great energy, as we have a considerable increase in mass. We can see that, in general, particles at light speed show no mass for our observation systems. Photons possess only kinetic energy. We should remember that, by the classical laws of physics, particles without mass do not generate gravity. But even without mass, these particles suffer the effects of gravity on their trajectories. The same thing occurs with dispersed massive particles: they also do not generate gravity, but are subject to it, with their trajectories following the space-time generated by the gravitationally active masses in the vicinity.

                Any non-massive particle will always be undefined in our time reference, as there is no way to bring it into the present. Particles at light speed have no mass and are always undefined for our time reference. A photon is always at light speed ‘c’: if it had mass, it would possess infinite energy. For this reason, its mass is zero. Given that, mass is intimately connected with time in the QTG, we can conclude that a photon (or its electromagnetic wave) is completely undefined in present time or in relation to the LTR. The greater the mass of an object or particle, the greater its tendency towards temporal non-definition.

                We can conclude, therefore, that the generation of time and gravity is a property of matter or simply of particles or objects with non-zero rest mass that are in interaction, because this results in the creation of space-time.

                As energy is equal to force times distance, we can see that space is required for energy to exist, because it results from interactions or from the known fundamental forces in space. Energy is only perceived in space-time. For an object or particle, therefore, the magnitude of its mass is proportional to the intensity with which these interactions, operating in space-time, are defined in the present or in relation to the LTR.

                An example given by Roger Penrose in his book The Large, the Small and the Human Mind, seen in chapter 8 of the QTG and illustrated in Figure 4, helps in the understanding of the definition of mass in the QTG.

                If we use GR to analyze the total gravitational potential energy of two systems of objects that are identical in gravitation (as represented by Figure 4 of chapter 8 of the QTG), we see that these two distinct systems will have different total potential energies. System B will have a greater gravitational potential energy, as a consequence of the greater distance between the objects in B.

                In GR, gravitational potential energy conspires against the quantity of mass in the two systems. Given that mass is a given potential energy divided by the square of the speed of light, system B will have greater mass. Under certain circumstances, the mass-energy relation, analyzed according to GR, gives surprising results. We should accept, therefore, that this energy is variable under GR.

                The total potential energy of these two systems is different, because energy is not localized in GR. The classical rules of physics tend to be violated by GR. In the QTG, it is mass that is not localized. Dark matter is a consequence of this, as seen in chapter 7 of the QTG.

                In the QTG, the gravity generated by bodies interacts negatively. That is, the closer the bodies, the lower the gravity generated between them, because we have a greater temporal definition between the bodies, as shown in chapter 8. On the other hand, greater distance between them contributes to the greater generation of gravity and thus of mass.

                As a result of the increased distance between objects, we have a reduced influence of one over the other. The atoms are the same, but what changes is the frequency of the time imposed by the gravitationally active masses. The time reference between the objects of system B will have reduced definition, freeing up the electrons of the atoms that make up the objects: their orbital radius will increase, as will the relativistic disequilibrium of the coulomb and centrifugal forces, and the atoms in this new state will generate more gravity.

                We know that this contribution is very small, The gravitational energy generated in the atoms that make up these objects is converted into potential energy, which gives an apparent increase in the mass of the objects, as found under GR. This mass, however, is relative: the greater the distance between the objects, the greater the apparent mass, as with dark matter.

                The conservation of energy is respected under the QTG, by not delegating the full responsibility for the generation of gravity to the mass, but rather to the interactions between masses. This slight difference in potential energies establishes the difference between the QTG and the classical physical theories.

                We conclude that the same quantities of mass analyzed in two systems in different gravities will have different total masses, with their total energy conserved. The magnitude of the mass is thus dependent on time, which is proportional to the intensity with which its interactions in space-time are defined in the present or in relation to the LTR.