And yet, how terrible. This work, apart from the final equation;
Some equation can help us understand inertia, a fundamental property of matter, and a principle of equivalence found in relativity that relates inertia with gravity as both as the same thing. Even though it is one of Einstein’s most controversial principles under scrutiny of validity, we should still remain loyal it is correct.
$$P=Mv$$
Momentum is equal to mass times velocity
$$F=Ma$$
Force equals mass times acceleration
1) That mass equals an inertial system.
2) The greater the mass the less a body accelerates under force.
So the equation $$P=Mv$$ is related to $$F=Ma$$ when describing inertia, because the tendency to keep momentum is drastically resistant with the mass of the body. So inertia turns out to be a resistance of an object moving through spacetime, or simply in one dimension.
So, according to relativity, it’s the geometry of spacetime that is inertia, as even distortions are predicted from such geometry. So inertia is caused by the acceleration of an object moving below $$c$$, and has a rest mass.
All indication seem to be pointing to the conclusion that the gravitational mass is somehow the same thing as inertial mass itself. Einstein himself began his general relativity by stating that gravitational mass was not only the same as inertial mass, but in his special theories, he also linked that inertial mass was closely related to relativistic mass.
But since gravitational mass has a rest mass, whilst relativistic mass does not, there is the question of inertia properly applying to both types of fluctuations. It would seem that there is an innate property consistent with gravitational mass and inertia, than there really is of inertia and relativistic mass. The notion that mass has a resistance when moving through spacetime, whilst the relativistic material objects have no resistance at all i.e. a photon, or a gluon.
Relativistic Mass
… Is really just a measure of change in energy; and relativistic mass governs all systems. This is a major principle that even systems of pointlike particles have in them energy, like photon energy. Luxon Theory is the observed phenomena that all particles of mass are but forms of trapped light. The theory is universally-accepted as being correct, since we have observed particles and their antipartners reducing each other back to pure photon energy.
The fact the photon is an electromagnetic fluctuation, it must be assumed there is some kind of mechanism for a photon to transmutate into matter, for matter to return back to their original states; again, electromagnetic fluctuations of gamma energy.
Mathematically, the problem right now is how a photon can even flux into a particle with rest mass, since the math describing a photon is very different to lets say, an electron. Despite this, we have observed light creating matter in particle accelerators. The first proof of this was observed by scientists in September 1997. Since then we have comfortably accepted all matter are different forms of ‘’trapped light.’’
Photon has an energy $$E=hf$$, and so does mass itself, $$E=Mc^{2}$$. So a mechanism begs to be answered. A photon can have momentum and this is related to energy and mass as $$E^{2} = M^{2}c^{4} + p^{2}c^{2}$$, but the mass in this equation is still zero for a photon though $$E = pc$$. So, since we know there is a limited particle model, with right now about 410 known particles on the standard model, there must be a finite limit for the photon to flux into a specific type of particle, which follows the specific quantum action of particle decay.
A previous state of a particle before decay, let’s a say a neutron into a proton, electron, ... In $$\beta$$+ decay, as found in a Feynman diagram, follows this exact process because of the initial state of decay: A neutron. The energy contained in a particle contains a quantum memory of their previous states, because in any particle fluctuation, we must begin to talk about ‘’the photon changing the flux into a new state of matter, rather than dealing with both particles as separate.
The reason why we must assume this, is because the anti-state gives a solution for the matter to return into their original states of photons. The functions involved here seems intriguing enough to presume it is all linked to the actual production of mass itself, and is the same as Inertia.
An Electromagnetic Coupling with Gravitational Force
The fundamental gravitational effect on the Coulomb Self-Energy of a system, like a point charge has been calculated in many modern theories, where the total mass of the system in question takes form quite large; infinite to be exact, and it indicates that it depends only on the charge itself, and no so much the mass itself.
In a specific non-Higgs model, there is even suggestion that this could be an acceptable mechanism for a particle to acquire mass, by saying an electromagnetic phenom is acting on the ‘’innate’’ property of the particle, and only can do so when it possess non-gravitational interactions from quite possibly the zero-point vacuum.
The first appearance of this theory came from Andrei D. Sakharov suggested as much in 1968, an idea which was addressed 20 years later by Puthoff.
The implication here must be assumable that energy provided to the system can also flux and sustain the property of a particle with rest mass, with a non-zero range. But to this, I also add that even the generation of mass must also include a type of gravitational-electric-magneto coupling. This may be the mechanism and cause for inertia in general.
The electromagnetic fluctuation of the zero-point field could act on the charge of the particle as an innate property. As also explained, I mention that there need to be a finite number of fluctuations it can create. The wavelength of the photon may be a useful determining factor of the mass-flux process itself v = fλ. There are already exists a gravitational and electromagnetic coupling.
There is an indication that there might be a relation between charge and mass when concerning the Luxon Theory state of transmutation into rest mass. Photons don’t even interact with each other, but some extent must do, because for photons to turn into matter, it needs the interaction of other photons. Whilst this remains a strange phenomena, we can say a few things for sure, when you take into account the initial state of a photon, before it changes into a particle with rest mass:
$$ \delta (\gamma \gamma \rightarrow \gamma \gamma) delta$$
$$E^{1}=W/c^{2}$$
Where a change in initial energy gives rise to a mass, where the increase is found by W/c2. The invariant mass of a system is found after the change $$\gamma E1$$, but when it can be measured, can be seen from any mechanics, with energy and mass. Naturally, we can now talk about when the system has a non-zero kinetic energy when $$\gamma > 1$$;
$$K= \int_{\gamma < 1} dW=m^{0}c^{2} \int_{\gamma = 1}=1/2m^{0}v^{2}$$
Since photon scattering is assumed as a mechanism for rest mass creation, we must assume there is a very high energy, and a final, or even a total energy.
$$ \gamma mc^{2}=mc^{2} + K$$
Is the total energy of the system, and the kinetic energy of the system will contribute to the rest mass. Only when 2 m0c2 does it take into account particle antiparticle production.
And as I have explained before, the prior state of the photon may very well have an influence on the type of particle it coheres into, and wave length now played a part:
$$\Delta f \lambda=t^{2}S^{f}-t^{1}S^{0}$$
The mechanism is seen as a change in the state of energy, from an initial state of energy DE1 to a final state of DM2 in a time of 0<t<r/c, which is equal to the integral over a change in charge times a change in frequency. The net force is found as;
$$F^{net}=t^{2}+t^{1}$$
The net force will give rise to what I call, a gravitational decoherence, and since I relate the wave length being directly responsible with the type of mass that it inexorably fluxes into, then the coherence equation would be given as:
$$Mg \Delta \lambda / \lambda^{2} ~1$$
And to calculate it’s amplitude, we would use the normal amplitude equation:
$$ P \epsilon = \int \epsilon |\psi (x)|dx$$
Where a $$\Delta t= \delta^{c}$$. The probability of the energy fluxing into mass can be found as an integral:
$$P^{12}= \int t^{1}(S^{0}) t^{2}(S^{0})=|(\Delta S^{0})t>,|\Delta S^{f})t*>$$