 ## Derivation of the equivalence of energy and mass

My Idea that matter is gravitationally self-trapped light is simply an expression of Einstein´s famous formula E = Mc2. When a particle meets an antiparticle to create pure light, the photons that make up the particle and the antiparticle simply escape their traps."

Bob Toben, Fred Wolf and Jack Sarfatti: Space-time and beyond, 1975

Within my definition of mass ( mi : = |p| / |c| ), the equivalence of energy and mass is obvious. It follows from the relations:

 [ I ] mi : = |p| / |c| [ II ] E : = p c From [I] and [II] follows : [ III ] E = mi c2

Mass and energy are inseparably linked to each other, because both of them have the luxon momentum as the base of their definition.

This formula was many times misunderstood and wrongly explained.
Mass cannot be converted to energy and energy cannot be converted to mass. Nevertheless, a certain energy is always linked to a certain mass. During the explosion of the Hiroshima bomb not a single gram of mass was converted to energy. Mass cannot be changed to energy, as dollars can be changed to gold.
During an atom bomb explosion a certain part of the rest mass of the uranium is converted to pure movement mass (the mass of the luxons), or, a part of the rest energy is converted to movement energy (the energy of luxons).
There is no conversion of mass into energy during an explosion.

The liberated luxons, the gamma rays have a certain inertia.

Photons do not only have energy, but inertia, too.

The sum of the inertia in all liberated photons corresponds exactly to the quantity of (rest) mass which is gone after the explosion. It is the gram of uranium that has been set free in the form of luxons. The overall quantity of mass did not change during the explosion.

Each matter with rest mass consists of particles with light velocity. That means: Every matter consists of luxons. What really happens is this: An atom bomb explosion set a certain part of these inner luxons free.

### Captive luxons appears to have inertial mass

A thermos flask filled with light (bouncing around its inner surface) has greater inertia than an empty one - if you push against the thermos, you will be creating a transient concentration of light at your end of the flask, and you'll feel the increased radiation pressure that this causes at your end of the flask pushing the flask back against your hand. The full flask has a greater resistance to applied force (=increased inertia).

Erk`s Relativity pages
Let's respect a hollow body equipped in the inside with nearly ideal mirrors. This hollow body is so well isolated that nothing from its inside can come out. In the hollow body there is an electric torch. When the torch is switched on, it emits light. This light, these luxons are reflected by the mirror. Thus, the whole body partially consists of luxons. Since these luxons have energy, the luxons moving freely inside the body form a certain amount of the mass of it. Luxon momentum cannot be differentiated from tardyon mass, when they are trapped within a limited volume. Thus, the difference between luxons and tardyons is not an essential difference at all.
Is any type of experiment conceivable which allows to determine whether the torch is switched on or not?

We weigh out the hollow body, we accelerate it near to the velocity of light. But all efforts stay unsuccessful. There is no possibility to determine a difference between a tardyon mass and the momentum of the luxons inside the hollow body.
Inertia is inertia. Let's assume that the hollow body would react in any other form with the torch inside it switched on (except for a different centre of gravity): This would mean a break of the law of conservation of mass.
The reflected light beam inside the mirrored hollow body create a certain inertia. Thus it has a certain amount of the mass of the body. The reflected luxons form a "luxon gas" with a certain inertia inside the body.
The weight of the body did not change by switching on the torch. There is no experiment able to determine whether or not the torch is switched on by simply measuring the mass of the body.

Thus, luxons have the ability to show characteristics of (rest) mass. Their momentum cannot be differentiated from the mass of tardyons, as long as they are trapped in a limited volume. Tardyons are continuously interacting luxons chained to each other by their interaction in a limited volume.
The whole energy of the luxons increases by the same factor with the velocity of the observer, as the rest energy of tardyons does. This is logical, because the rest energy (inertia) of the tardyons, after all, is the energy (inertia) of the inner, trapped luxons.

The relativistic rest energy increase of tardyons follows exactly from the relativistic energy increase of captive luxons. The relativistic rest energy increase of a glueball follows from the energy increase of its inner gluons, i.e. luxons.

From the point of view of a moved inertial system, also the apparent mass of these captive luxons is bigger by the factor: Take a look to a similar argumentation of Erk`s Relativity pages right here: ### Captive luxons appears to have heavy mass You find the proof for this on the page " Light is Heavy" of M.B. van der Mark and G.W. ’t Hooft: M.B. van der Mark and G.W. ’t Hooft wrote:
This example shows that the equation E=mc2 expresses the equivalence of mass and energy and not the generation of energy as a reaction product from mass. The confusion that sometimes arises can often be traced back to the mix-up between the words “mass“ and “matter“. Matter can be transformed into radiation. Matter is taking the role of energy container, radiation is some sort of released, “free“ energy, that must fly through space. [...]
The smaller the length scales, the stronger the forces involved and the higher the (binding) energies, and hence the corresponding masses, relative to the rest masses of the constituents. We could wonder whether this finds it climax at a point where an elementary material particle is build of constituents that have zero rest mass, with only kinetic and potential energy to make up for its mass. That this should be the case for the electron, but at the same time seems quite impossible , is well known .
What is intriguing is that matter’s most basic building blocks, the elementary particles, all have non-zero spin, intrinsic angular momentum, which seems to imply that they all must have some sort of intrinsic dynamics. Hypothetical structures which do not have internal dynamics, such as point particles and hard spheres, do not exist. So what is matter really made of then? In the Dirac theory, the electron is like electromagnetic energy quivering at light speed, just like a photon in a box . If really so, matter is light. [...]
Rest mass never applies to a system at complete rest, because such systems do not exist; there will always be internal dynamics.

Despite the dfference in frequency, at any point in space-time these two oscillations must still be in phase, just as they are in the proper frame. This provides a possible physical origin for the postulated law of the "harmony of phases" first proposed by de Broglie,[57, 58] which lies at the origin of quantum mechanics.

J.G. Williamson and M.B. van der Mark: Is the electron a photon with toroidal topology? (PDF)
So, the luxon theory solves a problem which marks the beginning of the development of wave mechanics.

Silva and Lochak write (Silva/Lochak 1969):

As we remember, at the beginning of wave mechanics there was the idea to regard every particle of the mass m as the origin of a periodical phenomenon of the frequency v. In order to express this in a quantitative way: De Broglie linked Einstein's formula E=mc2; with Planck's formula and thus received the formula m c 2 = h v
This formula tries to link, in a very general form, the quantum postulate with the principle of relativity.

To meet the principle of relativity means that this law has to be the same for all observers which move parallel and uniformly with respect to each other. Nevertheless, neither the mass nor the frequency can be called relativistic invariants, i.e. values which do not change from one observer to another. Thus, they have to change in a way to meet the equation they are in. But a severe difficulty arises within that. Indeed: If mass has a certain value mo for an observer who is at rest with relation to the particle, its value is bigger for any observer who is moving. On the other hand, if the observer at rest defines the frequency vo of the periodic movement which is linked to the particle, for any other observer it will have an inferior value. This is the famous effect of the clock difference. From this, it has to be followed that the law mentioned above can be true for a special observer who then defines the cyclic frequency which is linked to the particle. Nevertheless, it has then to be wrong for all other observers. It can be said that such a law is relativistically covariant.

In a certain sense, wave mechanics rose from a theorem of de Broglie, according to which everything elapses in a way as if there was a wave which propagates at a velocity much higher than the velocity of the particle. It must be stationary and have the frequency vo for the observer at rest. For any other observer it must continuously be in phase with the inner cyclic movement of the particle. He showed that the frequency of this wave is transformed as well as the mass from one observer to the other, and that therefore the quantum relation m c 2 = h v becomes relativistically covariant, if the cyclic frequency in it, which from now on is designated vc , is substituted by the frequency v of that wave.
The frequency of a tardyon transforms as well as its inertia, because the frequency of its luxons transforms as well as its inertia!
This follows from the fact that the overall energy of the luxons emitted by a light source transforms exactly like the mass of a tardyon. Otherwise, the law of conservation of energy would be disregarded.

There is actually a wave which "propagates at a velocity much higher than the velocity of the particle" and is stationary. This is the wave of the inner luxons!