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
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
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.
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
Is any type of experiment conceivable which allows to determine whether the torch
is switched on or not?
Luxon momentum cannot be differentiated
mass, when they are trapped within a limited volume. Thus, the
difference between luxons and tardyons is not an essential
difference at all.
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
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.
So, the luxon theory solves a problem which marks the beginning of the development
of wave mechanics.
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)
Silva and Lochak write (Silva/Lochak
The frequency of a tardyon transforms as well as its inertia, because the
frequency of its luxons transforms as well as its inertia!
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
In order to express this in a quantitative way: De Broglie linked Einstein's
; 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
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
of that wave.
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!