*Einstein has been
credited with discovering the ‘equivalence of matter and energy’ in September
of 1905. He ultimately rationalized his
way to a very different concept in December 1907. There is a relationship between matter and
energy, but in spite of the *ad hoc *equation E = mc ^{2}, it is not
complete equivalence. Rather, such
relationship is only ‘partial convertibility.’
In any event, such relationship should not be considered to be a
relativistic concept, and most of Einstein’s conclusions concerning mass,
matter and energy were based on the prior work of others.*

**A. What is
Energy, Mass and Matter?**

Energy on the macro level can be broadly defined as any fundamental physical process that can perform work or make something physically happen. This definition can be made somewhat more meaningful by brief descriptions and oversimplified illustrations of the major manifestations of energy, which often can be readily converted from one form of energy to another.

1.
__Gravitational__ energy is exemplified by the mutual attractions and
resulting gravitational accelerations of all material bodies, respectively in
proportion to and inversely to the proportion of their masses, and relative to the
inverse square of their distances apart.
One practical terrestrial application is water falling from the top of a
dam, which turns a dynamo and generates electricity. Another is the rise and fall of tidal waters,
which also can be applied to perform work.

2.
__Chemical__ energy holds combinations of atoms together as
molecules. The release of this energy
can be manifested by explosions, fires and other chemical interactions.

3.
__Heat__ energy results when atomic particles wiggle or vibrate “in a
random and confused manner.” [1] (Feynman, 1963, p. 4-6) A practical application is the heating of
water with a fire that produces steam pressure that drives a mechanical engine,
which in turn produces work.

4.
__Electrical__ energy is manifested by the pushing and pulling of
electric charges. (*Id*.

5.
__Radiant__ energy is transmitted by electromagnetic radiation in the
form of light, heat waves, x-rays, radio waves, gamma waves, etc. (see Chapter 6 and Figure 6.9) EM radiation received from the Sun can be
converted to electricity by solar voltaic cells, or it can be stored in the
form of plants, animals or fossil fuels (oil, coal, natural gas) and later
burned to produce heat and ultimately work.
Plants convert solar energy and chemical energy into matter (stored
energy) by the process of photosynthesis.
Animals convert solar energy, chemical energy and the stored energy of
plants and other animals into matter by the processes of life, growth and
reproduction.

6.
__Elastic__ energy is exemplified by the potential force of a spring
under tension. (*Id*.

7.
__Kinetic__ energy is “the energy of motion” of a body or subatomic
particle.[2] (*Id*., p. 4-5) Practical macro applications include wind
power that can propel sailing ships or turn windmills, a rifle bullet that can
cause destruction, and the motion of a truck, a ship, an airplane or a rocket,
which can transport a load of matter.

8. There are also several types of
__nuclear energy __which we should briefly consider separately.

a. __Natural
Radioactive Decay__. The unstable
nucleus of naturally occurring heavy atoms (such as radium or uranium-235)
spontaneously emit subatomic particles such as an electron (beta decay) and
thereby transforms itself into a different nuclide.[3] This process is sometimes described as
‘spontaneous fission,’ which means a partial disintegration of the
nucleus. Radioactive decay releases a
small fraction of the __binding energy__ that holds the nucleus together
(sometimes called ‘disintegration energy’), and the energy released is very
much greater than for a similar chemical process. Over great intervals of time this natural
radioactive decay process continues to produce different nuclides progressively
down the periodic table of elements until a stable nuclide of lead (^{206}Pb)
is eventually reached. (see Halliday, pp.
1147 – 1153, 1168 – 1169, A-5 to A-7)

b. __Nuclear
Fission__. Nuclei of atoms are
composed of positively charged protons and neutral neutrons. The ‘binding energy’ (the total internal
energy of the nucleus) holds these two particles together.[4] In order to keep the Coulomb repulsive force
of the positively charged protons from splitting the nucleus apart, the
neutrons (with their associated ‘strong force’) progressively outnumber the
protons as we proceed up the periodic table of elements.[5] Nuclear fission occurs when the massive
unstable nucleus of a heavy element (i.e. nuclide ^{235}U) splits and
its protons and neutrons are reassembled into two stable middle mass nuclei.[6] (*Id*., pp. 1143 – 1146) During this process large amounts of binding
energy are released, and the energy released per atom is roughly a million
times larger than that of similar chemical events. (*Id*.*Id*., pp. 1171 –
1172) The by-product of controlled
nuclear fission is heat, which boils water.
The steam pressure operates a turbine, which drives a generator of
electricity that in turn produces work.
(*Id*., pp. 1172 – 1173)

c. __Thermonuclear
Fusion__. Binding energy can also be
released where two light hydrogen nuclei are combined or fused to form a single
heavier nucleus, thus creating a different element (usually helium). This process, called thermonuclear fusion, is
the reverse of fission. It occurs
naturally inside the Sun and other stars, and results in solar radiation. (Halliday, pp. 1146, 1175) Thermonuclear fusion requires much more bulk
than nuclear fission. It also requires
much higher temperatures to ignite and sustain a chain reaction. Therefore, a nuclear fission bomb is used as
its trigger. (*Id*., pp. 1175 –
1176, 1178) The energy released by a
thermonuclear fusion event is roughly 20 million times the energy released by a
similar chemical event. But there is one
major problem. “A sustained and
controllable thermonuclear power source—a fusion reactor—is proving much more
difficult to achieve.”[7] (*Id*., p. 1178)

It follows from the above discussion that energy in all of its observed forms results from actions on the quantum level. When energy in any form excites electrons and raises their energy state, other forms of energy are observed. For example, the act of rubbing amber with a cloth (relative motion) may transfer electrons to the cloth creating positive ions that result in static electricity. An electric current results from directing the random motions of electrons (a charge) in a particular direction, i.e. along a wire, or a lightning bolt from clouds to the ground. Chemical and biological reactions, electricity, and rotary motion can induce the excitement of electrons and result in heat or light. “Sources of light depend ultimately on the motion of electrons.” (Halliday, p. 890)

What is matter? For the purposes of this chapter, let us define matter as all of the atoms, atomic particles, galaxies, stars, planets, asteroids, comets, and other celestial bodies existing in the cosmos. Matter does not include any independent form of electromagnetism, such as electric charges, electric currents, electricity, magnetism, EM fields, light, photons or EM radiation.

What are the concepts and definitions
of mass? In classical physics, ‘mass’
was a definition of the quantity of matter that existed for a particular
purpose. For example, the ‘inertial
mass’ of a material body was defined as the theoretical measure of its inertia
(resistance) to being accelerated by a force (applied energy).[8] On the other hand, the ‘gravitational mass’
of a material body was defined as its proportional force of attraction with
respect to another material body, diminished by the square of their distance
apart. This latter measure was first
articulated by

**B.
Einstein’s 1905 Concepts Concerning Mass and Energy**

All of the concepts contained in Einstein’s Section 10 and
in his September 1905 treatise were generally known by physicists at the turn
of the 19^{th} century, such as Kaufmann, Abraham, Lorentz, Poincaré,
Heavyside, Bucherer and Max Planck. They
had been experimenting with and theorizing about the relationship between the
kinetic energy and the electromagnetic energy of the electron and its
electromagnetic mass and inertia for years.
Before 1905, they knew of the equation E = m*c*^{2} in some of its various forms, that electromagnetic
mass (an electromagnetic resistance) was a measure of an electron’s
electromagnetic energy and its electromagnetic inertia, and that even when the
electron was at rest it contained a new form of energy which was associated
solely with its atomic structure.[10] (see Sobel, p. 205) Some physicists, including Abraham and
Einstein, also believed that light had some form or magnitude of mass, which
was capable of imparting a force or pressure on a body that received such light.

The major difference between the experiments and theories
of the other physicists and Einstein’s relativistic theories of 1905 was that
Einstein was mathematically attempting *ad
hoc* to apply and __generalize__ the concepts of electromagnetic mass and
the energy and inertia of an electron to the ponderable mass of atomic matter. As Sobel puts it:

“The
theory of relativity, in 1905, showed that the increase in mass with velocity
is to be expected on __general grounds __as a consequence of the new
transformation principles of space and time [the Lorentz transformations]; it
applies not only to the electron but to any particle, __any matter__, __whether
electrically charged or not__.” (*Id*., pp. 205 – 206)

Einstein
was also attempting *ad hoc* to
extrapolate this general conclusion to include the phenomena of light and EM
radiation.

After reviewing his June 30, 1905 Special Relativity paper for several weeks, Einstein wrote to his colleague, Habicht, and conjectured as follows:

“…a __consequence__
of the work on electrodynamics has suddenly occurred to me, namely, that the principle
of relativity in conjunction with Maxwell’s fundamental equations requires that
the mass of a body is a direct measure of its energy content—__that light
transfers mass__.[11] An appreciable __decrease in mass__ must
occur in radium.”[12] (see Miller, p. 333; Folsing, p. 196)

What do the above conjectures by Einstein tell
us? First of all, they demonstrate that
Einstein falsely equated the material atomic particle radiation of radium with
the non-material electromagnetic radiation of light, and falsely concluded that
in both cases the result would be a decrease in the mass of the emitting body,
because “light transfers mass.”[13] Why did Einstein make this generalized
assertion? Probably because in his
September 1905 paper he was going to attempt to demonstrate the *ad hoc* concept which he asserted in § 10
of his Special Theory…that Relativistic Mass and Relativistic Kinetic Energy
should __generally__ apply to the ponderable mass of a material body, as
well as to the electromagnetic mass (resistance or inertia) of an election.[14] The reason that Einstein gave for this
proposed *ad hoc* generalization made
absolutely no sense. It was:

“because a ponderable
material point can be made into an electron (in our sense of the word) by the
addition of an electric charge, *no matter
how small*.”[15] (Einstien, 1905 [

Secondly, the consequence that suddenly occurred to Einstein, “namely…that light transfers mass,” implies that Einstein believed that light (and EM radiation in general) contained a magnitude of mass.[16] This must have been the consequence that suddenly occurred to Einstein, because otherwise the phrase “that light transfers mass” would have been a non sequitur with respect to the prior phrase that it follows.[17]

These thoughts were further developed by Einstein
into a short 3-page follow-up paper to his Special Theory entitled, “Is the
Inertia of a Body Dependant Upon its Energy Content.” (Einstein, 1905e [Dover, 1952, pp. 69 –
71]) It was received by the editors of *Annalen
der Physik* on September 27, 1905, and was published in their next edition.

Einstein began this
three-page thought experiment with the following statement: “The results of the previous investigation
lead to a very interesting conclusion, which is here to be deduced.”[18] (*Id*., p. 69) Thereafter, Einstein stated that based upon
the Maxwell-Hertz field equations for empty space and his own expanded
principle of relativity he had deduced in § 8 of his Special Theory the
equation for the energy of a light ray L_{0} emitted from the
stationary inertial system K, as measured in inertial system k relatively
moving at v. This equation was:[19]

^{“ }

where *c* denotes the velocity of light.[20] We shall make use of this result in what
follows.” (Einstein, 1905e [Dover, 1952,
p. 69])

One might ask: What relevance did the result which Einstein
deduced in § 8 have for his September 1905 paper? In § 8, Einstein deduced that the energy of
the light which was emitted by system K and which was incident upon the moving
mirror in moving system k was different than the energy of the light leaving
the surface of the mirror in k. By the
principle of the conservation of energy, Einstein speculated that such
difference in energy must be “the __work__ done by the __pressure__ of
light” on the mirror.[21] (Einstein, 1905d [

We know from our prior
discussion of the classical concept of energy in Chapter 31D that work results
from a force, that a force (i.e. pressure) results from the motion (kinetic
energy) of a mass, and that the work done on an object (i.e. a mirror) by a moving
mass is equal to the change in kinetic energy of the mass. Einstein must have put all of the above concepts
and deductions together, along with his deductions of Relativistic Mass and Relativistic
Kinetic Energy in § 10, and concluded that the __energy of a light ray must
have a magnitude of mass__. There is
no other rational explanation for Einstein’s above quote in § 8 about “the work
done by the pressure of light,” for Einstein’s 1905 conclusion to Habicht “that
light transfers mass,” and for Einstein’s similar conclusions at the end of his
September 1905 thought experiment.
Resnick’s statement that Einstein’s equation, E_{0} = m*c*^{2}, “asserts that energy has
mass,” also tends to confirm the author’s above conclusions. (see Resnick, 1992, p. 167)

Let us now return to Einstein’s September 1905
thought experiment. After his above
described preliminary comments, Einstein imagined that a body __at rest__ in
inertial system K had an energy of E_{0} (as properly measured in K),
and that it had an energy of H_{0} (as measured by coordinates in
system k which had a relative velocity of v).[22] Why was the body __at rest__ in system K
in his September 1905 paper, whereas in § 10 of his Special Theory the electron
was slowly accelerated in system K?
Probably because when Einstein reflected on § 10, he realized that if
the kinetic energy W of the electron was m*c*^{2} times some
factor relating to the relative velocity of the electron, then it follows
algebraically that without that relative velocity factor the total energy of
the electron relativistically __at rest__ should be E_{0} = m_{0}*c*^{2}
in system K.

The body at rest then emitted two light rays of
energy ½ L each in two opposite directions,[23]
and thereafter the energy of the body was E_{1} and H_{1} as
measured in K and k, respectively.
Applying the relativistic transformation equations for the energy of a
light ray which he obtained from § 8 of his Special Theory to E_{0} and
H_{0}, Einstein eventually (after much algebraic manipulation) arrived
at the following equation:[24]

(*Id*., pp. 70 – 71) Einstein then conjectured: “The kinetic energy of the body __with
respect to k diminishes__ as a result of the emission of light, and the
amount of diminution is independent of the properties of the body.[25] Moreover, the difference K_{0} – K_{1},
like the kinetic energy of the electron (§ 10), __depends on the velocity__.”[26] (*Id*.,
p. 71) Therefore, “K_{0} – K_{1}
= ½ L/*c*^{2} v^{2}.” (*Id*.*If a body gives off the energy L in the form of radiation, its mass
diminishes by L/c^{2}*.” (

It follows from the above, that the
body’s mass m_{0} (like its kinetic energy k_{0}) only
diminishes by L/*c*^{2} __as
measured by coordinates in system k__.
In other words, such diminution of mass is at least partly an
illusionary relativistic decrease which only occurs because of the relative
velocity and because of Einstein’s contrived system of measurement.

With the above considerations in mind, let us slightly revise what
Einstein stated after he concluded that the body’s “*mass diminishes by L/c ^{2}*.”

“The fact that the energy withdrawn from the body becomes energy of [light] radiation evidently makes no difference,[27] so that we are led to the more general conclusion that

The mass of a
body [in K as measured by coordinates in system k] is a measure of its
energy-content; if the energy [in K as measured by coordinates in system k] changes
by L, the mass changes in the same sense by L/9x10^{20}.” (Einstein, 1905e [Dover, 1952, p. 71])

One might ask: What relevance do distorted coordinate measurements of mass and energy made in system k have to do with anything?

The biggest problems with these derivations, speculations, rationalizations
and conclusions by Einstein are: 1) they
are all completely *ad hoc*; 2) they depend upon the *ad hoc* concepts of Relativistic Mass and Relativistic Kinetic
Energy, which we demonstrated in Chapter 31 are empirically invalid; 3) they depend upon Electromagnetic Mass,
which is only an electromagnetic resistance and an electromagnetic form of
inertia; 4) they depend upon the
empirically invalid *ad hoc* concept
that light has a magnitude of material mass, and finally 5) they depend upon Einstein’s artificial and
distorting relativistic system of measurement.
How can conclusions and concepts which are based upon so many false
assumptions and *ad hoc* concepts have
any validity?

How and why did Einstein suddenly interject the word ‘mass’ into the
discussion? All prior discussions in his
September 1905 paper had been all about light, energy and radiation. Was this merely a non sequitur? Not really.
The ‘mass’ that Einstein was referring to was not the ponderable mass of
a material body. It was only the
‘electromagnetic mass’ in his concept of Relativistic Mass, which he was
attempting to generalize so that it could apply to a “ponderable material
point.” (see Chapters 17 and 31B) However, this attempted *ad hoc* generalization has no reasonable validity either.

Prior to 1905, Kaufmann
(in unpublished calculations) “defined the electron’s kinetic energy as the
difference between the electron’s total and rest energies.” (Miller, p. 313) Therefore, “this definition of kinetic
energy…was in use before the appearance of Einstein’s” relativistic equation
for kinetic energy. (*Id*.*Id*.*Id*.

Regardless of their *ad
hoc* nature, all of Einstein’s assertions and conclusions in his September
1905 paper were also quite ambiguous.
For example, what did Einstein mean by the term ‘inertia’?

1. Did he mean the inertial resistance of matter to being moved, measured by the formula F = ma?

2. Did he mean the electromagnetic inertia (resistance) of an electromagnetic field to a charged particle or body moving through it?

3. Did he mean the motion or momentum of a body through empty space, apparently without applied rectilinear force (inertial motion)?

4. Was he using inertia as a synonym for mass?

5. Did he mean some combination of the above, or something else?

What did Einstein mean by the term ‘mass’?

1. Did he mean atomic matter measured as inertial mass by the formula F = ma?

2. Did he mean the ‘apparent mass’ of an electromagnetic resistance?

3. Did he only mean that the electromagnetic
mass diminishes by L/*c*^{2}?

4. Did he mean the rigid or deformable body of a particle, such as an electron?

5. Did he mean the magnitude of mass that he assumed that a light ray possessed?

6. Did he mean some combination of the above, or something else?

What did Einstein mean by the term ‘energy content’?

1. Did he mean ‘mass-energy;’ the total energy stored in matter?

2. Did he mean every form of energy that can be associated with matter?

3. Did he mean the electromagnetic charge of a particle or body?

4. Did he mean that kinetic energy is ‘contained’ within a body?[28]

5. Did he mean some combination of the above, or something else?

What did Einstein mean by the phrase “a measure of”?

1. Did he mean the complete equivalence and complete convertibility of the two phenomena (matter and energy)? If so, how did he get to this conclusion?

2. Did he mean only a partial convertibility of matter into energy?

3. Did he only mean some indefinite amount of mass or energy, the magnitude of which can only be determined empirically on a case-by-case basis?

4. Did he mean some combination of the above, or something else?

What did Einstein mean by the term ‘energy of radiation?’

1. Was he describing a new and separate general classification of energy?

2. Did he mean the energy of any type of radiation: atomic (i.e. radium) or electromagnetic (light)?

3. Was he describing the different type of energy of EM radiation and the toxic energy from disintegrating atoms?

4. Did he mean some combination of the above, or something else?

What did Einstein mean by the phrase ‘light (or radiation) transfers mass (or inertia)?’

1. Did he mean that light transfers electromagnetic mass and electromagnetic inertia?

2. Was he assuming that light has a magnitude of material mass?

3. Was he assuming that the pressure of light on an absorbing body causes the body to move inertially?

4. Was he only referring to the atomic radiation emitted by disintegrating radium?

5. Did he mean some combination of the above, or something else?

Did Einstein even know what he was conjecturing? In his September 1905 article, Miller
concludes that Einstein “focused on the problem that he thought to be of basic
importance—the nature of radiation.”
(Miller, p. 333) Were all of the
ambiguous conjectures in his September 1905 article merely Einstein’s attempts
to better understand the nature of radiation?
His mathematical conjectures that “mass diminishes by L/*c*^{2}”
and that “the mass of a body is a measure of its energy content” could easily be
interpreted to be merely __supportive__ of his ultimate and general conclusion
concerning the nature of radiation—“radiation conveys inertia between emitting
and absorbing bodies.” (*Id*.

Later, of course, Einstein’s conjecture that “mass
diminishes by L/*c*^{2}” was interpreted to empirically mean m =
L/*c*^{2}, and thereafter E = m*c*^{2} (the
equivalence of matter and energy).[29] Einstein’s conjectures of: “the fact that the energy withdrawn from the
body becomes energy of radiation __evidently makes no difference__, so that
we are led to the more general conclusion that the mass of a body is __a
measure of__ its energy-content,” were also later interpreted by Einstein and
many of his followers to mean “the __equivalence__ of [material] mass with
any form of energy.”[30] (Miller, p. 333) Same problems and same comments.

**C. Numerous problems with E _{0} = m_{0}c^{2} and with E = mc^{2}.**

The problems with Einstein’s September 1905 thought experiment, along with the above gratuitous interpretations and ‘in hindsight’ conclusions, include the following:

1. First and foremost, the thought experiment
that Einstein concocted in his September 1905 paper was completely *ad hoc*.
It was based on all of the empirically invalid *ad hoc* assumptions and relativistic concepts contained in the
kinematic part of his Special Theory. It
was also derived from the *ad hoc* and
empirically invalid equations, conclusions and concepts contained in the
dynamical part of his Special Theory.

2. Einstein referred to the energy of the
stationary body (before its emission of light) by the relativistic algebraic
symbol E_{0} (or rest energy), a relative velocity dependent quantity
in Special Relativity. Therefore, in
order to remain consistent with Special Relativity, the mass of the stationary body
should have been algebraically designated m_{0} (for rest mass), a
relative velocity dependent quantity. In
fact, Einstein later designated the kinetic energy of the body with the
relativistic algebraic symbol K_{0} (for rest kinetic energy), because (as
Einstein asserted) it depends on the relative velocity when measured by
coordinates in system k. (Einstein,
1905e [_{0} = m_{0}/*c*^{2}.

But this relative velocity
dependent equation would only be valid for an observer properly measuring in
system K.[31] Only the distant observer in system k would
measure the energy and the mass to increase with relative velocity, and these
measurements would only be an __artifact__ of observation and they would
only result from Einstein’s bizarre system of measurement. (see Goldberg, pp. 141, 147) How can this artificial process result in a
law or relationship of nature?

3. With equation E_{0} = m_{0}*c*^{2}, the properly measured
energy in system K would not be equivalent to the variable magnitude of mass
measured by coordinates in system k, and the variable magnitude of energy
measured by coordinates in system k would not be equivalent to the properly
measured mass in system K. How can these
bizarre, contrived and conflicting relativistic measurements result in a
fundamental relationship of nature?

4. The ‘mass’ (m_{0}) that
Einstein was referring to throughout § 10 of his Special Theory and throughout
his September 1905 paper (except with respect to radium) was only an ‘electromagnetic
mass’ masquerading as Relativistic Mass, which as we have previously discovered
in Chapter 17 was really only an electromagnetic ‘resistance’ that
algebraically was only characterized to be a mass in order to remain somewhat
consistent with F = ma. Electromagnetic
mass was nothing like the ponderable __material__ inertial mass that

Photons of light radiation, if they exist, are *a priori*
__massless__ particles or quanta of energy.[33] (Okun, 1989, p. 34) Radioactive atomic particles __with material
mass__ that are emitted from radium undoubtedly would cause the mass of a
material body composed of radium to diminish.
But how can the __massless__ particles of EM radiation (light)
diminish the mass of a material body by L/*c*^{2}, or by any other
magnitude? (*Id*.

Contrary to Einstein’s assertion, the fact that the energy
withdrawn from the body becomes the energy of massless electromagnetic
radiation __does__ make a huge difference.
It is not the same as the material atomic radiation of particles given
off by unstable elements such as radium (uranium and plutonium), which
particles *a priori* do have material mass. Einstein could not be led from his thought
experiment concerning massless photons to a more general conclusion that “the
[ponderable material] mass of a body is a measure of its energy content.” Nor could he be led to the conclusions that
“[massless] light radiation transfers mass,” or that “[massless light]
radiation conveys inertia between the emitting and absorbing bodies.” Nor could Einstein be led to the general
conclusion that all energy and all mass are totally equivalent: E = m*c*^{2}. Therefore, Einstein’s assertion that it makes
no difference what the type of energy is was a major false premise for his
September 1905 theory, and his later theories about the ‘inertia of energy.’

5. In his September 1905 thought experiment,
Einstein arbitrarily __equated__ at least four very different types of
energy. A) There was E_{0} (rest
energy) and E_{1}, which stood for the total of all energies associated
with a body respectively before and after the emission of light as __properly__
measured in system K. B) There was H_{0}
and H_{1}, which stood for the total of all energies associated with a
body respectively before and after the emission of light, as __relativistically__
measured by coordinates in system k. C) There
was L_{0}, which stood for the energy of light radiation emitted in two
opposite directions from the body at rest, as properly measured in system
K. D) There must also have been the
different magnitude L, which would stand for the energy of the two light rays,
as measured by coordinates in system k.
E) There was K_{0} and K_{1}, which stood respectively
for the kinetic energy of motion of the body before and after the emission of
light, as respectively properly measured in system K and by coordinates in
system k (or by Lorentz transformations).
F) Finally, there was the toxic and radioactive energy of atomic
radiation emitted from the disintegrating nuclei of the atoms of radium salts.

Einstein conjectured
that “the fact that the energy withdrawn from the body becomes energy of
radiation __evidently__ makes no difference.” (Einstein, 1905e [*ad hoc* idea and what was the
justification for it? There was
none. It was simply pure speculation on
Einstein’s part. Einstein’s attempted
generalization of energy was also a fundamental false premise for his September
1905 paper.

How can the energy of EM radiation (i.e. light) be the same as the energy of the atom? Light cannot produce an atomic explosion because it has no magnitude of mass, it is not composed of atoms, and it is not radioactive. It cannot even be converted into fissionable uranium or plutonium in order to produce an atomic explosion. By the same token, kinetic energy, the energy of a body’s motion, is only theoretical potential energy which is theoretically capable of performing work. Theoretical kinetic energy cannot produce an atomic explosion, because it is only theoretical, because it is independent from the mass of the moving body, and because it is not composed of atoms. Nor can kinetic energy even be converted into fissionable material such as uranium or plutonium.[34] Light radiation and atomic radiation are also very different phenomena for another reason. One is radioactive and toxic, and the other is not. It becomes obvious that such energies are not all the same.

6. Einstein asserted that the mass
and the kinetic energy of motion of the stationary body would diminish as a
result of the __emission__ of light where L is the energy given off “in the
form of radiation.” (Einstein, 1905e
[Dover, 1925, p. 71]) He also asserted
that this diminution, K_{0} – K_{1}, “depends on the velocity”
of the body. (*Id*.

has no clear meaning.

There is another
problem with such equation. If the
difference K_{0} – K_{1}
depends solely upon the relative velocity of the inertial reference frames and
if such relative velocity approximates zero, then one is left with: K_{0} – K_{1} = ½ L/*c*^{2}
0^{2} = 0. It does not follow
from this last equation that m = L/*c*^{2}, because there would be
no diminution of kinetic energy, therefore L would be meaningless or zero, and
mass m would also be zero. In this case,
E = m*c*^{2} would also be zero and meaningless. In addition, Einstein derived his equation, K_{0}
– K_{1} = ½ L/*c*^{2 }v^{2}, by application of the
*ad hoc* and meaningless Lorentz
transformations, therefore his equation for the kinetic energy at any velocity
must also be *ad hoc*, totally flawed
and meaningless.

7. All of the derived equations in Einstein’s September 1905 thought experiment directly or indirectly result from the algebraic symbol ½L which he arbitrarily gave to the energy of light waves emitted from the body. Why did Einstein use this symbol? It only refers to the energy of a light ray, which is very different than the theoretical potential kinetic energy of a moving body or the toxic atomic energy emitted from radium.[35]

Based on ½L, Einstein ultimately derived m = L/*c*^{2}. If he was only referring to electromagnetic
mass in an EM field then this equation could have some meaning, but it has no
meaning for the atomic mass of a material body.
Material mass m cannot be equated with light energy, *inter alia*, because light does not have
any magnitude of mass. On the other
hand, if Einstein was talking about material mass, then how can he get
from m = L/*c*^{2}, where L is the energy of a massless light ray, to m
= E/*c*^{2}, where E is the
total energy of a material body? All of
these facts lead the skeptic to the conclusion that either Einstein’s final
equation (m = L/*c*^{2}) was
meaningless, or the interpretation of it (E = m/*c*^{2}) was *ad hoc*
and contrived.

**D. Revisions to Einstein’s Section 10 and his
September 1905 theories.**

Over the next three years, Einstein would re-rationalize
and change Section 10 of his Special Theory and his September 1905 theories in
many ways, always attempting to generalize his conclusions in Section 10 to
apply to ponderable masses of material bodies.
In May 1906, Einstein published a follow-up paper to this September 1905
paper, on what he called ‘The Inertia of Energy.’[36] (Einstein, 1906 [Collected Papers, Vol. 2,
pp. 200 – 206]) At the beginning of his
May 1906 paper, Einstein described a conclusion of his September 1905 paper, as
follows: “the mass of a body changes
with the change in its energy content, __no matter what kind of change of
energy__ this may be.” [37] (*Id*., p. 200) This conclusion basically describes the __conversion__
of one form of energy into another form, not the __equivalence__ of mass and
energy. For example, it describes what
happens when a body burns and part of its matter (mass) is converted into heat
and gases.

Thereafter, Einstein acknowledged that the considerations
necessary to prove the purpose of his May 1906 paper were “in the main already
contained in a work by H. Poincaré.”[38] (*Id*.*c*^{2}]
by considering a photon…that is emitted at one end of a hollow cylinder and
absorbed at the other end…”[39] (Okun, 1989, p. 34) However, as Okun asserted:

“The
conclusion of [Einstein’s May 1906] paper was that light with energy *E*
transfers mass *m = E/c ^{2}* and that to

Thus,
Einstein’s conclusion was both empirically incorrect and internally
inconsistent, because how can “the absorption of a __massless__ particle
change the mass of the absorbing body?”[40] (*Id*.

In May 1907, Einstein wrote a third paper on the ‘Inertia of Energy.’ In the first paragraph of this paper, Einstein again described conclusions that he believed needed to be drawn from his September 1905 paper:

“…the inertia of a body increases or decreases with its energy content…

“…to
an increase in the body’s energy ΔE there must always correspond an increase
in the mass ΔE/*c*^{2}…”
(Einstein, 1907 [Collected Papers, Vol. 2, p. 238])

These conclusions were nothing more than a repeat of the conclusions from his May 1906 paper. The criticisms of them are also the same.

Immediately thereafter, Einstein told his readers what the subject of his May 1907 paper would be:

“the
circumstance that the special case discussed [in the September 1905 paper]
necessitates an assumption of such extraordinary generality (about the
dependence of the inertia on the energy), demands that the necessity and
justification of this assumption be examined in a more general way.” (*Id*.

The
‘extraordinary assumption’ that Einstein was referring to and conjecturing
about was that the dependence of inertia on energy must also apply to __ponderable
material masses__ as well as to electromagnetic masses (resistances).[42]
He then stated that he had “taken the first step in this respect” in his May
1906 paper that dealt with the inertia of energy and “the constancy of the
motion [momentum] of the center of gravity” of a ponderable mass. (*Id*.

Einstein thereafter described
another imaginary case where an external electromagnetic field transferred
kinetic energy to the ponderable mass of a rigid body moving at a constant
velocity. (*Id*., pp. 240 – 243) An avowed reason for this thought experiment
was to show that the equation for the kinetic energy (K_{0}) of the
body at rest (in § 10 of his Special Theory) “does not hold any longer if the
body is acted upon by external” electromagnetic forces.[43] (*Id*., p. 240) He then also considered the ‘self’
“electromagnetic field produced by the electric masses of the body”[44]
and concluded that the inertial mass of the electrified body (i.e. an electron)
had increased by E/*c*^{2}.
Einstein the conjectured *ad hoc*: “The law of the inertia of energy is thus
confirmed” for ponderable masses.[45] (*Id*., pp. 243 – 246) One must give Einstein credit for being
persistent, even though the substance of his persistence is not correct.

In his December 1907 Jahrbuch
article, Einstein wrote a fourth article on the same subject, this time
entitled: ‘On the Dependence of Mass
[Inertia] upon Energy.’[46] In this article, Einstein compared the energy
E of a ponderable physical system with inertial mass, to the kinetic energy K
of an electron with __electromagnetic mass μ__ and concluded that “with
regard to the dependence of the energy on the translational velocity” they
behave the same.[47] (Einstein, 1907e [Collected Papers, Vol. 2,
p. 286]) In other words, Einstein
conjectured that the energy of a ponderable inertial mass and the kinetic
energy of an electron’s electromagnetic resistance are both velocity dependent,
and __in this regard__ they become the same.[48] Einstein then conjectured:

“This
result is of extraordinary theoretical importance because the inertial mass and
the energy of a physical system appear __in it__ as __things of the same
kind__.[49] __With respect to inertia, a mass μ is equivalent to an energy
content of magnitude μc__^{2}.”
[50] (*Id*.

In
effect, Einstein was stating: “With
respect to inertia, an apparent electromagnetic mass μ is __equivalent__ to an energy content of a magnitude
electromagnetic resistance μ
times *c*^{2}.”

This was Einstein’s real statement of mass-energy equivalence. In effect it was an EM resistance-EM energy equivalence. Now we know what Einstein was talking about in his September 1905 paper.

Thereafter, Einstein continued his conjecture about inertial mass, electromagnetic resistance and energy.

“Since
we can arbitrarily assign the zero-point of *E _{0}* [relativistic rest energy], we are

In
other words, just because Einstein was having difficulty arbitrarily distinguishing
between an inertial mass and an apparent electromagnetic mass (a resistance),
he decided to abandon his original false concept of EM mass and *ad hoc* decided to “consider any inertial
mass as a reserve of energy” instead. (*Id*., p. 287) Einstein was obviously very confused about the
entire subject of mass, resistance, inertia, energy, electromagnetism and
matter, and very frustrated in his *ad hoc*
attempts to generalize EM mass to include a ponderable material inertial mass.

The concept of ‘inertial mass as a reserve of energy’ is now called ‘mass
energy,’ the energy which is stored in material bodies at rest, and which may
be partially converted to other forms or manifestations of energy. In other words: “An object has energy from its sheer *existence*.” (Feynman, 1963, p. 4-7) But, if we apply this concept to uranium-238
it has little or no meaning, because this isotope is not fissionable. If we cannot release any of the energy in a
chunk of pure ^{238}U, what is the practical (or even the theoretical)
meaning of the concept that the energy of ^{238}U is equivalent to its
mass times *c*^{2}?[53] The same question applies to enriched uranium
where the percentage of fissionable uranium-235 is increased, but still only a
tiny amount of enriched uranium can be converted to energy. Even inside the Sun at its current
temperatures, helium and many other heavier elements cannot naturally be
converted into energy. (Halliday, p.
1178)

Nevertheless, the relativists claim
that Einstein’s “equivalence of mass and energy has been beautifully verified
by experiments in which matter is annihilated—converted totally to
energy.” (Feynman, 1963, p. 15-11) Regardless of these claims of equivalence,
these experiments rely almost completely upon theoretical assumptions,
inferences and interpretations, and (as Dingle stated) they only hang together
if Special Relativity is applied to them and is assumed to be valid. Let us assume, for sake of argument, that
anti-matter actually exists, and that when two identical subatomic particles
with opposite charges (i.e. an electron and a positron) are made to collide
under artificially controlled conditions, they can change into different
particles and/or a form of energy (i.e. gamma rays). (*Id*.

The relativists claim that all four of Einstein’s papers
on the inertia of energy, taken together, result in the assertion of the total
equivalence of the ponderable inertial mass of matter and its energy
content. However, we have repeatedly
demonstrated that this is not what Einstein was __directly__ asserting in
such papers. Rather, he was merely
trying to __indirectly__ generalize an electromagnetic mass to include the
ponderable inertial mass of a material body, by analogies and *ad hoc* persuasions. The clarifications in his December 1907
Jahrbuch article describe this difference.
They should have been the ‘coup d’ grave’ for Einstein’s attempted
artificial generalizations.

However, by 1916,
Einstein grew much bolder. In his book, *Relativity*, he __directly__ reinterpreted
his prior papers on the ‘inertia of energy’ to mean and include __ponderable
inertial mass__, and he expanded his concepts of the mass-energy relationship
*ad hoc*, with the following axiomatic and
relativistic conjectures:

“In accordance with the theory of
relativity the kinetic energy of a material point of mass *m* is no longer given by the well-known expression

,

but [by] the expression

.

This expression approaches infinity
as the velocity *v* approaches the
velocity of light *c*. [see Chart 16.___ and Figure 16.2B] The velocity must therefore always remain less
than *c*, however great may be the
energies used to produce the acceleration.”
(Einstein, *Relativity*, p. 50)

“A body moving with the velocity *v*, which absorbs an amount of energy *E _{0}* in the form of radiation
without suffering an alteration in velocity in the process, has, as a
consequence, its energy increased by an amount [54]

.” (*Id*., pp. 51 – 52)^{}

“If a body takes up an amount of
energy *E _{0}*, then its

Einstein finally achieved his
generalization *ad hoc* by __edict__.

Apparently, all of these conjectures only relate to __one__ frame, the
frame where the energy and the inertial mass are properly measured. Therefore, *a priori*, after 1916 the magnitudes of mass and energy are no
longer relativistic or distorted.
Presumably, such conjectures also include the energy of massless light
and EM radiation. But, again, how can
the inertial mass of a body increase when it absorbs a __massless__ photon
or quanta of light energy? (see Okun,
1989, p. 34)

So what does the theoretical concept of the equivalence of mass and
energy really mean? In general, such
theoretical equivalence is only a mathematical consequence of a dubious
equation (E = m*c*^{2}) and an
equally dubious theoretical goal.
Empirically, in nature, the equivalence of mass and energy only means a
minimal or partial __convertibility__ under certain circumstances.[56] Without substantial further explanation and
equivocation, the formulas E = m*c*^{2} or E_{0} = m*c*^{2}
or E_{0} = m_{0}*c*^{2}
do not describe or confirm any of their claimed empirical results.

**E. What is the real relationship between the
mass of matter and its energy?**

There is a long-standing principle
of physics known as the conservation of energy, which we briefly discussed in
Chapter 31D. Among other things, it may
be interpreted to state that one form of energy may be __partially converted__
into another form, but that energy itself can never be created nor destroyed. (see Resnick, 1992, p. 164) The previous descriptions of energy in this
Chapter appear to demonstrate this principle.
The facts that energy may be stored in matter (atoms), that matter
(atomic particles) may be energized, and that a small part of the matter can be
converted into energy are consistent with the principle of energy
conservation. But such partial
convertibility does not mean that the two phenomena (matter and energy) are
equivalent or the same thing. Each
phenomenon has its own properties. Atoms
are not light and protons are not photons.
Photons or quanta of light cannot be split or fused to produce enormous
amounts of nuclear energy. They are not
equivalent to the nucleus of an atom.
There is a relationship between the two phenomena (matter and energy),
but it is clearly __not__ total equivalence.

A body of matter that has been agitated or energized (i.e. by heat) has more energy (wiggling atoms) than when not energized (heated). Therefore, under any definition of mass or energy, the mass-energy of the heated body has increased. The same (or a similar process) may occur with a body that has been accelerated, a body that is being gravitationally pulled by another body, a body that has been agitated by a chemical interaction, by an electric charge, by an electromagnetic field, by a magnetic force, by atomic radioactivity, or by solar radiant energy. In all of these cases the matter (atomic particles) of the body has been ‘energized,’ and its atoms wiggle more. This energized state may be manifested in many ways (i.e. by the emission of heat, by the emission of light, by a chemical reaction, by radioactivity, etc.) and such manifestations of energy may be at least partially convertible into other categories or forms of energy.

However, this scenario does not mean
that the neutrons, protons, electrons and atoms that comprise the material body
have increased or changed in size, density or number. What can happen is when heat energy (for
example) is applied to a body or a gas, the ‘vibration energy’ of its atoms
increases as the temperature rises. This
increase in vibration energy normally causes the __separation__ between the
atoms to increase, and thus the __volume__ of the entire body or gas
expands.[57] (Resnick, 1992, p. 503) But this does not mean that the energized
matter (its inertial mass) is __equivalent__ to all of the various types of
energy applied to it or associated with it, including the potential release of
the nuclear binding energy attributed to the possible fusion or fission of the
nuclei of its atoms. During a nuclear
fission event, less than 5% of the enriched uranium is fissionable, and much
less than that (i.e. one gram) is converted to energy. (see Feynman, 1963, p. 15-11) Even during a thermonuclear fusion event,
only a tiny amount of the original matter in the bomb is converted to various
forms of energy.

What is the meaning of E = m*c*^{2}, which was derived *ad hoc* from E_{0} = m_{0}*c*^{2}, from Einstein’s September 1905 thought experiment,
and from his related conjectures? E = m*c*^{2} has been interpreted and
conjectured by Einstein and his followers to mean the total physical
equivalence of energy and material mass.
Even if this conclusion was true, it cannot be based on Einstein’s *ad hoc* relativistic equation E_{0}
= m_{0}*c*^{2}. On its face, E = m*c*^{2} asserts that classical non-velocity dependent energy
E is equal in magnitude to classical non-velocity dependant material mass m
times *c*^{2}. E_{0} = m_{0}*c*^{2}, on the other hand,
asserts that the Relativistic Energy and the Relativistic Mass of a body change
in magnitude depending upon relative velocity, as measured by a distant
inertial observer.

In
fact, E = m*c*^{2} is only an
artificial construct. It was only
intended by Einstein as a rough approximation, expression or illustration of
the enormous potential energy contained within any lump of atomic matter. As Einstein once stated: “E = m*c*^{2
}…showed that a very small amount of mass [matter] may be converted into a
very large amount of energy…” Similarly,
in 1946, Einstein summarized what he meant by the equation E = m*c*^{2}.

“It
is customary to express the equivalence of mass and energy (though somewhat __inexactly__)
by the formula *E = mc ^{2}*, in
which

As
such an __inexact__ approximation and as a metaphor, E = m*c*^{2} has great meaning. But such equation cannot be, and was never
intended to be, applied literally. For
example, a lump of non-fissionable coal (carbon) and a lump of fissionable
uranium-235 (both having the same weight or inertial mass), contain vastly
different quantities of convertible energy.
The convertible energy contained in a lump of coal might be described as
E = 1/1,000,000m*c*^{2} when
compared to the convertible energy contained in a lump of fissionable
uranium-235.

The word ‘equivalence,’ when applied
to energy and mass, only has a highly theoretical, metaphorical and speculative
meaning. It asserts that __if__ we
were able to access all of the atomic and other energy theoretically contained
in a lump of coal and convert it into an explosion so that all of its matter
was annihilated and totally converted into the energy of the explosion, then
its mass would to some extent be equivalent to its energy released.

But since we are not capable of performing such magic of total conversion, and probably never will be, such theoretical equivalence has no practical meaning. The only practical relationship between mass and energy that we now have (theoretical particle annihilations aside), and possibly ever will have, is that of ‘partial convertibility.’ In other words, ‘equivalence’ means: to what extent can we convert or release part of the theoretical energy contained in a lump of matter; equivalence is only a theoretical dream.

The fact that a negatively charged electron and a theoretical positively charged electron (a positron) may collide in a particle accelerator and theoretically be totally converted into other particles and gamma rays (energy), does not even demonstrate the equivalence of the original particle as compared to the two surviving particles and their energy, let alone the equivalence of the matter of the Earth and its energy.[58] The highly theoretical ‘annihilation’ of two subatomic particles and their dubious total conversion to another form, does not translate into the concept that all of the matter of the cosmos may be totally converted into energy.[59]

The Sun has been trying to turn all of its hydrogen into
energy for the past 5 billion years and still over half of it remains as
hydrogen. The rest has been converted
into helium and a few other heavier elements, plus a constant stream of EM
radiation (i.e. light) and particle radiation (i.e. cosmic particles such as
neutrinos). When a giant star, much
larger than the Sun, has exhausted most of its hydrogen, *a priori* it may suddenly disintegrate and explode as a supernova
with energy propagated and star fragments being propelled in all possible
directions at several thousand km/sec, leaving a white dwarf, a neutron star or
pulsar in its wake. Thus, after the
giant star has been substantially annihilated (it no longer exists as a giant
star), only a relatively small part of it has actually been converted into
energy. Again, this __partial
convertibility__ of matter is also dramatically demonstrated by a fission
bomb, where only about one gram of the original bomb material is converted into
energy. (see Feynman, 1963, p. 15-11)

How did Einstein interpret the presence of *c*^{2} in the
equation E = m*c*^{2}? In a
1946 treatise on E = m*c*^{2}, Einstein
explained what the factor *c*^{2} meant to him: It showed that there is “a vast amount of
energy for every unit of mass.”
(Einstein, 1946 [Ideas and Opinions, 1954, p. 375]) In other words, the factor *c*^{2} just showed that a very
small amount of mass [matter] may be __converted__ into a very large amount
of energy.

As Einstein himself acknowledged in 1946, the equation E = m*c*^{2}
was only a mathematical way of making a general statement or approximation that
an undetermined magnitude of energy can be released from an undetermined
magnitude of matter (mass), depending upon the specific mass/energy conversion
involved. For example, the magnitude of
energy (m*c*^{2}) would be small where radiation is naturally
emitted by the radioactive decay of radium, and this conversion might be
approximated by the equation E = 1/100,000m*c*^{2}. The magnitude of m*c*^{2} would
be larger for the nuclear generation of electricity, and this conversion might
be approximated by the equation: E =
1/10,000m*c*^{2}. On the other
hand, the magnitude of m*c*^{2} would be relatively enormous for a
*c*^{2 }or even E = 1/100m*c*^{2}. But certainly not E = 100%m*c*^{2},
because there is always a substantial quantity of original mass or matter left
over from any such explosion, such as a neutron star or a white dwarf. For all of the above reasons, E = m*c*^{2}
was never intended to signify a __specific__ magnitude of energy or
convertibility. Rather, it only attempts to describe a __general__
mass-energy relationship and some possible convertibilities.[60]

Einstein did not use the term or concept of ‘equivalence’ in his
September 1905 paper. The phrase ‘a
measure of’ is completely ambiguous as to what sort or magnitude of measure
Einstein might reasonably be suggesting.
Such phrase is certainly not equal to the term: ‘equivalence.’ Any implied conclusion concerning the
equivalence of the ponderable inertial mass of matter and its energy was
completely based on Einstein’s mathematics and his *ad hoc* conjectures,
because it was not supported by any empirical data. He only generally suggested that his theory
(whatever it was) might be tested by the radioactive particle emissions of
radium.[61] (Einstein, 1905e [Dover, 1952, p. 71]) Einstein’s suggestion that atomic radiation
released from radium may test his theory merely predicts a kind “of
circumstance under which energy and mass are exchanged but gives no insight
into the nature of the process.”[62]
(Goldberg, p. 159) In any event, as we
have just demonstrated, the so-called equivalence of mass and energy (in
nature) empirically means at most only __partial convertibility__.

**F. Who really
discovered the mass-matter-energy relationship?**

A general statement may be made that
the discovery of the mass-matter-energy relationship was in fact a long drawn
out __process__ and that many scientists contributed to its early and
current state of understanding, including Einstein. The earliest clue might have been when
philosophers realized the proportional relationship between the energy
necessary to move a body and its resulting motion.

Now fast-forward two centuries.
During the period between 1880 and 1904, British physicist J. J.
Thompson,[63]Austrian
physicist F. Hasenöhrl, American physicist D. F. Comstock, Max Plank and Max
Abraham in *Id*.,
p. 154) Such experimenters gave similar
descriptions between the __inertia__ of such trapped radiation and the energy
of the system. (*Id*.

In 1889, British physicist Oliver Heavyside derived the equation E = ¾m*c*^{2}. (Pavlovic, Section 23.6.2) The equation E = ¾m*c*^{2} was
generally interpreted as the mass content of the energy of the radiation. (*Id*., pp. 154 – 155) Because m*c*^{2} had an
ambiguous, variable and undetermined value, Heavysides’s equation could easily
be considered as equivalent to E = m*c*^{2}. In a 1900 paper, French scientist Henri
Poincaré derived the equation E = m*c*^{2} in an implicit form.[65] (Pavlovic, Section 23.6.2) Since Resnick concludes that the equation E_{0}
= m*c*^{2} “asserts that energy
has mass” (Resnick, 1992, p. 167), why are not Heavyside and Poincaré
considered to be the fathers of the mass-energy relationship and of the concept
of mass and energy are equivalent?

In 1904, a prize-winning paper by Friedrich Hasenöhrl (1874 – 1915) was
published in Annalen der Physik[66]
and showed “that radiation enclosed in a vacuum has to be credited with an __apparent
mass__, __proportional__ to the energy of the enclosed radiation.” This statement implied that mass and energy
are in some way equivalent, and Folsing concludes that Einstein must have read
Hasenöhrl’s paper. (Folsing, pp. 196,
197; Jammer, p. 72) Also during 1904,
numerous research projects on the relationship between mass and energy were
being conducted by scientists at various locations, including Einstein’s own
Patent Office in

It thus becomes obvious that the origin of the concept of a relationship, convertibility and/or equivalence of mass, matter and energy “emerged from a program of scientific research.” (see Goldberg, p. 156) Einstein could certainly be considered as a member of this group program, but he only joined it toward the tail end, not at the beginning. Yet he is often credited as being the founder of the mass-energy relationship, whatever it is, and even the father of the atomic bomb.[68]

The equation, E = m*c*^{2}, has of course become the most
famous equation in physics, especially for the general public. Pavlovic concluded, that:

“it is this equation
that has contributed most to Einstein’s fame and the fame of the theory of
relativity, although it is __not a relativistic equation nor was it derived by
Einstein__.” (Pavlovic, Section 23)

These latter conclusions by Pavlovic may also surprise many readers, but not the author. (see Chapters 32B and 32C, supra)

Pavlovic asserts that Einstein did not quantify or prove his general
conclusions concerning the mass-energy relationship, and that he did not derive
E = m*c*^{2} correctly.
(Pavlovic, Sections 23.6.3 and 23.7)
There is substantial support for Pavlovic’s assertions. In 1907, Max Planck published a manuscript in
which he stated that Einstein’s 1905 derivation of E = m*c*^{2 }included
assumptions only valid to the first approximation. (Jammer, 2000, pp. 64 – 65) In 1952, Herbert Ives claimed that Einstein’s
1905 derivation was a logical fallacy and circular, because it arbitrarily
introduced a relation that was “the very relation the derivation was supposed
to yield.” (*Id*., pp. 62 –
65) Einstein himself was not satisfied
with his 1905 so-called derivation, but despite his many later efforts, he was
unable to arrive at a general proof for the relation it asserted. (*Id*., pp. 66 – 67)

In a 1922 letter, Einstein acknowledged and asserted: “that the idea that mass and energy are the
same had long ago been proclaimed by many authors, but it is __only__ the
theory of relativity that gave a __true proof__ of this equivalence.” (Jammer, 2000, p. 72) This was not a correct claim by Einstein, for
the following reasons. Einstein’s
relativistic proofs were only mathematical (not empirical); they falsely
assumed that light has a magnitude of material mass, and they only dealt with
Relativistic Mass and Relativistic Kinetic Energy, neither of which
exists. It is true that Einstein
repeatedly used the Lorentz transformations to derive some variation of E = m*c*^{2},
but the Lorentz transformations by themselves are not Special Relativity, and
using them is not the only way to achieve such derivation. For example, in 1907, Max Plank published a
paper wherein he deduced the equivalence of mass and energy based on concepts
obtained from his black body experiments.
(Miller, pp. 340 – 342) Fritz
Rohrlich in 1990 and Ralph Baierlein in 1991 derived the mass-energy
equivalence relation from the classical Doppler effect (without applying the
Lorentz transformation). (*Id*.,
pp. 68 – 71) In 1988, Feigenbaum and
Mermin claimed a derivation of the mass-energy relation “without ever leaving
the realm of mechanics.” (*Id*.,
pp. 74 – 76) Even Einstein in 1906
derived the relation to a first approximation using only principles of
classical mechanics. (*Id*., pp. 77
– 79)

In any event, as Pavlovic correctly points out, the equation E = m*c*^{2}
itself has nothing to do with relativity, and should not be considered as a
part of Special Relativity. It is purely
a classical equation that asserts the general relationship between mass and
energy at various magnitudes of the variables.
Even mass ‘m’ in the equation refers to classical mass, rather than
relativistic mass.[69] (see Pavlovic, Section 23.8) A correct relativistic formula for the
theoretical mass-energy relationship of equivalence would be E_{0} = m_{0}*c*^{2} (or the equivalent), where
E_{0} is the proper (velocity dependent) rest energy of a body and m_{0}
is the body’s proper (velocity dependent) rest mass.[70]

In 1916, Einstein attempted, *ad
hoc*, to convert E = m*c*^{2} into a relativistic equation by
adding the Lorentz transformation factor to it as a denominator, vis.:

E = __ ____mc ^{2 }__

√1- v^{2}/*c*^{2 }

According to
Einstein, this new equation describes what happens when the energy, the mass
and/or the velocity of a material object changes. [71]
(Einstein, *Relativity*, p. 50)
There may be some empirical support for this conjecture by Einstein, but
certainly it is not as a result of the Lorentz transformation. If the Lorentz transformation factor, √1
– v^{2}/*c*^{2}, is *ad hoc* (Chapter 27); invalid
for Length Contraction and for the Dilation of Time (Chapter 28); and invalid
for Relativistic Mass, Relativistic Momentum and Relativistic Kinetic Energy
(Chapter 31); why should we suddenly believe that it is valid with respect to
mass and energy?

Thus, the conclusions attributed to Einstein—that the mass or matter of a
material body is a __direct__ measure of its energy content and that a
body’s matter can be totally converted to energy (*Id*.

[1] The wiggling of such atoms is sometimes characterized as ‘vibration energy.’

[2] The theoretical vibrating motions of a subatomic particle (i.e. an electron) are considered to be a form of kinetic energy.

[3] A ‘nuclide’ is defined as a different species of nucleus. (Halliday, p. 1143)

[4] ‘Binding energy is comprised of the ‘strong force’ between the particles, the Coulomb repulsive force between the positively charged protons, and the kinetic energies of the two particles. (Halliday, p. 1145)

[5] For
example, lithium (the third lightest element after hydrogen and helium) has
three protons and four neutrons, whereas ^{238}U (the heaviest
naturally occurring element) has 92 protons and 146 neutrons. (Halliday, pp. 1143 – 1144)

[6] The idea
of an atomic fission bomb is to cause a chain reaction of fission events that
will propagate itself. The fuel ^{235}U
(which normally constitutes only 0.7% of natural uranium) is usually enriched
to several percent, because the remaining ^{238}U is not fissionable by
thermal neutrons. (Halliday, p. 1171)

[7] At least
two generations of scientists and engineers have tried and failed to develop a
controlled, sustained fusion process using lasers to ignite a pellet of a
bubble of plasma (of other materials than hydrogen, such as deuterium, tritium,
and/or boron), using intense magnetic fields to contain the reaction. (see wikipedia.org/wiki/Fusion_power) The hydrogen fusion process that occurs
naturally inside the Sun is also naturally controlled, because rare
proton-proton collisions, which form a deuteron (^{2}H), occur just
frequently enough to release the even flow of binding energy that we
observe. (Halliday, p. 1177)

[8] The inertial mass m of a body in empty space (where there is no resistance of the medium) is equal to the force F applied to the body divided by the acceleration a: m = F/a. In the medium of empty space, the inertial mass of a body is a constant quantity. However, on the Earth this formula overstates the mass of a material body relative to the force applied or the resulting acceleration due to the resistance (R) of its medium or environment (i.e. the friction of air and/or of a surface) which is often factored in as part of the mass. Thus, the formula must be changed to m – R = F/a, or its equivalent, in order to properly account for R. (see Chapter 17)

[9] More recently, mass (on a sub-atomic level) has been described (in part) as “the effect of the interaction between particles and the Higgs field.” (Close, 2002, p. 193)

[10] In his Special Theory, Einstein and his followers later called this new internal energy of the atom, ‘rest energy.’

[11] Einstein referred to this theoretical concept “that light transfers mass” as “an amusing and attractive thought.” (Miller, p. 333)

[12] Radium
is an unstable radioactive metallic element that naturally gives off atomic
particle radiation. It was discovered by
Marie and Pierre Curie in 1898.
Radium-226 has a half-life of 1,602 years and decays into the element
radon. (see Oxford Dictionary of
Physics, p. 408) Such atomic particle
radiation would *a priori* result in a decrease in the inertial mass of
such radium, but this has nothing to do with __light__ (EM) transferring
mass. On the contrary, everything still
exists with radium. Part of the radium
has just been __converted__ to a different form: atomic particle radiation.

[13] In fact, in his September 1905 paper Einstein refers to the ‘energy of radiation’ in generic terms as if it applied generally both to light and radium; and he concluded that “radiation conveys inertia between the emitting and absorbing bodies,” where he also equated ‘inertia’ and ‘mass.’ As it turns out, one might conclude that Einstein really didn’t know what he was talking about.

[14]
Remember that in § 10 of his Special Theory, Einstein conjectured *ad hoc *that the relativistic
electromagnetic mass and the relativistic kinetic energy that he mathematically
derived and deduced for the electron should also apply to ponderable material
masses. (Einstein, 1905d [Dover, 1952,
pp. 63, 64])

[15] This silly justification constitutes a false premise for his entire September 1905 paper.

[16] In due course, we will demonstrate how Einstein deduced from § 8 and § 10 of his Special Theory that light must contain a magnitude of mass.

[17] Thus, it becomes obvious that the directly preceding phrase “the mass of a body is a direct measure of its energy content” was not the consequence nor the primary concept which Einstein was attempting to demonstrate in his September 1905 paper. It was merely a supportive concept and a step in Einstein’s mathematical generalization that ‘light has and transfers mass’ (or that ‘radiation has and conveys inertia’). Both of these general conclusions would be consistent with the then prevailing concepts of electromagnetic mass and electromagnetic inertia.

[18] As we shall soon discover, the previous investigations that Einstein was mainly referring to were those in § 8 and § 10 of his June 1905 Special Theory.

[19] Remember that this equation was substantially similar to Einstein’s formula for the relativistic Doppler effect of light and for the relativistic aberration of starlight in Section 7 of his Special Theory.

[20] Such equation does not define what the magnitude of energy of a light ray is. It only asserts that the energy of a light ray emitted from stationary system K, whatever its magnitude might be, will be different when measured in system k moving at v.

[21] Actually such difference was probably only due to his application of the Lorentz transformations to the emitted light from system K, or to the lesser frequency of the light received by the receding mirror. (see Chapter 30B)

[22] If we
Lorentz transform E_{0} from K to k, then H_{0} is different
than E_{0}. What is the physical
reason for this *ad hoc* change? There is none.

[23] In other words, the inertially moving body at rest in K emitted “pulses of [light] radiation at angles Φ and Φ + 180º with respect to the x-axis of K.” (Miller, p. 333)

[24] The
rest kinetic energy of the body before the emission of light radiation was K_{0}
= H_{0} – E_{0}. The
kinetic energy of the body in system K after the emission of light radiation
was K_{1} = H_{1} – E_{1}. (see Einstein, 1905e [

[25] Here
Einstein is only talking about the diminution of the kinetic energy of the body
__as measured by coordinates in system k__.
Therefore, such diminution is partly an illusionary relativistic
decrease which only occurs because of the relative velocity (as Einstein
pointed out in the next sentence), and because of Einstein’s bizarre system of
measurement.

[26] But which is it: the emission of light or the relative velocity which diminishes the kinetic energy? We will discuss this issue in the next section.

[27] This was a false premise, because if light does not have a magnitude of mass (which we now know to be the case), then this fact does make a huge difference for all of Einstein’s mass-energy conclusions contained in his September 1905 paper.

[28] How can
the energy of motion of a mass be physically __contained within__ a
body? When a force (energy) moves a body
in empty space, energy is conserved by the body’s kinetic energy of motion, but
is the atomic density of the body’s inertial mass increased? Of course not.

[29] But why
not *c*^{2} = mE, the velocity
of light squared equals electromagnetic mass times the energy of the
electromagnetic field? m = L/*c*^{2} only refers to the
electromagnetic energy of the two emitted light rays in a thought experiment
about light and radiation, and some possible electromagnetic mass involved, not
the vastly different E (any form of energy, including atomic energy). How could m = L/*c*^{2} mean the equivalence of material mass and energy, if
light L does not have any magnitude of material mass?

[30] Even
with this very gratuitous *ad hoc* interpretation,
we must still define what the word ‘equivalence’ means.

[31] Feynman agreed with the author, that Einstein was
dealing with Relativistic Mass and the equation E_{0} = m_{0}*c*^{2}. Feynman stated in his lecture: “We start with a body at rest, when its __energy
is m _{0}c^{2}__.” (Feynman, 1963, p. 15-10)

[32] ‘Lavoissier’s law’ concerned the conservation of inertial mass in chemical reactions. (Miller, p. 357)

[33] “The
photon has a rest mass of precisely zero.”
(Sobel, p. 206) “Thus we have
infinity times zero” (*Id*.__zero
for the mass__ of a propagating light ray in a vacuum.

[34] The same is basically true of gravitational energy, and its potential pulling power.

[35] The radioactive radiation from the disintegration of an atomic nucleus has atomic mass, kinetic energy only has potential and theoretical mass, and light energy has no magnitude of mass whatsoever.

[36] In 1921, Einstein further explained what he meant by
“the inertia of energy:” “It was found
that __inertia__ is not a property of __matter__…but a property of __energy__.”[36] (Einstein, 1921 [Nature, Vol. 106, p. 783]) Does this mean that the energy potential of
gravity has inertia? Does this mean that
a hydrogen bomb before it explodes has more inertia than an equal volume or
weight of lead?

[37] Like
his September 1905 paper, Einstein’s May 1906 paper was based solely upon
electromagnetic theory, his principle of relativity, and the principle of
energy conservation. (Einstein, 1906
[Collected Papers, Vol. 2, p. 200]) The
stated *ad hoc* purpose of his May 1906
paper was to demonstrate that his September 1905 paper was a necessary
condition for the conservation of motion (momentum). (*Id*.; see Miller, p. 334) But if momentum is mv (where m is material
mass), then there is no connection between the conservation of momentum and
Einstein’s September 1905 paper.

[38]
Einstein cited “Poincaré in Lorentz-Festschrift (1900): 252 – 278.”
In his 1900 paper, “Poincaré derived the equation E = m*c*^{2}
in an implicit form.” (Pavlovic, Section
23.6.2)

[39] This thought experiment has become a standard thought demonstration for Einstein’s ‘inertia of energy’ concept. (Miller, p. 334)

[40] What was the reason for this incorrect assertion by Einstein? Originally, because “only by attributing a mass to the radiation emitted or absorbed,” could Einstein conserve the motion (momentum) of a mass which he needed for his proof in his May 1906 paper. (see Miller, p. 334; Einstein, 1906 [Collected Papers, Vol. 2, p. 206]) However, later it also became useful for his Theory of General Relativity. (Okun, 1989, p. 34)

[41] Okun
also pointed out that in 1912, Tolman derived relativistic mass as m_{0}/√1
– v^{2}/*c*^{2} and Wolfgang Pauli adopted it and E = m*c*^{2}
for his widely read 1921 textbook, *The Theory of Relativity*. As a result, now almost everyone except
elementary particle physicists accepts these equations as correct relativistic
terminology. (Okun, 1989, p. 35)

[42] Einstein had previously conjectured this same assumption in § 10 of his Special Theory with respect to the longitudinal and transversal masses of electromagnetic mass and the kinetic energy of an electron. (Einstein, 1905d [Dover, 1952, pp. 63, 64])

[43] The *ad hoc* implication being that such
external EM forces transfer mass and inertia to such body.

[44] The
self EM field produced by the __electromagnetic mass__ (resistance) of an
electron is what Einstein was referring to.
(see Chapter 17)

[45] Not so. Merely describing an electron as an electrified ponderable body with an inertial mass, or describing an electromagnetic resistance as an inertial mass, does not result in Einstein’s desired generalization and confirmation.

[46] Note that Einstein again equated the word ‘mass’ with ‘inertia’ in this title.

[47] This,
of course, was consistent with Einstein’s ‘principle of relativity,’ that the
laws of nature (and the ways they may change) are independent of, and not
affected by, uniform translatory motion (velocity). (see Einstein, 1905e [

[48] Of course an electromagnetic resistance is velocity dependent, because without the velocity of an electric charge there is no EM resistance. However, the same is not true with a ponderable inertial mass. Therefore, Einstein’s attempted analogy of equivalence of an electromagnetic resistance and an inertial mass fails. Even if, for sake of argument, an electromagnetic resistance and an inertial mass were relative velocity dependent, this does not mean that they are “things of the same kind.” Relative velocity dependent ‘length’ and ‘time intervals’ in Einstein’s Special Theory are not ‘things of the same kind.’

[49] Here,
again, Einstein was (by __analogy__) attempting to __equate__ inertial
mass with electromagnetic mass. But
Einstein’s desires and __persistence__ cannot make it so. Inertial mass is of course defined as the
magnitude of __resistance__ of a body to being moved by a force. But a material resistance and an EM
resistance do not have the same cause: a
material mass.

[50] Here, as usual, Einstein was referring to the ‘apparent’ electromagnetic mass μ of an electron, which is actually an EM resistance. Again, he was arbitrarily comparing and interchanging an inertial mass with an electromagnetic mass, like apples with watermelons.

[51] Far
more natural than what? Far more natural
than considering electromagnetic energy as equivalent to electromagnetic mass
(a resistance) times *c*^{2}.

[52] In his
1921 article in Nature Magazine, after much theorizing and many experiments by
others, Einstein re-interpreted this statement to mean: “a body of mass m is to be regarded as a
store of energy of magnitude m*c*^{2}.” (Einstein, 1921 [Nature, Vol. 106, p.
783]) However, because both m’s in this
1921 statement refer to Relativistic Mass as measured by coordinates by a
distant observer in system S' moving at relative velocity v, this 1921
statement is also meaningless.

[53] Lead
and numerous other elements heavier than iron (^{56}Fe) are in the same
category as ^{238}U in this regard.

[54] “*E*_{0} is the energy taken up, as
judged from a co-ordinate system moving with the body.” (*Id*.,
p. 51)

[55] Here,
Einstein __directly__ and axiomatically generalized his concept of
electromagnetic mass to include the __ponderable inertial mass__ of a
material body, almost as if it was a postulate.
In 1921, Einstein even conjectured that his papers on the inertia of
energy were “of fundamental importance [with respect to] the __nature of
inertial mass__.” (Einstein, 1921
[Nature, p. 783])

[56] For example, over eons of time the Sun converts only a small part of its hydrogen into helium and into radiation energy.

[57] However, certain temperature regions of some crystalline solids may even contract. (Resnick, 1992, p. 503)

[58] This
process is often mischaracterized as ‘annihilation,’ suggesting that something
has been destroyed and no longer exists.
The same is true with respect to two protons that collide inside the Sun
and form a deuteron (^{2}H), a neutrino, and a positron (or two gamma
ray photons), and release energy in the process. (Halliday, p. 1177)

[59] Good luck trying to totally convert a lump of lead or a neutron star into energy. On the other hand, the assertion that matter and energy are equivalent states of the same phenomenon may have merit.

[60] E = m*c*^{2}
is therefore only a metaphor, a general approximation for a mass-energy
relationship. The factor *c*^{2}
only signifies that the atomic energy stored in a piece of matter is many, many
times greater than the chemical energy that it may contain or release.

[61] Radioactive particle emissions and EM wave emissions are two completely different types of radiation.

[62] This insight came from those who developed the atom bomb. But, to refer to Einstein as the father of the atomic bomb is like referring “to Isaac Newton as the father of the intercontinental ballistic missile.” (Goldberg, p. 156)

[63] In 1881, Thompson discussed the association between mass and energy in an electromagnetic theory.

[64] Abraham was the first to propose a magnitude for ‘light pressure.’ (Goldberg, p. 154) In 1905, Einstein also theorized in § 8 of his Special Theory about “the work done by the pressure of light…” (Einstein, 1905d [Dover, 1952, p. 59]) Both of these theories undoubtedly were based upon the false assumption that light possesses both mass (m) and momentum (mv). Also, this is probably the reason that Einstein concluded in his 1905e paper with the conclusion that light radiation conveys inertia.

[65] Also during the period 1880 – 1904, J. J. Thompson, Heavyside, Kaufmann, Abraham, Lorentz, Poincaré, Einstein, and others were experimenting with and theorizing about a phenomenon they called electromagnetic mass, which was related to EM charges, currents, radiation and other forms of EM energy. (see Chapters 17 and 31)

[66] Volume 15, pp. 344 – 370. Einstein was an avid reader of and contributor to this scientific journal.

[67] Einstein understood and wrote in the French language. (Jammer, 2000, p. 72, fn 23)

[68] It was
not until the mid 1920’s that the concepts of quantum mechanics were created by
Born, Heisenberg, Dirac, Schrödinger and others. It was not until the mid 1930’s that the real
technical work on atomic energy began with the work of Italian-American
scientist Enrico Fermi and others, and continued for a decade until August 1945
and Hiroshima. E = m*c*^{2}
may be a very rough first approximation for the energy released by a fission
bomb. Heavyside’s E = ¾m*c*^{2}
may be just as valid. E = m*c*^{2}
may even be a better first approximation for the energy released by a fusion
bomb. However, all of these equations
are merely extremely rough and ambiguous approximations. Referring to any of these early scientists,
much less Einstein, as the father of the atomic bomb is ludicrous. The only thing that Einstein did with regard
to the atomic bomb was to sign a letter (because of his great prestige) drafted
by nuclear scientists that informed President Roosevelt that such a device was
possible. (Cropper, p. 354)

[69]
However, in order to be a relativistic equation consistent with Einstein’s
Special Theory, it should be written: E_{0}
= m_{0}*c*^{2} or the
equivalent, in order to show that it is velocity dependent. (see Einstein, 1905 [

[70] It was
in his September 1905e paper that Einstein began the practice of adding a
subscript zero to indicate that the object or phenomena to be relativistically
measured was __at rest__ in an inertial reference system.

[71] This new equation leads to a relevant question: Is this manipulation of algebraic symbols endowed with any physical meaning?

[72] Much of the confusion depends upon what is meant by the words: equivalence, annihilation and convertibility.