*In Section 10 of his Special Theory, Einstein theoretically applied his
relativistic kinematic concepts to the mass of an electron. He imagined and described a new type of
electromagnetic mass for the electron, the magnitude of which varied depending
upon its relative velocity. This *ad
hoc *theory, which is now called
Relativistic Mass, was the basis for his other relativistic concepts of
dynamics and mechanics: Relativistic Momentum,
Relativistic Force, and Relativistic Energy.
Relativistic Mass also became the mass for Einstein’s September 1905
mass-energy paper (E = mc ^{2}). However,
none of these *ad hoc

**A.
Einstein’s electromagnetic concept of relativistic mass.**

Einstein’s Lorentz transformations succeeded in making his absolutely
constant velocity of light at *c* mathematically invariant (or
covariant) in all inertial reference frames, but only at the price of making classical
mechanics no longer invariant in such frames when transformed by Lorentz
transformations. “What had been gained
on one side had been lost on the other.”
(D’Abro, 1950, p. 156) Einstein’s
only way out of this theoretical dilemma, and to retain mathematical
consistency for his Special Theory, was “to assume [*ad hoc*] that the classical laws [of mechanics] were incorrect.”[1] (*Id*.

“Accordingly,”
states D’Abro, “the problem confronting Einstein was to __formulate new laws
of mechanics__ which would be invariant under the Lorentz-Einstein
transformations, and which at the same time would tend to coincide with the
classical mechanical laws when low velocities were considered. This last restriction stemmed from the fact
that for low velocities the classical laws of mechanics were known to be very
approximately correct.” (*Id*.

“Einstein obtained the revised
mechanical laws” by conjecturing that the magnitudes of most physical phenomena
(including length and time intervals) were dependent upon relative velocity.[2] (*Id*) Einstein continued his attempt to change all
of the classical laws of mechanics in Section 10 of his Special Theory with his
*ad hoc* velocity dependent concept of

“In classical physics inertial mass m_{i} is
an inherent characteristic property of a particle and…is independent of the
particle’s motion.” (Jammer, 2000, p.
41) In contrast, Einstein’s theoretical concept
of Relativistic Mass m_{r}, as described in Section 10 of his 1905
Special Theory, was a velocity-dependent mass which depends on the __relative velocity__
of the moving reference frame as measured by Einstein’s relativistic kinematics
from one inertial reference frame to another.
Jammer described Relativistic Mass by “the equation m_{r} = m_{0}/(1
– u^{2}/*c*^{2})-˝,” where m_{0} represents the
proper mass of a particle at rest in relatively moving reference frame k, u is
the velocity of the particle as measured from the relatively stationary reference
frame K, and *c* is the velocity of light. [4] (*Id*.

In Section 10 of his Special Theory, entitled the
‘Dynamics of the Slowly Accelerated Electron,’ Einstein conducted another
thought experiment. He imagined “an
electrically charged particle…an ‘electron’…in motion in an electromagnetic
field…” (Einstein, 1905d [Dover, 1952,
p. 61]) Einstein stated that he was seeking
the law of motion of the slowly accelerated electron.[5] (*Id*.

At this point, we must ask the following questions. Why did Einstein choose an electron in an
electromagnetic field for the subject of his discussion of Relativistic Mass,
whereas before in his Special Theory he had usually referred to a ponderable body
in empty space? [6] The apparent answer is because the mass which
Einstein was going to imagine and describe in Section 10 was the highly
theoretical ‘electromagnetic mass’ of an electron moving in an electromagnetic
field. In other words, such ‘mass’ was
actually an electromagnetic __resistance__ or __inertia__ masquerading as
a material mass (see Chapter 17), rather than the ponderable (weighable) inertial
mass of a ponderable (weighable) material body.
As Abraham acknowledged in 1902:

“the __inertia__ of
the electron originates in the electromagnetic field.”

“the __mass of the
electron is of purely electromagnetic nature__.” (see Jammer, 1961, p. 151)

In this regard, Miller pointed out that in the
original German version of his Special Theory, Einstein used the symbol ‘µ’ for
‘m’ “even though in the German language scientific literature this symbol was
usually reserved for the __electromagnetic mass__.” (Miller, p. 308) This fact, as well as Einstein’s abrupt
switch from a rigid body in space to an electron in an electromagnetic field,
and his later references to ‘longitudinal mass’ and ‘transverse mass,’ which
are only applicable to an electromagnetic mass, strongly implies to the author
that throughout almost all of Section 10 Einstein was only discussing an ‘electromagnetic
mass’ (an electromagnetic __resistance__), rather than the inertial mass of
ponderable matter. In fact, Einstein
twice acknowledged that the author’s interpretation is correct. In the middle of Section 10, Einstein
conjectured that the longitudinal mass and the transverse mass “__are also
valid for ponderable__ material points” (Einstein, 1905d [Dover, 1952, p. 63]),
and toward the end of Section 10, he conjectured that the kinetic energy of the
electron’s mass __must also apply to “ponderable masses__ as well.” (*Id*.,
p. 64)

Why did Einstein decide to use and analyze an electromagnetic
mass (a resistance) rather than the ponderable mass of a weighable body? Because Kaufmann’s 1901 – 1902 experimental
data suggested that electromagnetic mass __varied__ depending upon the
velocity of the electron; whereas, there was absolutely no empirical evidence
that the ponderable mass of a rigid body ever varied because of its
velocity. Thus, an analysis of the
ponderable mass of a rigid body would not have furthered Einstein’s relativistic
agenda.

In Section 10, Einstein began his thought experiment
by imagining that the electron was at rest in moving inertial reference system
k. He conjectured that the slightly
accelerated motion of the electron in system k was described by three
equations, and that “m [is] the mass of the electron, __as long as its motion
is slow__.”[7] (Einstein, 1905d [Dover, 1952, p. 61]) Thereafter, Einstein applied the Lorentz
transformations and the transformations which he found in Section 6, and
transformed the equations for the electron’s motion in k to the stationary reference
system K. He then asserted that a
‘pondermotive force’ was acting on the electron and was accelerating the
electron in accordance with the equation F = ma. [8] (*Id*.,
p. 62)

But wait a minute.
In Section 6 of his Special Theory, Einstein had denied that there was
an ‘electromotive force’ that acts on a point charge moving in an electromagnetic
field.[9] Instead he asserted that the force acting
upon the electron was nothing more than the ‘electric force.’ (see Chapter 30A) Why is this case any different? Why is it not the ‘electric force’ of the
electromagnetic field which is acting on the electric charged particle (the
electron)?[10] Einstein probably mischaracterized such force
as ‘pondermotive’ so that he could later conjecture that the electromagnetic
mass of the electron also applied to ponderable masses. A ‘pondermotive’ force means a ‘weight moving
force’ such as __other
values__ for the masses.”[11] (Einstein, 1905d [

Remember that the concepts of
longitudinal mass and transverse mass were invented by Abraham in 1903 in order
to describe Kaufmann’s 1901 – 1902 experiments with the __electromagnetic__
mass of electrons and the data which he collected and published in 1902. (see Chapter 17) At the end of his April 1904 treatise,
Lorentz also referred to the “electromagnetic masses” of electrons which
Kaufmann and Abraham had found, and Lorentz asserted that the values which he himself
had found (based on his April 1904 theories) for the same masses agreed with
Kaufmann’s measurements “nearly as well as with those of Abraham.” (see Lorentz, 1904c [

Einstein asserted in § 10 that he took
“the ordinary point of view” in his inquiry “as to the ‘longitudinal’ and the
‘transverse’ mass of the moving electron.”[12] (Einstein, 1905d [

(*Id*., p. 63)

In order to
derive these equations, Einstein called his ‘pondermotive force’ simply ‘the
force acting upon the electron,’[14]
he maintained the equation F = ma, and he decided “that the accelerations are
to be measured in the stationary system K.”[15] (*Id*.

According to Einstein’s concepts of longitudinal mass
and transverse mass, as the relative velocity v of system k increases so does
the mass of the electron (as measured in K), and when v approaches *c* the
mass m_{r} of the electron in k (as measured in K) increases toward
infinity.[16] (see Chart 31.1 and Figure 31.2) As will be seen on Chart 31.1A and Figure 31.2, Einstein’s
values for longitudinal mass match Lorentz’s April 1904 values __exactly__,[17]
but they differ dramatically from Abraham’s values. Remember from Chapter 17 that Abraham had
determined that Kaufmann’s ‘longitudinal mass’ was meaningless and
immeasurable. So why did Einstein derive
a formula for Longitudinal Mass and thus imply that it did have meaning and was
measurable? Most likely because he did
not know about Abraham’s conjecture and was merely mimicking the theories of
Kaufmann, Abraham and Lorentz without much scrutiny or original thought. On the other hand, Einstein’s values for
transverse mass differ dramatically from both Abraham’s and Lorentz’s
values. (see Chart 31.1B)

Miller believed that Einstein’s variations with respect to Lorentz’s magnitudes for transverse mass required an explanation, and that the question why Einstein did not provide one in his Special Theory was a mystery. (Miller, p. 312) However, there is very little mystery for the author. Any such explanation by Einstein might have signaled that he had read Lorentz’s April 1904 treatise and that he had ‘borrowed’ many of its concepts, especially the Lorentz transformation equations, which he claimed to have derived from his two fundamental postulates.

Shortly thereafter, Einstein conjectured that these results for the increase in (electromagnetic) mass of the electron are also valid for ponderable matter. (Einstein, 1905d [Dover, 1952, p. 63) In Einstein’s own words:

“We remark that these
results as to the mass are also valid for __ponderable material__ points,
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.”[18] (*Id*.

On the contrary, as we previously explained, all that Einstein was
dealing with were the __resistances__ provided by the electromagnetic field
to the motion of an electron through it, which when using the formula F = ma
mathematically results in increases in mass m.
These electromagnetic resistances had been mischaracterized by everyone
during the latter part of the 19^{th} century as ‘apparent’ masses in
order to remain consistent with Euler’s incorrect formula F = ma for the determination
of the masses. This incorrect
characterization was perfect for Einstein’s theory of Relativistic Mass,
because such electromagnetic ‘apparent’ masses (re-characterized as ponderable
masses) would __vary with velocity__ in his Special Theory.[19] (Chapter 17)
This is the major reason why Einstein wanted to maintain the equation F
= ma.

But, if there were no real increases in the mass of an electron due to such electromagnetic resistances, how could Einstein’s concept of a variable mass for the electron depending upon relative velocity be extended to (and be empirically valid for) the mass of ponderable matter? It could not. In light of the above discussion, we must ask the question: Does Einstein’s Relativistic Mass even exist?

**B.
Does Einstein’s Relativistic Mass Exist?**

In early 1906, German scientist, Max Planck, showed that with a different definition of force (vis. the rate of change of momentum) Einstein’s equations (from which he derived transverse mass) could be written in a different form. From this different form for Einstein’s equations, Planck also derived a different equation for transverse mass:[20]

m_{r} = m_{r}Y_{u}
= m_{0}(1 – u^{2}/*c*^{2}) ^{–˝}

(Jammer, 2000, pp. 43 – 44)

During the period 1909 – 1912, in order to demonstrate that the relativistic formulas for mass and momentum could be derived from mechanics principles, as well as electromagnetic principles, American mathematical physicist Richard Tolman (1881 - 1948) invented a series of relativistic thought experiments wherein identical bodies collided. (Jammer, 1961, pp. 161 – 162) He applied the mechanics principles of conservation of mass and momentum, and Einstein’s relativistic addition theorem of velocities to such thought experiments, and derived the same equation for transverse mass as Planck did.[21] (Jammer, 2000, p. 46)

There is little doubt that Planck’s derivations, Tolman’s method of derivation, and Jammer’s derivations are mathematically correct and internally consistent with Einstein’s theories and formulas. The only real questions are: Do any of these relativistic derivations, equations and computations mean anything? Does Einstein’s mathematical Relativistic Mass have any relevance to reality? Does Relativistic Momentum derived from Relativistic Mass have any empirical meaning? Is there any empirical evidence that ponderable inertial mass is velocity-dependent?

First of all, we must
remember that Einstein was not just asserting that mass was velocity dependent,
but rather he was asserting that it was __relative velocity__ dependent. One must then ask the question: What does relative velocity have to do with
anything? Every co-moving body in the
Cosmos has a relative velocity with respect to every other co-moving body. But very few of such relative velocities have
any relevant meaning.

According to Einstein’s Special Theory, the
measurement of the magnitude of the mass of a body depends upon the relative
motion of the observer “with respect to the body of reference chosen in the
particular case.”[22] (Einstein, *Relativity*, p. 60) This means that the measured mass of a body
will depend upon which body of reference is __chosen__ and which observer is
doing the measuring with respect to the relative motion in the particular
case. In other words, according to
Einstein, the same ponderable inertial mass of a material body can __vary__
from m_{0} to a magnitude approaching infinity in each reference frame
depending upon who is doing the measuring.

How does the chosen body of reference know that it
has been chosen by an observer, and by which observer? According to Einstein, every body in the
Cosmos has an infinite number of different mass values depending upon which infinite
observer is doing the measuring? If the observer
doing the choosing of the body of reference changes his mind and chooses a
different body of reference, will the magnitude of the body’s mass that is
being measured __instantaneously__ change to a different magnitude of mass? How does the mass of just one co-moving body
(i.e. the chosen body of reference) increase the mass of just one other
co-moving body to the exclusion of all of the others? By what process does this selective increase
of mass occur, and how does it occur at a distance? Does Einstein’s Relativistic Mass concept
have any real or physical meaning with respect to anything? The answer is no.

Secondly, one must ask the question: What relevance does electromagnetic mass,
which is nothing more than an electromagnetic resistance or inertia, have to do
with the material mass of ponderable bodies?
Einstein’s attempts to turn an electromagnetic resistance and its
related experiments (by Kaufmann and others) into the ponderable mass of a
material body may have fooled those who wanted to be fooled, but they do not
fool the author. Of course, the relative
velocity of an electromagnetic resistance has nothing to do with a ponderable
mass.[23] For this reason alone, Einstein’s contrived *ad hoc* concept of Relativistic Mass has
no empirical validity.

Thirdly, D’Abro described Einstein’s concept of Relativistic Mass, and its above described problems, in the following manner:

“According to Einstein,
the electron increases in mass only in so far as it is in __relative motion__
with respect to the observer. Were the
observer to be attached to the flying electron no increase in mass would exist;
it would be the electron left behind which would now __appear__ to have
suffered the increase. Thus mass follows
distance, duration and electromagnetic field in being __a relative__ having __no
definite magnitude__ of itself and being essentially dependent on the
conditions of __observation__.”
(D’Abro, 1950, p. 160)

Does any of this description make any empirical sense? Of course not.

Goldberg also made the following insightful comments about Einstein’s illusionary concept of Relativistic Mass:

“We must consider the
measurement of mass within the special theory of relativity from two different __perspectives__,
one in which the mass is at rest with respect to us, and one in which the mass
is moving at a high rate of speed relative to us.”[24] (Goldberg, p. 143)

“In the Einstein
theory…the increase in mass had nothing to do with a specific theory of the
electron. In fact it derived only from
the __measurements of lengths and times__ and was a kinematic result.”[25] (*Id*.,
p. 141)

“Does the mass of
objects moving with respect to the observer who is measuring __actually__
increase? Within the theory of
relativity this question has __no meaning__.
We might coin a phrase: ‘__Actually
is as actually measures__.’”[26] (*Id*.,
p. 147)

“For __as with all
other parameters__ that are treated within the theory of relativity, the
change in mass says nothing essential about the body itself, but results as an __artifact
of the way distances and times are measured__ for the same events by
different inertial observers.”[27] (*Id*.

In other words, the mathematical illusions which result from the Lorentz transformations and Einstein’s other bizarre kinematic methods of measuring the magnitudes of physical phenomena (i.e. mass) do not actually change such physical magnitudes. The observer (measurer) who is moving away from the object or the physical phenomenon to be measured only mathematically perceives a different magnitude because of the unrealistic and unscientific way that Einstein requires distances and times to be measured in his Special Theory.

Based on the above, one might ask: Why did Einstein require such obviously distorted
measurements for his Special Theory,[28]
and why must we continue to utilize them especially if we know that they are
deformations of reality?[29] It becomes obvious that if Einstein had not
invented his radical, bizarre and empirically invalid methods of measuring
(described in Chapters 25 through 29), and had not applied them to mass, then
there never would have been a concept or artifact of

For many years after
1905, relativists (and especially particle physicists) defended Einstein’s
concept of Relativistic Mass on the ground that it was important “when dealing
with atomic and subatomic particles.”
(see Jammer, 2000, p. 54) Feynman
attempted to explain such importance, vis. that Relativistic Mass provides the
inertia in a particle accelerator which allows particle physicists to __interpret__
both the magnitude of the mass and the magnitude of the velocity of the
accelerated particle. Based on
Relativistic Mass, Feynman conjectured that when a force constantly acts on the
mass of a body, the body keeps picking up momentum rather than speed. This Relativistic Momentum continually
increases because the Relativistic Mass is increasing. However, as the mass approaches velocity *c*
there is practically no change of velocity, but Relativistic Momentum continues
to increase toward infinity. (Feynman,
1963, p. 15-9) In Feynman’s own words:

“Whenever a force
produces very little change in the velocity of a body, we say that the body has
a great deal of __inertia__, and that is exactly what our formula for
relativistic mass says—it says that the inertia is very great when v is nearly
as great as *c*.[31]

“As an example of this
effect, to deflect the high speed electrons in the synchrotron…, we need a
magnetic field that is 2000 times stronger than would be expected on the basis
of _{i} should be 2000 times m_{0} means that…v differs from *c*
by one part in 8,000,000…[32]

“Whenever electrons are
going that fast their masses are enormous, but their speed cannot exceed the
speed of light.”[33] (*Id*.

The increase of a particle’s or a
body’s rest mass with velocity, or with relative velocity, has never been
empirically demonstrated on a macro level: at speeds that are small compared to *c* this conjecture is not even
theoretically detectible. (see Sobel, p.
206) In a modern particle accelerator, a
particle is __interpreted__ in accordance with Special Relativity to have “a
speed of more than 99.99999999 percent of the speed of light.” (*Id*.,
p. 252, F.N. 6) However, without Special
Relativity a particle can have no interpretation of its velocity or its mass,
whatsoever. Since we have already
demonstrated that every concept of Special Relativity is *ad hoc*, an illusion, and empirically meaningless, why should we
have __any__ faith at all in such relativistic interpretations on any
level: micro or macro?

Let us pause for a moment from discussing all of these theories, equations, experiments and their relativistic interpretations, in order to determine what we are really talking about and what we are really attempting to demonstrate. Dingle asked: “What do we mean when we speak of the mass of an electron?” (Dingle, 1972, p. 141) He answered:

“We certainly do not put
an electron in a balance-pan and compare it with weights in the other pan. We could not do so because not only can we
not capture an electron but also __we do not know what it is__. A hundred years ago the word denoted a rather
vaguely conceived unit of electricity of unknown character. By the end of the nineteenth century it
seemed to have been definitely revealed as a particle of negative electricity
with measurable properties of the kind familiar in ordinary matter, but thirty
years later it was found to possess undeniably wave-like characteristics. The idea then arose that it was a sort of
mist of electricity, and Eddington probably gave it the most candid description
as ‘something unknown doing we don’t know what’. We are no wiser today; nevertheless, we speak
of the mass of an electron as though it were equivalent to the mass of a lump
of lead.” (*Id*., pp. 141 – 142)

Dingle then asked the
question: “What, then, can we mean when
we say that special relativity receives __confirmation__ from the
verification of its prediction that the mass of a body increases with its
velocity?” (*Id*., p. 142)

“What we confirm by the
experiments (i.e. by the observations and our inferences from them) is that the
whole __complex of conceptions__ that yields the __highly metaphorical ‘mass’
and ‘velocity’__ hangs together __if we include special relativity__ (or
Lorentz’s theory) as a part of it.”[34] (*Id*.

Because Special Relativity is an integral part of that complex of
conceptions, such a ‘confirmation’ “proves nothing at all. It is like claiming, as a proof that a man
always speaks the truth, the fact that he says he does.” (*Id*.

It becomes obvious that
the mass of an electron, its increase with velocity, and even the velocity
itself are merely speculations, metaphors and interpretations of experiments
based largely upon relativistic equations for mass, momentum, force and energy
and upon Einstein’s other relativistic concepts. What else would one expect for a result,
other than a ‘__self confirmation__’ of Special Relativity?

Let us now do a little
theorizing, speculating and interpreting of our own. All of the above theories and experiments that
deal with electrons being accelerated in an electromagnetic field and which
result in an ‘apparent’ increase of mass with velocity, sounds a great deal
like the __electromagnetic mass__ theories and experiments that occurred
just before Einstein wrote his Special Theory in 1905. (Chapter 17)
But, again, it later turned out that the apparent electromagnetic mass
was only the resistance of the electromagnetic field acting upon the electron
moving through it. This resistance had
been interpreted as a mass so that the equation F = ma could remain valid. However, it was really just a form of
‘electromagnetic __inertia__’ masquerading as a mass, and Euler’s equation F
= ma should have been modified to F = (m – R)a, or the equivalent, in order to correctly
account for the resistance (R).

Now, factor in Feynman’s
analogy of a force which “produces very little change in the velocity of a
body; we say that the body has a great deal of inertia.” If the ‘apparent Relativistic Mass’ in such
high-energy particle experiments is instead __re-interpreted__ as an
electromagnetic resistance (or inertia as J. J. Thompson called it), then all
of such high-energy particle experiments which supposedly confirm Relativistic
Dynamics (the Relativistic Mass of a particle, its relativistic velocity and its
relativistic energy) would instead confirm the meaningless new
interpretation. The modified classical formula
F = (m – R)a would also describe this new interpretation.

Some relativists still
defend Relativistic Mass on heuristic or aesthetic grounds, i.e. “it paints a
picture of nature that is beautiful in its simplicity.” (Jammer, 2000, p. 55) However, others outright “reject the
legitimacy of m_{r}” and find it “objectionable that the mass of a
particle decreases or increases for __no physical reason__,” or find it “unreasonable…that
the mass of a particle…should depend on purely geometrical details such as the
spatial direction of the force…” (*Id*.,
pp. 53 – 54) Some even “reject m_{r},
on the grounds that it gives the impression that the effects of relativity are
due to ‘something happening’ to the particle, whereas they are of course due to
the properties of space-time.”[35] (*Id*., pp. 54, 55) Still others find it ‘misleading’ and ‘not
necessary’ at all. (*Id*., p. 54)

Jammer concluded that
“the general trend, especially in the literature on elementary particle
physics, is toward the elimination of m_{r}” entirely.[36]
(Jammer, 2000, p. 55) The “most vigorous
campaign ever waged against the concept of relativistic mass” began in 1989
when prominent Russian particle physicist Lev Okun emphatically declared that:

“in the modern language
of relativity there is only one mass, the Newtonian mass m, which __does not
vary with velocity__,” and “there is only one mass in physics which __does
not depend on the reference frame__.”[37] (*Id*., p. 51)

Relativistic Mass cannot exist for many other
reasons. For example, it depends upon
Einstein’s Lorentz transformations, which we have demonstrated to be *ad hoc*
and empirically meaningless in Chapter 27.
It also depends upon all of Einstein’s fundamental postulates and his
relativistic concepts of kinematics, all of which we have demonstrated to be *ad hoc* and empirically meaningless. (see Chapters 21 through 29) In addition, remember the *ad hoc* reason why we began this
discussion of Relativistic Mass:
Einstein needed to arbitrarily characterize all of the phenomena
involved with classical mechanics, including length, time, velocity and mass,
so that they could be considered to be relative velocity dependent in order
that they would be __consistent__ with his impossible second postulate
concerning the absolutely constant velocity of light at *c* and with the Lorentz transformations.

If Relativistic Mass does not exist, is not empirically
valid, and the only remaining mass is classical inertial mass, this is yet
another huge inconsistency and contradiction to Einstein’s entire Special
Theory. *Inter alia*, the natural law of mass would, therefore, not be mathematically
covariant with respect to Lorentz transformations. Remember Einstein’s edict described in
Chapter 27:

“General laws of nature are co-variant with respect to Lorentz transformations…This is a definite mathematical condition that the theory of relativity demands of a natural law…

“If a general law of
nature were to be found which did not satisfy this condition, then at least one
of the two fundamental assumptions of the theory would have been
disproved.” (Einstein, *Relativity*,
p. 48)

Well, we have now found yet another law of nature which does not satisfy Einstein’s requirement of co-variance. That natural law is mass.

If mass is not mathematically covariant, then neither
are the other concepts of Relativistic Dynamics: Relativistic Momentum, Relativistic Force, Relativistic
Energy, Relativistic Acceleration, and E_{0} = m_{0}*c*^{2}, which also depend upon Relativistic
Mass and relative velocity. Thus, the *ad hoc* and artificial concepts of
Relativistic Dynamics and Relativistic Mechanics become things of the past. Ultimately, Einstein’s entire relativistic
house of cards collapses completely.

**Relativistic Momentum. A Most Revealing Section!**

In Newtonian mechanics, the law of force F was sometimes described by the
rate of change of momentum, F = d(mv)/dt, where mass m was the constant
inertial mass. (Feynman, 1963, p. 15-8)

However, after 1905, Einstein and his relativistic followers decided that
when theoretically viewed from two different inertial reference frames and
measured by his relativistic kinematics, the magnitude of momentum was not
conserved in both reference frames and that this violated Einstein’s principle
of relativity.[38] Resnick demonstrated how this
non-conservation of momentum was contrived.
In a thought experiment, Resnick showed that when two identical billiard
balls (each with the same inertial mass and velocity) collide in a perfectly
elastic collision, that momentum is conserved for the observer situated in the
same inertial system S as the collision, which observer makes proper physical
measurements of such collision.[39] (see Figure 31.3A) Resnick then Lorentz transformed the initial
and final velocities of such collision to a distant inertial reference system
S' using Einstein’s relativistic composition of velocity transformations. (see Chapter 29) This Lorentz transformation procedure, of
course, mathematically changed and distorted all of the relevant magnitudes of
the collision which was performed in system S so that momentum of such
collision would not __appear__ to be conserved for the observer in S'. (see Figure 31.3B) Thereafter, Resnick decided that the observer
in S' “will conclude [from the distorted collision viewed in S'] that momentum
is not conserved,” and that this violated Einstein’s principle of relativity.[40] (Resnick, 1992, p. 482)

For this reason, Resnick stated that “if we are to retain the
conservation of momentum as a general law consistent with Einstein’s first
postulate, we must find a __new definition of momentum__.”[41] (*Id*.*Id*.

Not surprisingly, this new relativistic definition or formula for
momentum turned out to be p = mv = m_{0}v/√1 – v^{2}/*c*^{2}. (see Feynman, 1963, p. 15-8) “Momentum is still given by mv,” but (stated
Feynman) the new mass m in such formula for Relativistic Momentum is Einstein’s
velocity dependant Relativistic Mass, m_{0.}[43] (*Id*.*Id*.

At the end of his article on Relativistic Momentum, Resnick further insulted our intelligence. He claimed that the above relativistic formula for momentum was in exact agreement with experimental data collected from high energy linear accelerators, which when plotted showed a curve where the assumed momenta of electrons is a function of their assumed velocity.[44] (see Figure 31.3C) In the process, however, Resnick forgot to inform us that the assumptions of momentum and velocity for such electrons which resulted in such curve had been determined solely by interpretations based on and consistent with the concepts of Special Relativity. Therefore, all that such curve really attempted to confirm was that certain concepts of Special Relativity (i.e. the Relativistic Addition of Velocities and Time Dilation) were consistent with and mathematically confirmed another concept of Special Relativity (i.e. Relativistic Momentum and its associated velocities). In effect, that Special Relativity confirmed itself.

How stupid do the relativists think we are? Resnick took a perfectly valid terrestrial
collision experiment which conserved momentum, and then Lorentz transformed it
to another distant reference frame which, of course, changed all of its
magnitudes and distorted such collision so that momentum would no longer appear
to be conserved when viewed by S'. (Figures 31.3A & 31.3B) He then decided to scrap the perfectly
correct Newtonian law of momentum mv and replace it with an *ad hoc* relativistic law for
momentum. When the distorted collision
experiment in S' was then mathematically compared with such relativistic law of
momentum, they were of course consistent for any inertial reference system
moving at any relative velocity v. Then
Feynman explained and validated this very obvious mathematical subterfuge.

Are the relativists now so arrogant as to believe that no one else on the planet has a brain; that no one else can see through their artificial and transparent mathematical deceptions? After all, the relativists artificially caused observer S' to falsely believe that momentum had not been conserved during the collision in system S, by intentionally sending observer S' distorted magnitudes for such collision by means of Lorentz transformations. What result other than relativistic consistency should any such relativist expect?[45]

It turns out that Relativistic Momentum is not an isolated example of
this obvious subterfuge. On the
contrary, __all__ Lorentz transformed physical phenomena from one reference
frame to another also result in substantially similar transparent mathematical
deceptions. Therefore, all of the dozens
upon dozens of distorted relativistic concepts and distorted mathematical consequences
that result from these Lorentz transformation processes are completely *ad hoc*, artificial and meaningless. Is this science? Of course not; it is pseudo science.

In one of his
lectures, Feynman attempted to demonstrate that Einstein’s equations for mass
and momentum were valid and correct.
Feynman stated that the Newtonian law of force “is the rate of change of
momentum, or F = d(mv)/dt,” where mv is momentum. (Feynman, 1963, p. 15-9) “In Newtonian mechanics [momentum] is
proportional to the speed…[and it increases until the body] goes faster than
light.”[46] (*Id*.

In a modern synchrotron, if we theoretically accelerate a particle with a tremendous electric current we should increase the charge of the particle to many times the charge of a natural electron in order to greatly increase its velocity. If the path of this highly charged particle is then deflected by a magnetic field which is 2,000 times stronger than normal, this super strong magnetic field should apply 2,000 times the normal electromagnetic resistance to the velocity of the particle.

If we analyze this scenario with the unmodified Newtonian equation for force, this much greater electromagnetic resistance R must be accounted for somewhere, and the only logical place is an increase in the particle’s mass m. On the other hand, if this scenario is analyzed with the properly modified Newtonian equation for force, F = d(m[v – R])/d/t, then the very great electromagnetic resistance can be accounted for by the R and the lesser velocity v, and the mass m of the particle will remain constant.[48]

Feynman also stated that Einstein’s relativistic law of momentum is

p = *m*v
= __ m_{0}v__

√1
– v^{2}/*c*^{2},

“where the ‘rest mass’ *m*_{0} represents the mass of a
body that is not moving” and *m* is
“the mass of a body [which] increases with velocity.” (*Id*.,
pp. 15-1 and 15-9) Feynman then went on
to conjecture:

“In relativity, the body keeps
picking up, not speed, but momentum, which can continually increase __because
the mass is increasing__. After a
while there is practically no acceleration in the sense of a change of
velocity, but the momentum continues to increase.” (Feynman, 1963, p. 15-9)

“But when *v* is almost equal to *c*,
the square-root expression approaches zero, and the momentum therefore goes
toward infinity.” (*Id*.

“[At this point] the mass of the
electrons in the synchrotron is 2000 times as great as their normal mass, and
is as great as that of a proton! That
means that…the electrons are getting pretty close to the speed of light.” (*Id*.

“When the electrons are going that
fast their __masses are enormous__, but their speed cannot exceed the speed
of light.” (*Id*.

The problem with this scenario is that Feynman has again forgotten the resistance R. In the synchrotron, if we accelerate a particle with a tremendous electric current in order to increase its velocity, we should increase the charge of the particle to many times the charge of a natural electron. If this very highly charged particle is then deflected by a magnetic field which is 2000 times stronger than normal, it should apply 2000 times the normal electromagnetic resistance R to the velocity of the particle.

If
we analyze this scenario with Einstein’s unmodified equation for momentum, this
much greater electromagnetic resistance R must be accounted for somewhere, and
the only logical place is an increase in the mass *m* of the particle. On the
other hand, if this scenario is analyzed with Einstein’s properly modified
equation for momentum

p = *m(*v–R)
= __m___{0}(v–R)

√1
– (v-R)^{2}/*c*^{2}

then the very great electromagnetic
resistance can be accounted for by the R and the lesser velocity v, and the
mass *m* of the particle will remain
constant. Including the R in the above
middle equation solves the empirical problem.
Therefore, there is no reason for Einstein’s relativistic equations for
mass or momentum.

The primary reason that the author is writing this treatise is so that
his readers will ultimately realize that all of Einstein’s Special Theory of
Relativity, all of its bizarre relativistic concepts and its distorted mathematical
consequences, are nothing more than a huge collection of transparent
mathematical deceptions and their *ad hoc*
results. In other words, Einstein’s
Special Theory in its entirety was simply a monumental and malignant
mathematical hoax, cleverly and diabolically conceived for only one primary
meaningless purpose: to mathematically
attempt to demonstrate that Einstein’s impossible absolutely constant velocity
of light at *c* relative to all
inertial reference frames moving linearly at v should be considered to be a
general law of nature. (see Chapter 21) These distortions, subterfuges, and deceptions
which have distorted most of physics, along with Einstein’s entire *ad hoc* Special Theory, must now be
discarded.

**D. Relativistic Kinetic Energy**

The concept of energy was developed
during the 19^{th} century.
During the early 1800s, heat (a form of energy also known as thermal
energy) was considered to be “a material substance, a fluid called *caloric*.” (Goldberg, p. 63) After this inauspicious false start, great
progress ensued. However, it was not
until the end of the 19^{th} century that “the concept of energy, which
is nothing more than the ability to do work,” became fully developed and
generalized.[49] (*Id*.,
p. 414)

The concept of the ‘conservation of
energy’ was developed in parallel with the concept of energy. It states that “in any isolated system, the
total energy remains constant.” Whereas,
energy may be converted from one form to another, when all processes are
accounted for there are no net gains or losses.[50] (*Id*.

“At any time, the energy of the system is given by the kinetic energy of motion, [any electromagnetic energy], the various forms of potential energy that might be found in the system [such as gravitational energy], and the heat being generated as a result of the interaction of the various parts.”[51] (Goldberg, p. 414)

In classical physics, kinetic energy, K = ˝mv^{2}, was defined as
the energy of motion of a body, where m was the body’s inertial mass.[52] (Miller, p. 313) Resnick defined the classical kinetic energy
of a particle in motion as “the work done by an external force in increasing
the speed of the particle from zero to some value of u.” (Resnick, 1968, p. 120) It is axiomatic that the work done by a body’s
motion is equal to the change in its kinetic energy. Therefore, “should the work be zero whatever
kinetic energy the body has would be unchanged.”[53] (Goldberg, p. 402)

With this brief
background in place, let us now return to Einstein. In the second half of § 10 of his Special
Theory, Einstein deduced “the kinetic energy of the electron” from his *ad hoc* equations and rationalizations
concerning

“If an electron moves
from rest…under the action of an electrostatic force…as the electron is to be
slowly accelerated…the __energy withdrawn from the electrostatic field__
must be put down as equal to the __energy of motion W__ of the electron…we
therefore obtain W = m*c*^{2}[1/√1 – v^{2}/*c*^{2}
–1].”[54] (*Id*.

“Thus, when v = *c*,
W becomes infinite. Velocities greater
than that of light have—as in our previous results—no possibility of
existence.”[55] (*Id*., pp. 63 – 64)

If the energy withdrawn from the electrostatic field
by the electron’s motion through it results in Einstein’s above equation for
velocity dependent relativistic kinetic energy, then the mass m in such
equation must be an ‘electromagnetic mass.’
In other words, it must be the resistance of the electrostatic field
(medium) to the motion of the electron through it, or an ‘electromagnetic
inertia.’ In effect, the mass m in the
above equation must be Einstein’s relative velocity dependent

The author asserts the following: When energy creates a force which is applied to do work, i.e. to accelerate the mass m of a body to velocity v, the energy applied is conserved in the greater kinetic energy of motion and momentum mv of the mass of the more rapidly moving body which has the potential to do more work than before. But this process does not change or increase the body’s mass (the number of atoms which constitute the material body or their weight). (see Chapter 32)

It is not difficult to see in Einstein’s above equation
for kinetic energy the origin of the equation:
E = m*c*^{2}. It
follows from the above discussion that any assertion of a relationship between
mass and energy in Einstein’s September 1905e paper was really that rest energy
E_{0} equals electromagnetic mass m_{0} (a resistance) times *c*^{2}. Rather than being a revolutionary empirical
assertion of equivalence, E_{0} = m_{0}*c*^{2} was merely an *ad
hoc*, empirically invalid and meaningless relativistic conjecture by
Einstein. (Chapter 32)

Immediately thereafter, “from his theory for the
motion of an electron in an electromagnetic field” (Miller, p. 313), and from his
derivation of Relativistic Mass, Einstein conjectured that: “This expression for the kinetic energy must
also, by virtue of the argument stated above, apply to __ponderable masses__
as well.”[57] (Einstein, 1905d [Dover, 1952, p. 64]) Any empirical skeptic would immediately
scream: WHY?

Einstein then further conjectured the existence of three resulting ‘properties’ of the motion of the electron:

First: “It is possible by our theory to determine
the __velocity of the electron__ from the ratio of the __magnetic power of
deflexion__ A_{m} to the electric power of deflexion A_{e},
for any velocity, by applying the law A_{m}/A_{e} = v/*c*.”[58] (*Id*.

This so-called property of determining the velocity of a deflected electron in a magnetic field based on a deflection ratio was merely a mathematical description of what theoretically occurred in Kaufmann’s 1901 – 1902 electron deflection experiments.[59] (see Goldberg, p. 134) Kaufmann’s method of measuring the magnetic deflections of electrons (greatly refined and improved) is now the primary method that particle physicists use to interpret the velocities and masses of electrons and other particles in their particle accelerators.

However, we must now ask
the questions: How valid is such
relativistic method for determining the interpreted tremendous velocities of
magnetic deflected masses of atomic particles in particle accelerators, if such
masses are really only electromagnetic resistances and electromagnetic inertia
masquerading as a ponderable mass; and if Einstein’s relativistic formula was
derived in such an *ad hoc* and
artificial manner? Could it be that
particle physicists are only theoretically accelerating and virtually deflecting
electromagnetic resistances and electromagnetic inertia, and that the resulting
photographed ‘tracks’ (interpreted as new particles and their interactions) are
really meaningless? Could it be that
such interpreted velocities are also only theoretical, virtual and meaningless? (see Chapters 34 and 35)

The details for Einstein’s second conjectured ‘property’
of the electron’s motion (the relationship between the potential difference
between the momentum traversed by the electron and its acquired velocity v)
“were the same as the ones that led to” his relativistic equation for kinetic
energy.[60] (Miller, p. 314; see Einstein, 1905d [Dover,
1952, p. 64]) Einstein’s third
conjectured ‘property’ predicted “that an electron injected normally into a
constant magnetic field executed circular motion with a radius that was a
function of its velocity.”[61] (Miller, p. 314; Einstein, 1905d [Dover,
1952, p. 64]) Einstein ended § 10 of his
Special Theory with his final mathematical conjecture: “These [last] three relationships are a
complete expression for the laws according to which, by the theory here
advanced, the electron must move.”[62] (*Id*.,
pp. 64 – 65)

Miller concluded that
the last three conjectures (or relationships) followed from Einstein’s
Relativity of Simultaneity (Miller, p. 314), which we have demonstrated is
empirically invalid. (see Chapters 25,
26 and 28) Miller was also baffled by
them because: 1) “the ratio A_{m}/A_{e}
[v/*c*] seemed to be __indigenous__
to any theory based on Lorentz’s force equation;” and 2) Einstein’s last two conjectures directly
contradicted “Kaufmann’s (1901 – 1903) experiments on injecting electrons
normally into parallel electric and magnetic fields.” (*Id*.

By analogy to his discussion of momentum (described in Section C of this chapter and as illustrated by the collisions in Figures 31.3A and 31.3B), Resnick attempted to show why “special relativity gives us a different approach to kinetic energy.” (Resnick, 1992, p. 483) Resnick asserted that:

“if we use the classical
expression ˝mv^{2}, the collision [which conserved kinetic energy in
the S frame] does not conserve kinetic energy in the S' frame…this situation
violates the relativity of kinetic energy if we are to preserve the law of
conservation of energy and the relativity postulate.” (*Id*.

Resnick also asserted
that the classical formula, K = ˝mv^{2}, which allows kinetic energy to
increase without limit, implies that velocity likewise may increase without
limit, thereby violating Einstein’s second postulate which demands that a
material body may not exceed the speed of light at *c*. (*Id*., pp. 483 – 484; also see French, pp. 6 – 7)

“We must therefore find
a way to redefine kinetic energy, so that the kinetic energy of a particle can
be increased without limit while its speed remains less than *c*.”
(Resnick, 1992, p. 484)

The relativistic formula for kinetic energy turns out to be the relative
velocity dependent quantity K = m_{0}*c*^{2}/√1 – v^{2}/*c*^{2} – m_{0}*c*^{2}, which reduces to ˝m_{0}*c*^{2} when speeds are much lower
than c. Resnick stated that such
relativistic formula can also be expressed as K = E – E_{0}, where E is
the total relativistic energy E = m*c*^{2}/√1
– v^{2}/*c*^{2}, and
rest energy E_{0} is E_{0} = m_{0}*c*^{2}.[63] (*Id*.*Id*.

At this point, Resnick
returned to his collision thought experiment in an attempt to prove his
conjecture that classical kinetic energy (K = ˝mv^{2}) in the S frame
(Figure 31.3A) was not conserved when Lorentz transformed to the S' frame. First, Resnick used the velocities given in Figure 31.3B for the S'
frame, and showed that according to observer S', the kinetic energies before
and after the collision (computed according to the classical K = ˝mv^{2})
produce two different quantities for K; thus the collision apparently does not
conserve classical kinetic energy in S'.
(*Id*., p. 483) Secondly, using the relativistic formula for
kinetic energy, K = m_{0}*c*^{2}/√1
– v^{2}/*c*^{2} – m_{0}*c*^{2}, Resnick showed that relativistic
kinetic energy is conserved in the S' frame of the collision.[64]

Again, as with
Relativistic Momentum, the author must ask the question: How stupid do the relativists think we
are? Resnick took a perfectly valid
collision experiment which conserved kinetic energy in the S frame using the
classical equation K = ˝mv^{2}.
(Figure 31.3A) He then Lorentz transformed the initial and
final velocities of such collision to another distant reference frame S', which
of course changed all of its magnitudes and distorted such collision so that
kinetic energy would no longer appear to be conserved when viewed by S'. (Figure 31.3B) He then decided to scrap the perfectly
correct classical law of kinetic energy, K = ˝mv^{2}, and to replace it
with an *ad hoc* relativistic formula
for kinetic energy. When the distorted
collision experiment in S' was then mathematically compared with such
relativistic formula for kinetic energy, they were of course consistent for any
inertial reference system moving at any relative velocity of v. What a coincidence.[65]

Are the relativists now so blatantly arrogant as to believe that on one else can see through this obvious mathematical subterfuge…this artificial and transparent mathematical deception? After all, Resnick artificially caused observer S' to falsely believe that kinetic energy had not been conserved during the collision in system S by intentionally sending observer S' distorted magnitudes for such collision by means of Lorentz transformations. Should it be a shock to anyone that the transformed and now distorted collision in system S' appeared not to conserve kinetic energy? What result other than relativistic consistency should Resnick expect in S'? Again, this is not science; it is pseudoscience! In fact, Relativistic Energy, like Relativistic Mass and Relativistic Momentum, rises to the status of a monumental and diabolical hoax.

It is patently obvious to
any fair-minded person that if the same collision experiment had been conducted
__separately__ in accordance with the classical formula K = ˝mv^{2}
in two different reference frames, kinetic energy would have been conserved in
each frame. It is only when the Lorentz
transformations are misapplied to distort the situation that classical kinetic
energy can never be conserved.[66] Again, all of these mathematical subterfuges,
deceptions and distortions, along with Einstein’s entire *ad hoc* Special Theory, must immediately be discarded onto the
scientific trash pile of outlandish myths.

**E.
Relativistic Force, Relativistic Acceleration, etc.**

In Newtonian mechanics, the force F in

F = d/dt(p) = d/dt(m_{0}u/√1
– v^{2}/*c*^{2}).”

(Resnick, 1968, p. 119) This new
expression of force “is not equivalent to writing F = *m*a…[we do not] simply
multiply the acceleration by the relativistic mass.”[67] (*Id*., p. 120)

Resnick then conjectured
that this new relativistic definition of force correctly describes the motion
of high-energy charged particles in a particle accelerator where F is
interpreted to be the Lorentz electromagnetic force q(E = u x B). With respect to such Lorentz force equation,
E is the electric field, B is the magnetic field, u is the particle velocity
(all measured in the same reference frame), and q is the constant invariant electric
charge of the particle.[68] (*Id*.)
More *ad hoc* relativistic
conjectures.

Resnick also derived
from the relativistic equation for force a relativistic equation for
acceleration that, in general, states that “acceleration a is not parallel to
the force in relativity.” (Resnick,
1968, p. 124) The two exceptions
are: 1) “when F and a are parallel to
the velocity u” (the mass is then called ‘longitudinal mass’); and 2) “when F and a are perpendicular to the
velocity u” (the formula for the mass is then called ‘transverse mass’). (*Id*., p. 125) More meaningless bootstrap conjectures.

On the other hand, if the *ad hoc* concepts of Relativistic Mass and Relativistic Momentum are
empirically invalid and meaningless, as we have just demonstrated, then so also
must be such formula for Relativistic Force which incorporates such invalid and
meaningless relativistic concepts. It
follows that any formula for Relativistic Acceleration which is produced by
such Relativistic Force must also suffer the same fate.

Regardless of Einstein’s conjectures and his follower’s derivations,
computations and further conjectures concerning relativistic force and
relativistic acceleration, these concepts cannot be valid for all of the
reasons set forth in the previous chapters of this treatise and the previous
sections on Relativistic Mass, Relativistic Momentum and Relativistic Energy. They are based on the empirically invalid
Lorentz transformations (Chapter 27), and the invalid concepts of relative
velocity dependent Relativistic Mass, and on all of the other *ad hoc*,
artificial, and meaningless concepts that constitute Einstein’s Special Theory.

All of Resnick’s conjectures contained in this chapter are perfect examples of the way that all relativists attempt to bootstrap their way from one false relativistic concept to another. All of Resnick’s mathematics and rationalizations are neat and convincing within the framework of Special Relativity, except for one thing: they are all based on false assumptions, and are all logically and empirically incorrect. [69]

All of the so-called experimental confirmations of Relativistic mass and Relativistic Dynamics only deal with charged theoretical particles (i.e. electrons) in high-energy particle accelerators, and their results are all interpretations based on Einstein’s relativistic formulae. (see Zhang, p. 233) One might ask, what relevance do circular relativistic interpretations of the theoretical electromagnetic resistances, energies and inertias of electrons have with respect to the ponderable masses of material bodies? What (if anything) do they really confirm?

By the 1920s, Einstein and his relativistic mathematical physicist
followers had become so bold that they began to conjecture all kinds of wild *ad hoc* ideas in order to expand Einstein’s
Special Theory. For example:

“Owing to the
general validity of the Lorentz-Einstein transformations, it becomes __permissible
to apply them to all manner of phenomena__.
__In this way__ it was found that temperature, pressure and many
other __physical magnitudes__ turned out to be relatives.” (D’Abro, 1950, p. 160)

In other words, all of such phenomena become relative velocity dependent relativistic concepts of physics. This unscientific process cannot be allowed to continue.

[1] The real
reason for this dilemma was that Einstein’s impossible concept of the
absolutely constant velocity of light at *c*
relative to everything was empirically invalid, as were his Lorentz
transformations. (see Chapters 21 and
27) Classical mechanics, though not
completely theoretically correct, was not the real culprit.

[2] This
conjecture was completely *ad hoc*, and
like Einstein’s many other *ad hoc*
conjectures, it never should have been made.

[3] Where
did Einstein get the *ad hoc* idea that
the magnitude of physical phenomena might be dependent upon relative
velocity? Possibly from Lorentz’s
transformation equations in his April 1904 treatise which asserted that the
constant velocity of light at *c* in
Michelson’s experiments was somehow dependent upon the velocity of the Earth
relative to the Sun and the ether.
However, we now know that this assertion was incorrect, because we now
know the real reasons for Michelson’s paradoxical null results, which have
nothing to do with any relative velocity dependent phenomena. (see Chapter 16) Possibly Einstein got such *ad hoc* idea from Kaufmann’s 1901 – 1902
experiments which asserted that electromagnetic mass varied depending upon the
velocity of an electron.

[4] This
equation appeared in Lorentz’s April 1904 treatise. (Jammer, 2000, p. 42) Such equation for Relativistic Mass may also
be written as: m = m_{0} /
√1 – v^{2}/*c*^{2}. (see Feynman, 1963, p. 15-1)

[5] Why was
Einstein so interested in keeping the electron __slowly__ accelerated? Probably so that when he conjectured that the
motion and mass of the electron should also apply to ponderable material
objects, the speed of such electron would appear to be within the normal range
of speeds for material terrestrial objects.
This might make such *ad hoc*
conjecture appear to be more credible.

[6] The word
‘ponderable’ means: ‘that can be __weighed__.’ (Webster’s Dictionary, p. 1049) Almost everything in Einstein’s Special Theory
before Section 10 dealt with a rigid or solid body as an irreducible
entity. But in § 10 Einstein switched
“to the notion of a *point* electron moving according to the kinematics
derived in Part I of the relativity paper.”
(Miller, p. 305)

[7] This statement means that at low speeds, the mass of the electron was substantially the same as the non-velocity dependent classical mass m.

[8] The
phrase, ‘as long as its motion is slow,’ also implied to Miller “that, as a
result of the __relativity of simultaneity__, we can expect certain changes
to occur in the mathematical formulation of this law”… m = F/a. (Miller, p. 308)

[9] According to the electron theory: “Conductors of electricity, for example silver or copper metal, contain electrons which are free to move through the metal under the influence of electrical forces. Electrons are the fundamental entities of electric charge. When they move, they constitute an electric current. Should the electron, in its motion, be in the vicinity of a magnetic field, a force should be exerted on the electron in a direction opposed to its motion. This type of force is referred to as electromagnetic inertia of the electron.” (Goldberg, p. 134)

[10] Again, this is what Abraham acknowledged in 1902: “the inertia of the electron originates in the electromagnetic field.” “The mass of the electron is of purely electromagnetic nature.” (Jammer, 1961, p. 151)

[11]
Einstein needed to obtain the same or similar values for longitudinal and
transverse mass for his Special Theory, as was previously obtained by Kaufmann,
Abraham and Lorentz, in order not to appear too *ad hoc*. Einstein appears to
contradict himself two paragraphs later when (instead of a pondermotive force)
he described the motion of the electron “under the action of an __electrostatic
force__” and “the energy withdrawn from the electrostatic field” by the
motion of the electron. (Einstein, 1905d
[

[12] The
‘ordinary point of view’ “was Abraham’s in which the electron’s mass was a __two-component
quantity__ that depended upon the orientation of the external forces and was __totally
electromagnetic in origin__.” (Miller,
p. 309)

[13] In
order to remain consistent with the rest of his Special Theory, the m in each
equation should have been m_{0}, the proper rest mass in system k.

[14]
According to Einstein, this force “followed from the relativity of
electromagnetic fields.” (Miller, p.
309) This concept was, of course, *ad
hoc*. Einstein considered the force
he used as equivalent to Lorentz’s force law, and he referred to Lorentz’s
derivation of it as a major achievement.
(Miller, pp. 309 – 310) For a
description of Lorentz’s electromagnetic force law see Resnick, 1968, p. 120.

[15] The
accelerations of the electron in the moving system k needed to be measured in
the stationary reference system K in order to obtain the Relativistic Mass,
because if measured in system k the mass would only be the proper rest mass m_{0}.

[16] Since
momentum becomes m_{0}v, the momentum of the particle likewise
theoretically increases toward infinity in Einstein’s Special Theory.

[17] This is further evidence for our conclusions in Chapter 27 that Einstein had read Lorentz’s April 1904 treatise well before he published his Special Theory, and that he copied many of Lorentz’s concepts in his Special Theory.

[18] This conversion of a material point into an electron was, of course, nothing more than Einstein’s imagination of hyperbole at work. Einstein’s ‘sense of the word’ electron was, of course, fantasy.

[19] As the author explained in Chapter 17, Euler’s formula (F = ma) should have been modified to

F = (m – R)a, or the equivalent, in order to account for the environmental resistances to motion (R), to show the correct force, mass and acceleration, and to prevent such resistances R from being mathematically characterized as increases in mass.

[20] In his
2000 book, entitled *Mass*, Jammer then
rewrote Planck’s scalar equation as a vector equation, redefined “force as the
(time) rate of change of momentum,” and derived the relativistic formula for
momentum: p = m_{0}Y_{u}U. (Jammer, 2000, p. 44) The symbol “Y_{u} stands for (1 – u^{2}/*c*^{2})^{-˝}.” (*Id*.,
p. 53)

[21]
Tolman’s method for deriving Relativistic Mass has generally been adopted by
the scientific community. (Jammer, 2000,
p. 46) In order to demonstrate the
internal consistency of Einstein’s relativistic mass concept, Jammer (in his
2000 book) also mathematically demonstrated that “the equation m = m_{0}Y_{u}
is a __direct consequence of the Lorentz transformation__.” (*Id*., pp. 49 – 50)

[22] As we
learned in Chapter 28, the only reason that motion effects such measurement is
because of Einstein’s 1905 methods of hand and eye measurements of coordinates,
where it is physically impossible to measure the front end and the rear end of
a moving rod, simultaneously. (see
Resnick, 1992), pp. 480 – 481) This is
not a very good reason to change all of mechanics and much of physics,
especially in the 21^{st} century when such hand and eye measurements
are completely obsolete.

[23] Even if
there was a ponderable mass that was dependent upon relative velocity this
would have violated the mechanical co-variance of Galileo’s principle of
relativity, which Einstein claimed he was attempting to reconcile with the
constant velocity of light at *c*. (see Chapters 19 and 24) Unless, of course, if we applied Einstein’s
empirically invalid kinematic measurements to the situation.

[24] But why
must we do this? Mass is not a telephone
pole which we perceive to have a different height if it is next to us and if it
is one hundred yards away. In the case
of the telephone pole, our __speed__ does not change our perspective and
perception of its height; only __distance__ does. Why is mass any different?

[25] Even
Born and Resnick admitted that Einstein’s concept of Length Contraction did not
result in a __physical shortening__ of a rigid rod. Such shortening was only __an illusion__
of coordinate measurement when __relative motion__ between the measurer and
the object to be measured was involved. __Illusions__
of shortening, etc., have no place in physics.
(see Chapters 26 and 28)

[26] These ludicrous comments have no meaning with respect to our telephone pole analogy. The telephone pole does not physically change in height just because we perceive it to by our eye measurements. Such measurements of an illusion cannot change reality. We might coin another phrase: “Actuality is as actuality measures reality, not an illusion.”

[27] This same type of artifact (i.e. an illusion) results from our eye measurements of a telephone pole at two different distances, but it is a meaningless artifact. Einstein’s ridiculous methods of measuring illusions cannot change physical reality.

[28] We
already know the answer to this question.
Einstein needed such distortions in order to construct his Special
Theory, to make his bizarre relativistic concepts appear mathematically
plausible, and above all to remain mathematically consistent with his
impossible absolutely constant velocity of light at *c* relative to everything.
(see Chapters 21 – 29)

[29] We must continue to use such distorted measurements only if we desire to continue to apply Einstein’s empirically invalid and meaningless Special Theory to physics.

[30] These conclusions also equally apply to Einstein’s other distorted measurements of length, time intervals, addition of velocities, etc., etc.

[31] What really causes this great increase in inertia? In a high-energy particle accelerator it is most likely the resistance of the electromagnetic field acting on the accelerated charged particles, i.e. electrons. In other words, it is nothing more than an electromagnetic mass (an electromagnetic resistance). (see Chapter 17)

[32] Feynman
assumed that he was dealing with the electron’s inertial mass m_{i};
but he was most likely only dealing with the electron’s electromagnetic mass
(or resistance). Remember Abraham’s
acknowledgement: “the mass of the
electron is of purely electromagnetic nature.”
(Jammer, 1961, p. 151)

[33] All of
these *ad hoc* interpretations by
Feynman are, of course, based solely upon Einstein’s Special Theory and his
concept of Relativistic Mass, which we have just demonstrated is a mathematical
illusion, a resistance, and does not physically exist as a material mass.

[34] This ‘complex of conceptions’ is none other than what we currently call ‘quantum mechanics,’ ‘particle physics,’ ‘quantum field theory,’ and ‘superstring theory.’ (see Chapters 34 and 35)

[35] This
statement is, of course, a direct admission that Relativistic Mass does not
empirically exist. In Chapter 33 we will
demonstrate that Minkowski’s *ad hoc*
Spacetime geometry is also empirically invalid and empirically
meaningless. Therefore, Jammer’s
conjectures that Spacetime has properties are also meaningless.

[36] On the
other hand, some textbooks still cling to the concept of

[37] If Relativistic Mass does not exist, then how do particle physicists determine the mass and the velocity of an accelerated particle? What happens to the remaining concepts of Relativistic Dynamics (momentum, force and energy) which are dependent upon Relativistic Mass? We shall soon answer these questions.

[38] The fiction that observer S' makes hand and eye coordinate measurements of the momentum of a collision in another frame of reference S is, of course, an absurdity.

[39] This is
exactly the way that momentum is __empirically__ demonstrated to be
conserved in a theoretically perfectly elastic collision anywhere on Earth.

[40] Obviously, a much more precise method of determining whether momentum is conserved in two different reference frames is to conduct the same collision experiment in each frame and properly measure the relevant magnitudes within each frame.

[41] Why
should we want the conservation of momentum to be consistent with Einstein’s
first postulate when we demonstrated in Chapter 24 that it was *ad hoc* and empirically invalid? It should be enough that such conservation of
momentum is consistent with Galileo’s Relativity and with the Galilean
transformation equations.

[42] In other words, we empirically know perfectly well from 200 years of experience on Earth that p = mv always works the same way, and that momentum is always conserved in a theoretically perfectly elastic collision (absent external forces).

[43] On the
other hand, if the new mass is relative velocity dependent Relativistic Mass m_{0},
then it follows: 1) that Relativistic
Momentum must also be relative velocity dependent, and 2) that Relativistic Momentum must be
empirically invalid and meaningless, because we know from the prior sections A
and B of this chapter that *ad hoc*
Relativistic Mass is empirically invalid, an illusion, and a myth.

[44] The applicable relativistic curve should have been the one shown as Figure 16.3B, not the one which Resnick displayed on Figure 31.3C, because it was a result of division (not multiplication) and the Lorentz transformations.

[45]
Relativistic Momentum cannot exist for many other reasons. For example, it depends upon Einstein’s two
fundamental postulates and his kinematic method of measuring, which we have
demonstrated to be artificial, illogical and empirically invalid in Chapters 21
and 29. It depends upon the validity and
existence of ‘electromagnetic mass,’ which we have demonstrated in Chapter 17
to be only an ‘apparent mass’ and in reality only an electromagnetic resistance
or inertia. It also depends upon the
existence of Relativistic Mass, which we have just demonstrated earlier in this
chapter to be a myth. Above all, it
depends upon Einstein’s Lorentz transformations, which we have demonstrated to
be *ad hoc* and meaningless in Chapter 27.

[46] This might be theoretically possible in empty space far from large gravitating bodies.

[47] Resistance comes in many forms, including: friction, colliding with air particles, the force of gravity, and electromagnetic resistance.

[48]
Nowhere, in any literature, can the author find any mention that any definition
of ‘inertial mass’ has included within it any __additional__ resistance of
any kind. Of course, we are not talking
about the concept of ‘electromagnetic mass,’ which in reality is nothing more
than an electromagnetic resistance R masquerading as a material inertial mass
m. (see Chapter 17)

[49] ‘Work’
W is generally defined in physics as “the product of the __force__ [acting]
on an object and the __distance__ the object moves in the direction of the
force.” (Goldberg, p. 405)

[50] “Rather
than losses or additions, there are only __conversions__ between potential,
chemical, mechanical, electrical, magnetic, light, sound and heat
energies.” (Goldberg, p. 64)

[51] The
final breakthrough for the concept of energy conservation took place in the
late 19^{th} century when it was ultimately realized that heat “was a
manifestation of the…interactions of the atoms and molecules that make up all
matter” (Goldberg, p. 64), and included friction and air resistance which were
all part of the isolated system. (*Id*., p. 414)

[52] Goldberg describes how the formula for kinetic energy K was arrived at and how this concept was developed. (Goldberg, pp. 400 – 413)

[53] In a theoretically perfectly elastic collision, “the net effect is that the kinetic energy after the collision is the same as before the collision.” (Goldberg, p. 404)

[54] One might ask: Why did Einstein use the symbol W for the kinetic energy of the electron, instead of the correct symbol K for kinetic energy? W is the symbol for work! The author’s only response is: Why did Einstein do anything that he did?

[55] Miller
points out that: “One of
Lorentz’s…assumptions [in his April 1904 thesis] was that the velocity of
material bodies could not exceed *c*…”
(Miller, p. 313) This is yet
another example of Einstein copying concepts from Lorentz’s April 1904
mathematical thesis. Nevertheless,
Einstein’s equations for kinetic energy do not __prove__ his *ad hoc* relativistic conjecture
concerning a maximum velocity.

[56] For this reason alone the above equation for kinetic energy cannot be empirically valid.

[57] Miller
stated that this “bold conjecture, provided __a basis__ for the previous one
(that the mass of all bodies behaves like the electron’s mass).” (Miller, p. 313) The author has had great difficulty in
finding such a __basis__, other than circular reasoning. It is true that both circular *ad hoc* conjectures acknowledge that
Relativistic Mass was really nothing more than an electromagnetic mass, an
electromagnetic resistance, and they both were mutually supportive. But circular reasoning is never a valid basis
for anything.

[58]
Einstein then conjectured what __theoretically__ occurs in a modern particle
accelerator: “This relationship may be
tested experimentally, since the velocity of the electron can be directly
measured, e.g. by means of rapidly oscillating electric and magnetic fields.” (Einstein, 1905d [

[59] In Kaufmann’s deflection experiments the very similar ratio was “the charge of the electron to its mass as a function of the electron’s speed…,” and it was “found that the ratio decreased as the speed of the electrons increased.” (Goldberg, p. 134)

[60] This conjecture also has similar implications for particle physics and other mathematical theories.

[61] This mathematical conjecture is a basis for interpreting the curvilinear cloud chamber tracks of assumed atomic particles to mean certain things, including their electric charge.

[62] How can
these mathematical relationships have any empirical validity if Einstein’s
Special Theory (upon which they are based) is completely *ad hoc*, empirically invalid and meaningless?

[63] “The rest energy is in effect the total relativistic energy of a particle measured in a frame of reference in which the particle is at rest.” (Resnick, 1992, p. 484)

[64] Specifically, Resnick concluded that “because the rest energies of the initial and final particles are equal in this collision [as measured in S'], conservation of total relativistic energy is equivalent to conservation of kinetic energy,” due to the fact that no new particles were produced by such collision.

[65]
Relativistic Kinetic Energy also cannot exist for many other reasons. For example, it depends upon Einstein’s two
fundamental postulates and his kinematic method of measuring, which we have
demonstrated to be artificial, illogical and empirically invalid in Chapters 21
and 29. It depends upon the validity and
existence of ‘electromagnetic mass,’ which we have demonstrated in Chapter 17
to be only an ‘apparent mass’ and in reality only an electromagnetic resistance
or inertia. It also depends upon the
existence of Relativistic Mass, which we have just demonstrated earlier in this
chapter to be a myth. Above all, it
depends upon Einstein’s Lorentz transformations, which we have demonstrated to
be *ad hoc* and meaningless in Chapter 27.

[66] The same conclusion would apply to inertial mass, classical momentum, length, and every other physical phenomenon which Einstein and his Special Theory have distorted.

[67] The reason for this limitation was Einstein’s theory that no material object can reach or surpass the velocity of light, and his relativistic formula for the compilation of two velocities in the same direction which mathematically ‘confirms’ his theory. (see Chapter 29)

[68] One might ask: Why is the magnitude of the physical concept of an electric charge not relative velocity dependent within Einstein’s Special Theory? What is the reason for this relativistic exception or inconsistency? The answer is probably because Einstein needed an electric charge to be independent of its velocity so that he could confirm Kaufmann’s assumption of such independence and use Kaufmann’s experimental data to confirm his own relativistic dynamic theories. (see Chapter 31F)

[69] We are not just picking on Resnick. His ideas and analyses are typical of all relativists.