*After Einstein described his theoretical concepts of relativistic kinematics
in Part I of his Special Theory, he applied them to certain electromagnetic and
optical phenomena in Part II of his Special Theory, entitled the
“Electrodynamical Part.” Einstein’s main
purposes in Part II were: 1) to attempt
to justify and confirm his *ad hoc*
relativistic and mathematical concepts by applying them to so-called
experimental data, and 2) to extend his
relativistic kinematics to mechanics, electrodynamics, electricity and
beyond. In this Chapter 30 and in
Chapter 31, we will demonstrate that Einstein did not succeed in this endeavor.*

**A.
****The invariance of Maxwell’s equations for empty
space, and a description for the induction of an electric current.**

The next Section 6 of Einstein’s Special Theory was entitled:

“§ 6. Transformation of the Maxwell-Hertz Equations for Empty Space. On the Nature of the Electromotive Forces Occurring in a Magnetic Field During Motion.” (Einstein, 1905d [Dover, 1952, p. 51])

In Section 6, Einstein had two primary goals. First, to demonstrate that the Maxwell-Hertz equations for empty space,[1] when properly transformed, are invariant (or rather ‘covariant’) in all inertial frames of reference. Second, to attempt to resolve the “asymmetry in the case of magnet and conductors in relative motion” (Miller, p. 270); this was the problem that Einstein cited at the beginning of his Special Theory. The Maxwell-Hertz equations are written as follows:

^{“} ” (Miller,
p. 12)

A threshold question
is: Why did Einstein choose Hertz’s 1890
ether reformulation of Maxwell’s equations rather than Lorentz’s 1892 ether reformulation?[2] Most likely the answer is that Hertz’s four
Maxwellian equations applied __both__ to Maxwell’s theory of
electromagnetism in the presence of charges (i.e. electric currents), as well
as to Maxwell’s theory of electromagnetism in the absence of charges (i.e.
light and EM radiation); whereas, Lorentz required a separate set of four
equations to describe Maxwell’s theory of electrodynamics in the presence of
charges. (see Figure 6.3) Thus, with the Maxwell-Hertz equations
Einstein could discuss both the invariance of such equations when applied in
empty space (i.e. light and EM radiation) and with respect to the induction of
an electrical current.[3]

As the title for Section 6 implies, Einstein limited his discussion during the first two pages of Section 6 to the invariance of Maxwell’s “equations of electrodynamics for the case of radiation [i.e. light] in ‘free space’…in the absence of charges.”[4] (Miller, p. 270) Einstein discussed the invariance of Maxwell’s equations in the presence of electric charges (and electric currents), and the invariance of such electric charges, separately in Section 9 of his Special Theory (see Miller, pp. 305 – 307), which we will discuss in Section D of this chapter.

Einstein began Section 6
by assuming that “the Maxwell-Hertz equations for empty space hold good for the
stationary [inertial] system K…”
[Einstein, 1905d [*c*] in…the resting [inertial] system K.” (Miller, p. 271)

Einstein then applied
the Lorentz transformation equations to the above Maxwell-Hertz equations with
respect to inertial reference system k moving with velocity v relative to
system K. (Einstein, 1905d [Dover, 1952,
p. 52]) This process, of course,
distorted the Maxwell-Hertz equations in system k. (see Einstein, 1905d [*Id*.,
p. 53) He then reformulated the
equations so that the reformulation would apply in both inertial systems. (*Id*.,
pp. 53 – 54) In other words, after all of such algebraic
manipulations Einstein’s modified Maxwell-Hertz equations for light were
algebraically ‘covariant’ in both inertial frames.[5]

But why did Einstein go through this *ad hoc* and artificial process? What relevance do any transformation
equations have with respect to non-material light? What relevance do covariant algebraic
equations have with respect to anything?
Einstein’s attempted justification was that:

“the __principle of
relativity requires__ that if the Maxwell-Hertz equations for empty space
hold good in system K, they also hold good in system *k*.”[6] (*Id*.

In
1905, at the beginning of his Special Theory, Einstein axiomatically described *ad
hoc* his expanded principle of Galileo’s Relativity, which included electrodynamics
and optics as well as mechanics.
Einstein’s expanded principle of relativity was described as a __postulate__
(an unchallengeable statement which must be accepted on face value). It was asserted without any justification for
such radical generalization.[7] The
year before, in 1904, Henri Poincaré had asserted a similar generalized
‘principle of relativity’ which also included electrodynamics and optics (see
Chapter 16B), and Einstein was cleverly attempting to ride on Poincaré’s
coattails.[8] However, by 1916, Einstein found it necessary
to attempt to justify such generalization of Galileo’s Relativity. (see Chapter 24) As we have previously demonstrated in detail
in Chapters 16B and 24, both Poincaré’s and Einstein’s generalizations of
Galileo’s material principle of relativity (Chapter 5) were completely *ad
hoc*, meaningless, and empirically invalid, despite Einstein’s 1916
attempted justification.

Because
Einstein’s *ad hoc* principle of relativity had no empirical verification,
he had no scientific justification to declare that “if the Maxwell-Hertz
equations for empty space hold good in system K, they also hold good in system
k.” Einstein needed his expanded postulate
of relativity in order to axiomatically make such declaration. He also needed such postulate in order to
justify applying transformation equations from one inertial reference frame to
another, so that observers in each system could theoretically measure
magnitudes of all physical phenomena in the other system. In other words, without an empirically valid
expanded principle and postulate of relativity, Einstein had no relativistic
Special Theory whatsoever.

For all of the above reasons,
Einstein could not justifiably apply the principle of relativity and the
Lorentz transformations to the Maxwell-Hertz equations*. *Nevertheless, Einstein did misapply the
principle of relativity, he did adopt the Lorentz transformations, and he did misapply
them to light and to the Maxwell-Hertz equations for light. Therefore, we must respond to these invalid, irrelevant
and unnecessary acts, to Einstein’s bizarre conclusions, and to the resulting
mathematical consequences.[9]

Guilini points out that
this non-mechanical covariance was established before Einstein by Lorentz in
1904, by Poincaré in 1905 and by Voigt in 1887; but “nobody before Einstein __connected__
these results to the principle of relativity.”
(Guilini, p. 81) The reason for
this failure to connect such non-mechanical covariant results to the principle
of relativity was (as we have again just explained) that such algebraic __electromagnetic__
results do not apply to Galileo’s mechanics concept of material
relativity. The two concepts (Maxwell’s
electromagnetic equations for non-material light and Galileo’s mechanics
concept of material inertial relativity) are completely incompatible and mutually
irrelevant. (Chapters 5, 6, 23 and 24)

Theoretically, when one applies the Lorentz transformations to anything, a Length Contraction of matter and a Dilation of Time results. (see Chapters 26 and 28) But Einstein did not mention either of these relativistic mathematical consequences with respect to the covariance of the Maxwell-Hertz equations for empty space. Not to worry, his resourceful followers have taken up the imaginary theoretical slack.

According to Guilini,
the Length Contraction manifests itself with respect to the Maxwell-Hertz
equations by the __spherical__ point charges in a Coulomb field contracting
in the direction of relative velocity so that at v = 0.8*c* they become horizontally weakened ellipsoids. (Figure 30.1) Similarly, the Time Dilation supposedly
manifests itself by a reciprocal enhancement (strengthening or elongation) of
the point charge’s vertical component which in turn results in a desired
variation in the charged particle’s ionization (decay) rate. (see Guilini, pp. 83 – 85) Aside from such imaginary and dubious conjectures,
has either of such relativistic effects ever been detected or observed? Of course not.

Toward the end of
Section 6 of his Special Theory, Einstein interpreted such covariant Maxwellian
equations for empty space (i.e. light) in terms of a moving electrical charge
and the principle of relativity.[10] Einstein then determined that the mysterious
‘electromotive force’ that was generally described for the induction of an
electric current was none other than an electric force, and “that electric and
magnetic forces do not exist independently of” relative motion.[11] (Einstein, 1905d [

Did all of the above
mathematical theorizing make Maxwell’s transmission velocity of light at *c* in a vacuum empirically __invariant__
with respect to all linearly moving inertial reference frames? Remember that this was Einstein’s primary
goal for his Special Theory. (see
Chapters 18 through 21) The answer
is: of course not. [12]

**B. Einstein’s relativistic Doppler effect of light.**

In Chapter 8 we explained the concept of the current
classical Doppler effect of light in empty space. We empirically discovered that as luminous
bodies in space __approach__ one another, the light waves emitted by one
body are received __more frequently__ by an observer on the other body, and
vice-versa. Conversely, as such luminous
bodies __separate__ from one another the light waves emitted by one body are
received __less frequently__ by an observer on the other body, and
vice-versa. These two different
phenomena are empirically manifested, when light is received in a spectroscope
on Earth, by a red shift of spectral lines for such separation, and by a blue
shift of spectral lines for such approach.
(see Figure 8.3)

Special Relativity declares that such classical
Doppler effect of light is a meaningless concept, because *inter alia* at one time in the past it incorporated and referred to
the fictitious medium of ether. (see
Gill, p. 6) On the contrary, once the
fictitious concept of ether is eliminated, the classical Doppler effect of
light remains just as valid as Maxwell’s transmission velocity of light at *c* in a vacuum is without the concept of
ether.

Nevertheless, in Section 7 of his 1905 Special
Theory, Einstein invented an abstract mathematical version of the classical and
empirical Doppler effect of light.
Why? In order to apply his Lorentz
transformations and his kinematic theories to this long accepted optical
phenomenon so that it would remain mathematically consistent with his two empirically
invalid fundamental postulates and his *ad
hoc* relativistic kinematics; and also so he could claim that the empirical
Doppler effect of light was an experimental confirmation of Special Relativity.

In *ad hoc*
fashion, Einstein determined the equations for a light wave of frequency *v* emitted from an infinitely distant co-moving
star. Einstein axiomatically applied the
Lorentz transformations to such equations as well as the transformations which
he found in Section 6 for electric and magnetic forces. He then concluded that where “the connecting line
‘source-observer’ makes the angle *Φ*
with the velocity of the observer” on Earth moving with velocity v, “the frequency
*v*' of the light perceived by the
observer is given by the equation

.

This is Doppler’s principle for any velocities whatever.[13] When *Φ*
= 0 the equation assumes the perspicuous form

”[14] (Einstein, 1905d [Dover, 1952, p. 56])

The implication from the above scenario is that Einstein’s relativistic formula is able to mathematically predict the empirical Doppler effect of light, and thus all observed Doppler effects of light are experimental confirmations of Special Relativity.

Dingle interpreted Einstein’s relativistic Doppler equations to mean the following:

“The formula has the
required characteristic that it gives opposite frequency changes for approach
and recession, and is a function of __the relative velocity of the bodies only__. But this view of the matter __compels__ us
to assume that the observer, and not the source of light, is the moving
body. If the source moves and the
observer remains at rest, it requires [a different equation].[15] The two ways of regarding the motion are thus
not equivalent, and __the postulate of relativity is violated__.” (Dingle, 1961, p. 24)

There are also other problems.

Einstein’s relativistic
concept, of course, begs the questions:
Is there a relative motion between bodies, in which directions are such
bodies moving, and what is the magnitude of their relative velocity? For the answer to these questions we must __first
empirically determine__ the classical Doppler effect of light by observing
the magnitude of blueshifts or redshifts, interpreting their meaning and computing
their magnitudes. Do these additional prerequisite
requirements __not__ suggest incomplete, conjectured and circular
relativistic reasoning on the part of Einstein?

Based on Einstein’s Special Theory, Dingle asserted that: “we have no basis for assuming any [Doppler] formula at all.” (Dingle, 1961, p. 22)

“The postulate of constant light velocity speaks only of the velocity of light; it does not require that light shall even show a periodicity [frequency]. That we infer quite independently from experiment [vis. by theory], and therefore the Doppler effect can have only an empirical basis.”

“it would be entirely
consistent with Einstein’s theory if there were no Doppler effect at all—i.e.
if motion had no effect on the observed frequency of light.” (*Id*.

Nor does Einstein’s
Special Theory express any relation between frequency and velocity. (*Id*.

Regardless of all of
Einstein’s *ad hoc* deductions,
rationalizations, and transformations, the relativistic Doppler formula cannot
be correct because the Lorentz transformations, the other transformations and the
relativistic concepts upon which it was based, are all *ad hoc* and meaningless false assumptions. (see Chapters 21 through 29) For example, one can see from the denominator
of Einstein’s relativistic Doppler equations, as Einstein specifically pointed
out in Section 5 of his Special Theory, that the relative velocity between
bodies can never mathematically exceed *c*. On the other hand, this feature of his
relativistic Doppler formula posed seemingly insolvable problems and conflicts
for Einstein and other relativists during the 1930’s when distant galaxies were
interpreted (based upon their gigantic redshifts) to be receding from Earth at
several times the velocity of light.
These interpretations of gigantic recession velocities of all the
galaxies are called ‘the expanding universe theory.’ (see Figure 30.3) In apparent desperation, Einstein and his
followers suggested *ad hoc* that
perhaps the non-material __space__ of the Universe was doing the expanding
and that it merely carried the material galaxies along with it. (see Einstein, *Relativity*, p. 153) This ridiculous attempted solution to the
conflict was referred to as the ‘expansion of space’ theory. (see Eddington, 1933)

Perhaps the most
self-contradictory assertion of Einstein’s relativistic Doppler effect of light
is its assertion that such relativistic effects are __due solely to the
relative velocity__ between two luminous bodies in space. In other words, according to Einstein and his
followers, the only thing that is relevant to the relativistic Doppler effect
of light is such relative velocity. Einstein
denied that there is any meaning to a unique motion or velocity of one luminous
body (the source or the observer), or to an identifiable time of such unique motion,
when such motions are considered separately.
In other words, Einstein and his followers “claimed that all that enters
into the picture is the relative motion between source and observer, and to ask
which one moves is to ask an unanswerable question.”[16] (see Gill, p. 14)

Dingle agreed with the first part of Gill’s
conclusion: “the relativity postulate requires
that [Einstein’s relativistic Doppler effect] must not enable us to distinguish
in an __absolute sense__ between the motion of the emitter with respect to
the receiver and that of the receiver with respect to the emitter.” (Dingle, 1961, pp. 21 – 22) French even praised Einstein’s Doppler
formula as being a simpler way of expressing the phenomena in that it only
depended upon __relative motion__ without any distinction as to which body
was doing the moving. (French, p. 134)

Resnick in turn asserted that: “the theory of relativity introduces an __intrinsic__
simplification over the classical interpretation of [the Doppler effect] in
that the two separate cases which are different in classical theory, (namely,
source at rest—moving observer and observer at rest—moving source) are __identical__
in relativity.” (Resnick, 1968, p.
91) In other words, in Special
Relativity there is __no observational distinction between the two cases__. This claim of __identity__ has also been
made by many other relativists. For
example, “the relativistic result is a kind of __unification__ of the
moving-source and moving-observer results…”[17] (French, p. 137)

It follows from the above discussion that (in Einstein’s symmetrical relativistic
Doppler theory) the relative velocity of the source and the observer produces __one
and the same effect__ (either a blue shift or a red shift), and that either
the “observation of the movement [motion] is __immediate in both cases__, or
it is delayed in both cases.” (Dingle,
1972, p. 216) Which is it?

We know from our own experience that the observation of such motion in
Einstein’s theory must theoretically be __immediate in both cases__. Why?
Because:

“We know that, with respect to a distant star, the orbital motion of
the Earth round the Sun causes an alternation of approach and recession. The Doppler effect corresponding to this is
observed to synchronize with the [Earth’s] orbital motion in every case, so we
know that, when the [terrestrial] __observer moves, the effect is seen
immediately__…” (*Id*.

This empirical fact contradicts
Einstein’s assertion that the unique velocity of the __observer__, when
considered separately, has no meaning for the Doppler effect of light. Other empirical facts (such as blue shifts of
supernovae and alternating blue and red light shifts of binary stars) also
contradict the assertions of the relativists:
that the unique velocity of the __source body__, when considered
separately, has no meaning for the Doppler effect of light. (see Chapter 8C and Figure 8.4)

In
addition, because our experience tells us that the solar orbital motion of the
Earth results in __immediate__ blueshifts and redshifts in the light
received by a terrestrial observer from a distant star: “That means that [Einstein’s relativistic
Doppler] effect must also be seen __immediately__ [symmetrically] when the
star moves, __otherwise there would be an observable [non-symmetrical] distinction
between the two cases__.” (Dingle,
1972, p. 216) Therefore, also according
to Einstein’s Special Theory, “every Doppler effect observed is __a result of
a motion occurring at the time (instant) of observation__, no matter how far
away the source of light may be.” (*Id*.,
p. 217)

This fact
presents two more extraordinarily serious contradictions for Einstein’s
relativistic Doppler theory. First, in
Einstein’s relativistic Special Theory, Maxwell’s and Römer’s distance/time
delay of the finite light signal at c must be __irrelevant__ to Einstein’s Special Theory, because the
light shift caused by a distant motion of the source can be seen immediately
(instantaneously) on Earth with no distance/time delay.[18] Secondly, this means that the __transmission
of information__ (vis. the blue shift velocity of fragments from a distant
exploding star) is __instantaneous__ for the terrestrial observer, and thus such
transmission dramatically exceeds the finite velocity of light at *c*,
which Special Relativity claims cannot happen.

The above
empirical contradictions demonstrate *inter
alia* that the classical Doppler
effect of light is correct, and that Einstein’s simplistic, symmetrical and
relativistic Doppler theory is invalid.
Rather than being an application and confirmation of Einstein’s
relativistic concepts, Einstein’s relativistic Doppler effect of light is self
contradictory, and it also contradicts the rest of his Special Theory.[19] On the other hand, if the relativistic
Doppler effect is correct then information can be instantaneously transferred
over great distances (much faster than the velocity of light) which contradicts
Special Relativity which asserts that this result cannot happen. (Chapter 29)
Either way, Einstein’s Special Theory is contradicted.

C. The relativistic formula for stellar aberration.

After Einstein theoretically applied his Lorentz transformations to the light from a distant star in order to arrive at his formula for the relativistic Doppler effect of light in Section 7, he conjectured that the relativistic formula for the aberration of starlight “in its most general form” is:[20]

cos *ф *= cos *ф *– v/*c*

1 – cos *ф *•_{ }v/*c *

(Einstein, 1905d [Dover, 1952,
p. 56])* *The denominator
was due to Einstein’s concept of the Relativity of Simultaneity (Miller, p.
286), which we demonstrated in Chapters 26 and 28 is *ad hoc* and empirically invalid.

Einstein’s above conclusion has been explained by many of his followers, as follows. If we make the analogy that light from a distant star is like a rain of photons, then the direction of such rain will change relative to an astronomer/observer on Earth arbitrarily moving at v in its solar orbit relative to such rain. Therefore, the change in the relative direction of such rain of photons can be calculated to the first order of approximation from such relativistic formula. (French, pp. 132 – 134; Zhang, p. 153; Hoffmann, 1983, pp. 47 – 48) The implications from the above conjectures are that Einstein’s relativistic aberration formula predicts and approximates Bradley’s 1728 aberration of starlight experiment (which was determined empirically), and therefore Bradley’s work was an experimental confirmation of Special Relativity. (Miller, p. 286)

On the contrary, Bradley’s 1728 aberration of starlight
had two components: 1) the telescope had
to be tilted to a certain angle, vis. the constant angle of aberration, in
order to keep the star in the center of the scope, and 2) as a result the direction of the starlight
relative to the Sun appeared to constantly change during the Earth’s annual
solar orbit. (see Chapter 7D and Figure 7.6) Einstein’s relativistic formula only
described the latter. Einstein’s
relativistic formula cannot even be applied until the constant angle of
aberration ‘a’ and the velocity v of the receiver (i.e. the Earth) have been
empirically determined. Also, the mere
mathematical approximation and description of an age-old empirical discovery is
obviously not a __prediction__ of what happened in the past.[21]

In any event, Bradley’s work in 1728 is not an experimental
confirmation of Special Relativity in general or of the empirical validity of
the *ad hoc* Lorentz transformation in
particular.[22] The only assertion of Special Relativity that
Bradley’s experiment did confirm was the second part of Einstein’s second
postulate: that the velocity of light is
independent of the motion (velocity) of its source body.[23] However, as we have repeatedly pointed out,
this assertion was never in doubt by 1905.
For all of the above reasons, Einstein’s *ad hoc* relativistic formula for stellar aberration is *ad hoc*, empirically invalid and above
all meaningless.

**D.
Einstein’s Relativistic Transverse Doppler Effect**

In 1906, Johannes Stark
(the publisher of Einstein’s December 1907 *Jahrbuch*
article) observed a shift in the periodic spectral lines of high velocity
hydrogen canal rays (particles) emitted substantially __perpendicular__ to
the observer, which he interpreted to be a Doppler shift. The observed frequency of such spectral lines
(*v*) was apparently less than the
emitted frequency (*v*_{0}). (Zhang, p. 183; Einstein, 1907 [Collected
Papers, Vol. 2, p. 263]) In early 1907,
Einstein interpreted the canal ray ions that produced such periodic spectra to
be “a fast moving clock.” He also
claimed that such theoretical transverse Doppler effect could be predicted from
his concept of ‘Time Dilation’: “a
uniformly moving clock runs at a slower rate as judged from a ‘stationary’
system…”[24] (*Id*., p. 232) Note that Einstein was using one *ad hoc*
concept (Time Dilation) as the foundation and justification for another *ad
hoc* concept (the transverse Doppler effect). Circular reasoning?

In his December 1907 *Jahrbuch*
article, Einstein again referred to this “very interesting application” of his
‘Time Dilation concept’:

“Since the oscillation
process that corresponds to a spectral line is to be considered an intra-atomic
process whose frequency is determined by the ion alone, we may consider such an
ion as a clock of a certain frequency *v*_{0}…

“the effect of motion on the light frequency…reduces the (apparent) proper frequency of the emitting ions [particles] in accordance with the relation

[*v* = *v*_{0}√1
– v^{2}/*c*^{2}].”
(*Id*., p. 263)

“If…the connecting line
‘source of light-observer’ forms an angle Ψ [so that the direction of the
light is not perpendicular] relative to the observer, then the frequency *v* of the source of the light perceived
by the observer is given by the equation[25]

.
” (*Id*., pp. 266 – 267)

Einstein’s so-called transverse
Doppler effect “is a purely relativistic effect with no classical counterpart.”[26] (Resnick, 1992, p. 897) Generally, it is only an __unobservable__
‘second order effect’ and theoretically it only occurs when “the relative
motion of the source and the observer is at __right angles__ to the
direction of propagation of the wave fronts…[T]he observed frequency *v* is always lower than the frequency *v _{0}* emitted by the source.”[27] (

“we see a given number of oscillations in a time that is longer than the proper time. Or, equivalently, we see a smaller number of oscillations in our unit time than is seen in the unit time of the proper frame. Therefore, we observe a lower frequency than the proper frequency.” (Resnick, 1968, p. 91)

In other words, the distant
stationary observer S theoretically measures a longer (dilated) time period
between less frequently received longer light waves than the observer S' moving
with the particle properly measures during a proper time interval. (see Resnick, 1992, p. 898) “Thus any confirmation of the transverse
Doppler effect can therefore be taken as another confirmation of relativistic
time dilation.” (*Id*.; Bohm, p.
80) Again, we have one unobservable *ad hoc* relativistic effect confirming
another unobservable *ad hoc*
relativistic effect, but we know that Time Dilation does not empirically exist. (Chapters 26 and 28)

In 1937, Ives and Stillwell
conducted a canal ray (accelerated positive ions) experiment based on the
existence of __ether__ which the relativists claimed confirmed Einstein’s
transverse Doppler effect; whereas, Ives himself claimed that the results
instead verified a different theory.[28] (Miller, p. 212) Here we have the relativists claiming that an
experiment confirms one of their concepts, and the person who devised and
conducted the experiment denying such confirmation. Gill concluded that: “Evidence for the correctness of the [Doppler]
formulae to the second order in *v/c* [the
transverse Doppler effect] depends on specially designed experiments which are
few in number and not high in precision.” [29] (see Gill, p. 140)

Miller concluded that, with his theoretical
transverse Doppler effect, Einstein went far beyond his intent in 1905, and in
1907 he defined a clock as “__any periodic process__—for example, an atomic
oscillator emitting a frequency…” (*Id*.*ad hoc* interpretations and
applications for his relativistic concepts.

For example, if any periodic process
(in nature or otherwise) could be interpreted to be a clock, and if any such
moving clock could be interpreted to be slowing down, then the concepts of Time
Dilation in particular, and Special Relativity in general, could be expanded to
other phenomena without any restraints or limitations. This is exactly what happened with the
quantum mechanics explanation of why fast moving theoretical atomic particles
(pions and muons) are believed to decay slower than expected on their way
toward Earth. It was, of course, because
of Time Dilation. (see Chapter 37) Einstein also felt free to use such expanded
interpretations and *ad hoc* applications
of Special Relativity to help concoct his General Theory of Relativity (see
Einstein, *Relativity*, pp. 88 – 91), even though General Relativity
contradicts Special Relativity. (Chapter
40)

Regardless of dubious
interpretations and claimed experimental confirmations, we know that Stark’s
1906 observations and Ives’ 1937 results were not the result of relativistic
Time Dilation or any relativistic transverse Doppler effect. Why?
Because in Chapters 26 and 28 we demonstrated that the Relativity of Simultaneity
and Time Dilation were *ad hoc* and
empirically invalid. Also, in Chapter 27
we demonstrated that the Lorentz transformations (which mathematically produced
the theoretical consequence of Time Dilation) were also *ad hoc*, empirically invalid and meaningless. Without these foundational concepts to
support it, or as its premise, no transverse Doppler effect can even
theoretically exist. The conclusion is
clear: Einstein’s unobservable relativistic
transverse Doppler effect is just another mathematical fantasy.

**E. The energy and pressure of light on an
inertially moving mirror.**

In early 1904, Abraham published a widely read paper
entitled: “On the Theory of Radiation
and of the Pressure of Radiation.” In it
Abraham “deduced equations…for the characteristics of radiation reflected from
a perfectly reflecting surface in inertial motion relative to the __ether__,
and for the __light pressure__ on this surface…”[30] (Miller, p. 298) In his 40-page paper, “Abraham discussed all
of his results in great detail.” (*Id*., pp. 291, 300) Very importantly, in order “To obtain exact
results… he used only one reference system, __fixed in the ether__.” (*Id*.,
p. 298)

Then, in 1905, in Section 8 of his Special theory, Einstein decided to take a shot at these problems and conjectures. Einstein first deduced “the energy of light per unit of volume” in the stationary system K. (Einstein, 1905d [Dover, 1952, p. 57]) Because of “the relativity of time and length observers in K and k do not measure the same volumes of the light complex.” (Miller, p. 292) Therefore, Einstein deduced that “the energy…of a light complex [will] vary with the state of motion of the observer in accordance with the…law: [31]

.

(Einstein, 1905d [Dover, 1952, p. 58])

Einstein then conjectured:

“It
is remarkable that the energy and the frequency of a light complex vary with
the state of motion of the observer in accordance with the same law.”[32] (*Id*.

On the contrary, the energy and the frequency of a propagating light ray generally do not vary in accordance with the same law. The energy of an emitted light wave normally does not vary as it propagates through the vacuum of empty space from a star to Earth. However, if it encounters particles of matter during its journey it could convert a fraction of its energy to heat during the process of absorption and re-emission. After a great number of such encounters the diminished energy level of the light ray may be manifested by a redshift observed on Earth.[33]

On the other hand, the observed
frequency of a propagating light wave *a
priori* can vary depending upon the __linear__ motion of the
observer. If the observer moves toward
the linearly propagating light ray, *a
priori* the frequency of its waves will __appear__ to increase, and this
will be manifested by an observed blueshift.
Conversely, if the observer moves away from the linearly propagating
light ray, *a priori* the frequency of
its waves will __appear__ to decrease, and this will be manifested by an
observed redshift (the Doppler effect of light).[34] In these situations, the energy of the light
wave which is __received__ by the linearly moving observer may increase or
decrease,[35] but the
energy possessed by the light wave itself does not __physically__ change;
the energy possessed by the light wave (whatever it may be) remains constant as
it propagates, regardless of any relative motion by the observer (its potential
recipient). Thus, the law that governs
the change in energy of a light ray is very different than the law that governs
its observed frequency.[36]

Einstein then deduced the necessary relativistic
transformation equations for the energy of a light complex and transformed the light
waves from K to the surface of a perfectly reflecting mirror on inertial system
k moving at v relative to K, and then back to K. (see Figure 31.4) The theoretical result was that the energy of
the light waves incident upon the moving mirror was greater than the energy of
the reflected light.[37] Einstein concluded that the difference was
due to the work done by the __pressure__ of the light on the mirror.[38] (Einstein, 1905d [Dover, 1952, p. 59]) Einstein ended Section 8 with the following conjecture:

“What
is essential is, that the electric and magnetic force of the light which is __influenced
by a moving body__,[39]
be transformed into a system of co-ordinates at rest relatively to the
body. By this means all problems in the
optics of moving bodies will be reduced to a series of problems in the optics
of stationary bodies.”[40] (*Id*.

Miller asserted that Einstein’s
results in Section 8 were __equivalent__ to Abraham’s results in his early
1904 paper. (Miller, p. 298) But how could this be? Abraham theoretically measured his light rays
relative to the stationary ether, whereas Einstein applied relativistic
equations to his light rays and denied the existence of ether.

It turns out that both Abraham and
Einstein applied their light rays to a system theoretically at rest. Abraham’s system at rest was the hypothetical
ether that does not exist. Einstein’s
system at rest was his axiomatic velocity of light at exactly *c* in every inertial system regardless of
its linear motion. Thus, light
propagated at *c* from K is theoretically
received at the mirror in k at *c* ‘__as
if the surface were at rest__.’ (see
Miller, p. 300) And Einstein’s
relativistic transformation equations make this virtual result mathematically
so.

Actually, and empirically, as we
learned in Chapter 21, the light propagating from K at velocity *c* relative to the medium of the
intervening space also propagates toward the mirror at k (moving away from K)
at *c* – v. (see Figure 30.4A) Therefore, neither Abraham’s impossible ether
solution nor Einstein’s impossible absolutely constant velocity of light at *c* explanation is correct or
equivalent. Most likely, both were
completely *ad hoc*, arbitrary and
meaningless.[41]

**F.
The invariance of an electrical charge.**

In Section 9 of his
Special Theory, Einstein first attempted to demonstrate the invariance of the
Maxwell-Hertz equations in the presence of an electric charge. (see Einstein, 1905d [*Id*., p. 60) He also assumed
that the Maxwell-Hertz equations were valid in the stationary system K. (*Id*.

Einstein then transformed the Maxwell-Hertz equations to system k with the Lorentz transformations (with the assistance of the electromagnetic field transformation equations that he used in Section 6), but this was still insufficient to achieve his desired covariance. Einstein found that this time he also had to use an additional transformation equation for the charge density in order to achieve covariance.[42] (Miller, p. 306) After this convoluted transformation process, Einstein concluded that “the electrodynamic foundation of Lorentz’s theory of the electrodynamics of moving bodies is in agreement with the principle of relativity.” [43] (Einstein, 1905d, [Dover, 1952, p. 60])

Einstein then easily deduced the constancy and invariance of any electrical charge from such covariant equations. He stated:

“If an electrically charged body is in motion anywhere in space without altering its charge when regarded from a system of co-ordinates moving with the body, its charge also remains—when regarded from the ‘stationary’ system K—constant.” (Einstein, 1905d [Dover, 1952, p. 61])

But how could such electric charge remain the same if it was contracted and its time was dilated by all of such relativistic transformations?[44]

It turns out that Poincaré had developed an identical
mathematical proof of the invariance of an electrical charge in early 1905, but
it assumed a stationary ether.[45] (Miller, p. 307) Intuition, logic and classical physics would
also produce the same result without any transformations. If all inertial frames are __equivalent__
states of motion, why should an electric charge vary from one inertial frame to
another? There is no viable physical
reason. This conclusion should also
apply to all other physical phenomena (including length, time, mass, etc.) as
it did in classical physics. The
conclusion is clear: No physical
phenomenon is velocity dependent, with the possible exception that the constant
velocity of light at *c* relative to the
vacuum of empty space is also *c* ± v
relative to linearly moving bodies.

Why did Einstein want to demonstrate the mathematical
invariance of an electric charge? One
reason probably was because Kaufmann __assumed__ the invariance of electric
charge for his experiments about electromagnetic mass in 1901 – 1902, and
Einstein used Kaufmann’s experiments and his concept of electromagnetic mass as
the foundation for his own concept of Relativistic Mass in Section 10 of his
Special Theory. It would be natural for
Einstein to want to bolster Kaufmann’s critical assumption which Einstein
needed to adopt for his Special Theory.
(see Chapter 31A)

[1] The term
‘Maxwell-Hertz field equations’ was coined by Abraham in 1902-03. (Miller, p. 24) In 1890, Hertz axiomatically proposed that
the electrodynamics of moving bodies could be described by four equations
(which are shown by Miller on p. 12 of his book) and that they were invariant
in different reference frames. (*Id*., pp. 12, 14) Hertz wrote his equations relative to a
system that was theoretically fixed in the __ether__, and he assumed that
when such system moved the ether was totally dragged along. (*Id*.,
p. 13)

[2] The Maxwell-Lorentz equations are shown on Figure 6.3. Another question is: How mathematically valid is either set of equations since they were formulated with respect to the hypothetical stationary ether, which does not exist? Remember that when the Michelson & Morley experiment was analyzed and computed relative to the stationary ether, the result was completely wrong (see Chapters 9 and 12), and its paradoxical null result plunged physics into a theoretical tailspin (i.e. Special Relativity) from which it has yet to recover.

[3] There is
also another possibility. Einstein may
not have known much (if anything) about Lorentz’s 1892 reformulation of
Maxwell’s equations in June 1905. In
order to become a patent clerk in 1902, Einstein read __just enough__ about
Maxwellian electromagnetism from Föppl’s 1894 text on the Hertz-Heavyside
version of Maxwell’s theory and from Hertz’s 1892 book in order to pass the
patent exam. (see Miller, pp. 142, 148,
165) In his 1892 book Hertz opined that
“Maxwell’s theory __is__ Maxwell’s system of equations,” which, of course,
is not correct. (see Chapter 6) From studying his Special Theory, it is
evident that Einstein didn’t know much about Maxwell’s theory of
electromagnetism and optics beyond the so-called Maxwell-Hertz equations.

[4] The last page of Section 6 dealt primarily with Einstein’s problems concerning the induction of a point charge of electricity.

[5]
Actually, Einstein was required “to undertake additional transformations
besides those concerning the space and time coordinates, in order to maintain
the __covariance__ of the equations of electromagnetism.” (Miller, p. 271)

[6] Here
Einstein was just assuming the validity of his *ad hoc* principle of relativity with respect to electromagnetics and
optics.

[7] Einstein
raised his expanded principle of relativity “to the status of a postulate” in
his Special Theory for one primary reason:
so that it __could not be challenged__ when he applied it in his
Special Theory.

[8] Poincaré was a legendary mathematical physicist and his similar expanded ‘principle of relativity’ gave Einstein’s postulate and principle of relativity an air of credibility.

[9] Very
importantly, all of the above analyses and conclusions apply equally to every
other relativistic concept described in this treatise. All of Einstein’s concepts and mathematical
conclusions that rely on either of his two *ad
hoc* postulates are in turn themselves *ad
hoc*, irrelevant and empirically invalid.

[10] One might ask: what relevance does an electric charge or current and the mechanics principle of relativity have to light? The answer, of course, is none.

[11] For Einstein, these conjectures removed the asymmetries which he referred to in the opening paragraph of his Special Theory. They also cleared up the problems that he had with the description of ‘unipolar induction’ which he read about in Föppl’s text. (see Miller, pp. 144 – 150, 276 – 280)

[12]
Maxwell’s transmission velocity of light is always c with respect to its medium
of a vacuum in empty space, but relative to linearly moving bodies it is quite
naturally always *c* ± v. (Chapter 21)

[13] Figure
30.2 graphically depicts the frequency *v*'
as a function of the velocity v and the angle Φ in such equation.

[14] Neither
of Einstein’s equations actually describes the specific magnitude of any
frequency. They merely describe the
theoretically different emitted frequency *v*
of the light wave when the observed frequency *v*' is known. Actually *v* should be *v _{0}* in both equations, because the emitted frequency of
the light at its source (the star) constitutes its proper ‘rest
frequency.’ (see Miller, p. 286)

[15] We will soon be informed of another reason why we are compelled to the above conclusion.

[16] On the contrary, in Chapter 8 we have demonstrated that there are some situations where there is an observable distinction.

[17] The
mathematical relativists also attempt to justify the relativistic effect because
of its “special __symmetry__ that the previous result lacks.” (French, p. 137) But what has symmetry got to do with
anything?

[18] This fact, if true, would even contradict Special Relativity.

[19] For
example, it contradicts the validity of the __Lorentz transformations__ that
produced Einstein’s mathematical Doppler effect. (see Chapter 27) It contradicts Einstein’s first postulate
that Galileo’s principle of relativity applies to light in all cases. (Chapters 20, 21 & 24) It contradicts Einstein’s second postulate
that ‘light propagates with a definite velocity *c*’ (Chapter 21), and his
relativistic formula for the ‘computation of velocities’ (i.e. that nothing can
exceed velocity *c*). (Chapter
29) Finally, it contradicts Einstein’s
‘aberration of light’ concept, because both it and his relativistic Doppler
effects are based on substantially the same algebraic equations. (Chapters 30C and 37)

[20]
Einstein went on to mathematically determine the “electric and magnetic force”
of the light waves, and then conjectured:
“It follows from these results that to an observer approaching a source
of light with the velocity *c*, this source of light must appear of
infinite intensity.” (Einstein, 1905d
[Dover, pp. 56 – 57]) Miller claimed
that this conjecture was offered by Einstein as an example of the unphysical
results that would occur when v = *c*. (Miller, pp. 285 – 286, 288)

[21] In addition, there is no empirical way to test with any accuracy which approximation (Bradley’s or Einstein’s) is more accurate. Feynman conjectured that Bradley’s empirical result was not as accurate as Einstein’s formula because Bradley’s ruler was contracted, but that Einstein’s formula takes this length contraction into account. (Feynman, 1963, p. 34-10) On the other hand, we know that length contraction is an empirically invalid concept (see Chapters 26 and 28), so Feynman’s conjecture is nonsense.

[22] On the
contrary, because Einstein’s relativistic aberration formula was obtained by
application of the *ad hoc* Lorentz
transformations, and because we know that such transformations are empirically
invalid (see Chapters 16 and 27), Bradley’s aberration formula must be more
empirically correct.

[23] We know that this fact is true, because the angle of aberration is always the same for all light received from every possible star in the MW Galaxy.

[24] Assuming that Stark’s measurements were reasonably accurate there has to be a physical reason for such frequency change, but it certainly is not Time Dilation. In Chapters 26 and 28 we demonstrated that Time Dilation is an empirically invalid concept, and that empirically it does not exist. It is just a myth.

[25] French conjectured that any deviation from the transverse would cause the normal linear Doppler effect “to swamp the” transverse Doppler effect so that it cannot be observed. (French, p. 144) How convenient!

[26] It is
also pure conjecture. The reason why the
transverse Doppler effect “does not vanish in the relativistic theory is
basically that the period of light [between waves] can be regarded as a kind of
‘clock’…so that in the change from one reference frame to another moving at a
speed *v*, relative to the first, there remains an increase of this period
in the ratio 1/√1 – (v^{2}/*c*^{2}).” (Bohm, p. 80)
More conjecture.

[27] Miller conjectured that: “Stark’s 1906 experiment lacked sufficient accuracy for detecting the transverse Doppler shift [to the second order] in the spectral lines emitted by the moving canal rays (hydrogen ions).” (Miller, p. 250; Einstein 1907 [Collected Papers, Vol. 2, p. 232])

[28] “Ives remained a vigorous anti-relativist to the end of his life.” (Miller, p. 250)

[29] Nevertheless, Gill supported the transverse Doppler effect, not so much because of the imprecise Ives-Stillwell experiment, but mainly because of “the general success of the Special Theory of Relativity, and the failure of rival theories.” (Gill, pp. 140 – 141) This type of unscientific deference to Special Relativity is not uncommon. We shall discuss the Ives-Stillwell experiment in greater detail in Chapter 37.

[30] Abraham must have falsely assumed that light had a magnitude of mass which caused such pressure or force. (see infra)

[31] Einstein did not deduce a specific variation for the energy of any light ray. All that such equation asserted was that if the energy of the light ray varied, then the magnitude of such variance would depend upon the angle of the light ray relative to the observer, and that such magnitude would be different at the source than when received by the observer depending upon the relative velocity.

[32] The reason for this conjecture was that Einstein’s formula for the relativistic energy of a light complex was exactly the same as his relativistic formula for the Doppler effect of light. Was the connection between light wave frequency and energy not already common knowledge in 1905? See Chapter 7.

[33] This theoretical phenomenon has been given the unfortunate name ‘tired light’ by Eddington and other cosmologists.

[34] *A priori *the length of the light waves
emitted by the source may be __physically__ lengthened or shortened by the
relative linear motion of the source, which would produce the same effect for
an observer on Earth, albeit a delayed effect depending upon the relative
distance between the two bodies.

[35] In Chapter 7 we suggested a reason for this theoretical phenomenon. The more frequently a light wave containing the same quantity of photons (or quanta) is received (in other words, the shorter the wavelength), the more EM energy will be received at a certain point.

[36] Einstein was always striving for simplicity and fewer hypotheses in physics. However, too often simplicity is achieved at the cost of correctness.

[37] If this was true, it was probably due to Einstein’s relativistic transformations.

[38] It is
probable that at this time Einstein also assumed that light had a magnitude of
mass. (see Chapter 32) Another question: Why did Einstein not attempt to transform the
__pressure__ of the light? Why is the
physical phenomenon of pressure not also velocity dependent? What is the reason for this relativistic
inconsistency?

[39] Einstein never told us the theoretical process by which such forces are “influenced by a moving body.”

[40] Except that the relativistic transformation process changes and distorts the problems that need to be solved.

[41]
Einstein’s explanation was also meaningless because *inter alia* it includes and requires the empirically invalid
relativistic concepts of the Relativity of Time, the Relativity of Length
(Chapter 26), the Lorentz transformations (Chapter 27), Einstein’s relativistic
kinematics (Chapter 28), and Einstein’s relativistic composition of velocities
(Chapter 29).

[42] If
Einstein has to keep inventing new *ad hoc*
transformation equations for every different situation in order to achieve
covariance (as he also did in Section 6), then covariance begins to take on the
character of arbitrary algebraic manipulation

[43] This was an elaborate indirect way to demonstrate the invariance of Lorentz’s relativistic concepts contained in his April 1904 treatise, without having to refer directly to them.

[44] See
Guilini’s *ad hoc* claim in Chapter 30A
that spherical point charges (when Lorentz transformed) become ellipsoids.

[45] Once the concept of ether is eliminated, it becomes the same concept as Einstein’s. Was Poincaré’s proof of the invariance of electric charge Einstein’s source; and if so, why did he not give Poincaré credit?