Maxwell’s Equations and Special Relativity Theory 2

Special Relativity Theory

Enter Einstein in 1905 with his famous paper on SRT(4).Contrary

to popular
belief, he was not attempting to address the 1887

Michelson-Morley (M-M)
null-result, and was reportedly unaware

of it at the time(5).In effect, he
borrowed, and then redefined,

the Lorentz transformation in order to address the
invariance

problem with the Maxwell Equations. He also stated two
postulates.

Einstein’s First Postulate was a restatement of the principle

of
relativity (not to be confused with the Theory of Relativity).

The principle of
relativity is the antiptolemaic epitome of

enlightenment and common sense, and
was known during the time

of Galileo, if not earlier. It was first stated by
Newton in

his Principia(6)over three hundred years ago. In essence, it

says
that the laws of physics, when properly formulated, remain

equally valid in all
(inertial) frames moving with uniform

velocity with respect to each other. All
physicists accept

this principle without reservation.

Einstein’s Second Postulate states that the velocity of light

is independent
of the state of motion of its emitting source.

Actually, this is not at all an
unusual proposal, and it

would be expected of a medium-based (aether) theory. The

analogy to sound waves is irresistible. When a train whistle

blows, the
speed of sound is independent of the speed of the

train, but not of the velocity
of the wind carrying the sound

to the observer. Here, the air molecules are the
medium, and

they play the equivalent role of the aether for

electromagnetism.
But SRT is not an aether-based theory, at

least not directly. (General
relativity uses the concept of

"curved spacetime." Matter supposedly causes the
curving of

"space," and "curved space" causes the bending of light rays.

From a
metaphysical standpoint, curved space-time is just as

audacious and arbitrary as
the nebulous aether of the nineteenth

century.) And although not explicitly
stated by Einstein, some

thought will convince the reader that the Second
Postulate, when

combined with the principle of relativity, results in a velocity

of light that is also independent of the receiver (the observer),

because
the emitting source can take on any velocity including

that of the receiver. So
here we have a prediction resulting in

a sharp departure from our everyday
experience.

It has been stated that Einstein independently derived

the Lorentz
transformation using his two postulates, but this

is not true. Taken alone, they
are insufficient to derive the

Lorentz transformation uniquely. Further
assumptions must be

made to do so; otherwise, several alternative
transformations

can be derived from them.(7) Nevertheless, in 1905 this was a

tentative start toward a salvage operation of the Maxwell

Equations for
observations at high speeds, and physicists were

willing to overlook the smell
of covariance, and the use of an

ad hoc transformation, if it would rescue the
Holy Grail. As

Phipps has pointed out,(8) this was a bizarre turn of events, for

there were competing theories at the time, theories capable of

remedying the
situation without the need to tamper with the

time-honored concepts of space and
time. This is all the more

poignant, considering the fact that the Lorentz
transformation

intermixes and scrambles space and time, something that is

unfounded and erroneous.

Problems and Paradoxes of SRT

Before we present alternative theories that could
be used to

replace SRT, it is important to discuss the serious problems

and
paradoxes associated with the use of SRT. The full impact

of this most unusual
theory is rarely discussed, and the

first warning signs of trouble appeared
shortly after the

1905 paper was published. For simplicity, a single Lorentz

transformation is normally applied along one coordinate axis.

But what about
the more general case of two linear, but

nonaligned (non-collinear)
translations? You might assume

that this merely adds complexity to the
calculation, but

not so- the theory breaks down. The results depend upon the

order in which the two translations are applied. For example,

apply two
transformations in succession, with the velocities

of the two systems pointed in
different directions, say,

along the x axis and then along the y-axis. Next,
repeat the

calculation by reversing the order, e.g., the y-axis and

then the
x-axis. The result is different. Hence the Lorentz

transformation fails to obey
the commutative law of mathematics,

(a+b = b+a) and a definitive answer eludes
us. This is a paradox,

an absurdity.

Thomas Rotation

Theoreticians were brought in to resuscitate SRT and they

administered the so-called "Thomas Rotation" ("Thomas Precession,"

when
applied to the electron). This is a rotation of coordinate

axes introduced to
compensate for the error between the two results

mentioned above. It might seem
a bit odd that an inertial system,

that is, a moving system with fixed velocity
and no acceleration

nor rotation, should begin to rotate! Furthermore, where did
this

rotational energy come from? Is this a real effect, or is it some

sort of
mathematical artifact, some indication that the Lorentz

transformation (and
hence SRI) is in error?

Some years later, a theoretical prediction(9) for Thomas
Rotation

was published in the British journal Nature, and an experiment

was
conducted by Phipps to determine whether it really existed.

The experiment
produced a null result, and despite the photographic

evidence, it was refused
publication in Nature. Consequently, the

results were published
elsewhere.(10,11) There is also a theoretical

basis for refutation of the Thomas
Rotation.(12)

The Ehrenfest Paradox

If phantom rotation wasn’t bad enough, the next disease
to afflict

SRT was the rigid body problem, otherwise known as the "Ehrenfest

Paradox." Einstein had originally intended SRI to apply to rigid

bodies
only. Ehrenfest asked the question, "What happens when we

have an idealized
rigid disk, and we set it into rotation?"(13)

The outer edge of the disk can be
divided into infinitesimal

segments such that they appear to be moving with a
linear velocity

with respect ro an observer in the laboratory. How would the

Lorentz contraction affect such an object, as viewed by the

observer? The
radius must contract somehow.

In 1910, the first generally accepted answer (now
called the

Herglotz-Noether theorem) said that, since the disk was rigid, it

could not rotate! Of course, there were those who decried this sort

of
non-solution solution, so the next answer to bubble to the surface

said the disk
could rotate if it was somewhat elastic, and not made of

rigid material. So once
again, we have a radical departure from

everyday experience. Newtonian mechanics
has absolutely no problem

with rigid spinning bodies, while Einstein’s approach
expressly

forbids them on purely mathematical grounds.

The Lorentz Contraction

There is also the pole-vaulter paradox, the lever
parado and a

host of other variants. What these all have in common is the
Lorentz

contraction. But do atomic particles shrink in the direction of
their

motion, as viewed by an external observer? Do macro-objects really

shrink?
The author of the Lorentz transformation considered the

contraction effect to
apply only to a deformable electron based on

an aether-stresi theory.(14) He
never intended for his mathematical-

equivalence contraction formula to be
extrapolated to all matter as

a reality. This might explain why H.A. Lorentz was
adamantiy opposed

to SRT until his death in 1928. He intended it to explain the
electron’s

non-uniform concentration (bunching) of electric field lines

perpendicular to its direction of acceleration. In electrical

engineering,
this is similar to the "skin-effect" at macroscopic

levels.(15), pp.149-151 But
length contraction plays no role.

During the first half of the twentieth century,
physicists were eager

to put the Lorentz contraction to the test, and see if the
phenomenon

really existed. Several experiments were performed,16-18 but no
variation

in length was observed. Recently, a modern space-based test has been

proposed by Renshaw.(19) To date, no direct experimental verification of

relativistic length contraction has ever been measured.

The Twin-Paradox

The twin-paradox (also known as the clock-paradox) is without
a

doubt the most famous paradox associated with SRT. Once upon a

time, there
were two twin brothers. One twin ventured into outer

space at relativistic
speeds, while the other twin stayed home.

As extrapolated by SRT, the Lorentz
transformation causes time

itself to slow down, not just for moving subatomic
particles,

but for atoms and molecules, and for bigger objects, say, people!

To
continue with the story, the space traveling twin eventually

reverses course to
return to Earth. Upon his arrival, he discovers

that his Earth-bound brother has
aged many years, while he has aged

only a few. This is considered to be a
paradox because each twin

(each observer) can claim that it is the other who
moves at high

speed as viewed in his own reference frame.

So in SRT, how can one
age more than the other? The

symmetry-breaking event is alleged to be the fact
that the

space traveling twin must reverse course in order to return.

This
causes him undergo accelerations and decelerations that

the other does not
experience. No clear explanation is given

as to why this would break symmetry
and slow the aging process,

especially over a many year period, where the actual
time

involved in acceleration could be quite small.

In reality, there is little
doubt that both twins would age at the

same rate. So there really is no paradox
because there is no

time-dilation. This myth is perhaps the greatest
extrapolation of

elementary observation in the history of science. Let’s take a
careful

look at the evidence supporting the timedilation aspects of SRT.

(There is no time-dilation. This myth is perhaps

the greatest extrapolation of
elementary observation

to the history of science.)

Time-Dilation

The alleged proof for time-dilation is claimed to be among the
most

confirmed experiments in physics. Yet a careful dissection of these

experiments reveals an equally plausible alternative explanation, one

that
does not require time to be a dependent variable.(20-21) There are

three types
of experiments that address this issue, the rate of

radioactive decay of
high-speed mesons in linear motion(22)and in

circular orbit,(23) the transport
of atomic clocks around the globe,

24-25 and (indirectly via) the relativistic
Doppler formula.(20) As

Beckmann has pointed out, in all cases the experimenters
have failed

to ask, let alone answer, whether time itself is dilated, or whether

internal processes are simply slowed by moving through a gravitational

field.(15) PP77-81 To date, no direct experimental verification of

relativistic timedilation has ever been measured.

Do we know what the
"innards" of a high-speed meson consist of?

Nope. Do we know what causes natural
radioactive decay? Not really.

It can be characterized mathematically by a
Poisson distribution,

but the actual internal "trigger" for a particular decay
is unknown.

Could the rate of decay be affected by angular accelerations, or by

traversing a gravitational potential? Think about the last time you

rode an
amusement park ride. Weren’t you affected?

In 1761, the British Royal Navy
awarded John Harrison a cash prize

of 9,000 £ (over $2,000,000 in today’s
currency) for inventing a

navigation-quality timepiece with enough accuracy to
withstand tile

pitching and rolling seas ot the Atlantic. The magnitude of the
residual

error has diminished over the centuries, but the basic problem remains.

We cannot construct an ideal clock using actual materials, even if we

use
cesium atoms by definition. To emphasize this point, let’s take a

look at a
grandfather clock. If we transport such a clock eastward

around the globe, it
will slow down. But if we transport it westward,

it will speed up. The
grandfather clock relies upon the force of gravity

to control the timekeeping
rhythm of its pendulum, in inverse proportion

to the square root of "g." When
transported westward against the rotation

of the earth, the centrifugal force of
the earth’s rotation is diminished

and the effect of its gravity field is
strengthened, if ever so slightly.

Hence the clock speeds up in an increased
gravitational field. And of

course, if flown eastward with the earth’s rotation,
its centrifugal force

is strengthened and the clock slows down a little.
Time-dilation? Of course

not. We explain the outcome of the experiment by
analyzing the "innards" of

the clock. But the influence of gravity applies to
more than just pendulum

clocks. For example in the famous Hafele-Keating
experiment,(25) the atomic

clock transported eastward lost 59 ns, but the atomic
clock transported

westward gained 273 ns, compared to the stationary laboratory
standard.

All physical devices used for time keeping are subject to error when

accelerated, decelerated, or constrained to move linearly through a

variation in gravitational potential.

So if we can’t rely upon experiment,
let’s do the next best thing and

look to theory for an answer. What does
electrodynamics have to say?

Oleg Jefimenko (of Generalizations of Coulomb and
Biot-Savart laws(26)

fame) has answered this question most eloquently. Using
conventional

electrodynamic theory,(27) he has analyzed the interactions of
charged

particles. The simple arrangement shown in Figure 1 can be used as an

oscillatory particle-clock. In many cases, these "particle-clocks"

behave
precisely as predicted by SRT, apparently a brilliant and

stunning confirmation
of the theory. But when this same particle

clock is oriented 90 degrees to its
direction of motion, it behaves

differently. This is not predicted by SRT
(apparently a shocking and

stunning defeat?). In the case of Jefimenko’s
particle clocks, they

slow down for purely conventional reasons, having nothing
to do with

time-dilation. Some clocks slow in accordance with the Lorentz

transformation and some do not. But SRT adopts the Lorentz transformation

exactly, without any wiggle room. In the final analysis, the concept

and
definition of time is metaphysical. It ought not to be subjected

to the whims of
anyone’s pet theory.

Alternative Theories

Einstein’s SRT tampers with space and time in order to
force the

speed of light to be constant with respect to all observers. And

it
pays the price. The theory is reminiscent of a balloon animal.

If squeezed at
one end, it expands at the other, yielding an overall

concervation of paradox.
At least five alternatives to SRT have been

proposed:

1.The speed of light is constant with respect to an unentrained

(or partially
entrained) aether. (This is the equivalent of an more

particularly, it must not
make the absolute reference frame and

violates the principle of relativity.)

2. The speed of light is constant with respect to

the emitting source. This is
the Ritzian "ballistic" theory

where the speed of light is (v+c), like
projectiles fired from

a moving tank (and the antithesis of the Second
Postulate).

3. The speed of light is constant with respect to a fully

entrained
ether.

4. The speed of light is constant with respect to the dominant

local or
gravitational field, as proposed more recently by

Beckmann.(15)

5. The speed of
light is constant with respect to the absorber

(the detector), as proposed more
recently by Phipps.(8)

Long ago, the great optical experimentalist, Albert A. Michelson,

disproved
the first two of these five theories. Note that the M-M

experiment was
compatible with all of these theories with the

exception of number 1. In a
separate experiment, Michelson showed

conclusively that number 2 was
untenable?(28) So contrary to popular

myth, Michelson believed that he had
actually confirmed the existence

of the aether, via theory number 3.

Beckmann
has noted that number 3 and number 4 are nearly equivalent

theories, if you
replace the outdated term "aether" with his more

radical idea of "gravity."
Beckmann’s theory (number 4) squares with

all of the experimental evidence,
because in every case, the observer

has always been tied to the Earth-bound
frame of reference. (The

double-star evidence does not refute his theory.) The
light emitted

(from binary stars revolving about a common center of mass) would

indeed travel with two different velocities initially, and this would

cause
spectral anomalies that are not observed. But the light rays

would merge to a
common velocity as the gravitational fields from

the two stars merged into one
dominant field.(15), P-37 And the dominant

field would change yet again upon
encountering an observer in the

Earth’s gravitational field. Beckmann’s theory
and SRT predict the

same answers to first-order in (v/c), and a decisive
experiment

would have to be performed at second-order, (v/c)^2

In his
outstanding book,(8) Phipps argues forcefully and confidently

for his absorber
theory (number 5) by starting with some of the original

ideas of Heinrich Hertz.
Hertz proposed a minor modification to the

Maxwell Equations in order to make
them invariant to the Galilean

transformation. The modification involved a
simple and straight forward

change from partial derivatives (@/@t) to time
derivatives (d/dt) in

Faraday’s and Ampere’s Laws. This had the excellent effect
of adding

a velocity parameter to the Maxwell Equations (a very pragmatic

modification for dealing with moving inertial frames, wouldn’t you say?).

But unfortunately, Hertz assigned the wrong definition to his new velocity

term, one having to do with the fashionable aether wind of the nineteenth

century. As a result, his "Hertzian Theory" was shot down by experiment.

To
make matters worse, his untimely death in 1894 from blood poisoning,

at the age
of thirty-six, made it impossible for him to catch his mistake

and reassign
proper meaning to the new parameter.

Phipps has continued this work by assigning
the velocity of the detector

to this Hertzian parameter. Phipps goes on to
propose an experiment which

can decide between SRT and his theory. Furthermore,
his experiment can

determine the victor at first-order in (v/c). This sheds some
light on

why experiment has not yet determined a winner among the various
theories

mentioned. With the available technology, experiments at first-order
are

extremely difficult to do, and experiments at second-order are
impossible.

In view of the problems with SRT and the availability of
alternatives, is

it any wonder that there were (and are) several noted
authorities who would

have nothing to do with SRT? Some of the famous ones
included Dingle, Essen,

Ives, Mach, Russell, and Rutherford. (My apologies to
anyone I may have

missed (or included) in the Who’s Who Directory of Heretical
Physics.)

Michelson was even rumored to have said, "I have created a monster."
Wheeler

and Feynman also toyed with the idea of an acausal absorber theory to
replace

SRT. And late in life, Einstein was said to have had second thoughts.

It
is interesting to note that the speed of light is approximately the

same as the
escape velocity from an idealized electron in a Bohr orbit.(29)

Perhaps it will
turn out that theories number 2, 4, and 5 are all correct

within their
respective gravitational spheres of influence.

(Physics, if it is to understand the real world, must build

on the two
primitive and undefinable pillars [space and time].

It must not tamper with them
in order to accommodate higher

concepts. It must not redefine the unthinkable
more particulary,

it most make the primitive pillars observer-dependent.