Journal of Theoretics Vol.36

Restricted
Relativity
A Detailed
Account of the Main Objections
Author: Ali A.
Faraj <a_a_faraj@hotmail.com>
Abstract: In
this paper the cogency and relative strength of Einstein's
Special Relativity Theory (SRT) are evaluated. Additionally, the conceptual framework of
SRT is
reviewed in some detail. This exposition may also serve as a brief review
of the criticism that has been directed against SRT during the
second half of the last century.
Keywords:
electromagnetic, theory, aether.
Introduction
Maxwell's electromagnetic theory requires an "aether" [preferred
spelling so as not to confuse with the anesthetic gas]. Without a carrying medium such as the
aether, the wave concept of light
becomes incomprehensible. The dynamic properties of the aether are wellknown and considered by many to be ad hoc and superfluous.^{1} Within the context of this discussion, only the kinematical
aspects of the aether are relevant. These are certainly more transparent and
internally consistent. A few points need to be emphasized about the
kinematical characteristics of this medium:
 There is nothing in
Maxwell's theory that prohibits the motion of the observable part of the
universe along with its aether, with a constant speed in some direction.
Motions relative to the Maxwellian
aether therefore, are not
equivalent in any strict sense, to motions relative to Newtonian space.
 In Maxwell's theory,
every motion of a physical object must be relative to the aether. That is
because a symmetrical assignment of motions in this case, renders longrange
measurements of motions by optical means useless. Also the motion of the aether
leads to mirage motions of stationary bodies easily noticeable in
shortrange measurements. Since no such mirage motion is ever observed, the
above generalization is admissible.
 The notion of a
stationary aether with respect to moving bodies, does not exclude however,
the possibility of independently contracting or expanding aether at a cosmic
scale. In fact, phenomena explainable by the conventional model of 'expanding
universe' are equally explainable by the idea of 'expanding aether'.
Since the velocity of light relative to the aether
is always equal to c , the ethereal velocity of an isolated system in
which the observer is at rest, can be measured in terms of displacement.
Now, the velocity of the earth around the sun is wellestablished from dynamic perspective. Experimental attempts to determine this velocity on
the basis of Maxwell's theory have failed. Positive experimental results do
exist, although they do not unambiguously accord with the prediction of the
theory.^{2}
Many theoretical projects have been
undertaken to resolve this quandary, ranging from directly adjusting the
physical parameters of the aether to adopting the
corpuscular theory of Newton. The general consensus however, is
that the kinematical asymmetries predicted by Maxwell's theory are basically
correct,
albeit concealed by some effect. This concealment, according
to the Lorentz theory, is due to the contraction in the physical dimensions
of moving objects in the direction of their motion. Dilation in local time
is dismissed as a mere algebraic curiosity. By contrast, according to SRT, the concealment of asymmetries is due to changes in space
and time caused by relative motions. In this theory the loss in depth
inflected on the modified electrodynamics is offset by extending its scope
to areas that were previously considered to be in the domain of mechanics.
The proposed modification of universal logic constructs, like space and time, is bound to stir up considerable
objections. The main objective of this paper is to investigate those
objections and to evaluate their weight and relevance
in context.
Postulate of
Relativity
This postulate is a collection of relatively
independent assumptions:
A. The laws of nature are the same
with respect to reference frames in uniform motion.
This assumption is a special case that lies at the foundations of Natural
Philosophy (The study of the laws of nature
in the universe).
Obviously, such an assumption cannot be
falsified because whatever exceptions are encountered, they are
automatically utilized in developing more general laws of the natural world.
Consequently,
violations to this axiomatic rule, if found, will not necessarily
be fatal
to SRT or any other theory for that matter.
B. No experiment inside a
physical system can reveal its space motion.
This assumption is in fact a statistical
conclusion based on fairly large, but by no means encompassing, samples of
physical situations. It emerged during the Galilean campaign against the
Ptolemaic System. It has been used ever since by various competing schools
against the aether hypothesis. As a principle, however, it has little or no
logical force of its own.^{3} That is because
the number of potential phenomena inside a physical system, which may reveal
its motion, is unlimited and it cannot possibly be exhausted. It should also
be
pointed out that not only are
the supporters of SRT, who have used
this assumption, but also the proponents of the corpuscular model have used
it as well against the wave theory. This is despite the fact that all
corpuscular theories predict the feasibility of measuring absolute
velocities, not just relative to the aether, but also relative to immobile space
in the Newtonian sense.
On a corpuscular theory, by carefully
measuring variations in the apparent diameters of rotating
spheres (inside a
moving system) as a function of perspective, one can in principle find the velocity relative to Newtonian space. In any case, exceptions to the
above assumption, if found, will probably destroy the conventional
form of SRT, and weaken the case against bringing back the aether.
C. Two observers in uniform
motion must measure exactly the same value of relative velocity between
their coordinate systems.
This is by far the most important assumption
in the cluster of the relativity postulate. Any violation of this axiom, simply
renders the Lorentz equations useless.
D. Temporal and spatial distortions as computed
via
the Lorentz transformation, must be reciprocal
between two coordinate systems in uniform relative motion.
The failure of this assumption will destroy
the metrical interpretation of Einstein's theory. At present, it is widely
acknowledged that measurement distortions are real in a moving system, and
illusory in its stationary counterpart. That is the reciprocity in the
theory, is part ontological and part metrical. This consensus has been
developed almost unconsciously in the wake of the Dingle campaign against SRT
during the 1960s.
E. Each member of a group of
observers in relative motion, can equally assert he is the one who is at
rest and that it is the others that are
moving.
This assumption, of course, flies against a
whole set of known procedures that are routinely used to identify states of rest and
movement in the physical world. For instance, from dynamical
considerations alone, one knows for sure that the Earth is moving relative
to the sun and not the other way around. Nevertheless, this assumption is not
entirely worthless. It points to a background difficulty associated with
measurements in absolute space. For the practicalminded, absolute space
presents a notorious problem,
because if it exists, it is rigid and immobile, yet one can not go out and
grab it. Every point is exactly the same to every observer whether they be
in motion or at rest. It is the homogeneous continuum at its worst.
Postulate of Constancy
In all inertial systems, the
velocity of light is the same.
This postulate is composed of three
independent assumptions:
1. The velocity of light is always
c, regardless of the light
transmitter's velocity at the time of emission.
As long as light is assumed to be a wave
phenomenon, this assumption is misplaced and redundant. The independence of
velocity of light relative to the velocity of its source, is simply a
result direct deduction from the wave concept. Nonetheless, the validity of
this assumption is very crucial for SRT. Maxwell's theory
for example, if this assumption is invalid, can be easily saved by a helper
hypothesis such as the hypothesis of 'Tubes of Force' used by J. J.
Thomson in his theorizing about the ballistic theory.^{5}
None of that is available to Einstein's theory. If the assumption is proved
experimentally to be incorrect, the theory just collapses.
2. The velocity of light is
independent from the velocity of the observer.
The dependency of every
velocity, measured
by an observer, on the rate of change in the displacement of that observer
with time, is one of the most selfevident truths encountered anywhere in
physics. A direct denial of such a truth, therefore, is out of the question.
What Einstein has done in this case, is to assume that the simple truth is
concealed by length contraction and time dilation. Theoretically, it works.
If someone insists that all airplanes bound for Rome have the same speed, he
will undoubtedly account for the ensuing discrepancies when given the
luxury of elastic space and time.
3. The velocity of light is
absolute. No material body can be accelerated to a velocity that
is equal to or
exceeds the velocity of light.
The assumption of a limiting velocity that
cannot be exceeded, is of course a borrowed analogy from thermodynamics
in reference to the absolutezero temperature. It appears unjustifiable and paradoxical.^{6}
However, within the framework of the current
theory, there is no other alternative. Velocities greater than c, lead to
time compression and gross violations of the law of causality.
Lorentz's Equations
To assume that a composite
quantity (e.g.
velocity of light) is constant and its basic units variable, is
quantitatively the equivalent to taking it for granted in reverse. The various
sets of equations that can be deduced from the above symmetry are limited
only by imposing a purpose. Since the objective here is to hide Maxwellian
asymmetries, some additional information is needed. One must know how the velocity of light along longitudinal and transversal paths, is calculated
for a moving system based on Maxwell's theory. One also must be
informed somehow that all of the
attempts to detect the ethereal velocity of Earth,
have been unsuccessful. A convenient way to compute ethereal inequalities of a moving system, is to
apply
them in terms of traveltime differences
between round trips along closed paths.
If L is the path length in the
direction of a system that is
moving with a velocity v, then according to
Maxwell's theory, the total time of a round trip along the longitudinal
path, t_{1} is:
t_{1} = 2Lc / (c^{2}
 v^{2})
(1)
and along an equal path in transversal
direction, t_{2} is:
t_{2} = 2L / (c^{2}
 v^{2})^{1 /2}
(2)
Now, if all attempts to detect ethereal
asymmetries have failed, then the failure can mean only one thing:
that t_{1}
= t_{2} . If one is still assuming that Maxwell's theory is valid,
then t_{1} = t_{2} either because the longitudinal path is
contracting, or because the transversal path is expanding. Quantitatively,
length expansion is more complicated than length contraction
as it requires
taking care of length expansion not only along one dimension, but also
through an angle of 360 degrees around the velocity vector of a moving
system. Furthermore, transversal expansion cannot be used to account for
other optical phenomena such as the Doppler Effect and the Fresnel
convection. Longitudinal contraction, therefore, is the right choice.
Total longitudinal and transversal paths of
a light beam in a moving system are readily available via the
multiplication of t_{1} and t_{2} by the
velocity of light in vacuum, respectively. By assuming that they are equal,
one can obtain the socalled Lorentz factor, f :
f
= t_{2} / t_{1} = [1  (v^{2} / c^{2})]^{½}
(3)
This factor is then used to create a
Lorentzian analogue to the Galilean equations
for the two Einsteinian
coordinate systems, xyzt and x'y'z't', in uniform relative motion:
x'
= (x  vt) / [1  (v^{2} / c^{2})]^{½}
(4),
y'
= y
(5),
z'
= z
(6),
t'
= [t  (vx / c^{2})] / [1  (v^{2} / c^{2})]^{½}
(7) .^{7}
If an object is moving with a constant
velocity u relative to one of the two coordinate systems, then its
relative velocity u' as observed from the other system is
u'
= (v + u) / [1 + (vu / c^{2})]
(8) .^{8}
Now, we must note two major difficulties for
the theory under discussion:
 According to the above
equations, all things, as viewed from the other system, run slow. All
motions, physical and physiological processes, clocks, cause and effect
nexus, etc., go sluggish, on the basis of these equations . Why do all
velocities within the system, slow down, but not the velocity of the system
as whole? It has been, of course, exempted by the third assumption in the
relativity postulate. Einstein's theory, therefore, appears to be
selfcontradictory. It presupposes absolute space and time in order to move
forward.^{9} That is not unexpected. The whole
concept of relative motion is a Galilean creation. The current theory does
not redefine the concept nor does it contain any new procedure for
measuring relative velocities between moving systems.
 Length contraction by
the Lorentz factor, does not entirely
eliminate Maxwellian asymmetries. The
transversal path in the MichelsonMorley experiment, for instance, is an
isosceles triangle with a base that lies along the longitudinal direction.
It must therefore be contracting by the same factor as well. The total
transversal path in this experiment, P_{trans}, is
P_{trans}
= 2 [L^{2} + (vt_{2} / 2)^{2}]^{1/2}
(9)
The displacement ( vt_{2} )
is in the longitudinal direction, and it must be contracting by the Lorentz
factor. Since time flow is the same for the whole system, the factor of
its slowdown cancels out, upon computing the ratio of the two paths. Thus, if
it is assumed that only the arms of the apparatus are contracting, then after
contraction, the ratio between the longitudinal path P_{long}
and the transversal path P_{trans}_{ }, is
P_{long} / P_{trans}
= [(c^{2}  v^{2} f^{2} )
/ (c^{2}  v^{2} )] ^{½}
= [1 + (v^{4} / c^{4} )/f^{2}]
^{½} (10a) ,
where f is the Lorentz factor. On
the other hand, if it is assumed that the whole horizontal path is
contracting, then the ratio between the longitudinal path P_{long}
and the transversal path P_{trans}_{ }, after contraction is
P_{long} / P_{trans}
= cf / (c^{2}  v^{2} f^{2}
)^{½} = {f^{2} / [f^{2} + (v^{4}
/ c^{4} )]} ^{½}
(10b)
.
In both cases, a moving observer is
therefore able, in principle, to notice that the
velocity of light is not the same in
all directions, contrary to the second assumption in the constancy
postulate.
In his 1905 paper, Einstein started
out with the
notion of total contraction but then switched to the Lorentzian notion of
partial contraction, without stating clearly his motivation.^{9} It should be
noted however, that it is not enough to assert
that c is invariant. Length contraction and time slowdown are the basic
requirements for the postulated invariability of velocity of light in every coordinate system. The problem is that no coherent set of equations can be
constructed to achieve that goal in a selfconsistent manner under all
circumstances.
Universal Simultaneity
Maxwellian asymmetries can be grouped into
two categories: plane asymmetries and linear asymmetries. Plane
asymmetries, although they are not completely concealed as demonstrated
above, are practically made unaccessible to
experimental testing by the Lorentz equations. Those equations however, cannot be used in any way
to hide linear asymmetries. Within the framework of the present theory, the
exclusion of universal simultaneity is the only way to conceal linear
asymmetries. The procedure is illustrated by Einstein's imaginary train.
Consider a point O midway between two distant points A and B, along a
railway station. Then imagine a very long train traveling with a constant
velocity v. When the A' (front end of the train) coincides with A (its
rear end), B' with B, and its midpoint O' coincides with O, then two flashes
of light are sent.^{10} There are three
theories applicable to this situation, namely the
Maxwell theory, the
Emission theory, and the Einstein theory. Two cases have to be considered
here:
I. The two sources of light
are located at A and B respectively.
In the reference frame of the railway
station, the three theories agree that the two flashes arrive simultaneously
at O, after a time t
has elapsed since emission, i.e.
t = AB / 2c
(11)
.
In the reference frame of the moving train,
Maxwell's theory and the Emission theory maintain that flash A arrives at O'
after a period t_{1}:
t_{1 }= A'B' / 2(c
+ v) (12)
.
Flash B arrives at O' after a period t_{2}:
t_{2 }= A'B' / 2(c
 v)
(13)
.
By contrast, Einstein's theory asserts that
the two flashes arrive at O' after a period t',
t' = A'B' / 2c
(14)
.
They did not arrive simultaneously at O',
not because their velocities relative to the moving train were
different but because, according to this theory with respect to the moving frame of
reference, flash A was emitted earlier and flash B later than the time of
emission as measured in the stationary reference
frame of the railway station.
Earlier
and later, it's just like that! The problem, of course, is
that there is no quantitative method for determining by how much they are
earlier or by how much they are later, on the basis of this theory. As a
result, Einstein's operational procedure, which works just fine within a
single coordinate system, breaks down
completely when it comes to
synchronizing clocks in relative motion.
II. The sources of light
are mounted at A' and B' respectively:
1. According to Maxwell's
theory, the two flashes arrive simultaneously at O, after a period t:
t = AB / 2c
(15)
Relative to the moving train, flash A'
arrives at O' after a period t'_{1 }as
shown by:
t'_{1 }= A'B' /
2(c + v) (16)
Flash B' arrives at O', after a period t'_{2
}as shown here:
t'_{2 }= A'B' /
2(c  v) (17)
Therefore
for this theory, it makes no difference whether the
source of light is stationary or moving.
2. According to the
Emission theory, flash A' arrives at O, after a time t_{A' }:
t_{A' }=
AB / 2 (c  v)
(18)
Flash B' arrives at O, after t_{B' }:
t_{B' }=
AB / 2(c + v)
(19)
In the reference frame of the moving train,
flash A' arrives at O', after a period t'_{A' }:
t'_{A' }=
(A'B' / 2)  v t'_{A' }) / (c
 v) = A'B' / 2c
(20)
Flash B' arrives at O', after a period t'_{B'
},
t'_{B' }= (A'B'
/ 2) + v t'_{B' }) / (c + v) = A'B' / 2c
(21)
Therefore, according to this theory, the two
flashes arrive simultaneously at O'.
3. According to Einstein's
theory, the flashes arrive simultaneously at O', after a period t':
t' = A'B' / 2c
(22)
With respect to the railway station, the
actual travel time for the two flashes t, is the same, i.e.
t = AB / 2c
(23)
The two flashes arrive one after the other
at O, only because they were emitted this way, as observed from the
stationary frame of reference of the railway station.
Thus Einstein's theory has removed the
problem of Maxwellian asymmetries from the domain of physics
and dropped it
into the realm of formal logic. After imposing an elasticity of time by the
Lorentz transformation, thereby
denies the validity of universal simultaneity,
and it does
not seem too audacious in the context of this theory. The consequences of
this action may not be harmful in the short run but
in the long run, they could be very damaging to any theory. Through the ages, no hypothesis
has ever held its ground for long against the enormous pressure exerted by
the universal principles of Reason.^{11}
It should be clear from the above comparison
of the three theories, that relative simultaneity and the severe
limitations placed on the synchronization of timemeasuring instruments, are
peculiar aspects of the Einstein theory.^{12}
Synchronizing clocks, in order to establish temporal relations between
events, poses no problem whatsoever within the framework of the other two
theories. It should be noted, however, that temporal relations, when based
on actual measurements not on assumed initial conditions, are never exact.
Universal simultaneity, therefore, always implies a certain level of
accuracy. Accordingly, the probability of two events remaining simultaneous
beyond this implied level, approaches zero
as the degree of precision in
measuring time approaches infinity.
Modification of Mechanics
According to Maxwell's theory, the velocity
of all ethereal disturbances is constant. Constancy of ethereal velocity
has an immediate consequence. Curvature of tracks is employed in the
measurement of chargetomass ratios for charged particles in motion
perpendicular to the electric and magnetic fields. The observed variability of
those ratios, therefore, must be on the basis of this theory caused by
variable mass, i.e.
m' = m / [1  (v^{2}
/ c^{2})]^{½}
(24)
where m is the rest mass of the
particle, and v is its velocity as deduced from the path curvature.
Clearly, the deduced velocity is hypothetical, and a byproduct of adjusting
the theoretical parameters to fit the observations.^{13}
Einstein's theory has generalized this case and extended its scope to
include mechanics.
Thus for an object of mass m and
velocity v , the linear momentum p and the kinetic energy E
are
p = mv / [1  (v^{2}
/ c^{2})]^{½}
(25)
and
E = m c^{2}
/ [1  (v^{2} / c^{2})]^{½}
(26)
.^{14}
Obviously, this modification is necessary. Without it, the third assumption
of the constancy postulate would be disposed with, by
experiment at once.
In other words, if velocity of light is an upper limit for all velocities,
then variability of mass is the only available alternative to account for
unlimited linear momentums and kinetic energies of moving materials.
Finally, the equivalence of mass and energy is deduced from the previous
formulae. The procedure seems arbitrary,^{9}
but there is little doubt that the existence of many hypothetical entities
in particle physics depends entirely on those modifications.
It should be pointed out that the
redefinition of the concept of mass has been proposed earlier by E. Mach who
considered the given definition in Principia unsatisfactory and
circular. He proposed a redefinition in terms of interaction with distant matter.
This, however, is even more circular and unsatisfactory. The circularity of
Principia is benign and harmless,
while the Machian circularity is
vicious and malignant in that a body cannot have a mass without interaction with
distant matter and it cannot interact with distant matter without first
having
mass.
Increasing spheres of influence may soften
this circularity, nevertheless, Mach himself has little patience for such
fundamental locality. In fact, he does not challenge Newton's law of
gravity.^{15} His gravitational field,
therefore, is a virtual solid body extending to infinity. It behaves as
single unit and when it moves, the universe is instantly informed of that
movement.
Dingle's
Paradox
According to Einstein's theory,
two similar clocks, A and B, in uniform relative motion, work at different
rates. Since this situation is symmetrical, it follows that if A is faster
than B, then B must be faster than A. This is impossible. The theory,
therefore, must be false.^{3}
H. Dingle has worked out the details, and
transformed this paradox from vaguely conceived idea, to a bullying device
of the first order to silence his opponents. Like Galileo before him, Dingle
is a great believer in the power of Reason, and was
clearly frustrated by the
inertia of his contemporaries. In any case, he has succeeded in restoring
respect to Newtonian absolutes and linking his own name with the clock
paradox forever.
Dingle's paradox destroys the reciprocity of
real effects, and forces the defenders of the theory to make one of two
difficult choices, both of which
would reduce absolute time
and absolute space to mere 'shadows':
A. Temporal and spacial
distortions are optical illusions.
From the standpoint of logic, this option is
very appealing. It restores the harmony between the two Einstein
postulates, leaving the concealment of the Maxwell asymmetries intact and
weeding out all claims against absolute space, absolute time, and absolute
velocity. Currently, this choice is the least popular, but there can be
no doubt about its importance as the last line of defense for the current
theory.
B. The dilation
of time and
contraction of length are real in the moving system and illusory in its
stationary counterpart.
This popular option destroys the second and
the fifth assumptions in the relativity postulate, and restores the
Maxwellian asymmetries at a different level. As mentioned earlier,
Einstein's theory takes for granted the Galilean concept of relative motion
between coordinate systems. As far as the banishment of Newtonian absolutes
from physics is concerned, this concept is a Trojan horse. The concept is
neither simple nor axiomatic. Relative velocity is a combined velocity. The
following points can be made about this velocity:
 For every value of the
relative velocity v, there is an infinite number of actual
velocities that can be combined in infinite number of ways, to produce the
observed resultant velocity. The relative velocity of two systems velocity
could be, for example, the resultant of (v + 0), (0 +
v), (0.5v +0.5v), (2v  v), (v
+ 2v), or (100v  99v).
 Relative velocity as
measured by any observer, is a mixture of two types of velocities, namely,
actual velocity and apparent velocity. The actual velocity is the velocity
of the external system. The apparent velocity is the reflection of the
observer's own velocity on the external system.
 Absolute velocity is a
generalization by induction from actual velocities. To deny the validity of
absolute velocities in kinematics, therefore, is as pointless as denying the
validity of limits in calculus.
According to the above choice, real
Einsteinian effects are produced by actual velocities, and the illusory ones
are caused by apparent velocities. It is wellknown that the reunion of two
Einsteinian observers, ends always in a disaster for the relativity
postulate.^{9} It reintroduces the notorious
asymmetries of Maxwell. Even without a reunion, the theory still faces difficulty. The reciprocity of the results, real or illusory, obtained by
employing the Lorentz transformation, is tacitly based on the assumption of
equal units of length and equal intervals of time in the two systems. What
each observer observes in the other system, is simply those units and
intervals multiplied by the Lorentz factor and the reciprocal of the Lorentz
factor, respectively. If, for example, the intrinsic duration of a
particular process is t, then its duration as viewed from the other system
is slowed down by the reciprocal of the Lorentz factor. The observer
compares the duration of this process with the duration of a similar process
in his own system, and concludes that it is longer by the reciprocal of the
Lorentz factor. Now, if the time in a system moving with the actual velocity
is intrinsically slower, and the time in a counterpart moving with the
apparent velocity is intrinsically faster, then how can the apparent
reciprocity be preserved? The only way to preserve reciprocity, in this
case, is to postulate that the apparentlymoving observer sees real slowdown
of duration, and the actuallymoving observer observes the intrinsically faster durations multiplied, not by the reciprocal of the
Lorentz factor, but by the square of the reciprocal of the Lorentz factor.
Obviously, this procedure is ad hoc, and its main purpose is to keep the
appearances of symmetry between Einsteinian coordinate systems.
Acceleration provides no way out of the
above difficulty. Accelerations and decelerations, in this case, have
nonvarying effects on clocks. Therefore, they cannot be used to account for accumulative differences in
the time flow of the Lorentz equations, in any consistent way.
A very popular variation on the Dingle
paradox, is the socalled 'twin paradox'. The clock, in this case, is
biological. Two identical twins, one stays on Earth, and the other is
ejected with c[1  10^{99}] towards the galaxy of
Andromeda. This form of the Dingle paradox certainly has some psychological
elements attached to it. As deduced from the Lorentz equations, the
traveling twin shall live for eons as
observed by the twin remaining on Earth. Interestingly, the space twin will
experience a normal lifespan even though the Earth bound twin sees his
brother living for eons. So it is more a time travel into the future rather
than an extension of mortality.
The special case above is very convenient
for highlighting the central difficulty posed by the Dingle Paradox. As it
is known, many of the socalled resolutions have been geared primarily
towards justifying the reappearance of the old asymmetries in this paradox.
But that is a secondary and minor problem. In a nutshell, the
primary and the most daunting problem is the following: Those
asymmetries, in their new disguise, provide the experimenter with exactly
the same opportunity to carry out exactly the same unsuccessful attempts as
the old Maxwellian asymmetries. In particular, these new
asymmetries can be easily plugged into the Lorentz Equations to compute no
less than the absolute velocity of the Earth without any reference to any
thing else in the universe. It is
clearly a violation of the Relativity
Postulate. Let's assume, for a moment, that Earth is moving with a
constant speed of 0.555c relative to Mach's Distant Matter. Using only
spaceships, multiple identical twins, and Einstein's Theory of Relativity,
can we determine that velocity? The answer is yes. Spaceships are wellbehaved projectiles.
They acquire the velocity of their launching pad in the Einsteinian sense,
that is. Another important note is that no time reverse is allowed by
Einstein's theory albeit postulated by many modern SRT theorists such as Kip
Thorne, that time for an object traveling away from the observer will slow
down, while time for an object traveling towards the observer will speed up,
leaving the two twins the same age when they are reunited on Earth.^{17}
For all
practical purposes, the idea of motion
being relative to the universe, is nothing
but a grandiose metaphor for the notion of motions relative to Newtonian
space. It is true that one cannot determine, by practical
means, whether the Earth is moving relative to the
universe or that if the universe
is moving relative to the Earth.^{18}
Also one cannot determine by the same means,
whether or not the Earth
is rotating relative to Absolute Space, or whether Absolute Space is
rotating with respect to Earth. Of course, the idea of rotating or moving
space is a sheer nonsense. But the motion of the entire universe (its space
included) is no less nonsensical. In any case, the idea of velocities
relative to the universe, is the reinstallment and triumphant return of the
notion of the absolute velocities of kinematics.
General
Remarks
The representation of Einstein's theory in
the form of postulates and deductions, has some resemblance to the method
employed in Euclid's geometry. This similarity, however, is superficial. The
Euclidean method is strictly topdown and deductive. Take for granted
Euclid's axioms and the consequences followed by logical necessity. This is
not the case with the Einsteinian postulates. Unlike the axioms, these
postulates are not at the top of the conceptual hierarchy. Also,
they are not
simple, abstract, or even selfevident. Furthermore, Einstein's postulates
require modifications of space and time. Because these concepts are higher
and more general than the postulates of relativity and constancy, the
required reformulation can only be done by induction. Thus, by Euclidean
standards, the representation above is upside down. This upsidedown method
is the main cause for making arbitrary decisions by Einstein at every turn
in his theory.^{9}
Induction and deduction are, of course,
complementary. That is, to extract the abstract from the concrete, induction
must be used, and to reach the concrete through the abstract, deduction must
be employed. Induction is basically, guessing. There are no wellestablished
procedures, no formal rules, and certainly no logical necessity. Induction,
however, is not a game of free associations. For the inductive method to
work properly, the following conditions have to be fulfilled:
 Inferences must be based
on specified sets of concrete cases.
 These sets of actual
situations must be deducible from the inferences. If they are non sequitur,
then the inductive process has failed.
 Inferences must not have
consequences that conflict with experience and observation.
 Inferences must not
contradict other inferences higher on the conceptual scale. Because these
are based on larger samples of concrete situations, it is highly unlikely
that offending inferences of this sort are correct.
 The inductive aspects of
the scientific method, are also subject to further restrictions imposed by
Baconian procedures.
Although induction and deduction are
complementary, induction is by far the most fundamental. The roots of every
idea in every field, can be always traced back to induction. Even if it is
proved that all or some of the general principles of reasoning are
hardwired
into the human brain, these principles are still independently reproducible
by induction.
Clearly, the number of potential inferences
that can be drawn from a given set of physical phenomena, is infinite. The
state of absolute conceptual perfection, therefore, is only a potentiality.
It is true that in physics, the claim of nearing the end has
been made from time to time. Examined closely, however, this claim is often
just an other way of saying: 'The current theories and research
programs have been exhausted. They offer no opportunity for discovery.
Change them'.
Moving upward, along the conceptual pyramid,
one notices a trend of convergence and drastic drop in the number of
potential inferences to finally find an upper limit for the abstraction process.
In other words, the levels of generalization are steep and limited. At the
top of the hierarchy, there are only very few independent concepts that
cannot be abstracted any further. These include the three logical laws (Is,
Or, Excluded Middle), the three essences (Space, Time,
Matter), and the Law of Causality. They are
simple, axiomatic, selfevident, and their denial presupposes their
validity.
Throughout history, there have been
countless attempts to break away from those perceived shackles. They all
have one thing in common. After an initial flurry of activities, those
attempts, without exception, always end up in stagnation, superstition, and
selfimposed blindness and deafness towards very essential aspects of
reality.
Since the days of Thales and Anaximander of
Miletus, it has been a rule of thumb in Natural Philosophy, that phenomena
of matter must be explained by the dynamics of matter. No advance, in this
field, can be achieved by mixing up the essences, or by importing extraneous
hypotheses. Einstein's theory, clearly, violates this rule. Mixing up the
essences, in this case, is done in two separate steps. It is done in the
theory under discussion as well as by assuming the motion of matter effects space and
time. In his general theory, Einstein also assumes that space and time are
produced by gravity of matter . In both cases, beyond the initial
assumptions, there is not the slightest possibility of discovering
mechanisms or even developing a theoretical rationale, for this postulated
process.
The gap between space, time, and matter, is simply unbridgeable.
Furthermore, the proposed tests to verify these assumptions are anything but
relevant. For instance, the clocks may run faster or slower, for countless number of dynamical
reasons. Why should anyone ignore the dynamics of matter altogether and
make an unjustified jump to a
completely different essence in order to explain
the phenomenon? In addition, time by definition is a homogeneous continuum.
In other words, the flow of time already has all the capabilities to
accommodate all paces and rates for all processes at once. It is up to the
processes of matter themselves to choose the paces that suit them from this
universal continuum.
With regard to geometry, in the current
theory, Einstein works within the framework of Euclid's geometry. For his
theory of gravitation, however, he chooses as a
basis Riemannian
geometry. Riemann's geometry, of course, is based on removing the
impossibility of intersection imposed by the Euclidean axiom of parallelism.
Denying this impossibility, as well as extending its scope further, both
leads to two selfconsistent geometries that differ from each other, and from
that of Euclid in many respects. However, there is a catch. A denial of the
parallelism axiom implies inescapable
demotion in the abstract standards of
the definitions. That is, the points, the lines, etc., are no longer
absolutely abstract as in the Euclidean geometry, but rather
relatively abstract
and closer to the physical dimensions from which they have been abstracted
in the first place. This lowering in the standards, could be useful in
dealing with some particular problems such
as the trajectories of moving bodies, for
example. Geometries of this kind, however, are not rivals or substitutes for
Euclid's geometry in dealing with the spatial continuum. They don't even
come close to the level of universality and simplicity of Euclidean
geometry.
Conclusion
Theories and hypotheses in
physics are always exposed to endless challenges by observation and
experiment. Einstein's theory is no exception. Most of the assumptions of
its two postulates are under continuous threat of being experimentally invalidated. It is not inconceivable that a clock synchronized and thrown
at 0.999c will come back synchronized. In addition to this burden,
Einstein's theory as shown in this
paper, faces serious difficulties at two
fronts. From inside, the theory is plagued by internal inconsistencies,^{19} fuzzy logic,^{20} and
perpetual tension between its two postulates. From outside, the current
theory is subjected to a tremendous pressure by the universal concepts that
have been left behind. The theory has placed itself firmly against some of
the absolutes of Natural Philosophy. At the same time, it has done its best
to save the laws of logic and causality. The problem is that the general
principles of Natural Philosophy form a highly integrated package. Take it
all or leave it all. There is no possibility of choosing only the items that
one likes from this package and to
do so would be to invite irresolvable
contradictions.
Einstein's theory has been criticized by the importing of many metaphysical issues into the heartland of physics. It is
not easy to evaluate the possible effects of this import on the development
of physics in the long term. On one hand, one may say: "Let
mainstreamers wrestle with the eternal conundrums of metaphysics and build
up philosophical muscles." On the other hand, it is
welldocumented that the ancient Greeks, during the Hellenistic Era, had
engaged in just the same
playing around with essences and
principles, and the Dark Ages weren't far behind. The current state of physics should be a source of concern,
but not overwhelming so, as the present status quo is likely
to persist for the next hundred years.
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Acknowledgments
My thanks to JW, Rosen, and Leon, for
many interesting and stimulating discussions on Special Relativity and
related matters.
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