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**Restricted
Relativity**

**A Detailed Account of the Main
Objections**

**By**

**Ali A. Faraj**

**Abstract
**

The major objections
against Einstein's Special Theory of Relativity are the subject of this
discussion. The aim is to evaluate their cogency and relative strength within
their appropriate context. In addition, the conceptual framework of the theory
has been reviewed in some details. The current exposition may serve as a brief
review of the criticism that has been directed against this theory, during the
second half of the Twentieth Century.

Maxwell's electromagnetic
theory, necessarily, requires an ether. Without a carrying medium such as the
ether, the wave concept of light, in that theory, is incomprehensible. The
dynamical properties of the ether are well-known and considered by many to be ad
hoc and superfluous **[Grayson, 1964]**. Within the context of this
discussion, only the kinematical aspects of the ether are relevant. These are
certainly more transparent and internally consistent. Few points need to be
emphasized about the kinematical characteristics of this
medium:

**1.** Nothing, in Maxwell's theory, prohibits the motion of the observable
part of the universe along with its ether, with a constant speed in some
direction **[Spector, 1972]**. Motions relative to Maxwellian ether
therefore, are not equivalent in any strict sense, to motions relative to
Newtonian space.

**2.** In Maxwell's theory, the motion of every physical object must be
relative to the ether. That is because a symmetrical assignment of motions in
this case, renders long-range measurements of motions by optical means useless.
Also the motion of the ether leads to mirage motions of stationary bodies easily
noticeable in short-range measurements. Since no such mirage motion is ever
observed, the above generalization is admissible.

**3.**** **The notion of 'stationary ether' with respect to
moving bodies, does not exclude however, the possibility of independently
contracting or expanding ether at a cosmic scale. In fact, phenomena explainable
by the conventional model of *'expanding universe'* are equally
explainable by the idea of *'expanding ether'*.

Since velocity of light relative to the ether
is always equal to c , the ethereal velocity of an isolated system in which the
observer is at rest, therefore, can be measured in terms of displacement. Now,
the velocity of the earth around the sun is well-established from dynamical
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**
[Swenson, 1972]**.

Many theoretical projects
have been undertaken to resolve the anomaly, ranging from directly adjusting the
physical parameters of the ether to adopting the theorizing of Isaac Newton
about the corpuscular theory. The general consensus however, is this:
Kinematical asymmetries predicted by the Maxwell theory are basically correct.
They are only 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 mere algebraic curiosity.

By contrast, according to
the Einstein theory, 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
previously considered to be in the domain of mechanics.

The proposed modification
of universal logical 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 relative strength, in the
context of this theory.

This postulate is a
collection of several, relatively independent,
assumptions:

**A.**** ****Laws of nature are the same with
respect to reference frames in uniform motion.**

This assumption is a
special case of the well-known assumption that lies at the foundations of
Natural Philosophy, i.e. **Laws of nature are the same everywhere in the
universe.**

Obviously, such an
assumption cannot be possibly falsified. Because whatever exceptions are
encountered, they are automatically utilized in developing more general laws of
the natural world. That is after all the essence of progress in science.
Consequently, violations of this
axiomatic rule, if found, will not be necessarily fatal to Einstein's theory or
to any other theory for that matter.

**B.**** ****No experiment inside a physical
system can reveal its uniform space motion****. **

This assumption is in fact
a statistical conclusion based on fairly large, but by no means encompassing,
sample 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 ether hypothesis. As a principle, however, it has little or no
logical force of its own **[Dingle, 1972]**. That is because the
number of potential phenomena inside a physical system, which may reveal its
uniform motion, is unlimited and it cannot possibly be exhausted.

It should be pointed out
that not only the supporters of Einstein's theory 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
ether, but relative to immobile space in the Newtonian sense **[Cyrenika,
2000]**.

On a corpuscular theory, by
carefully measuring variations in apparent diameters of rotating spheres, inside
a moving system, as a function of perspective, one in principle can find out the
velocity relative to Newtonian space.

In any case, exceptions to
the above assumption, if are found, they will probably destroy the conventional
form of Einstein's theory, and weaken the case against bringing back the
ether.

**C.**** ****Two observers in uniform motion must
measure exactly the same value of relative velocity between their co-ordinate
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 absolutely
useless.

**D.**** ****Temporal and spatial distortions as
computed from the Lorentz transformation, must be reciprocal between two
co-ordinate 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 half ontological and half metrical. This consensus
has been developed almost unconsciously in the wake of the Dingle campaign
against Special Relativity during the sixties.

**E.**** ****Each member of a group of observers
in relative uniform motion, can equally assert he is the one who is at rest and
the others are moving, or he who is moving and the others are at
rest.**

This assumption, of course,
flies against a whole set of procedures 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, 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 practical-minded, absolute space presents a notorious
problem. They know, intuitively, it exists. They know it is rigid and immobile.
They just can't drive their hooks into it. Every point of it is exactly similar
to the rest. It is the homogeneous continuum at its worst.

**2. Postulate of
Constancy**

**In all inertial
systems, velocity of light is the same.**** **

This postulate is composed
of three independent assumptions:

**A.**** ****Velocity of light is always c,
regardless of whatever velocity, during the time of emission, the emitting body
might have. **

As long as light assumed to
be a wave phenomenon, this assumption is misplaced and redundant. The
independence of velocity of light, in this case, of the velocity of its source,
is simply a result directly deduced from the wave concept. Nonetheless, the
validity of this assumption is very crucial for the Einstein theory. 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 **[Thomson,
1910]**. None of that is available to Einstein's theory. If the
assumption is proved experimentally to be incorrect, the theory just collapses.

**B.**** ****Velocity of light is independent of
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 self-evident 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 slowdown. Theoretically, it
works. If someone insists that all airplanes bound for Rome have the same speed,
he will, presumably, account for the ensuing discrepancies, when given the
luxury of elastic space and time.

**C.**** ****Velocity of light is absolute. No
material body can be accelerated to a velocity equals to or exceeds the velocity
of light.**

The assumption of a
limiting velocity that cannot be exceeded, is of course, a borrowed analogy to
the absolute-zero temperature, from thermodynamics. It appears unjustifiable and
paradoxical **[Kraus, 1993]**.

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.

Nevertheless, for the
fundamental law of causality to
hinge upon the validity of such arbitrary assumption, is, undoubtedly, one of
the most unsatisfactory aspects of Einstein's theory. Not only, it opens the
door for all sorts of irrational conjectures, but also, it can, in the long run,
undermine the scientific enterprise itself. The fantastic explanations of
recently-discovered superluminal phenomena, illustrate this disturbing fact.

**3. Lorentz's
Equations**

From algebraic stand point,
to assume that a composite quantity, e.g. velocity of light, is constant and its
basic units variable, is quantitatively 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 velocity of light along longitudinal and transversal paths, is
calculated for a moving system, on the basis of Maxwell's theory. One also must
be informed somehow that all attempts to detect the ethereal velocity of Earth,
have been unsuccessful. A convenient way to compute ethereal inequalities, for a
moving system, is to be treated in terms of travel-time differences between
round trips along closed paths.

If *L* is the path
length in the direction of a system 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})**

and along an equal path in
transversal direction, *t _{2}* is:

**t _{2} = 2L /
(c^{2} - v^{2})^{1 /2}**

Now, if all attempts to
detect ethereal asymmetries have failed, then the failure can mean only one
thing: t_{1} = t_{2} . If one is still assuming the validity of
Maxwell's theory, 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. 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
through the multiplication of *t _{1} *and

** f**** = t _{2} / t_{1} =
**

This factor is then used to
create a Lorentzian analogue to the Galilean equations, for two Einsteinian
co-ordinate systems, x-y-z-t and x'-y'-z'-t', in uniform relative
motion:

** x'
= (x - vt) / [1 - (v ^{2} /
c^{2})]^{˝}**

** y'
= y****
(3.5),**

** z'
= z****
(3.6),**

** t'
= [t - (vx / c ^{2})] / [1 - (v^{2} /
c^{2})]^{˝}**

**[Born,
1962].**

If an object is moving with
a constant velocity *u* relative to one of the two co-ordinate systems,
then its relative velocity *u' *as observed* *from the other
system,

** u' =
(v + u) / [1 + (vu / c ^{2})]
**

**[Skinner,
1969].**

Now, we must note two major
difficulties for the theory under discussion:

**1.** 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 a whole? It has been, of course,
exempted by the third assumption of the relativity postulate. Einstein's theory,
therefore, appears to be self-contradictory. It presupposes absolute space and
time, in order to move forward **[Rudakov, 1981]**. That is not
unexpected. The whole concept of relative motion is a Galilean creation. The
current theory does not redefine the concept. It does not contain any new
procedure for measuring relative velocities between moving systems either.

**2.** Length contraction by the Lorentz
factor, does not eliminate entirely Maxwellian asymmetries. The transversal path
in the Michelson-Morley experiment, for instance, is an isosceles triangle with
a base that lies along the longitudinal direction. It must be, therefore,
contracting by the same factor as well. The total transversal path in this
experiment, *P _{trans}* is

** P _{trans}
= **

The displacement (
*vt _{2}* ) is in the longitudinal direction, and it must be
contracting by the Lorentz factor. Since the 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's assumed that only the arms of the apparatus are
contracting, then after contraction, the ratio between the longitudinal path

** P _{long} /
P_{trans} = [(c^{2} - v^{2}**

where *f* is the
Lorentz factor. On the other hand, if it's assumed that the whole horizontal
path is contracting, then the ratio between the longitudinal path
*P _{long}* , and the transversal path

** P _{long} /
P_{trans} = cf / (c^{2} - v^{2}**

In both cases, a moving
observer, therefore, is able in principle, to notice that 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 with the notion of total contraction, then switched to the Lorentzian
notion of partial contraction, without stating clearly his motivation
**[Rudakov, 1981].** It should be noted, however, that it is not
enough to assert that c is invariant. Length contraction and time slowdown are
the basic requirement for the postulated invariance of velocity of light in
every co-ordinate system. The problem is that no coherent set of equations can
be constructed to achieve that goal in a self-consistent manner under all
circumstances.

**4. Universal
Simultaneity **

Maxwellian asymmetries can
be grouped into two categories, i.e. plane asymmetries and linear asymmetries.
Plane asymmetries, although they are not completely concealed as demonstrated
above, are practically made by the Lorentz equations, inaccessible to
experimental testing. 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. Imagine a very long train traveling with a constant velocity
*v*. When the front-end of the train A' coincides with A, its rear-end B'
with B, and its mid-point O' coincides with O, two flashes of light are sent
**[Einstein, 1916]**. There are three theories applicable to this
situation, namely, Maxwell's 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*, elapsed since emission, i.e.

** t = AB /
2c
(4.1)**

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)
(4.2)**

Flash B arrives at O' after
a period *t _{2 }*,

** t _{2
}= A'B' / 2(c - v)
(4.3)**

By contrast, Einstein's
theory asserts that the two flashes arrive at O' after a period
*t'*,

** t' = A'B' / 2c
(4.4)**

They did not arrive
simultaneously at O', not because their velocities relative to the moving train
are 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 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
co-ordinate 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
(4.5)**

Relative to the moving
train, flash A' arrives at O' after a period *t' _{1
}*,

** t' _{1
}= A'B' / 2(c + v)
(4.6)**

Flash B' arrives at O',
after a period *t' _{2 }*,

** t' _{2
}= A'B' / 2(c - v)
(4.7)**

For this theory, therefore,
whether the source of light is stationary or moving, makes no difference at all.

**2.** According to the Emission theory,
flash A' arrives at O, after a time *t _{A'
}*,

* t_{A'
}*=

Flash B' arrives at O,
after *t _{B' }*,

* t_{B'
}*=

In the reference frame of
the moving train, flash A' arrives at O', after a period *t' _{A'
}*,

* t'_{A'
}*=

Flash B' arrives at O',
after a period *t' _{B' }*,

* t'_{B'
}*=

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
(4.12)**

With respect to the railway
station, the actual travel time for the two flashes *t*, is the same,
i.e.

**t = AB / 2c
(4.13)**

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 elasticity of time by
the Lorentz transformation, denying the validity of universal simultaneity, does
not seem too audacious, in the context of this theory. The consequences of this
action may not be harmful in the short run. In the long run, however, 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 **[Barter, 1953].**

It should be clear from the
above comparison between the three theories, that relative simultaneity and the
severe limitations placed on the synchronization of time-measuring instruments,
are peculiar aspects of the Einstein theory only** [Essen, 1971].**
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 remain simultaneous beyond this implied level, approaches zero, as the
degree of precision in measuring time, approaches
infinity.

**5. 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 charge-to-mass ratios for charged particles in motion
perpendicular to 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})]^{˝}**

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 by-product
of adjusting theoretical parameters to fit the observations **[Waldron,
1980]**. 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})]^{˝}**

** E =
m****c ^{2} / [1 - (v^{2} /
c^{2})]^{˝}**

**[Einstein,
1922].**
Obviously, this modification is necessary. Without it, the third assumption of
the constancy postulate, would have been 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 **[Rudakov, 1981]**, 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. He considers the given definition in Principia, unsatisfactory and
circular, and proposes 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. By comparison, the Machian circularity is
vicious and malignant: A body cannot have a mass without interaction with
distant matter, but it cannot interact with distant matter without having mass
first.

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* **[Phipps, 2000]**. 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.

**6. 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 ****[Dingle, 1972].**

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 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, neither of which is of any help for reducing
absolute time and absolute space to mere
*'shadows'*:

**A.**** ****Temporal and spatial distortions are
optical illusions.**

From the standpoint of
logic, this option is very appealing. It restores the harmony between the two
Einsteinian postulates, leaves the concealment of the Maxwellian asymmetries
intact, and weeds out all claims against absolute space, absolute time, and
absolute velocity. In the present, this choice is the least popular, but there
can be no doubt about its importance as the last line of defence for the current
theory.

**B.**** ****The slowdown 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 co-ordinate 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:

**1.** 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 *v* could be, for example,
the resultant of **(v + 0)****, ****(0 +
v)****,** **(0.5v +0.5v)****,
****(2v - v)****, ****(-v +
2v)****, or ****(100v - 99v)****.
**

**2.** The 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.

**3.** 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 well-known that the
re-union of two Einsteinian observers, ends always in a disaster for the
relativity postulate **[Rudakov, 1981]. **It re-introduces the
notorious asymmetries of Maxwell.

Even without a re-union,
the theory still faces a 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 apparently-moving observer
sees real slowdown of duration, and the actually-moving 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 co-ordinate systems.

Acceleration provides no
way out of the above difficulty. Accelerations and decelerations, in this case,
have non-varying effects on clocks **[Selleri et al, 1998]**.
Therefore, they cannot be used to account for accumulative differences in the
time flow of the Lorentz equations, in any consistent way. However, Einstein’s Theory of
Gravitation can be used to justify the destruction of reciprocity, by treating
acceleration, in this case, as a special kind of artificial gravity. In short, the original symmetry of the
theory, under discussion, is impossible to restore, due to this paradox, and it
is lost forever.

A very popular variation on
the Dingle paradox, is the so-called '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.
This postponement of his mortality is a great feat, even if the outcome is not
certain.

By terrestrial standards,
however, the life of the ejected twin is anything but pleasant. In addition to
the problem of how to survive wandering meteorites in outer space, he is
technically a frozen mummy in time. His world is extremely sluggish. His own
mind is unbelievably lazy. It takes him centuries to solve a simple problem such
as * '01 + 01 = 10 according
to the binary system'.* His perception of time is also dull.
Millenniums, for him, feel like seconds. What is the point of living millions of
years, if he can't have a feeling for it? By using the Lorentz equations, if he
is wicked enough, he may draw some pleasure from the conclusion: '

The special case above is
very convenient for highlighting the central difficulty posed by the Dingle
Paradox. As it is known, many of the so-called resolutions have been geared
primarily towards justifying the re-appearance of the old asymmetries in this
paradox. But that, in fact, 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's a clear violation of the Relativity Postulate.

Let's assume, for a moment,
that the earth is moving with a constant speed of 0.888c 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,
**'beautifully unexpected'**** **is yes. Spaceships are
well-behaved 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. The traveling twin may delay the ageing process
of his body indefinitely. But under no circumstance, he can get younger, undo
the ageing effect, or reverse the arrow of time. That, at least, is the official
stand of the current theory. Given these two stipulations, the road is now open
for finding out, experimentally, the velocity of Earth with respect to the
universe.

In Terrestrial Time, let
the round trip of each traveling twin, be two moths. Suppose it is
practically-possible to fire each spaceship with a constant velocity of 0.888c,
in some direction, relative to Earth. By constructing a random sample of various
directions, therefore, the basic asymmetry can be discovered. The twin traveling
in the direction of the earth motion, will come back younger than his siblings
by the expected amount. That is, if he is wise enough to turn his spacecraft
around without putting it at rest with respect to the universe.

On the other hand, the twin
ejected in the opposite direction, will return older. That is because, during
the first leg of his trip, his inertial time is running more quickly, compared
to that of his stay-at-home siblings. During the second leg of the trip, he is,
of course, moving faster, and hence his local time is running more slowly than
the Terrestrial Time. But the slowdown of the time of this second leg, can do
nothing to change the physiological effect already done by the fast-running time
of the first leg. He must, thus, come back older than his resident siblings.

Between these two extremes,
the age-difference function varies sinusoidally with direction. By comparing the
deviations of these measured values, from the values expected theoretically on
the assumption of Earth at rest with the universe, one can, in principle,
determine the velocity of the earth relative to the cosmos.

Now, for all practical
purposes, the idea of motions relative to the universe, is nothing but a
grandiose metaphor for the notion of motions relative to Newtonian space. It is
true that, in this case, one cannot determine, by practical means, whether the
earth is moving relative to the universe, or the universe is moving relative to
the earth **[Gardner, 1976].** But one, also, cannot determine, by
the same means, whether, for example, 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 a re-instalment and triumphant return of
the notion of absolute velocities of kinematics.

**7. 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 top-down and deductive. Take for
granted Euclid's axioms, and the consequences follow 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. They are not simple,
abstract, or self-evident. 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 be done only by induction. Thus, by Euclidean standards, the
representation above is upside down. This upside-down method is the main cause
for making arbitrary decisions by Einstein at every turn in his theory
**[Rudakov, 1981].**

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 well-established 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:

**1.** Inferences must be based on
specified sets of concrete cases.

**2.** These sets of actual situations
must be deducible from the inferences. If they are non sequitur, then the
inductive process has failed.

**3.** Inferences must not have
consequences that conflict with experience and
observation.

**4.** 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.

**5.** 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 hard-wired
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 in particular, 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 programmes 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 and finally 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, self-evident, 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
self-imposed 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, 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, those little instruments of human ingenuity, may run faster or slower,
for countless number of dynamical reasons. Why should anyone ignore the dynamics
of matter altogether, and make unjustified jump to 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, from the infinitely small to
the infinitely large, for all processes, all 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, the 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 lead to two
self-consistent 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 relatively abstract and closer to the physical
dimensions from which they have been abstracted in the first place. This
lowering of the standards, could be useful in dealing with some particular
problems, 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 the Euclidean geometry.

**8. Conclusion
**

Theories and hypotheses in
physics, as it is known, 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
falsified. It is not inconceivable that a clock synchronized and thrown with
0.999c, will come back sound and synchronized. In addition to this burden,
Einstein's theory as demonstrated above, faces serious difficulties at two
fronts.

From inside, the theory is
plagued by internal inconsistencies **[Babin, 2000]**, fuzzy logic
**[Shaozi, 2000]**, 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. To do so is to invite
irresolvable contradictions.

Einstein's theory has been
criticized by many of importing 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 main-streamers wrestle with the eternal conundrums
of metaphysics and build up philosophical muscles'*. On the other hand,
it is well-documented that the ancient Greeks, during the Hellenistic Era, had
engaged in just the same game of playing around with essences and principles,
and of course, the Dark Ages weren't far behind. On balance, therefore, the
current state of physics should be a source of some concern, but not of
overwhelming concern, at least, not before the present status quo persists for
the next hundred years.

**References**

**Babin, W. (2000). “****An Analysis of the
Theoretical Foundations of Special Relativity****”:**

** **http://wbabin.net/babin/webdoc1.htm

**Barter, E. G.
(1953). Relativity and Reality. New York: Philosophical
Library.**

**Born, Max. (1962).
Einstein's Theory of Relativity. New York: Dover Publications
Inc.**

**Cyrenika, A. A.
(2000). "****Principles of
Emission Theory****":**

http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1CYR.pdf

**Dingle, H. (1972).
Science at the Crossroads. London: Martin Brian &
O'Keeffe.**

**Einstein, A. (1961,
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House.**

**Einstein, A. (1974,
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**Essen, L. (1971).
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Press.**

**Gardner, M. (1976).
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**Grayson, H. W.
(1964). The Theory of Relativity Revisited. Philadelphia: Dorrance &
Company.**

**Kraus, G. (1993).
Has Hawking Erred? London: Janus.**

**Phipps, T. E. Jr.
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**

**Rudakov, N. (1981).
Fiction Stranger than Truth: In the Metaphysical Labyrinth of Relativity.
Australia: Hedges & Bell.**

**Selleri, F. and
others.(1998). Open Questions in Relativistic Physics. Montreal: C. Roy Keys
Inc.**

**Shaozi, Xu. (2000).
"No One Can Save the LT", Apeiron, Vol. 7, No. 1-2.**

**Skinner, R. (1969).
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**Swenson, L. S.
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**Thomson, J. J.
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**Waldron, R.
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** **

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