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Physical
Interpretations of Relativity Theory V,
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Updated on november 12th 2005 |
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Abstract
This
paper deals with some important aspects of a book entitled "Relativité
et substratum cosmique", which has been registered at the French Society
of Authors on November 14th 1995. Some questions just outlined in the book
are developed here. We
demonstrate that, contrary to what is often proclaimed (Whittaker and
others), Einstein's relativity is completely different from the theory of
Lorentz-Poincaré. Certainly, as demonstrated by Prokhovnik, they lead to
equivalent results in several essential aspects. But the equivalence presents
some limitations: for example Einstein's theory requires the constancy of the
speed of light in any inertial frame. As we will see, this requirement is not
compatible with different well established results of fundamental physics. On the
other hand, Lorentz's theory presents some difficult aspects which need to be
explained, resulting from the methods used to synchronize clocks (for example
synchronization procedure with light signals or slow clock transport). In
addition, the Lorentz-Poincaré transformations derived from the Lorentz
assumptions, are strictly valid exclusively when one of the frames under
consideration is the fundamental frame. In all other cases, the space-time
transformations take a different mathematical form. The
purpose of this paper is to provide a comparative analysis of the theories of
Einstein and Lorentz-Poincaré and to emphasize that. 1. The
theories are based on different assumptions and, although it has been
brilliantly demonstrated that they lead to equivalent results in several
essential aspects, there is a domain where the equivalence does not apply. 2. Both
theories present different limitations although these are not identical. Introduction
A number
of untruths regarding Special relativity are commonly taught or written in
scientific literature, namely : - Einstein
has definitively discarded the hypothesis of ether1. - The
principle of relativity of Poincaré has exactly the same meaning as that of Einstein.
The idea was expressed by Poincaré one year before Einstein. Poincaré was the
first to conceive the relativity theory without the help of ether2. - Einstein's
Special relativity is nothing other than a marriage of the ideas of Lorentz
and Poincaré (Whittaker)3. With the
help of quotations pronounced by the authors themselves, it is easy to
realize that these opinions are completely unfounded1. Look what
Poincaré said in his final days: "The
universe consists of electrons and ether and nothing else". Science
and Method, In 1912,
just before his death, he published an article in "Le Journal de
Physique" entitled "The relations of matter and ether"4. Contrary
to what is often taught even today, the opinion of Einstein on the ether has
completely changed from 1905 to 1920. This has been widely demonstrated by
Ludwig Kostro1. For example: "The
negation of ether is not necessarily required by the principle of Special
relativity. We may assume the existence of an ether, only we must give up
ascribing a definite state of motion to it... The theory of ether as such is
not in conflict with the special theory of relativity". A.
Einstein, conference at the Poincaré's relativity principle was expressed one year before Einstein,
but it had in no way the same meaning. Poincaré never
abandoned the idea of a privileged reference frame supporting the ether. This
principle could be expressed as follows: "It
is impossible by means of an experiment internal to a given inertial frame to
know its absolute motion". For
Poincaré the ether is necessary to convey the electromagnetic waves. This
makes the difference with Einstein who considers that no privileged reference
frame exists, and for whom the ether is not needed to propagate the
electromagnetic waves5. So, there
is a great difference between the concepts of Einstein and Poincaré, and to
accuse Einstein of plagiarism is pure fantasy. Poincaré believed in the ether
of Lorentz and wanted to reconcile it with the principle of relativity.
Einstein, considering this unrealistic, came up with the idea of photon and
adopted another concept of ether. The view of Einstein is shared nowadays by
different scientists such as F. Balibar who goes further than Einstein when
she says "The existence of quanta of light, energy without support, is
in contradiction to that of an ether necessary to convey the electromagnetic
waves". On the
other hand, several physicists come back today to the theory of Poincaré.
Moreover, different attempts with a view to reconciling the theories of
Einstein and Poincaré have been done6 . It is paradoxical that,
although based on different assumptions, the theories appear equivalent in
many respects. It is
important to determine to what degree the equivalence applies. The question
will be examined below. Also it
is important to appreciate whether the ether of Lorentz-Poincaré is really
compatible with the principle of relativity. Different authors give different
replies to this question2, 6, 7. Most of
them, but not all, consider the relativity principle as a fundamental concept
of physics. Finally,
we will try to estimate to what extent the theory of Lorentz-Poincaré and the
relativity theory, are consistent with other aspects of physics. Postulates
The
postulates of Lorentz and Einstein are completely different; those of Lorentz
can be summarized as follows8: - Existence
of an ether frame in a state of absolute rest. The speed of light is constant
and equal to C exclusively in this ether frame; it is different from C in all
other reference frames. However, for different reasons that will be
considered later, it looks constant. - Contraction
real and non reciprocal of rods moving with respect to this fundamental
frame. - Slowing
down of clocks, moving with respect to the ether frame. - Variation
of mass with speed. Lorentz
was obliged to make this assumption in order to justify that the contraction
of moving rods had never been observed experimentally. — Those
of Einstein are: - Equivalence
of all inertial frames for the description of the physical laws. - Constancy
of the speed of light in all inertial frames. These postulates imply
reciprocity of observations, reciprocal and observational (but not real)
contraction of moving rods, and relativity of time. Michelson’s
experiment
Michelson’s
experiment can be easily explained by means of Einstein’s Special
relativity. The two arms of the interferometer being equal, and C constant,
the transit time of light in both directions must be identical. Now, the
explanation given by Lorentz of the experiment is completely different. Let
us suppose that at a moment in its journey, one of the arms of the
interferometer moves along the x axis of a reference frame at rest in the
Cosmic Substratum (ether). The other arm is aligned along the y' axis
perpendicular to the direction of motion (see fig. 1).
Figure 1 —
We first consider the latter. Let us
designate the frame of the substratum (O, x, y, z) as S, and the Earth frame
(O’, x’, y’, z’) as S’. S’ moves with
respect to S with an (almost) rectilinear and uniform motion at speed v. From the
point of view of an observer at rest in frame S’, a light beam
traveling to and fro along the arm O’B, covers a distance 2L; but from
the point of view of an observer of reference frame S, the beam starts from
A, reflects in B, and then comes back to A’. (AA’ designates the
distance covered by the interferometer during a cycle of the beam). Since the
speed of light is supposed to be constant in the substratum we have: Now, from
the classical (Galilean) viewpoint, the time separating two events is
independent of the frame from which it is measured and, consequently, the
speed of light must be lower than C in frame S’. In effect, since However,
the measurement of the speed of light gives C in all inertial frames. So
there is a paradox. If one
supposes that C = const, then, the interval between the starting and the
arrival of the beam must be different in the two frames, and we will have and
Nevertheless,
from the point of view of the supporters of the Lorentzian approach, this
result is false. The real value of the speed of light in frame S' is given by That is How can
we explain that we find C and not C'? In order
to understand this, we must assume that the motion entails a slowing down of
the clocks. Therefore, any measurement of the time in a frame moving with
respect to the Cosmic Substratum, will be different from the universal time. The
relationship between the local (fictitious) time t, and the real (universal)
time T, is easily obtained from fig.1: Therefore,
for Lorentz there is no relativity of time, but rather a slowing down of the
clocks, moving with respect to the ether frame. The two
way transit time of light in arm O’B is: —
Let us now consider the arm parallel to the direction of motion (fig.2).
Figure 2 The
theoretical time needed by the light signal to travel back and forth along
this arm should be: In order
to explain that no interference was observed in the interferometer,
Fitzgerald and Lorentz were compelled to postulate a contraction of moving
lengths along the x axis, the contracted arm being: Now, we
can ask ourselves how Lorentz's theory can explain that the average two way speed of light along the x axis, is always found equal to C ? even though: There are
two reasons for this: 1. The
meter stick used to measure L is also contracted, so we cannot observe the
contraction, and therefore we make a systematic error in measuring the rod.
We find L and not 2. As
we have seen on the occasion of the study of the arm O’B, the clocks in
the "inertial" frame S’ slow down in such a way that the time noticed by
observer S must be multiplied by Finally,
the measured average two-way speed of light will be -
Important remark It is
essential to realize that C is not the real one way speed of light in
S’. It is the apparent (fictitious) average two way speed of light,
obtained as a result of the systematic errors made for the measurement we
have just seen. Moreover,
measuring exactly the one way speed of light presents real difficulties
since, to this end, we generally use clocks synchronized by means of
Poincaré-Einstein's method, or by slow clock transport. But as demonstrated
by Builder 9, both methods only enable the measurement of the two way
speed of light. Einstein and Lorentz transformations
regarding a light signal
It is
usual to consider that the Lorentz-Poincaré and Einstein transformations are
identical. Certainly their mathematical form is the same, but, as we shall
see, their physical meaning is completely different. It is not necessary here
to derive Einstein's transformations. This has been done by different well
known techniques. On the other hand the derivation of the Lorentz-Poincaré
transformations has been forgotten... In order to derive them, we use a
mathematical tool referring to "Zeno" different from those used by
these authors and which disclose some hidden aspects of them. Consider to this end the reference frames S and S' mentioned above. A long rod aligned
along the x axis is at rest in frame S’. Let us name v0 the
relative speed of S and S’. At the initial instant t0, O and
O’ are superimposed. At the same instant, a light ray starts from
OO’ and travels towards point P (We bear in mind that the speed of
light is supposed to be equal to C in the substratum S, and different from C
in all other frames (see figure 2)). When the
light ray has covered the distance L in the substratum, the rod has covered
the distance So that,
the total distance covered by the ray to reach the extremity of the rod is: The sum
of the series is: Now if we
take account of the Lorentz contraction From this
expression, we easily obtain the transit time of the signal according to
observer S. In the
ideal case where the measurements are carried out perfectly by observer S',
this finds also for t' So that t
= t' But, as
we have seen before, when observer S' measures the speed of light, he makes a
systematic error and finds C (consult formula 14 and the important remark
following it). This is also the case for L, since the rod is measured with a
contracted standard. So that, observer S' considers that the apparent time
needed by the ray to reach the extremity of the rod is We see
that, contrary to Einstein's approach, t'app is a fictitious
apparent time. Only t is the real time. Nevertheless, t'appis the
time measured by observer S'. This approach implies a slowing down of moving
clocks. From
expression (24) we easily obtain: and -
Important remarks
- We see that
the formulas 21 and 22 are correct since - If the
clocks had been synchronized perfectly, then, as a result of the slowing down
of moving clocks, we would have obtained (from formula 24): Formula
(28) is the one used by Tangherlini Mansouri and Sexl (see appendix 1). —
The above transformations (24 to 27) look compatible with the relativity
principle, and imply reciprocity of observations (apparent). But for Lorentz,
there is no real reciprocity. For example, the rods of the substratum do not
contract. The reciprocity is only apparent, and results from the
impossibility of synchronizing exactly the clocks in S' by means of the usual
methods. This
apparent reciprocity has been demonstrated by Prokhovnik10. It is
used as an argument to prove that the ether of Lorentz is compatible with the
principle of relativity. Nevertheless, the argument is not sufficient since
it has been applied to a particular case. In effect, in the example we have
just considered, one of the frames is at rest in the cosmic substratum. —
Let us now study a different case: that of two inertial frames S1
and S2 receding from the fundamental frame S0 along the
x axis (see figure 3).
Figure 3 The
relative speeds are v01, v02 and v12. A rod
of length According
to Lorentz, this time is the real transit time of the signal. Now, let
us determine the apparent transit time as measured by observer S1.
Using clocks synchronized by Einstein-Poincaré’s method, observer S1
measures in fact the apparent average transit time of the signal* (from
O' to B and from B to O'). Assuming
that the speed of light in S1 is C - v01, and in S2,
C - v02, the real transit time from O' to B can be easily
obtained. In effect, when the signal has covered in S1 a distance
equal to When the
signal has covered this distance in turn, frame S2 has moved away
from S1 a distance equal to: So that
the distance covered by the signal in S1 when it reaches the
extremity of the rod is
(Note
that in Lorentz's theory, the Galilean law of addition of velocities applies
to real speeds but not to fictitious speeds - see later). The real
transit time of the signal (for S1) from O' to B is then According
to Lorentz, it is the universal transit time (which is the same in all
inertial frames). Now, as we
have seen, there are great difficulties in measuring t1. The time
generally measured is the apparent average transit time Let us
designate the time needed by the signal to come back from B to O' as The distance
covered by the ray from B to O' is the same as from O' to B, but the speed of
light in the reverse direction (with respect to frame S1) is C + v01 So that We then
easily obtain: Since,
the clocks in reference frame S1 are slowed down with respect to
the clocks of reference frame S0, we must multiply t1app
by We then
obtain: We note
that for This is
in conformity with our expectations. In effect, when the speed of frame S1
is zero, S1 is at rest in the cosmic substratum and the Lorentz
transformation applies. For We also
note that v12 represents the real speed of S2 with
respect to S1 and that Indeed, in
Lorentz's theory, the Galilean law of addition of velocities applies to real
speeds. It does not apply to the average apparent (fictitious) speeds. (See
appendix 1). —
In order to compare Lorentz and Einstein theories, we must carry out some
transformations on expression (40). We easily obtain We see
that this expression depends on v01. It is therefore different
from Einstein's transformation relative to frames 1 and 2 which does not
depend on v01. In effect, Einstein's transformation regarding time
is Expression
(48) reduces to Lorentz's transformation only if Taking
account of the identity Multiplying
the numerator and the denominator by As we
have seen, v12 is the real speed. If v12 had been equal
to Expression
(49) characterizes Einstein's theory, which is therefore the only theory that
generally obeys the relativity principle. Now, is
the relativity principle an unquestionable concept physics? The
question will be examined in subsequent papers. The question of
reciprocity
One of
the most important difficulties of Einstein's theory concerns the question of
reciprocity. This does not affect Lorentz's theory, since it does not require
the constancy of the speed of light in any inertial frame. The
following example is particularly demonstrative of this11 —
Two rockets are receding symmetrically with respect to a point P. After
having covered the distance D, they reverse their direction and go back.
Finally they meet again at point P. Most of the journey is carried out with a
rectilinear and uniform motion. Two
mirrors A and B are placed in front of one another on the ceiling and on the
bottom of the two rockets. Let us call l the distance AB and A'B' (see
figure 4)
Figure 4 Now, let
us suppose that a light beam starts at time t = 0 from the mirrors A and A',
and travels towards the other (B and B'). After
reflection in B (or B'), the light beam comes back to A (or A') and is
reflected another time, and so on. The light beam and the mirrors constitute
elementary clocks that will be used for our study. Let us
consider first the point of view of observer 1, and suppose that the
light beam of rocket 1 has carried out 10 cycles during the journey (N.B.:
the number 10 has been chosen for convenience. Of course in a real experiment
it should be greater). As a
result of the complete symmetry of the trips, the light beam of rocket 2
experiences also 10 cycles (see figure 5)
Fig 5.
The path of the light beam in rocket 2 as observed by observer 1. The light
beam experiences 5 cycles from P to P' and 5 cycles from P' to P after the
reversal of the direction of the rocket. The path of
the signal in rocket 2 appears oblique to observer 1, so that the distance
covered by the light beam (2x10 L) appears longer to him than the
distance covered by the light beam in his own rocket (2x10 l) (see
figure 5).
Figure 6. Point of view of observers
1 and 2 Figure 7. Point of
view of observers 1 and 2 If we
suppose that C is constant, observer 1 will conclude from his calculation
that the duration of the journey of rocket 2, (2x10 T) is longer
than the journey of rocket 1. But
conversely, observer 2 will draw opposite conclusions (see
figures 5, 6, 7). Obviously the points of view of the two
observers are contradictory, and cannot be true at the same time The
theory of Lorentz is not affected by this flaw, since it does not consider
that the speed of light is constant in any inertial frame. Other limitations of
Einstein's theory
Einstein's
Special relativity suffers from some other flaws. These have been analyzed in
previous papers12. They can be summarized as follows : 1. The
theory is not compatible with the reciprocity of the speeds. Special
relativity implies a lack of reciprocity of the velocity between the photons
and the source of emission. By virtue
of reciprocity, the source should have a speed equal and opposite to the
photons. The reciprocity of the speeds is a fundamental principle of physics.
(The lack of reciprocity concerns the apparent (fictitious) speeds but not
the real speeds (see appendix: Transformations of Tangherlini)).
Nevertheless, Special relativity is compelled to give up the reciprocity,
because if a body had the speed C with respect to a photon, its mass would
become infinite. The
attitude generally adopted in order to resolve these difficulties consists in
denying the existence of a proper reference frame for the photon. This
negation is not based on logical grounds. If photons had no proper reference
frame, there could be no possibility of attributing a velocity to them, something
we do not hesitate to do. 2. Special
relativity implies a proper mass and a proper energy equal to zero for the
photon. Nevertheless,
since the photon is considered a particle, it is worth asking why it does not
possess proper energy (and therefore proper mass). The physicists who
conceived special relativity did not answer this question. 3. In
the course of an electronic transition with emission of a photon, special
relativity implies that the photon immediately reaches the velocity C. As we
have seen in previous papers, this assumption is not logical. In effect, if
one assumes according to Einstein that the photon is a particle, its initial
speed must be identical to that of the structure from which it comes. But we
know that this speed cannot be C, otherwise the mass of the structure would
be infinite. The same
remark can be applied to a photon which is reflected in a mirror. 4. As
we will show, the absolute constancy of the speed of light is not compatible
with Heisenberg's uncertainty relations (see appendix 2). Conclusion
As we
have seen, the theories of Einstein and Lorentz-Poincaré are not generally
equivalent. As shown by Prokhovnik6, there is an equivalence when
one of the reference frames involved is at rest in the Cosmic Substratum.
This can be extended to the cases where one of the frames moves at low speed
with respect to the Cosmic Substratum. (This should be the case for the Earth13, 14).
In all other cases, there is no equivalence. Lorentz-Poincaré's
transformations apply exactly exclusively when one of the frames involved is
the privileged frame. In all other cases the space-time transformations take
a form different from those of Lorentz-Poincaré. Einstein's
Special relativity suffers from other flaws that have already been
considered. So, we
are compelled to conclude that the two theories are different and that no one
is consistent with all aspects of physics. Appendixes
Appendix 1
1. Since
the lengths and the time are fictitious in Lorentz's theory, all the
measurements of the speeds in any frame not at rest in the Cosmic Substratum
are false. The law 2. The
theory of Tangherlini is considered equivalent to Lorentz's theory.
Nevertheless, in this approach the synchronization of clocks is supposed to
be carried out exactly. So we have: (The
latter expression replaces Lorentz's transformation of time In
Tangherlini's approach, only the slowing down of moving clocks is taken into
account. The
consequences are: - The
theory is not consistent with the relativity principle. (F. Selleri considers
that the principle of relativity has only conventional status depending on
the method of synchronization of clocks). - In
Tangherlini's approach the speeds are not reciprocal15. But we
have to be aware that this concerns the apparent speeds (which at the moment
of the measurement are subject to unavoidable errors, because the estimate
of the lengths and the time are false). Appendix 2
It is
important to try to determine whether the constancy of the speed of light is
compatible with quantum mechanics. The question has been taken up extensively
in a previous publication16. The demonstration can be summarized
as follows: Let us
consider a source of light sending out a monochromatic signal of frequency Let us
consider a brief interval of time However,
if we suppose that C is constant, then the position of the photons can be
known at every instant (indeed the uncertainty about the position So, the
constancy of the speed of light seems to be in disagreement with Heisenberg's
uncertainty relations. - Of
course, at first sight, some objections can be raised to our reasoning,
namely: 1. It
is impossible to know the initial position of a photon with respect to its
wave train after the opening of the diaphragm, since we cannot know at which
moment the photon jumps17. So, there is no incompatibility between
the constancy of the speed of light and Heisenberg's uncertainty relations. 2. In
order to know precisely enough the position of a photon, it is imperative to
open and close the diaphragm successively between instants - But,
are these objections adequate? At first sight they appear so. In fact, as we
shall see, this is not the case. In effect, objection 1 leads us to
suppose that some photons stay at rest inside the filament, which is not in
accordance with the constancy of the speed of light. The
(hypothetical) answer to this is that before their emission the photons did
not stay at rest but had not yet been created, and, as a consequence, they
could not be compelled to assume the speed C. This
answer is not pertinent from those who say that the opening and closing of
the diaphragm, are necessary and sufficient to know that all the wave-trains
are occupied. In effect, if a photon is not created, how can the closing of
the diaphragm (which is placed in front of the filament) give rise to its
creation inside the filament followed by its emission? (see
objection 2). So
if we know the initial position of the photon with respect to its wave-train
with an indeterminacy equal to So,
we can conclude that Heisenberg's uncertainty principle is not compatible
with the constancy of the speed of light. - Moreover,
if we do not know when the photon jumps and at the same time we suppose that
the speed of light is constant, then we must also assume that some photons
will be constrained to always occupy on the wave train a position where Let
us take two examples: a) A
monochromatic photon associated with a wave-train whose dimension is very
long (for example
Figure 8. Example of the
invariable position of a monochromatic photon The
photon always occupies the same position on the wave train. There is no equal
probability of finding the photon on every top of the wave-train (The equal
probability concerns a beam constituted of numerous wave-trains but not an
individual one). b) A
polychromatic wave As
a result of the fact that a photon can jump at any instant, the probability
that the photon occupies the position indicated by figure 9 is not zero.
Figure 9. Example of the
invariable position of the photon on the wave if C = const If C is
constant the photon will permanently occupy this position. This appears
unrealistic. Indeed, it seems to us that an organic relationship exists
between the photon, and the part of the wave where the probability density So, the
objections which have been raised to our arguments, cannot allow to conclude
that "Heisenberg's uncertainty relations"*** are compatible with the invariance
of the speed of light. Acknowledgements
I would
like to thank Pr M.C. Duffy for the efforts he makes in organizing an
innovating symposium open to philosophical ideas, and, on the other hand, for
having sent me two interesting papers, which shed light on several aspects of
ether theories. I am
grateful to Pr V. Bashkov for the care he has taken in reading one of my
publications and for his encouragement. I also
thank M. J. Babaud, late Pr B. Grossetęte, M. B. Guy, Dr
R. Hock, Dr P. Huber, M. V. Makarov, Dr G. Margalhaes, Pr
P. Marmet, for their interesting reflections and/or for their
encouragement regarding some aspects of my work. Bibliography 1. L.
Kostro, Proceedings of the P.I.R.T. Conference (1994), p.206, "A
critical examination of the generally accepted ideas". 2. For a discussion about this question, consult for example, M.A. Tonnelat, Hist |
, and the indeterminacy of the frequency remains constant. 
