Abstract
This paper aims at demonstrating that, contrary to what is often proclaimed (Whittaker and
others), Einstein's relativity is completely different from the theories of
Lorentz and 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 results of fundamental physics.
On the
other hand, Lorentz's theory presents some difficult aspects which need to be
explained. Due to the systematic measurement distortions resulting from lenth contracton, clock retardation and the methods used to synchronize clocks some corrections are necessary to disclose the real values of the physical data.
In
addition, the space-time transformations derived from the Lorentz
assumptions, (including the Galilean composition of velocities law applied to real speeds) take the usual mathematical form exclusively when one of the frames they connect is the fundamental frame. In all other cases, the space-time
transformations take a different mathematical form. The relativist composition of velocities law applies to speeds whose measurement is altered by the systematic distortions due to length contraction clock retardation and the synchronism discrepancy effect. The transformations reduce to the Galilean transformations when the measurement distortions are corerected.
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 else 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, Dover, NY, 1908.
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 University
of Leyden, 1920.
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 highlight 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 with 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 aether of Lorentz 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 theories of Lorentz and 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 in vacuo.
Vacuum M ichelson’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:
   (1)
where T is the time needed to cover the distance AB.
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 > L one cannot have at the same time:
and  (2)
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
(3)
and
 (4)
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
 (5)
That is
 (6)
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:
 (7)
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:
 (8)
—
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:
 (9)
 (10)
it is different from (8).
In order
to explain that no interference was observed in the interferometer,
Fitzgerald and Lorentz had the idea to postulate a contraction of moving
lengths along the x axis, the contracted arm being:
 (11)
as a consequence the two way transit time of light in the arm aligned
along the x axis, appears identical to that of arm O’B, that is :
 (12)
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:
 (13)
and not C !
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
 (14)
-
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 measurement of the two way
speed of light.
Einstein and Lorentz transformations
regarding a light signal
Many physists consider that the theories which assume the existence of an aether frame and Einstein's relativity are equivalent, yet, 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 transformations which assume the existence of an aether frame and the variability of the speed of light are not familiar. In order to derive them, we use a
mathematical tool referring to "Zeno" The method discloses some hidden aspects of these transformations.
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’ overlap. 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 assumed 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  ; as the ray reaches this distance in turn,
the rod has moved away from S a distance equal to  etc.
So that,
the total distance covered by the ray to reach the extremity of the rod is:
 (15)
 (16)
The sum
of the series is:
 (17)
Now if we
take account of the Lorentz contraction
 (18)
the distance covered by the ray will be in fact:
 (19)
 (20)
From this
expression, we easily obtain the transit time of the signal according to
observer S.
 (21)
In the
ideal case where the measurements are carried out perfectly by observer S',
this finds also for t'
 (22)
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
 (23)
since the length L is arbitrary, we can write . Then comparing t and  we obtain:
 (24)
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:
 (25)
and the reciprocal transformations
 (26)
and  (27)
-
Important remarks
- We see that
the formulas 21 and 22 are correct since  . But as far as  and  are
considered as the real coordinates, in frame S' we are misled.
- 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):
 (28)
(and not t' = t which does not imply the slowing down of the clocks of S')
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 has ben
used as an argument to prove that the aether of Lorentz is compatible with the
principle of relativity. But even though at first sight the principle seems to apply, we must be aware that this fact results from the systematic mesurement errors made when one measures the lengths and the time. The relativity principle does not apply when these errors are corrected and therefore it does not constitute a fundamental principle of physcs. It is contingent and depends on the measurement methods used as the following example will show.
—
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). This case is important since it is the case we generally encounter in practice.
Figure 3
The
relative speeds are v01, v02 and v12. A rod
of length  (when it is at rest in the fundamental frame)
will measure  in frame S2. At time t0=zero the three reference
frames overlap. At this very instant, a light ray starts from O, O'
and O" and travels along the x axis towards point B. In B, the signal is
reflected in a mirror firmly fixed to reference frame S1, and then comes back towards O'. As we have seen (formula 22), for
observer S0 the time needed by the signal to reach point B is
 (29)
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. Indeed, when the signal has covered in S1 a distance
equal to  , reference frame S2 has moved away from S1 a
distance:
 (30)
When the
signal has covered this distance in turn, frame S2 has moved away
from S1 a distance equal to:
 (31)
and so on.
So that
the distance covered by the signal in S1 when it reaches the
extremity of the rod is
(32)
 **
(33)
(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
 (34)
it is the same as the time t0 measured by observer S0
(see formula 29).
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 , (See
later).
Let us
designate the time needed by the signal to come back from B to O' as  . We have:
 (35)
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
 (36)
We then
easily obtain:
 (37)
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:
 (38)
 (39)
 (see
formula 23)
(40)
We note
that for  we obtain
 (41)
 (42)
 (43)
This is
in conformity with our expectations. Indeed, when the speed of frame S1
is zero, S1 is at rest in the cosmic substratum and the space-time transformation takes the form of a conventional
transformation..
For  we have
 (44)
indeed in this case S1 and S2 are not different and
 (45)
We also
note that v12 represents the real speed of S2 with
respect to S1 and that
 (46)
(we have already applied this law in our reasoning).
Indeed, in
Lorentz's theory, the Galilean law of addition of velocities applies to real
speeds. It does not apply to the apparent (fictitious) speeds. (See
appendix 1).
—
In order to compare the aether theory based on Lorentz's assumptions and Einstein theory, we must carry out some
transformations on expression (40). We easily obtain
 (47)
 (48)
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. Indeed, Einstein's transformation regarding time
is
 (49)
Expression
(48) reduces to a conventional transformation only if  (i.e., when
one of the frames under consideration is the fundamental frame).
In order to compare the aether theory based on Lorentz's assumptions and relativity theory we note that expression 40 can be written as follows:
 (50)
Multiplying
the numerator and the denominator by
 (51)
we obtain
 (52)
As we
have seen, v12 is the real speed. If v12 had been equal
to the apparent speed:
 (53)
as in Einstein's theory, we would have obtained
 (54)
with this apprent speed the theory would have seemed to obey the relativity principle.
Expression
(49) characterizes Einstein's theory, which regards the relativity principle as a basic postulate.
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
concerning the light ray of rocket 2
concerning the light
ray of rocket 1
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
aether theory based on Lorentz assumptions 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. Indeed, 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 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.
Poincaré's relativity principle does not apply to the physical laws determined with reliable standards. It seems to apply because the distortions affect the standards. It is therefore contingent and cannot be regarded as a fundamental principle of physics.
Einstein's
Special relativity suffers from other flaws that have already been
considered.
Appendixes
Appendix 1
1. Due to measurement distortions , all the
measurements of the speeds in any frame not at rest in the Cosmic Substratum
are false.
Let us designate as v the real speed of an" inertial" body with respect to the
Cosmic Substratum, and v0 the absolute speed of the Earth frame.
The law
 (55)
which is regarded as the real speed of the body relative to the aether frame in relativity theory is in fact the apparent speed,
the real speed being
 (56)
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:
 (57)
 (58)
(The
latter expression replaces Lorentz's transformation of time  which
implies a synchronization of clocks with light signals ).
In
Tangherlini's approach, as regards the time, 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  . At the
instant the diaphragm of the source is opened.
Let us
consider a brief interval of time  . Between and  a number of
photons leave the source. If we suppose that C = constant, their
position is well defined (to within about  , but conversely their frequency
is not, since we are dealing with extremely short wave-trains (and not
completely spread out) that cannot really be compared to sinusoids. Indeed,
the term sinusoid must be reserved for an ideal wave of infinite length. The
longer the wave train, the more it assumes the properties of a monochromatic
sinusoidal wave.
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 remains
constant) and, at the same time, as the wave spreads out, its frequency can
be defined more and more accurately.
So, the
constancy of the speed of light seems to be in disagreement with Heisenberg's
uncertainty relations.
This hypothesis supposes that the photons are emitted at the very instant where the diaphragm is open
- 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 shoud be 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 and  . We then
know the position of the photon with an indeterminacy equal to  , and the indeterminacy of the frequency remains constant.
- But, are these objections adequate? At first sight they appear so. In fact, as we shall see, this is not the case. Indeed, objection 1 leads us to suppose that some photons stay at rest inside the filament or have not yet been created at the instant when the diaphragm is open.
If the photons stay at rest inside the filament, the constancy of the speed of light is transgressed.
On the other hand if some photons have not been created at the instant when the diaphragm is open, and we don't know when they are created, objection N°2 makes us believe that the closing of the diaphragm generates magically their creation in the filament and that these photons will jump instantaneously behind the diaphram (and this before its closing !!!). Yet the diaphragm can be at a distance from the filament and therefore this imples that the photons move at infinite speed.
In conclusion: if the photons jump at the instant when the diaphragm is open, and assume a constant speed, Heisenberg's uncertainty principle will be transgressed.
On the other hand, if we don't know the initial position of a photon but we need to open and close the diaphragm to determine its position with a known uncertainty, Heisenberg's uncertainty principle can be obeyed but the constancy of the speed of light will be transgressed. (We should add that this reference to a magic behaviour of the photon is difficult to accept).
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  is weak. Indeed the speed of the photon is equal to the group velocity vg,
(vg = C = vf).
Let
us take two examples:
a) A
monochromatic photon associated with a wave-train whose dimension is very
long (for example 1 mile)(see
figure 8).
Figure 8. Example of the
invariable position of a monochromatic photon
with respect to its wave-train if C = const (case of a quasi sinusoidal wave).
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 a photon on the wave if C = const
(case of a polychromatic wave)
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  is at its
maximum. It is not easy to explain how a photon can be permanently outside
the centre of its wave-train.
Therefore the hypothesis of the absolute invariance of the speed of light is facing a number of objections. Apart from the fact that this speed may assume the value C only in the aether frame, it is highly probable that this regime cannot be reached immediately after the opening of the diaphragme, and that the speed requires a little time before being constant.
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. Grossetête, 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, Histoire du principe de
relativité, Flammarion, Paris (1971).
3. E.
Whittaker, A history of the theories of ether and electricity, Nelson , London (1951).
4. H. Poincaré, Journal de
Physique théorique et appliquée 2, 347, 1912, Science and Method, Dover, NY
(1908).
5. A. Einstein and L. Infeld,
L'évolution des idées en physique, Payot, Paris (1912) - F. Balibar, Le rôle
de l'ether dans la question du continu et du discontinu en physique. T.M. Salanskis and H. Sinacoeur
editors, Springer Verlag France.
6. S.
Prokhovnik, The logic of Special relativity, Cambridge University Press
(1967) - Light in Einstein's Universe, Reidel Dordrecht (1985).
7. F. Balibar, Einstein
(1905) de l'ether aux quantas, collection Philosophie, PUF (1992), p.79.
8. H.A.
Lorentz, Collected papers, P. Zeeman, A.D. Fokker editors.
9. S.
Prokhovnik, The logic of special relativity, Cambridge University Press
(1967), Appendix 5.
10. S.
Prokhovnik, reference 6 and private communication.
11. J.
Lévy, A preliminary study of the process has been presented by the author in
a poster session at the symposium "Fundamental problems in quantum
physics", Oviedo Spain, 29 august, 3 September
(1993).
12. J.
Lévy, Phys essays, 6, 241 (1993). Invariance of light speed, reality or
fiction, Offilib, 48, rue Gay Lussac 75240 Paris Cedex 05. Fundamental questions
in quantum physics and relativity. Hadronic Press 1993, p.160, see also ref.
19.
13. H.E.
Wilhelm, Phys essays, 6, 420(1993), p.431.
14. E.W.
Silvertooth, 10, 3 (1986)
15. F.
Selleri, Clocks synchronization and relativity, Fundamental questions in
quantum physics and relativity, Hadronic Press (1993), p.172.
16. J.
Lévy, Is the invariance of the speed of light compatible with quantum
mechanics ?, in "Advances in fundamental physics", a book
relative to the proceedings of the International Conference, Olympia,
September 27-30 (1993), Hadronic Press, Palm
Harbor FL 34684 USA.
(Note that p. 211 of the book, three lines before end of the page, the reader
should read  instead of  ).
17. Cl. Cohen-Tannoudji,
private communication.
Insofar as the speed of light is anisotropic, the measurement of the one-way transit time of light with clocks synchronized by the Einstein-Poincaré procedure is affected by a systemetic error. The method only enables the measurement of half thetwo-way transit time
(from O' to B and from B to O'). (See for example Prokhovnik
"The Logic of Special Relativity").
Notice that the measurement of
the distance O’B by observer S1 is carried out with a contracted
meter stick, so that he will find  in place of expression (33).
Note that according to
Heisenberg's uncertainty relations, the product  is of the
order of .
Return to top
|
