Abstract

Due to their conviction that the laws of nature must be identical in any "inertial" frame, the physicists of the beginning of the twentieth century were led to extend the relativity of Galilei to the electromagnetism of Maxwell, but this implied the abandonment of universal time and absolute simultaneity.

In a previous paper^[1] we have criticised, from a logical viewpoint, the criteria designed to demonstrate the relativity of simultaneity and we have proposed replacing them by other criteria. According to these, the relativity of simultaneity was called into question.

We propose here a rigorous experimental method designed to verify the simultaneity of two events. By means of this device we demonstrate that one can define an absolute simultaneity. The method also permits an exact synchronization of clocks. We then demonstrate that the relativity of time of Einstein's theory must be discarded. So the time appears to be absolute. On the other hand, Einstein's relativity principle appears to be an approximation only valid for bodies moving with respect to one another at low speeds.

On the contrary, the slowing down of the clocks moving with respect to the ether frame must be maintained. But this does not mean that Lorentz's theory can be retained without any changes.

Important note: We do not question the relativity principle as an abstract concept. Indeed, if frames were perfectly inertial, the principle would obviously apply.

In this text we will call "inertial" the frames in which a body at rest is not submitted to any perceptible external force, a term sanctionned by use. But, we must be aware that, insofar as an aether drift acts on them, the frames cannot be perfectly inertial, and therefore the relativity principle does not strictly apply.

 

 

 

 

I. Position of the problem

One of the concepts which has most drastically changed our vision of the world since the origin of philosophical thinking is the idea of "relativity of time". Until the beginning of this century, time was considered as absolute, flowing uniformly, and identical for all observers. Certainly, if one supposes that different stars are inhabited, one could suppose that the people living there, use units of time different from our own, adjusted to the rhythm of their central sun. Nevertheless, time by itself would not be affected. An appropriate conversion would be enough to come to an agreement.

Until the end of the nineteenth century this conception was the object of a large consensus. Better still, the idea that it could have been called into question looked deprived of any meaning. It was not before the advent of Maxwell's electromagnetic theory that the problem began to be addressed. Indeed, by using the Galilean transformations, (although these were universally accepted), one could realize that Maxwell's equations, which crown this theory, were not invariant under a change of "inertial" reference frame. In other words, the electromagnetic laws were different for one observer on earth and for another travelling inside a rocket, or for an inhabitant of another solar system.

The physicists could not content themselves with such a disparity. Knowing that their obsession was the discovery of the universal laws of nature, this result conflicted with their firm convictions. But, on the other hand, to call into question the Galilean relationships seemed to imply a heartbreaking revision of the concept of universal time.

The end of the nineteenth century and the beginning of the twentieth century were periods of deep reappraisal. The notions which looked the best established, seemed to collapse. The experiment of Michelson and Morley came at the right moment to increase this perplexity.

Different physicists, all around the world, set themselves the task of putting in order the sum of the newly appeared disparate notions. Voigt, Larmor, Lorentz, Poincaré, in turn, showed great concern about them. Lorentz was particularly shocked when he knew the null result of the Michelson experiment, which called into question the concept of ether. In order to save this, he formulated (at the same time as Fitzgerald) the hypothesis of a contraction of the lengths moving through the ether. Alas, the hypothesis could never be verified experimentally ; the experiments of Trouton and Noble, Rayleigh and Brace, Chase and Tomashek, those of Trouton and Rankine, and those of Wood Tomloson and essex proved all negative. Lorentz was then compelled to formulate other hypotheses in order to explain such negative results : at first, the variation of mass with speed, but this was not sufficient. It was necessary to postulate the existence of a local time needed for the consistency of the theory.

The sum of these hypotheses, finally ended in the formulation of a set of equations, improved and modified by Poincaré, and named by him "Lorentz transformations". This was the first breach against universal time. Nevertheless the latter was not really abolished since, for Lorentz, the idea of an absolute space (absolute inertial frame) was not called into question, and the time measured in this privileged frame was exclusively considered as the real time. The local time was described as fictitious, which implied that the measurement of the time is distorted. That is the reason why it is more appropriate to define the process as 'slowing down of clocks' rather than relativity of time.

It is at that moment that Poincaré took part in the debate. Poincaré acknowledged the Lorentz assumptions, but, at the same time, showing great concern about the fact that the laws of nature ought to be universal, he believed that the space-time transformations should take the same form in all"inertial" frames. The final form he gave to them, seemed to satisfy this requirement : indeed, using group theory to derive them, Poincaré obtained a set of transformations which assume a group structure. He then formulated his relativity principle. Although he was convinced that a preferred inertial system supporting the ether should exist, Poincaré was persuaded of the impossibility of distinguishing it from the other "inertial" frames. In order to derive his transformations based on group theory, Poincaré had to assume that the speeds should obey the relativist composition of velocities law. Yet his derivation does not highlight the fact that this law concerns the speeds altered by the measurement distortions rather than the real speeds.

Although these transformatons are generally referred to as the "Lorentz transformations", it is Poincaré who gave them their ddefinitive form, for this reason we designate them as Lorentz-Poincaré transformations.

We know today that if we take for granted the postulates of Lorentz, including the application of the Galilean composition of velocities law to real speeds (which was used by Lorentz to explain Michelson's experiment), the space-time transformations assume the same mathematical form as the transformations derived by Poincaré only when they connect the aether frame to any other "inertial" frame.They take a different form in all other cases^[2] and, as a consequence, the whole of these transformations do not constitute a group. Starting from these equations, it is nevertheless possible to give these transformations a mathematical form similar to the conventional transformations, yet their meaning is quite different since they connect coordinates which are altered by the measurement distortions, including the speeds (see Ref 2), they conceal hidden variables which are the Galilean transformations, they do not assume the isotropy of the speed of light.

The approach of Einstein proved very different. Einstein also showed great concern about the requirement of the universal character of the laws of nature. His relativity principle is based on hypotheses different from those of Lorentz and Poincaré. Since it assumes a total reciprocity of the observations (contraction observational and reciprocal of moving lengths), it is not affected by the same difficulties as that of Poincaré who assumed the existence of a preferred aether frame.

Einstein's transformations constitute a fully fledged group. In other words, Einstein succeeded in deriving a set of transformations that maintain invariant the laws of nature. His system was universally adopted because, at the time when the relativity theory was published, the universality of the laws of nature looked an unquestionable requirement.

The question asked in this text is the following : what is the price to pay for maintaining the universality of the laws of nature and should they be kept? This question, which could not be asked some decades before without raising a general outcry, is seriously envisaged today by numerous physicists.

In other words, is the application of the relativity principle really unquestionable in the physical world? For certain physicists it has no absolute meaning but only a conventional character^[3], in connection with a method of synchronization of clocks questionable and relative.

According to relativity theory, the relativity principle should be compatible with time dilation. We will try to see, in that which follows, if these two concepts are mutually compatible, and if Einstein's local time is in agreement with logic.

In order to make us understand the relativity of time, Einstein takes the classical example of the train and the two flashes of lightning that we have studied in detail in a previous paper^[1]. Let us recall it briefly here : two flashes of lightning strike at the two ends of a railway platform at the very instant when the middle of the train meets the middle of the platform (Einstein). The two flashes are reflected in mirrors and then travel in opposite direction towards the middle of the platform. According to Einstein, the two flashes are considered simultaneous if they reach the middle of the platform at the same instant. The same definition is also valid for the train, but the train moves towards one of the flashes and moves away from the other and, consequently, the middle of the train will be reached at different instants by the two flashes. Einstein concludes that two events which are simultaneous for one observer, are not simultaneous for another moving with respect to the first. From which the relativity of simultaneity.

In our previous article^[1], we have demonstrated that the assertion was incorrect, because it implied a confusion between the instantaneous flashes striking at the ends of the platform, and the light issuing from them. We have also defined differently the simultaneity after correction of the errors of judgment generated by the non instantaneous translation of light.

II. A new experimental test of simultaneity

We now propose another experimental test of simultaneity deprived of the defects of that of Einstein. Of course it is a matter of a thought experiment that may be difficult to carry out, but this does not deprive it of its character of logical foundation of thinking.

Let us consider a precision balance (of great sensitivity) longer than an ordinary one, and suppose that two identical rubber spheres, released from the same level, fall down and bounce instantaneously on its pans. If the beam of the balance remains steady during the experiment, one will be authorized to conclude that the spheres have met the pans at the same instant.^[4]

Let us suppose now that a train passes alongside the beam of the balance, and that the two ends of the train meet the pans at the very instant when the spheres bounce. Let us designate as A the rear of the train, as B its front, and as A' and B' the places of the corresponding pans (figure 1).

Figure 1

After the spheres have bounced, a recording device situated at the middle of the train, will receive the light issuing from B' before that issuing from A'. From this, one could conclude that two events simultaneous for the Earth, are not simultaneous for the train.

Nevertheless, an observer inside the train will realize that the beam of the balance has not moved. In consequence, he will deduce that the two spheres have met the pans at the same instant. There is no doubt that this criterion of simultaneity is better than that of Einstein, because it allows an instantaneous estimate which does not need the mediation provided by the photons. It permits the absolute simultaneity independent of the motion of the observer, to be rediscovered.

Moreover, the method should permit the clocks to be exactly synchronized. For that it could suffice placing two clocks in proximity to the two pans of the balance; if the spheres bounce without making the beam move, then it is the same time at the two ends of the balance : for example 8 o'clock. It will also be possible to synchronize the clocks of the train identically. To this end, it will suffice to make them indicate 8 o'clock when they pass in front of A' and B'.

Now, with the help of several identical closely related balances, it is theoretically possible to synchronize clocks distributed on the whole surface of the Globe.

Let us now consider a train equipped at its two ends with clocks synchronized with the clocks situated at A' and B'. Suppose now that the train continues on its way and, after a certain time, meets two other clocks perfectly synchronous with A' and B', aligned with them, and separated from one another with the same distance. The question asked now is to know if the clocks of the train will be synchronous with these two new clocks.

According to the relativity principle, this should be the case, because there is no reason to favour the terrestrial frame rather than the frame of the train.

This can be easily understood with the help of the following reasoning :

Let A and B be the clocks of the train, A' and B' the terrestrial clocks met first, and A" and B" the terrestrial clocks met secondly.

Let us recall that A' and B' and A" and B" have been synchronized beforehand. On the other hand A and B are synchronized with A' and B' when they pass in front of A' and B'. So, at this instant, the six clocks are synchronous.

If one supposes that the Earth frame is an "inertial" frame (which is only approximately true, but that we will consider absolutely true for the purpose in hand) the frame of the train and the Earth frame are equivalent. Therefore, the relativity principle imposes that when A and B will meet A" and B" they will indicate the same time.

This fact demonstrates that the relativity principle is not compatible with the relativity of time (contrary to what Einstein’s postulates suggest) and that it also excludes the slowing down of moving clocks.

Now, knowing that clock retardation is an experimental fact, we realize that the relativity principle does not strictly apply in the physical world. This result calls into question all the derivations of the space-time transformations which assume the application of the relativity principle or are in agreement with it, including our past derivation^[5]. (However the arguments in the same paper according to which the speed of the photon cannot always assume the value C remain unchanged).

Conversely, the existence of a privileged inertial frame could generate an assymetry responsible for a slowing down of a pair of clocks relative to the other. So the notion of local time (slowing down of clocks), proposed by Lorentz, appears justified. But it is a matter of a physical effect concerning the clocks rather than an effect regarding the time itself. This can explain the experiments regarding the half life of the muons or the pions^[6].

Nevertheless, although in agreement with the theory of Lorentz, this conclusion does not imply a total support for it for the reasons previously mentioned^[2]-[7]

Acknowledgements

I would like to thank Professor Franco Selleri for having given me the opportunity to participate in the debate raised around Special Relativity, on the occasion of this Conference.