Abstracts Details

A simple and rigorous proof of the Sagnac effect for the most general value of the synchronization parameter

e1 is given. If in the final result one adopts the relativistic *e _{1}* one can see that the relativistic theory is incompatible with the experimental evidence. Only the theory with

*e*predicts correctly the Sagnac effect. Of course the obtained results depend on the assumptions made, which look rather safe however.

_{1}= 0The conviction that relativistic simultaneity has a conventional nature is shared by many authors, but it will be shown that simultaneity exists in the physical reality and therefore cannot be conventional. If the coefficient - we call it e_{1} - of the space variable x in the Lorentz, or other, transformation of time had a conventional nature it should be possible to modify it without touching the empirical predictions of the theory: this expectation can be called Reichenbach-Jammer conjecture (?RJ conjecture?). Given that Einstein's principle of relativity leads necessarily to the Lorentz transformations, and thus also to a fixed nonzero value of e_{1}, the modification would imply a reformulation of the relativistic idea itself. With respect to the idealized expectation, based on the RJ conjecture, the concrete development of physics produces some exciting novelties. Several phenomena, in particular those taking place in accelerating frames (Sagnac effect, and all that), converge in a strong indication of e_{1} = 0. This implies absolute simultaneity and a new type of space and time transformations, which we call "inertial". We give eight proofs of absolute simultaneity, deduced from essentially independent normally accepted premises.

It is remarkable that almost a century after the discovery of the Sagnac effect no justification based on the two relativistic theories has been found. Hasselbach and Nicklaus, describing their own experiment, list about twenty different explanations of the effect and comment: "This great variety (if not disparity) in the derivation of the Sagnac phase shift constitutes one of the several controversies ... that have been surrounding the Sagnac effect since the earliest days of studying interferences in rotating frames of reference."

In the Sagnac 1913 experiment a platform was made to rotate uniformly around a vertical axis at a rate of 1-2 full rotations per second. In an interferometer mounted on the platform, two interfering light beams, reflected by four mirrors, propagated in opposite directions along a closed horizontal circuit defining a certain area. The rotating system included also the luminous source and a photographic plate recording the interference fringes.

The present paper reviews the results obtained in recent years by the author in relativistic physics. Historically the two theories of relativity were born from the clash of positivism and realism. The former current of thought used relativism as a weapon against ideas of realistic inclination, like Lorentz's. Paradoxes were the consequence in the new relativistic paradigm of emarginating realism. The recent understanding of the role of the conventional definition of simultaneity in relativistic physics has opened the doors to new lines of thought. Epistemologists have stressed that the coefficient of the space variable x in the Lorentz transformation of time (we call it e1) has a nonphysical ("conventional") nature. Therefore, it should be possible to modify e1 without touching the empirical predictions of the theory. Given that Einstein's principle of relativity leads necessarily to the Lorentz transformations, such a modification implies however a reformulation of the relativistic idea itself. With respect to this ideal picture, the concrete development of the research has produced some exciting surprises. Nature does not seem to be so indifferent about the value of e1, given that several phenomena, in particular those taking place on a rotating platform (Sagnac effect, and all that) converge in a strong indication of the value e1 = 0 .This implies absolute simultaneity and a new type of space and time transformations which we call "inertial". Today we count on six proofs of absolute simultaneity, which are essentially independent of one another (three are contained in the second part of the paper). The cosmological consequences of the new structure of space and time go against the big bang model. After our results relativism, although weakened, is not dead and keeps proposing itself under milder forms.

At the end of the XIX century Poincar? had the idea that one way velocities are not measurable. To measure them one needs synchronized clocks, but to synchronize clocks one needs to know the one way velocity of some signal. It seems a perfect logical loop, impossible to overcome. Einstein essentially adopted the idea when he defined the velocity of light as constant to formulate the TSR.

In 1927 the German philosopher of science Hans Reichenbach, discussed this definition concluding that even if essential for the TSR, it was “not epistemologically necessary.“

Half a century later, in the years 1977-1984, Max Jammer produced a very stimulating reconstruction of the debates about the notion of distant simultaneity. He stressed that one cannot know the simultaneity of distant events at all since simultaneity is arbitrary; and therefore we can lay down whatever definition we wish concerning it, without giving rise to any error. At this point several people must have felt that the Reichenbach-Jammer conjecture was too self-assured for a statement almost completely lacking empirical support. Researches trying to confirm/invalidate the conjecture actually started in several places.

If the coefficient of the space variable x in the Lorentz, or other, transformation of time (we call it e_{1}) had a conventional nature it should be possible to modify it without touching the empirical predictions of the theory. Given that Einstein’s principle of relativity leads necessarily to the Lorentz transformations, and thus also to a fixed value of e_{1} , such a modification would imply a reformulation of the relativistic idea itself. With respect to the idealized initial picture, the concrete development of research has produced some exciting novelties. Several phenomena, in particular those taking place on accelerating systems (Sagnac effect, and all that) converge in a strong indication of the value = e_{1}. This implies absolute simultaneity and a new type of space and time transformations, which we call "inertial". The cosmological consequences of the new structure of space and time go against the big bang model. After these results relativism, although weakened, is not dead, but survives in milder forms.

The experimental evidence for electromagnetic signals propagating with superluminal group velocity is recalled. Transformations of space and time depending on a synchronization parameter, e1, indicate the existence of a privileged inertial system. The Lorentz transformations are obtained for a particular e1 different from zero. No standard experiment on relativity depends on e1, but if accelerations are considered only e1 = 0 remains possible. The causal paradox generated by superluminal signals in the theory of relativity does not exist in the theory with

In the transformation of time between inertial reference frames the coefficient of the space variable, *e _{1}*, describes the possible choices of clock synchronization with its different values. In the first part of the paper we review the proof of a zero acceleration discontinuity for rotating platforms: the velocity of light relative to inertial reference frames agrees with the zero acceleration limit of the velocity of light relative to rotating platforms only by assuming

*e*= 0, that is by replacing the Lorentz by the "inertial" transformations based on absolute simultaneity. The second part of the paper contains the proof that the same discontinuity exists also for linearly accelerated reference frames. Absolute simultaneity again provides the cure.

_{1}Our recently proposed inertial transformations of the space and time variables based on absolute simultaneity imply the existence of a single isotropic inertial reference system ("privileged system").

We show, however, that a resynchronization of clocks in all inertial systems is possible leadind to a different, arbitrarily chosen, isotropic "privileged" system. Such a resynchronization does not modify any one of the empirical consequences of theory, which is thus compatible with a formulation of the relativity principle weskeer than adopted in Einstein's theory of special relativity.

Transformations of space and time depending on a synchronisation parameter, e_{1}, indicate the existence of a privileged inertial system S_{0}. The Lorentz transformations are obtained for a particular e_{1} different from zero. No classical experiment on inertial frames depends on the choice of e_{1}, but if accelerations are considered only e_{1} = 0 remains possible. The choice e_{1} = 0 provides a rational resolution of the long standing mystery connected with the relativistic interpretation of Sagnac effect.

The description of natural phenomena by observers in motion is a problem that many consider solved once and for all by the Lorentz transformations of the Theory of Special Relativity (TSR), though it was actually was left open. Consequences of my alternative transformations of the space and time variables are: (i) an explanation of the empirical data better than provided by the TSR; (ii) the elimination of those features of the TSR which give rise to paradoxes. This is obtained thanks to the recovery of a preferred inertial frame in which the Lorentz ether is at rest. In the present paper I expound the basic ideas of the research, leaving aside mathematical detail.

The description of natural phenomena by observers in motion is a problem that many consider solved by Lorentz transformations, but that actually was left open. Consequences of my alternative "inertial" transforamtions are: (i) an explanation of the empirical data better than provided by the Theory of Special Relativity (TSR); (ii) the elimination of those features of the TSR giving rise to paradoxes thanks to the recovery of a privileged inertial frame in which the Lorentz ether is at rest. The example of the "clock paradox" is discussed and a complete resolution is obtained by giving an exhaustive unified description of all possible situations. Velocity (and nothing else) is thus seen to be responsible for the differential retardation effect.

In the last ten years I have been working at the description of natural phenomena by observers in motion. It is a problem that many consider solved once for all by the Lorentz transformations of the Theory of Special Relativity (TSR in the following), but that actually was left open for reasons I will say. The result of this research is twofold: an explanation of the empirical data better than provided by the TSR, and the elimination of those features of the TSR which give rise to paradoxes; all this is obtained thanks to the liberation of time from the enslavement to space forced upon it in Minkowski space. The story is told in detail in a recent book [FS].

Atomic clocks distributed around the world communicate with one another by means of radio signals. The synchronization signals sent by a transmitting station always reach the receiving station 'on time', at any hour of the day and in any season, despite the motion of the Earth. For some authors this means that these signals propagate isotropically (with one way velocity c), even with respect to the Earth surface. In fact this may not be so; we show that the proper working of the network says nothing about the one way velocity, as it is consistent with another theory, empirically (almost) equivalent to special relativity, in which the one way speed of light has a directional dependence in moving frames.

Published in *Science Philosophy Interface*.

**Part 1.** Transformations of space and time between inertial systems have been constructed by assuming: (1) Invariance of the two way velocity of light; (2) Retardation by the usual velocity dependent factor for clocks moving with respect to an isotropical system. The so obtained transformations contain a free parameter e_{1}. Different values of e_{1} correspond to different theories of space-time phenomena. The Theory of Special Relativity (TSR) is recovered for a particular choice of e_{1}. Many experiments are insensitive to the choice of e_{1}: Michelson type, aberration, occultations of Jupiter satellites, radar ranging of planets and so on. There is however at least an exception (see part II).

**Part 2.** A physical quantity rho exists for which the TSR predicts rho: 1 relative to all inertial frames. Under extremely general conditions we show that rho={c+v)/(c-v) for all rotating disks having the same peripheral velocity v. This rho must hold in any small region near the disk rim and arbitrarily small acceleration a. Therefore the TSR gives rise to a discontinuity which is unacceptable because all empirical knowledge about inertial systems is obtained in frames with nonzero a, e.g. because of the Earth,s rotation. Elimination of the discontinuity is possible using the set of equivalent theories. The clock synchronization ambiguity in inertial systems is then solved: only e1=0 (corresponding to absolute simultaneity) gives rho-{c+v)/(c-v) when a goes to zero. Noninvariant values of the one way velocity of light are thus obtained and a new theoretical framework emerges in which space and time are not mixed and the usual relativistic paradoxes are absent.

Transformations of space and time between inertial systems are set up by starting from two empirically based assumptions: (1) The two-way velocity of light is the same in all inertial systems; (2) Clock retardation takes place with the usual velocity-dependent factor when clocks move with respect to an isotropic reference frame. The transformations thus obtained contain a free parameter *e _{1}*, the coefficient of

*x*in the transformation of time. The Theory of Special Relativity is recovered for a particular choice of

*e*. Different values of

_{1}*e*correspond to different theories of space and time, which are to a large extent empirically equivalent. We show that Michelson type experiments, aberration, occultation of Jupiter's satellites, and radar ranging of planets are insensitive to the choice of

_{1}*e*. Several other experiments lead to the same conclusion. An exception is discussed in Part II.

_{1}A physical quantity *p* exists for which the theory of special relativity (TSR) predicts *p* = 1 relative to all inertial frames. Under extremely general conditions we prove that *p* = (c +v)/(c - v) for all rotating disks having the same peripheral velocity v and *arbitrarily small acceleration a*. This value of *p* must hold in any small region near the disk rim. Therefore, the TSR gives rise to a discontinuity. The limit a -> 0 should instead be smooth, because all empirical knowledge about inertial systems is obtained in frames with a <> 0, e.g., because of the Earth's rotation. Elimination of the discontinuity is possible using the set of theories "equivalent" to TSR of Part I. The clock synchronization ambiguity in inertial systems is then solved: only *e _{1}* = 0 (corresponding to absolute simultaneity) gives

*p*= (c + v)/(c - v) when a -> 0. Non-invariant values of the one-way velocity of light are thus obtained.

Space and time transformations from a "stationary" isotropic inertial system S0 to any other inertial system S are shown to imply complete physical equivalence between the three possible pairs of assumptions chosen among the following: A1. Lorentz contraction of bodies moving with respect to S0; A2. Larmor retardation of clocks moving with respect to S0; A3. Two-way velocity of light equal to c in all inertial systems and in all directions. The empirical evidence supporting A2 and A3 is therefore in favour of A1 as well.

Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way speed of light. The conventionality of some features of relativity theory allows full compatibility with existing experimental evidence.

We consider an isotropical inertial reference frame ("stationary") and in it a uniformly rotating circular platform of radius * R*. The velocity of light

*relative to the rim of the platform is calculated and found to have values necessarily different from*

**c***. This*

**c***remains the same if*

**c***is increased but the peripheral velocity is kept constant. Since by so doing any small piece of the circumference can be considered better and better at rest in a ("moving") inertial system, the velocity of light relative to this system can be deduced. Noninvariant values are obtained and shown to coincide with the predictions of our recently published "inertial transformations".*

**R**An isotropic inertial reference frame ("stationary") is considererd, in which a circular disk of radius *R* rotates uniformly. The velocity of light [] relative to the rim of the disk is calculated under *very general *assumptions and found to satisfy []. This [] remains the same if *R* is increased but the peripheral velocity of the disk is kept constant. Since by so doing any small part of the circumference can be considered (for a short time) better and better at rest in a ("moving") inertial system, there is a discontinuity between accelerated reference frames with arbitrarily small acceleration and inertial frames, *if* the velocity of light is assumed to be *c* in the latter. Elimination of the discontinuity is shown to imply *fos inertial systems* a velocity of light [], necessarily equal to that obtained from recently published "inertial transformations."

After discussing in the first five sections the meaning and the difficulties of the priciple of relativity we present a new set of spacetime transformations between inertial systems ("inertial" transformations), based on three assumptions:

- The two-way velocity of light is c in all inertial systems and in all directions
- Time dilation effects take place with the usual relativistic factor
- Clocks are synchronized in the way chosen by nature itself, e.g., in the Sagnac effect

Recently pubblished space-time transformations between inertial systems (different from the Lorentz transormations) are reviewed. Energy and momentum are defined consistently with these new transformation laws. Formally they equal the usual relativistic expressions only in the privileged frame, but numerically they do so in all inertial frames. All the precise experimental data concerning thresholds for inelastic processes, particle masses, and so on, can thus be explained also within this new theoretical framework.

We construct a set T of space-time transformations between inertial system that are completely equivalent for explaining the experimental evidence, by starting from two empirically based assumptions: (1) The two-way velocity of light is c in all inertial sistems and in all directions; (2) Time dilation effects take place with the usual relativistic factor. The Lorentz transformation is an element of T and any two elements of T differ only as to a convention regarding clock synchronization. The simplest choice is to transform time indipendently of space coordinates (absolute synchronization) and can be called "inertial transformation". When accelerations are considered the equivalence is broken and the inertial transformation emerges as closest to physical reality.

The purpose of this paper is twofold: (1) to discuss the basis of the Lorentz transformations showing that the invariance of the velocity of light has in them a role even more important than usually believed, and (2) to find the complete set of theories empirically equivalent to the special theory of relativity (STR) under the assumption that the one-way velocity of light is not measurable.

In particular it will be shown that any modification of the coefficients of the Lorentz transformation, however small, gives rise to an ether theory, in the sense that the modified theory necessarily predicts the existence of a privileged frame that in principle can be detected experimentally, Therefore all the theories equivalent to STR but based on different transformation laws, must necessarily negate the validity of the relativity principle. We will come thus to the surprising conclusion that __if the one-way velocity of light is not measurable__, the content of the relativity principle is entirely conventional, since it can be affirmed or negated without any practical change in the predictive power of the theory.

The Einstein-de Broglie picture of wave-particle duality can provide an understandable foundation of quantum phenomena. We review the conceptual and experimental situation concerning this idea, as well as some recent proposals of experiments that could lead to the direct detection of the (empty) Einstein-de Broglie waves of photons and neutrons