As is well know from Einstein the choice of a criterion for distant simultaneity is equivalent to stipulating one-way speeds for the transit of light. It is shown that any choice of non-standard synchrony is equivalent to a Lorentz local time boost. From this and considerations from the hole argument, it follows that there is a non-trivial sense in which distant simultaneity is conventional, at least to the extent that the “gauge freedom” arising in the hole argument is non-trivial.

We analyze the possible implications of spacetime discreteness for the special and general relativity and quantum theory. It is argued that the existence of a minimum size of spacetime may explain the invariance of the speed of light in special relativity and Einstein’s equivalence principle in general relativity. Moreover, the discreteness of spacetime may also result in the collapse of the wave function in quantum mechanics, which may provide a possible solution to the quantum measurement problem. These interesting results might (...) have some important implications for a complete theory of quantum gravity. (shrink)

An important epistemological lesson can be learned from the impossibility to determine the one-way velocity of light and the immediate implication that simultaneity is conventional. The vicious circle -- to determine whether two distant events are simultaneous we need to know the one-way velocity of light between them, but to determine the one-way velocity of light we need to know that the two events are simultaneous -- is an indication of the need for a profound change of our view on (...) reality. (shrink)

Philosophy Compass, Volume 17, Issue 4, April 2022.

The conventionality of simultaneity thesis as established by Reichenbach and Grünbaum is related to the partial freedom in the definition of simultaneity in an inertial reference frame. An apparently altogether different issue is that of the conventionality of spatial geometry, or more generally the conventionality of chronogeometry when taking also into account the conventionality of the uniformity of time. Here we will consider Einstein’s version of the conventionality of geometry, according to which we might adopt a different spatial geometry and (...) a particular definition of equality of successive time intervals. The choice of a particular chronogeometry would not imply any change in a theory, since its “physical part” can be changed in a way that, regarding experimental results, the theory is the same. Here, we will make the case that the conventionality of simultaneity is closely related to Einstein’s conventionality of chronogeometry, as another conventional element leading to it. (shrink)

The purpose of the present paper is to develop kinematics of the special relativity with an anisotropy of the one-way speed of light. As distinct from a common approach, when the issue of anisotropy of the light propagation is placed into the context of conventionality of distant simultaneity, it is supposed that an anisotropy of the one-way speed of light is due to a real space anisotropy. In that situation, some assumptions used in developing the standard special relativity kinematics are (...) not valid so that the “anisotropic special relativity” kinematics should be developed based on the first principles, without refereeing to the relations of the standard relativity theory. In particular, using condition of invariance of the interval between two events becomes unfounded in the presence of anisotropy of space since the standard proofs drawing the interval invariance from the invariance of equation of light propagation are not valid in that situation. Instead, the invariance of the equation of light propagation, which is a physical law, should be taken as a first principle. A number of other physical requirements, associativity, reciprocity and so on are satisfied by the requirement that the transformations between the frames form a group. Finally, the correspondence principle is to be satisfied which implies that the coordinate transformations should turn into the Galilean transformations in the limit of small velocities. The above formulation based on the invariance and group property suggests applying the Lie group theory apparatus which includes the following steps: constructing determining equations for the infinitesimal group generators using the invariance condition; solving the determining equations; specifying the solutions using the correspondence principle; defining the finite transformations by solving the Lie equations; relating the group parameter to physical parameters. The transformations derived in such a way, as distinct from the transformations derived in the context of conventionality of distant simultaneity, cannot be converted into the standard Lorentz transformations by a coordinate change. The anisotropic nature of the presented transformations manifests itself in that they do not leave the interval invariant but only provide the conformal invariance of the interval. The relations that represent measurable effects include the conformal factor which depends on the relative velocity of the frames and the anisotropy degree. It is important to note the use of the correspondence principle as a heuristic principle which allows to relate the conformal factor to the anisotropy degree and thus completely specify the transformations and observable quantities. (shrink)

We explore the mathematical structure and the physical implications of a general four-dimensional symmetry framework which is consistent with the Poincaré—Einstein principle of relativity for physical laws and with experiments. In particular, we discuss a four-dimensional framework in which all observers in different frames use one and the same grid of clocks. The general framework includes special relativity and a recently proposed new four-dimensional symmetry with a nonuniversal light speed as two special simple cases. The connection between the properties of (...) light propagation and the convention concerning clock systems is also discussed, and is seen to be nonunique within the four-dimensional framework. (shrink)

In his first paper on the special theory of relativity, Einstein indicated that the question of whether or not two spatially separated events were simultaneous did not necessarily have a definite answer, but instead depended on the adoption of a convention for its resolution. Some later writers have argued that Einstein's choice of a convention is, in fact, the only possible choice within the framework of special relativistic physics, while others have maintained that alternative choices, although perhaps less convenient, are (...) indeed possible. (shrink)

In their article, “Relative Simultaneity in the Special Theory of Relativity,” Jackson and Pargetter have offered a method to determine distant simultaneity which they claim to be independent of any assumptions concerning one-way velocities and thus a basis for denying the conventionality of distant simultaneity within the framework of the Special Theory. In what follows, I shall argue that the case they make to support the claim to independence is mistaken.

Robert Torretti's objection is verificationism writ large. We reply that verificationism is to be rejected. Carlo Giannoni's objection is that our test for tilting fails because the rod might tilt and yet no current flow through its mid-point. We reply that nevertheless we can test for tilting because there would still be differences detectable with a glavanometer.

Within Special Relativity accelerated systems can be described as those systems in which standard clock synchronism does not hold. Therefore, the ε -generalized Lorentz equations derived by Winnie are the equations governing accelerated systems. The ε -generalized equation for time is used in analyzing two cases of the clock paradox: (1) the case in which a clock travels in a straight line, stops, and returns, and (2) the case in which a clock travels with uniform velocity in a circular path. (...) The treatment of case (1) of the paradox within this generalization of the Special Theory is compared with Møller's treatment of it within the General Theory. (shrink)

Gyrogroup theory and its applications is introduced and explored, exposing the fascinating interplay between Thomas precession of special relativity theory and hyperbolic geometry. The abstract Thomas precession, called Thomas gyration, gives rise to grouplike objects called gyrogroups [A, A. Ungar, Am. J. Phys.59, 824 (1991)] the underlying axions of which are presented. The prefix gyro extensively used in terms like gyrogroups, gyroassociative and gyrocommutative laws, gyroautomorphisms, and gyrosemidirect products, stems from their underlying abstract Thomas gyration. Thomas gyration is tailor made (...) for hyperbolic geometry. In a similar way that commutative groups underlie vector spaces, gyrocommutative gyrogroups underlie gyrovector spaces. Gyrovector spaces, in turn, provide a most natural setting for hyperbolic geometry in full analogy with vector spaces that provide the setting for Euclidean geometry. As such, their applicability to relativistic physics and its spacetime geometry is obvious. (shrink)

The role of the light postulate in special relativity is reexamined. The existing theory of relativity without light shows that one can deduce Lorentz-like transformations with an undetermined invariant speed based on homogeneity of space and time, isotropy of space and the principle of relativity. However, since the transformations can be Lorentzian or Galilean, depending on the finiteness of the invariant speed, a further postulate is needed to determine the speed in order to establish a real connection between the theory (...) and special relativity. In this paper, I argue that a certain discreteness of space-time, whose existence is strongly suggested by the combination of quantum theory and general relativity, may result in the existence of a maximum and invariant speed when combing with the principle of relativity, and thus it can determine the finiteness of the speed in the theory of relativity without light. According to this analysis, the speed constant c in special relativity is not the actual speed of light, but the ratio between the minimum length and the shortest time of discrete space-time. This suggests a more complete theory of relativity, the theory of relativity in discrete space-time, which is based on the principle of relativity and the constancy of the minimum size of discrete space-time. (shrink)