Formulation Of Special Relativity Research Articles

Why Not a Sound Postulate?

What, if anything, would be wrong with replacing the light postulate in Einstein’s 1905 formulation of special relativity with a ‘sound postulate’, stating that the speed of sound is independent of the speed of the source? After reviewing the historical reasons underlying the particular focus on light in the special theory, we consider the circumstances under which such a theory of ‘sonic relativity’ would be justified on empirical grounds. We then consider the philosophical upshots of ‘sonic relativity’ for four contemporary areas of investigation in the philosophy of spacetime: (i) global versus subsystem symmetries, (ii) dynamical versus geometrical approaches to spacetime, (iii) the possibility of a preferred frame in theories of quantum gravity, and (iv) spacetime functionalism.

Seven formulations of the kinematics of special relativity

We present a comprehensive discussion of the formulation of the kinematics of special relativity, i.e., the Lorentz transformation. We begin with a concise new proof that the principle of relativity implies that the transformation of event coordinates between inertial reference frames is linear. We then give a clear derivation of the pre-Lorentz transformation, which follows from the principle of relativity. We then show that the pre-Lorentz transformation and the inertial invariance of the speed of light together result in the Lorentz transformation. This, of course, is essentially the traditional formulation. We next present two additional formulations, one using Lorentz–Fitzgerald contraction and one using time dilation, instead of inertial invariance. This is reasonable since Lorentz–Fitzgerald contraction and time dilation are about as well established as and are arguably less abstract than inertial invariance, and thus may profitably be used instead of inertial invariance to complete the formulation. We then present a complete proof that the pre-Lorentz transformation and the requirement of closure upon composition together imply that the transformation is either a Galilean transformation or a generalized Lorentz transformation. This is noteworthy in that it gets ever so close to the Lorentz transformation without invoking light. In the course of this, we obtain a generalized velocity addition rule, which reduces to the velocity addition rule of special relativity. We next show that the generalized Lorentz transformation, together with inertial invariance, Lorentz–Fitzgerald contraction, and time dilation, used one at a time, yields three more formulations. We then show that the unspecified, nonzero, constant speed in the generalized Lorentz transformation can be determined without any reference to light, thereby obtaining a seventh formulation. Light plays no explicit role in the four formulations employing Lorentz–Fitzgerald contraction and time dilation and plays no role whatsoever in the seventh formulation. Thus, and this is a fact which should be strongly emphasized, the formulation of special relativity in no way depends upon the nature of electromagnetic radiation. We conclude by briefly discussing these seven formulations of the kinematics of special relativity and some associated implications.

Why the Sagnac effect favors absolute over relative simultaneity

We consider a thought experiment, equivalent to the Sagnac effect, where a light signal performs a round trip over a closed path. If special relativity (SR) adopts Einstein synchronization, the result of the experiment shows that the local light speed cannot be c in every section of the closed path. No inconsistencies are found when adopting absolute synchronization. Since Einstein and absolute synchronizations can be discriminated, the conventionality of the one-way speed of light holds no longer. Thus, as sustained by specialists, it might be a viable formulation of SR that reinstates the conservation of simultaneity, even though it allows for relativistic effects, such as time dilation. Such an approach may lead to the discovery of new effects and a better understanding of relativistic theories.

Speakable and Unspeakable in Special Relativity: the Ageing of the Twins in the Paradox

In previous papers, we have presented a general formulation of special relativity, based on a weaker statement of the postulates. In this work, the paradigmatic example of the twin paradox is discussed in detail. Within the present formulation of special relativity, a “non-paradoxical” interpretation of the asymmetric ageing of the twins emerges. It is based exclusively on the rhythms of the clocks, which are not related by the standard textbook expressions and shall not be confused with clock time readings. Moreover, the current approach exposes the irrelevance of the acceleration of the returning twin in the discussion of the paradox.

Invention of the Free Electron Laser

The 150 years since Maxwell's formulation of the field equations, Lorentz's formulation of his force law, and Einstein's formulation of special relativity have seen electrodynamics emerge as one of the most fundamental elements of scientific and technical progress in the 20th and 21st centuries. Beginning with the analysis and demonstration of Hertzian waves, these fundamental contributions have launched a series of recurring cycles of discovery and application, in which each new discovery has been exploited to support new applications, which in turn have facilitated additional new discoveries and so on, revolutionizing in the process major elements of our economy with yet more to come through the research now in progress. It is the purpose of this article to relate my recollections of the invention and development of the free electron laser (FEL) within the context of the pervasive influence of the science and technology of electrodynamics in the 20th century.

What does the “arrow of time” stand for?

One hundred and thirty years after the work of Ludwig Boltzmann on the interpretation of the irreversibility of physical phenomena, and one century after Einstein's formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becoming, i.e. the course of time and the arrow of time, two concepts that the formalisms of modern physics are careful to distinguish. The course of time is represented by a time line that leads us to define time as the producer of duration. It is customary to place on this time line a small arrow that, ironically, must not be confused with the “arrow of time”. This small arrow is only there to indicate that the course of time is oriented, has a well-defined direction, even if this direction is arbitrary. The arrow of time, on the other hand, indicates the possibility for physical systems to experience, over the course of time, changes or transforma-tions that prevent them from returning to their initial state forever. Contrary to what the ex-pression “arrow of time” suggests, it is there-fore not a property of time itself but a property of certain physical phenomena whose dynamic is irreversible. By its very definition, the arrow of time presupposes the existence of a well- established course of time within which – in addition – certain phenomena have their own temporal orientation. We think that it is worth-while to emphasize the difference between sev-eral issues traditionally subsumed under the label “the problem of the direction of time”. If the expressions “course of time”, “direction of time” and “arrow of time” were better defined, systematically distinguished from one another and always used in their strictest sense, the debate about time, irreversibility and becoming in physics would become clearer.

La hipótesis del cuanto de luz y la relatividad especial ¿Por qué Einstein no las relacionó en 1905?

We attempt to determine why Einstein did not mention his article on light-quanta hypothesis, written in March 1905, in his formulation of Special Relativity, devised just three months later. The main reasons we have found are the following: Einstein's different attitudes towards the existence of ether and absolute space; his permanent commitment to the ontological primacy of the electromagnetic field; the non-classical properties he ought to attribute to light-quanta; his hesitant stance about Maxwell electrodynamics as a complete and definitive representation of physical reality and at the same time, his suspection that a possible wave/particle duality would not lead to an unsolvable difficulty; his unstable and uncompromised attitude with respect to atomism; the more conservative, though less intuitive, character of Special Relativity; the different interpretation of the epistemological status of both theories and the marked differences in their formulation.

About the Confusion Between the Course of Time and the Arrow of Time

A conclusion drawn after a conference devoted (in 1995) to the “arrow of time” was the following: “Indeed, it seems not a very great exaggeration to say that the main problem with “the problem of the direction of time” is to figure out exactly what the problem is supposed to be !” What does that mean? That more than 130 years after the work of Ludwig Boltzmann on the interpretation of irreversibility of physical phenomena, and that one century after Einstein’s formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becoming, i.e. the course of time and the arrow of time, two concepts that the formalisms of modern physics are careful to distinguish.

Thomas Rotation and Thomas Precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. A straightforward derivation of the Fermi–Walker equation is also given. Besides the simplicity of calculations the absolute treatment of spacetime allows us to make a clear conceptual distinction between the phenomena of Thomas rotation and Thomas precession.

On the Appeal to a Pre-Established Harmony Between Pure Mathematics and Relativity Physics

Soon after its appearance in 1905, the Einsteinian relativity with its relativistically admissible 3-velocities was recognized by Vladimir Varicak in 1908 as the realization in physics of the hyperbolic geometry of Bolyai and Lobachevski. At the same time, however, during the years 1907–1909 Minkowski reformulated the Einsteinian relativity in terms of a space of 4-velocities that now bears his name. As a result, the special theory of relativity that we find in the mainstream literature is not the one originally formulated by Einstein but, rather, the one reformulated by Minkowski. Thus, in particular, one of the most powerful ideas of Einstein in 1905, the Einstein addition of relativistically admissible 3-velocities that need not be parallel, is unheard of in most texts on relativity physics. Following our recently published book, Beyond the Einstein Addition, Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces [1], the aim of this article is to employ the principle of pre-established harmony between mathematics and physics to demonstrate that the original Einsteinian relativity, as opposed to the Minkowskian relativity, is the legitimate formulation of special relativity whose time has returned.

A vector product formulation of special relativity and electromagnetism

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in “six-vector” form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's four equations expressed as one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated.

The second cardinal equation of dynamics for continua in special relativity

The second cardinal equation of dynamics is obtained in special relativity for a continuum in generic motion and acted upon by volume and surface forces. In the usual « synchronous » formulation of special relativity, the second cardinal equation is used in order to explain the presence of a moment of external forces acting on a body which is in uniform rectilinear translatory motion. This is done in general and applies to the particular cases as the classical problem by Lewis and Tolman.

Formulation of Special Relativity by Means of Galilean Transformations

Special relativity is formulated in terms of Galilean transformations. This is possible by using the principle of general covariance in the framework of special relativity. In particular the relativistic contraction of lengths and time dilation are discussed. It is further shown that classical electrodynamics also can be formulated consistently when using Galilean transformations. Finally, this result is illustrated by evaluating the field of a uniformly moving charge.