On the formal statement of the special principle of relativity

The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest generality

How to move an electromagnetic field?

As a first principle, it is the basic assumption of the standard relativistic formulation of classical electrodynamics (ED) that the physical laws describing the electromagnetic phenomena satisfy the relativity principle (RP). According to the standard view, this assumption is absolutely unproblematic, and its correctness is well confirmed, at least in a hypothetico-deductive sense, by means of the empirical confirmation of the consequences derived from it. In this paper, we will challenge this customary view as being somewhat simplistic. The RP is actually used in exceptional cases satisfying some special conditions. As we will see, however, it is quite problematic how the RP must be understood in the general case of a coupled particles + electromagnetic field system

Is the relativity principle consistent with classical electrodynamics? Towards a logico-empiricist reconstruction of a physical theory

The transformation rules for the basic electrodynamical quantities are routinely derived from the hypothesis that the relativity principle (RP) applies for Maxwell's electrodynamics. These derivations leave open several questions: (1) Is the RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of electrodynamics in one single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of electrodynamics in one single frame of reference? (1) and (2) are empirical questions; we will investigate problems (3) and (4). First we will develop a formalism of the RP. In the second part, we will deal with the operational definitions of the fundamental quantities. In the third part of the paper we will show that the proper transformation rules are indeed identical with the ones obtained by presuming the covariance, and that the covariance is indeed satisfied. Problem (3) raises conceptual problems to which there seems no satisfactory solution in electrodynamics; thus, contrary to the widespread views, the question we asked in the title has no obvious answer.Comment: 39 pages, 3 figures, LaTeX; more concise notations, elucidatory remarks and examples adde

On the formal statement of the special principle of relativity

The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest generality.Comment: 15 pages, 3 figure

Operational understanding of the covariance of classical electrodynamics

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamic quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations are regarded as unquestionable, they leave open the following fundamental question: Are the so-obtained transformation rules indeed identical with the true transformation laws of the empirically ascertained electrodynamic quantities? This is of course an empirical question. In this paper, we will answer this question in a purely theoretical framework by applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena, including what a moving observer must see when performs measurement operations with moving measuring devices. We will show that the real transformation laws are indeed identical with the ones obtained by presuming the covariance of the equations of electrodynamics, and that the covariance is indeed satisfied. Beforehand, however, we need to clarify the operational definitions of the fundamental electrodynamic quantities. As we will see, these semantic issues are not as trivial as one might think

Operational understanding of the covariance of classical electrodynamics

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the pre-assumption that the equations of electrodynamics are covariant against these---unknown---transformation rules. There are several problems to be raised concerning these derivations. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following fundamental question: Are the so-obtained transformation rules indeed identical with the true transformation rules of the fundamental electrodynamical quantities? In other words, is it indeed the case that the values calculated from the quantities in one inertial frame by means of the transformation rules we derived are equal to the values of the same quantities obtained by the same operations with the same measuring equipments when they are co-moving with the other inertial frame? This is of course an empirical question. In this paper, we will investigate the problem in a purely theoretical framework by applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena. We will show that the transformation rules of the electrodynamical quantities are indeed identical with the ones obtained by presuming the covariance of the equations of electrodynamics, and that the covariance is indeed satisfied. Beforehand, however, we need to clarify the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think