1,076 research outputs found
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
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
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
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
On the Persistence of the Electromagnetic Field
According to the standard realistic interpretation of classical electrodynamics, the electromagnetic field is conceived as a real physical entity existing in space and time. The problem we address in this paper is how to understand this spatiotemporal existence, that is, how to describe the persistence of a field-like physical entity like electromagnetic field. First, we provide a formal description of the notion of persistence: we derive an “equation of persistence” constituting a necessary condition that the spatiotemporal distributions of the fundamental attributes of a persisting physical entity must satisfy. We then prove a theorem according to which the vast majority of the solutions of Maxwell's equations, describing possible spatiotemporal distributions of the fundamental attributes of the electromagnetic field, violate the equation of persistence. Finally, we discuss the consequences of this result for the ontology of the electromagnetic field
How to Move an Electromagnetic Field?
The special relativity principle presupposes that the states of the physical
system concerned can be meaningfully characterized, at least locally, as such
in which the system is at rest or in motion with some velocity relative to an
arbitrary frame of reference. In the first part of the paper we show that
electrodynamic systems, in general, do not satisfy this condition. In the
second part of the paper we argue that exatly the same condition serves as a
necessary condition for the persistence of an extended physical object. As a
consequence, we argue, electromagnetic field strengths cannot be the
individuating properties of electromagnetic field---contrary to the standard
realistic interpretation of CED. In other words, CED is ontologically
incomplete.Comment: 14 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:0912.438
Questionable and Unquestionable in Quantum Mechanics
We derive the basic postulates of quantum physics from a few very simple
operational assumptions based exclusively on the relative frequencies of
observable events (measurement operations and measurement outcomes). We isolate
a notion which can be identified with the system's own state, in the sense that
it characterizes the system's probabilistic behavior against all possible
measurement operations. We investigate some important features of the possible
states of the system. All those investigations remain within the framework of
classical Kolmogorovian probability theory, meaning that any physical system
(traditionally categorized as classical or quantum) that can be described in
operational terms can be described within classical Kolmogorovian probability
theory. In the second part of the paper we show that anything that can be
described in operational terms can, if we wish, be represented in the Hilbert
space quantum mechanical formalism. The outcomes of each measurement can be
represented by a system of pairwise orthogonal closed subspaces spanning the
entire Hilbert space; the states of the system can be represented by pure state
operators, and the probabilities of the outcomes can be reproduced by the usual
trace formula. Each real valued quantity can be associated with a suitable
self-adjoint operator, such that the possible measurement results are the
eigenvalues and the outcome events are represented by the eigenspaces,
according to the spectral decomposition of the operator in question. This
suggests that the basic postulates of quantum theory are in fact analytic
statements: they do not tell us anything about a physical system beyond the
fact that the system can be described in operational terms. This is almost
true. At the end of the paper we discuss a few subtle points where the
representation we obtained is not completely identical with standard quantum
mechanics.Comment: 40 page
On the Persistence of the Electromagnetic Field
According to the standard realistic interpretation of classical electrodynamics, the electromagnetic field is conceived as a real physical entity existing in space and time. The problem we address in this paper is how to understand this spatiotemporal existence, that is, how to describe the persistence of a field-like physical entity like electromagnetic field. First, we provide a formal description of the notion of persistence: we derive an “equation of persistence” constituting a necessary condition that the spatiotemporal distributions of the fundamental attributes of a persisting physical entity must satisfy. We then prove a theorem according to which the vast majority of the solutions of Maxwell's equations, describing possible spatiotemporal distributions of the fundamental attributes of the electromagnetic field, violate the equation of persistence. Finally, we discuss the consequences of this result for the ontology of the electromagnetic field
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