arXiv subjects

Marton Gomori

Publications and source records attributed to Marton Gomori.

6 recordsLinked to original sources

arXiv2026

Trajectory of Probabilities, Probability on Trajectories, and the Stochastic-Quantum Correspondence

The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which assigns probabilities to possible histories. A lack of a clear distinction between these two probabilistic descriptions has given rise to a number of conceptual difficulties, particularly in recent analyses of stochastic-quantum correspondence. This paper provides a systematic account of their relationship. We define probability dynamics and stochastic process families together with a precise notion of implementation that connects the two descriptions. We show that implementations are generically non-unique, that every probability dynamics admits a Markovian implementation, and characterize when non-Markovian implementations are possible. We expose fallacies in common arguments for the linearity of probability dynamics based on the law of total probability and clarify the proper interpretation of ``transition matrices'' by distinguishing dynamics-level maps from the conditional probability matrices of implementing processes. We further introduce decomposability as the appropriate general notion of stepwise evolution for (possibly nonlinear) probability dynamics, relate it to divisibility in the linear case -- showing that the two can come apart -- and disentangle both notions from Markovianity and time-homogeneity. Finally, we connect these results to what we call statistical dynamics, in which linearity is indeed physically motivated, and contrast the framework with quantum mechanics.

quant-ph↗

arXiv2025

Questionable and Unquestionable in Quantum Mechanics

According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative frequencies expressible in operational terms using classical Kolmogorovian probability theory. In other words, a quantum theoretical description of a system should in principle be translatable into a purely operational-probabilistic description. However, our goal in this paper is different; we do not want to deal with the problem how to translate the known theory of quantum mechanics into operational terms, or to reconstruct the theory from postulates which can be interpreted in operational terms. Our aim is somewhat broader and points in the opposite direction. We start with a general scheme for the operational description of an arbitrary physical system. The description is based solely on the notion of observable events (measurement operations and measurement results) and on general, empirically established simple laws concerning their relative frequency. These laws are so simple and fundamental that they apply equally to any physical system. In the first part of the paper, we outline the basic elements of such an operational-probabilistic theory. In the second part, we discuss how this operational-probabilistic description compares to the quantum mechanical description and to what extent the standard Hilbert space quantum mechanics can be regarded as a reformulation of the general operational-probabilistic theory.

quant-ph↗

arXiv2014

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.

physics.hist-ph↗

arXiv2013

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.

physics.hist-ph↗

arXiv2011

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.

physics.hist-ph↗

arXiv2011

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.

physics.gen-ph↗