On the two aspects of time: The distinction and its implications

L. P. Horwitz*, R. I. Arshansky, A. C. Elitzur

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The contemporary view of the fundamental role of time in physics generally ignores its most obvious characteric, namely its flow. Studies in the foundations of relativistic mechanics during the past decade have shown that the dynamical evolution of a system can be treated in a manifestly covariant way, in terms of the solution of a system of canonical Hamilton type equations, by considering the space-time coordinates and momenta of events as its fundamental description. The evolution of the events, as functions of a universal invariant world, or historical, time, traces out the world lines that represent the phenomena (e.g., particles) which are observed in the laboratory. The positions in time of each of the events, i.e., the time of their potential detection, are, in this framework, controlled by this universal parameter τ, the time at which they are generated (and may proceed in the positive or negative sense). We find that the notion of the state of a system requires generalization; at any given τ, it involves information about the system at times t(τ) ≠ τ. The correlation of what may be measured at t(τ) with what is generated at τ is necessarily quite rigid, and is related covariantly to the spacelike correlations found in interference experiments. We find, furthermore, that interaction with Maxwell electromagnetism leads back to a static picture of the world, with no real evolution. As a consequence of this result, and the requirement of gauge invariance for the quantum mechanical evolution equation, we conclude that electromagnetism is described by a pre-Maxwell field, whose τ-integral (or asymptotic behavior as τ → ∞) may be identified with the Maxwell field. We therefore consider the world of events in space time, interacting through τ-dependent pre-Maxwell fields, as far as electrodynamics is concerned, as the objective dynamical reality. Our perception of the world, through laboratory detectors and our eyes, are based on integration over τ over intervals sufficiently large to obtain an a posteriori description of the phenomena which coincides with the Maxwell theory. Fundamental notions, such as the conservation of charge, rest on this construction. The decomposition of the common notion of time into two essentially different aspects, one associated with an unvarying flow, and the second with direct observation subject to dynamical modification, has profound philosophical consequences, of which we are able to explore here only a few.

Original languageEnglish
Pages (from-to)1159-1193
Number of pages35
JournalFoundations of Physics
Issue number12
StatePublished - Dec 1988


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