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arXiv:chao-dyn/9903010

Past events never come back

Xavier de Hemptinne

Published Mar 8, 1999• 0 citations
arXivHTMLPDF

Abstract

Time can be defined as the duration between events. It is irreversible. When used as a variable in quantifying the changing properties of matter, this irreversibility of time is incompatible with Newton's deterministic mechanics and with its quantum mechanical prolongation. Experimental evidence, involving rejection of the traditional isolation paradigm, points to a solution of this paradox. No system may be thought of as isolated. Irreversibility is imported from ``elsewhere''. The popular objection of the followers of determinism, consisting in extrapolating local behaviour to the scale of the universe and stressing alleged contradictions generated by the non-isolation hypothesis, is intellectually unacceptable. It is unjustifiable to draw conclusions by extrapolating beyond the domain of scientific observation.

DOI
10.48550/arxiv.chao-dyn/9903010

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Time can be defined as the duration between events. It is irreversible. When used as a variable in quantifying the changing properties of matter, this irreversibility of time is incompatible with Newton's deterministic mechanics and with its quantum mechanical prolongation. Experimental evidence, involving rejection of the traditional isolation paradigm, points to a solution of this paradox. No system may be thought of as isolated. Irreversibility is imported from ``elsewhere''. The popular objection of the followers of determinism, consisting in extrapolating local behaviour to the scale of the universe and stressing alleged contradictions generated by the non-isolation hypothesis, is intellectually unacceptable. It is unjustifiable to draw conclusions by extrapolating beyond the domain of scientific observation.
Time – what it is and its nature – has from the beginning held mysteries for layman, philosopher, and physicist alike. Periodic phenomena from motions of heavenly bodies and pendulums to quantal atomic clocks provide the means to measure time intervals, and Newton’s absolute time is a background flow against which classical and non-relativistic quantum physics is played out. While internally consistent, these two fields of physics are incompatible with the requirement of treating space and time on an equal footing. Quantum field theories provide the answer, as both treated as parameters, physics residing instead in the states and operators. But even in classical physics and quantum mechanics, time-independent descriptions provide an alternative to an explicitly time-dependent one. These, including a general method of approach called invariant imbedding, are discussed as alternative representations of an underlying reality that is the concern of physics.
The nature of time has long been debated in human history and nowadays is considered of central importance for understanding quantum gravity. We focus on and advocate the relational concept of time, which was put forward in the 17th century in opposition to Newton's absolute time, and only in 1990 explored in a quantum mechanical framework by Carlo Rovelli. After a historical introduction the mathematical models of time are carefully analyzed in chapter 1, followed by a discussion of the role of time played in fundamental theories. Using as an example nonrelativistic mechanics, the process of parametrization is explained, leading to a separation of a 'canonical time coordinate' from an arbitrary evolution parameter. The discussion of the role of time in special and general relativity as well as in quantum mechanics shows that more fundamental theories use less structure of time. This is followed by an exposition of the history of the relational concept of time, which negates the existence of an absolute duration and therefore often is called "timeless". Next it is shown how fundamental theories can be formulated and re-interpreted using this concept. We put emphasis on the hitherto neglected connection between relationalism and non-extensibility, while absolute time is shown to be unproblematic in classical mechanics just because of the possibility to extend the system without changing its nature. We conclude chapter 1 with a new axiomatic basis for the construction of time observables based on a simultaneity relation between 'observations', which are treated as a primitive concept and intuitively correspond to measurement events, but without knowing 'when' these events occur. There is no fundamental time observable; any observable qualifies as a time observable, if it allows to separate all instants. Chapter 2 gives a brief account of three main problems connected with time: a) The problem of the arrow of time. This has to be disentangled from the problem of irreversibility: a solution of the latter essentially excludes cyclic motions and is required for a solution of the former, which consists in showing that a fundamental direction between any two non-identical instants is physically meaningful. We give a formal definition of the arrow of time. This classical analysis is followed by a review of the problem of the arrow of time in quantum theory, where the situation becomes more complicated because of indeterminism. The discussion shows that there is no experimental evidence for a fundamental arrow of time, so that no contradiction with the relational concept of time arises. b) The problem of time measurement, which is of particular importance for the relational approach, in which time has no reality except if measured by a clock. In quantum theory useful time operators seem to be possible only within the more general formalism of positive operator valued measures (POVM). Clocks based on an oscillation mechanism do however require phase measurements; quantum phase operators can be defined as certain POVMs. Phase difference operators do also exist in the traditional Hilbert space formalism, if another quantization is used, as is done with relational quantization. c) The problem of quantum gravity is sketched only briefly. Chapter 3 introduces and discusses a model of Rovelli consisting of two oscillators with no external time. In this model one oscillator is considered as a clock and defines a relational time for the other one. In the first section we introduce this model and generalize it to a free massless scalar field in one dimension. We establish the relation between a single field mode and the infrared behaviour of the field through constants of motion. In the second section after a short review of canonical quantization we review Rovelli's quantization and generalize it to the free field. We could not prove the existence of the quantization map, but calculations using computer algebra indicate that the quantization does exist. For an enlarged algebra we are able to prove the nonexistence of a quantization map similar to a proof by Groenewold and van Hove. In chapter 4 we observe that a clock time always requires infinitely many degrees of freedom, and we make the hypothesis that a time observable is given by the infrared behaviour of quantum fields, leading to a classical notion of time when using algebraic quantum mechanics. This does however not solve the main problem of quantum relationalism: Which conditions determine a particular evolution?
This chapter contains a study of Heisenberg's views of the ontological content of quantum mechanics from I925 until the present day. During the quantum revolution of I925, he began by accepting a Berkeley-type empiricism in which the reality of a quantum mechanical system was reduced to that of a set of observation events, which were, however, acausally connected and in consequence did not constitute a stable phenomenal object of experimental knowledge. After 1955, he professed a modified form of Kantian philosophy whose starting point was the existence of universal and necessary scientific laws. Those universal and necessary scientific laws from which Kant started have been shown to belong only to restricted domains of intuitive experience (the domain of everyday life and classical physics). Heisenberg defines noumenal reality as the object of an intellectual intuition (episteme) which, however, is a kind of knowledge we do not possess. We know noumenal reality only through symbols in an intellectually patterned experience. There are two kinds of noumenal reality: there is the thing-in-itself which is the correlate of the phenomenal object, and there is the dunamis (or Aristotelian potentia or objective tendency) which is the correlate of the quantum mechanical system (e.g., elementary particle, atom, etc.). The latter is the noumenal correlate of the phenomenal or experienced union of subject and object taking place in the act of observation. The importance of universal symmetries in the expression of general laws of nature is stressed by Heisenberg, and these constitute for him the true basis for transcendental philosophy.
Modern physics speaks of observing quantum events as they unfold in real time, yet this claim contains a fundamental impossibility: observation requires duration, and by the time any measurement is complete, the event being measured has already passed. We introduce the concept of the existential instant — the infinitesimal moment of actual change that can never be directly observed because all measurement occurs in the past. As measurement resolution increases, we approach this instant asymptotically but can never arrive. This creates observational boundaries at both the microscopic and macroscopic scales where all structure collapses to points, not because reality is point-like at these extremes, but because we have reached the limits of what can be measured from our fixed observational bandwidth. Three foundational errors in modern physics — treating scale as static, misunderstanding consciousness as direct experience of the present, and ignoring observational limits — generate cascading false paradoxes including wave-particle duality, quantum uncertainty, the measurement problem, and cosmological tensions. When corrected through the framework of universal dynamic scale, these paradoxes dissolve, revealing them as artifacts of observational boundaries rather than properties of reality itself.