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arXiv:2205.11547 · Foundations of Physics

The Open Past in an Indeterministic Physics

Flavio Del Santo, Nicolas Gisin

Published Nov 26, 2022• 18 citations
arXivHTMLPDF

Abstract

Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally indeterminate, while also explaining the intuitive (and observed) asymmetry between the past-which can be remembered, at least partially-and the future-which is impossible to fully predict.

DOI
10.1007/s10701-022-00645-y

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Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally indeterminate, while also explaining the intuitive (and observed) asymmetry between the past-which can be remembered, at least partially-and the future-which is impossible to fully predict.
The dissertation is a defense of the following conditional claim: if there are objective collapses of the wavefunction, then the future is genuinely open. Although this is no radically new idea, the strategy I shall use to defend it is a new one. It proceeds in two main steps. First, building upon the recent literature on metaphysical indeterminacy in quantum mechanics, I argue for the view that systems in superposition have be interpreted as objectively indeterminate state of affairs. Second, I propose an alternative way to think of openness, according to which the future is open as of t, if and only if there is an indeterminate state of affair S at t, and S becomes determinate at t? (with t? later than t). To argue for the second step, I will give an analysis of the objective collapses of the wavefunction as the becoming determinate of previously indeterminate systems. Furthermore, in developing my arguments, I will also make some remarks concerning the ontology of objective collapse interpretations of quantum mechanics, the issue of whether metaphysical indeterminacy can be at some derivate level of reality, and the possibility of the openness of the future being an emergent phenomenon.
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name principle of infinite precision). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on finite information quantities (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem.'' We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').
This article focuses on three themes concerning determinism and indeterminism. The first is observational equivalence between deterministic and indeterministic models. The article discusses several results about observational equivalence and presents an argument on how to choose between deterministic and indeterministic models involving indirect evidence. The second is whether Newtonian physics is indeterministic. The article argues that the answer depends on what one takes Newtonian mechanics to be and highlights how contemporary debates on this issue differ from those in the nineteenth century. The third theme is how the method of arbitrary functions can be used to make sense of deterministic probabilities. The article discusses various ways of interpreting the initial probability distributions and argues that they are best understood as physical, biological, and other quantities characterizing the particular situation. The fact that the method of arbitrary functions deserves more attention than it has received so far is also emphasized.
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to "speak" of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms.
It is well known that the principles of quantum mechanics limit the possibilities of exact prediction as to the future path of a particle. It has sometimes been supposed, nevertheless, that the quantum mechanics would permit an exact description of the past path of a particle. \n \nThe purpose of the present note is to discuss a simple ideal experiment which shows that the possibility of describing the past pathof one particlewould lead to the predictions as to the future behaviour of a second particle of a kind not allowed in the quantum mechanics. It will hence be concluded that the principles of quantum mechanics actually involve an uncertainty in the description of past events which is analogous to the the uncertainty in the prediction of future events. And it will be shown for the case in hand, that this uncertainty in the description of the past arises from a limitation of the knowledge that can be obtained by measurement of momentum.
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of continued re-creation of the physical properties. The rate at which the system is re-created is a measure of the determinism of the measurements. The existence of uncertainties is better explained through this view, the meaning of incompatible observables becomes clearer and with the notion of re-creation and the origin of the Heisenberg uncertainty principle becomes more vivid.