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Determinism beyond time evolution


Physicists are increasingly beginning to take seriously the possibility of laws outside the traditional time-evolution paradigm; yet many popular definitions of determinism are still predicated on a time-evolution picture, making them manifestly unsuited to the diverse range of research programmes in modern physics. In this article, we use a constraint-based framework to set out a generalization of determinism which does not presuppose temporal evolution, distinguishing between strong, weak and delocalised holistic determinism. We discuss some interesting consequences of these generalized notions of determinism, and we show that this approach sheds new light on the long-standing debate surrounding the nature of objective chance.

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  1. Note that here and throughout this article we will use ‘objective chance’ to refer exclusively to chances which arise from the fundamental laws of nature, such as the probabilities arising from the Born rule within indeterministic interpretations of quantum mechanics - i.e. in this article ‘objective chance’ does not include higher-level emergent chances, chances derived via the method of arbitrary functions, deterministic probabilities or anything else that might in another context be called an objective chance.

  2. The flash ontology version of the GRW model is not deterministic in this sense, but in principle other models of this kind could be deterministic.

  3. This framework has been set up in such a way that there is a probabilistic step followed by a non-probabilistic step. However, in principle nothing very significant rides on the choice of ordering - one could imagine a similar framework which would work the other way round, and this would presumably give rise to a fairly similar set of definitions for determinism.


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This publication was made possible through the support of the ID 61466 grant from the John Templeton Foundation, as part of the ”The Quantum Information Structure of Spacetime (QISS)” Project ( The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.

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Correspondence to Emily Adlam.

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Appendix : Nomic frequentism

Appendix : Nomic frequentism

The ‘nomic frequentism’ proposal of Roberts (2009), which suggests that laws about probabilities should be understood in terms of laws of the form ‘R percent of the Fs are Gs’ has much in common with the frequency constraint approach that we have discussed in this article. However, there are a few key differences. First, Roberts presents nomic frequentism as a general analysis of all probabilities that appear in laws, including for example the laws of evolutionary biology, whereas we have suggested it only for the specific case of objective chances appearing in the fundamental laws of nature, and in particular quantum mechanics - we would expect that the laws of evolutionary biology could be satisfactorily understood in terms of subjective probabilities. Moreoever, we do not even claim that all of the objective chances appearing in the fundamental laws of nature must be attributed to frequency constraints; we merely observe that this is one possible way in which apparently probabilistic events could arise in a deterministic universe. So our account is in that sense considerably less general and ambitious than Roberts’.

Second, Roberts suggests that ‘eighty percent of As are Bs’ should be regarded as conceptually equivalent to a law like ‘All As are Bs,’ (or rather, the latter should be regarded a special case of the former). But there is one important conceptual difference: the constraint ‘All As are Bs’ does not seem to require any ‘communication’ between the As, as it is enough that each A has the intrinsic property of being a B, whereas ‘exactly eighty percent of As are Bs’ or even ‘approximately eighty percent of As are Bs’ does seem to require some sort of coordination, as in order to ensure that the relative frequency is exactly or approximately correct, it seems that each A must ‘know’ something about what the other As are doing. Thus frequency constraints seem to require some form of non-locality (as Roberts himself later observes), which means we are in quite a different conceptual space from standard laws like ‘all As are Bs.’

Third, Roberts’ solution to the apparent absence of counterfactual independence within nomic frequentism is to say that ‘the way a nomic frequentist will represent independence of distinct fair coin-tosses is by denying the existence of any law that implies that the conditional frequency of heads on one toss given the results of another toss is different from (50 percent).’ But as we have seen, it does not seem that this can be entirely correct: constraint frequentism does allow the violation of counterfactual independence in at least certain special cases. Roberts justifies his solution on the basis that knowing facts which violate counterfactual independence ‘would require (us) to have advance intelligence from the future,’ but this argument seems to depend implicitly on the assumption that we are in a Humean context where the only information which is relevant to inferences about a future event is an actual observation of the event itself. But if the laws which induce the frequency constraints are understood as laws which are ontologically prior to the Humean mosaic, and if we are able to make correct inferences about the laws based on observations of a limited subset of the mosaic, then we would in principle be able to know about violations of counterfactual independence without having any illegitimate information about events which have not yet occurred. This sort of ‘knowledge of the future’ is not really any different from the knowledge of the future that we get from more familiar sorts of scientific laws: the laws constrain the Humean mosaic, including the future, and thus by figuring out the laws we can make inferences about the future.

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Adlam, E. Determinism beyond time evolution. Euro Jnl Phil Sci 12, 73 (2022).

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  • Determinism
  • Time evolution
  • Constraints
  • Objective chance