Abstract
This paper claims that, to the extent that temporal direction figures in physics at all, it is found there as part of the extra-scientific language science employs. The asymmetry between “before” and “after” is not captured by the mathematics of any theory, nor can it be derived from the laws of any theory. This, I argue, is true even of theories whose laws are not time reversal invariant. Recognizing that physics does not yield temporal direction but receives it from the background in which physics develops and operates does not, however, expose any hitherto unknown limitations or deficiencies of physics. The claim is not about physics, but about metaphysical stances regarding physics, specifically, physicalism, which requires from physics to deliver more than it does, or should. Once the place of temporal direction in physics is understood, infamous difficulties can be addressed in a novel way. Issues emerging from the 2nd law of thermodynamics, such as the minimum problem, and the worry that the law generates outlandish predictions, are removed. A side benefit is the recognition that the past hypothesis is superfluous. A final conclusion of the paper is that the relationship between physics and everyday language, far from being a source of difficulties, is healthy and beneficial to both.
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Notes
For an insightful and elaborate discussion of this question see Sklar (1981).
In a 1952 letter to Ruth Levitova. Let me note that issues pertaining to relativity were left out of this paper, but are discussed in my (2018). Also, in the context of this paper I treat the reality of passage and the reality of presentness, of the now, as going together. However, since passage is not central to any of the theses presented here I merely state this without argument or explanation.
That in Minkowski spacetime diagrams time is represented by an imaginary coordinate does indeed distinguish time from space, but this distinction has nothing to do with temporal directionality. This is the place to mention that issues stemming from relativity theory are not discussed here at all.
The breakdown of CPT symmetry has no bearing on the present discussion, which concerns direction as it manifests itself in ordinary experience.
Due to Putnam.
Much of this has been stated before, e.g., in Price (1996).
Cf. Hemmo and Shenker (2016, 156–8).
In passing, let us note that turning to “causation” as the anchor of temporal asymmetries will not do because causation itself is absent from the math of the theory (I am ignoring here the minority views which hold causation as reduceable to or emergent from physics). Causal structures are superimposed from the outside, for instance, when the evolution of the system, as depicted on a coordinate system, is described in English (albeit mixed with technical mathematical/physical terms). Such narrations tell a story of events that unfold in directed time, but that is because TD is built into the English with which they are relayed.
The details have been presented numerous times both in science texts books and in the relevant philosophy of physics literature, and will simply be assumed here.
Josef Loschmidt, Boltzmann's colleague and friend, was one of the first to observe that the 2nd law generates the minimum problem. In addition to Loschmidt's hypothesis there is an argument, based on Liouville's theorem, according to which every past microstate of the system is bound to reappear in the future, thus duplicating the past in the future. I do not discuss this argument here, but the analysis offered in the text to LH can easily be carried over and applied to this argument as well.
To the best of my knowledge, with the possible exception of Julian Barbour, nobody denies the reality of TD.
In a somewhat similar vein Earman (2006) observes that “without [the] presumption [that our short-term memories are veridical] both common-sensical and scientific knowledge would be impossible, and issues about inferences to the more remote past would be moot” (p. 421), and he adds that “the importance of statistical mechanics in grounding our knowledge of the past should be downgraded, especially when Boltzmann entropy is being relied upon to do the grounding, but more generally as well.” (Ibid, pp. 420–21).
Earman’s criticism in this context is harsh: he speaks of the Past Hypothesis as having “a (wannabe) law status”, a “dogma” that is “not even false”, whose implementation “consists mainly in furious hand waving and wishful thinking” (2006, 400).
Here Earman's (2006) discussion is particularly poignant because it undermines a central line of argument that attempts to justify the hypothesis precisely by appealing to its explanatory power. See e.g., North (2011), p. 328. Note that the following argument applies equally to alternative formulations of the Past Hypothesis, such as in Wallace (2017).
Famously, the magnetic and electric potentials, initially introduced just for mathematical convenience and without any physical significance, turned out, following the Zeeman effect, to represent important quantum mechanical properties. Lie Groups too where initially regarded irrelevant to physics.
A project related to but different from the more general challenge of accounting for the applicability of math in science.
By Evelyn Lamb, January 27, 2014. The Fig. 76 is taken from Tom Stoppard’s absurdist play “Rosencrantz and Guildenstern Are Dead”, which opens with one of them tossing 76 straight “heads”.
Of course, the correct question to ask is not whether a sequence of 1,000,000 “heads” is possible—it is just as likely as any other sequence of “heads” and “tails”. The relevant question concerns the probability of diverging from 50% “heads” and 50% “tails”. The law of large numbers states that for an infinitely long sequence the probability of diverging is 0. It is surprising how fast the probabilities drop. The probability of diverging by just 2% percent (that is of getting over 510,000 or under 490,000 “heads”) is approximately 0.25%. The probability of getting over 750,000 “heads” is utterly negligible.
Similar queries are raised in Stefanon (2019).
Similar questions, pertaining to the application of probability in cosmology, can be found in Sahlén (2017), where it is observed that “Model inference in cosmology involves both evaluation of empirical statistical evidence and application of other interpretative principles… [that] are not in the themselves empirically testable by conventional Bayesian statistical tests” (on p. 444).
Just to remove misunderstanding, even if, as I am suggesting, there are physical reasons why such eventualities cannot occur, that does not imply that TD is found inside physics after all. As explained above, even if the laws of nature are not TRI, the “earlier”/“later” asymmetry cannot be reduced to the irreversibility of processes because the term “irreversible” assumes this asymmetry. The claim that some processes cannot occur likewise presupposes TD—it says that it cannot happen that a body in the biological state typical of 80 years old bodies will 40 years later be in the state of a body that is 40 years old, or that, we start flipping a coin and five minutes later find that it has landed 100.
Smolin's Time Reborn is an example of a profound attempt to reintroduced passing time, that is, time as it is known from experience, into physics, but on the basis of cosmology. I believe Smolin aims for a correct goal but choses the wrong path (for more see Dolev 2018). The correct path starts with an appreciation of the role of natural language in science.
Where it cannot do so, as in some remote theories of cosmology, it has to defend itself against skeptics who questions whether it even deserves to count as science.
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Dolev, Y. Why Physics is not Wrong on Temporal Directionality, and Why This is not Necessarily Good News for Physicalism. Found Sci 27, 1285–1300 (2022). https://doi.org/10.1007/s10699-021-09816-y
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DOI: https://doi.org/10.1007/s10699-021-09816-y