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ABSTRACT
Before the twentieth century, the Universe was usually imagined as a large spatially extended thing unfolding in time. The past was fixed and the future was open; unfolding was conceived as an asymmetric process of coming into being. Relativity introduced a new vision in which space and time are presented together as a single four-dimensional manifold of events. That, together with the fact that the fundamental laws of our classical theories are symmetric in time, made understanding why the past and future present themselves so differently in our experience one of the central challenges of physics. The last two centuries have seen a great deal of progress in understanding various of the so-called arrows of time: the thermodynamic arrow, the cosmological arrow, the arrow of knowledge or information. There remains an outstanding piece of this puzzle that has seen little progress, one that Roger Penrose described in his beautiful paper Singularities and Time-Asymmetry in 1979 as: “The arrow most difficult to comprehend … namely the feeling of relentless forward temporal progression, according to which potentialities seem to be transformed into actualities.”
I will propose that the insight needed to resolve the problem involves taking into account that we are part of the universe and that any attempt to model it as a totality involves self-reference. I will argue specifically that self-reference, against the background of a thermodynamic gradient, creates an instability in an embedded agent’s ability to know the future or even treat it as a potential object of knowledge. That instability captures the sense in which the future remains for her perpetually open and the passage of time resolves openness into the fixity of fact.
Notes
1 If ‘the Universe’ is used explicitly in the all-inclusive sense to mean ‘the totality of all that there is’, then the fact that the Universe includes us follows from the fact that we exist. If ‘the Universe’ is used to mean ‘all of material existence’ then whether the Universe includes us (i.e., whether self-reference arises in any description of the Universe) will seem to depend on whether we are ourselves physical things. Philosophers have sometimes used ‘the Universe’ ambiguously, sometimes meaning ‘all of existence’ and sometimes ‘all of material existence’, treating physics as providing us with (at least provisionally) an explicit representation of the Universe. If one is a dualist, a slightly more roundabout way of showing that self-reference will arise is needed. All that is needed for what follows is that you are an embodied intelligence, that your actions are part of what happens, and that your thoughts make a difference to what happens. See the section: “Taking Self-Reference into Account”.
2 This is the set up in the paradox of predictibility. See “An Essential Unpredictability in Human Behavior”, by Michael Scriven, from the book Scientific Psychology: Principles and Approaches, edited by Benjamin B. Wolman and Ernest Nagel,1965. Also Ismael, (2019) “Determinism, Counterpredictive Devices, and the Impossibility of Laplacean Intelligences” in The Monist, Special Issue edited by Gordon Belot.
3 Penrose, R. (1979) “Singularities and Time-Asymmetry”. In: Hawking, S.W. and Israel, W., Eds., General Relativity: An Einstein Centenary Survey, Cambridge University Press, Cambridge, 581-638.
4 There has been a mass of literature on the foundations of statistical mechanics since Albert’s book: some technical, some philosophical. There is widespread agreement that the classical laws together with some form of a probability distribution and some sort of hypothesis about the past will underwrite thermodynamic generalizations, but dispute about the form the probability distribution and the Past Hypothesis should take. See, for example, Wallace, D., “The Logic of The Past Hypothesis”, http://philsci-archive.pitt.edu/8894/, Earman, J. (2006). The ‘Past Hypothesis’: Not even false. Studies in the History and Philosophy of Modern Physics 37, 399–430. Myrvold, W. C. Beyond Chance and Credence, Oxford University Press, 2021. Winsberg, E., “Laws and Statistical Mechanics”, Philosophy of Science 71 (5):707-718 (2004). Frigg, R. (2008). “Typicality and the approach to equilibrium in Boltzmannian statistical mechanics”. http://philsci-archive.pitt.edu, and the wide-ranging commentary devoted specifically to Albert’s program in The Probability Map of the Universe: Essays on David Albert’s Time and Chance, Edited by Barry Loewer, Brad Weslake, Eric Winsberg, Harvard University Press, forthcoming. Another source of dispute concerns the fact that Albert presents the account at the global level, but there are (good) reasons for thinking it might be best told at the level of local adiabatically isolated subsystems of the world: those are the systems to which thermodynamics is applied and the probabilities have a clear statistical interpretation when applied to local subsystems. See Reichenbach’s The Direction of Time (Dover, New York, 1956), Rovelli, “Back to Reichenbach”, http://philsci-archive.pitt.edu/20148/, Fernandes, http://philsci-archive.pitt.edu/20955/. Leeds, Stephen. 2003. Foundations of Statistical Mechanics—Two Approaches. Philosophy of Science 70(1): 126−144. Albert is building on a tradition that goes back to Boltzmann, and much of which was present in There is also an alternative Gibbsian tradition. E.T., Jaynes, Gibbs vs Boltzmann Entropies, American Journal of Physics 33, 391 (1965); https://doi.org/10.1119/1.1971557, Gibbs and Boltzmann Entropy in Classical and Quantum Mechanics Sheldon Goldstein, Joel L. Lebowitz, Roderich Tumulka, and Nino Zangh, June 2, 2019, https://arxiv.org/pdf/1903.11870.pdf
5 Phase space is a continuous space containing six dimensions for every particle in the system, one for every dimension of position and momentum. The Boltzmannian entropy of a system is proportional to the log of the measure of microstates in phase space compatible with its macrostate, using the standard Lebesgue measure.
6 Microscopic knowledge will not typically help to reliably increase our macroscopic predictability. Out in the wild, microscopic variables are too sensitive and fragile to too many factors to be stabilized effectively as a source of prediction.
7 This is an active, but nascent area of investigation. See Hoerl, Christoph & Teresa McCormack (2018) “Animal Minds In Time: The question of episodic memory” in Kristin Andrews & Jacob Beck (eds.) The Routledge Handbook of Philosophy of Animal Minds Routledge pp. 56-64, Templer, Victoria L. & Robert R. Hampton (2013) “Episodic Memory in Nonhuman Animals” Current Biology 23 R801-R806, Tramacere, A., Allen, C. Temporal binding: digging into animal minds through time perception. Synthese 200, 1 (2022). https://doi.org/10.1007/s11229-022-03456-w. There are obvious difficulties of studying animal consciousness, because our knowledge is indirect and there is a bewildering variety from elephants and crows to gophers and fish.
8 See Time and Chance, Chapter 6 and After Physics, “The Difference Between the Past and Future”.
9 Any adequate account of the foundations of statistical mechanics is going to have to deliver this result; it is going to have to support the generic expectation of thermodynamic behavior to the future and underwrite inferences from records to the past. Note that these aren’t meant to describe self-conscious inferential practices of agent, but rather to make explicit the physics that underwrites their typically unreflective reliance on records.
10 After saying that the epistemic account is unsatisfactory, Penrose leaves off this train of thought and moves to a different way of trying to understand the intuitive nature of the difference between past and future, in terms of thinking of the past as providing reasons (or, as he says ‘causes’) of future events. “My attitude has been that a low entropy at one time may be regarded as providing a ‘reason’ for precise correlations.
11 The indexical here is for ease of exposition: we can replace it with an explicit specification of location and time. Notice, however, that the indexical is crucial to recognizing that the answer can’t be given truthfully.
12 A brief recap might be useful: self-reference arises naturally and inevitably for a system that is part of the domain that it is representing. An agent using information to guide behavior knows that some of what happens in the world it is representing is stuff that it does. It knows that its own knowledge-gathering activity is connected in the domain by way of its effect on behavior. And it knows that its behavior produces records. And it exploits the interaction effects of its beliefs with an eye to the records they will leave. If one can’t stabilize the answer to a question independently of giving the answer – i.e., if whether the answer that is true is going to depend on the answer that one gives - that creates interference. Interference can be immediate or attenuated. It can be negative or positive. Both examples above were examples of negative interference. But it is easy to change the examples to get positive interference. Just as there’s no way to be right in the question displayed in the original example, there’s no way to be wrong if we ask the computer ‘is the word that is about to appear on the monitor yes?’. Or better ‘what word is about to appear on the monitor?’. It doesn’t matter how you answer – yes or no – what you say will be true. The attenuated effects are going to depend on how the answer delivered is connected in the wider domain.
13 Chalmers, D., The Conscious Mind: In Search of a Fundamental Theory. New York: Oxford University Press, 1996.
14 There will be an essential incompleteness on pain of contradiction. That is the familiar Gödelian conclusion; any logical system powerful enough to permit self-representation is either inconsistent or complete.
15 This point is indifferent to disputes in the foundations of statistical mechanics. Whatever one’s preferred account of the foundations of statistical mechanics, that account will have to provide an understanding of the physics of traces. The practical asymmetry derives from the physics of traces; effects are expected records of occurrences. See Rovelli, C. “Memory and Entropy”, https://arxiv.org/abs/2003.06687 for a similar account of the relationship between records and agency. The paper also provides a very general account of the nature of traces from a statistical mechanical point of view.
16 There is a metaphysical picture of the world that frames much of common sense. We imagine that we live in a universe that is unfolding in time, that causal relations run from past to future and that is why we regard the past as fixed and the future as open. This metaphysical picture has not found a hospitable home in physics. The actual metaphysics of post-relativistic classical physics portrays the Universe as a four-dimensional manifold of events with no global conception of time. There is no unfolding and the laws don’t incorporate any intrinsic direction of determination. That means that we need a new way of understanding it, and that new way of understanding it is bound to seem alien and unintuitive.
17 This is for the same reason that the computer can’t truthfully answer questions about what will appear on its monitor without giving an answer. No amount of information is going to overcome the problem.
18 On the logic of this, see my, How Physics Makes Us Free (New York, NY: Oxford University Press, 2016) and “Decision and the open future,” in Adrian Bardon, ed., The Future of the Philosophy of Time (New York, NY: Routledge, 2012), 149–168. Routledge. James Joyce, “Levi on causal decision theory and the possibility of predicting one’s own actions,” Philosophical Studies 110:1 (2002), 69–102. James Joyce, “Are Newcomb problems really decisions?,” Synthese, 156:3 (2007), 537– 562. Huw Price, (2012)., “Causation, chance, and the rational significance of supernatural evidence,” Philosophical Review 121:4 (2012), 483–538. David Velleman, “Epistemic freedom,” Pacific Philosophical Quarterly 70 (1989), 73–97. Wlodek Rabinowicz, “Does practical deliberation crowd out self-prediction?,” Erkenntnis, 57:1 (2002):91–122. Brian Skyrms, The Dynamics of Rational Deliberation (Cambridge, MA: Harvard University Press, 1990). Isaac Levi, The Covenant of Reason: rationality and the commitments of thought (Cambridge, UK: Cambridge University Press, 1997). Yang Liu, Yang and Huw Price, “Ramsey and Joyce on Deliberation and Prediction,” Synthese https://doi.org/10.1007/s11229-018-01926-8 (2018). Yang Liu and Huw Price, “Heart of DARCness,” Australasian Journal of Philosophy DOI: 10.1080/00048402.2018.1427119 (2019). Alison Fernandes (2016) Varieties of Epistemic Freedom, Australasian Journal of Philosophy, 94:4, 736-751, DOI: 10.1080/00048402.2015.1116015. Anscombe famously asked what the difference is between prediction and intention, e.g., between ‘I’m going to be sick’ and ‘I’m going to go for a walk’? In epistemic terms, the signature of an intention is that it is a self-affirming act that interferes positively with what it predicts: Elizabeth Anscombe, Intention, (Cambridge, MA: Harvard University Press, 1957).
19 Of course, there is no view from outside; I mean simply the view of the Universe that is invariant under transformations between internal perspectives.
20 To be clear on what the ‘transformation of potentiality into actuality’ can mean. There is one world. The transformation of some particular event from potentiality to actuality has to be something that happens over time, so we have to be talking about how particular events look from different temporal perspectives. So if we are looking at some particular event – say who wins the NCAA tournament in 2025– prospectively, at the beginning of the tournament, there are many possibilities; retrospectively, at the end, there is only one.
21 See Ismael, “Rethinking Time and Determinism: what happens to determinism when you take relativity seriously, Time and Science, edited by Remy Lestienne and Paul Harris, World Scientific Publishing, forthcoming.