From solipsism to emergent time

July 8, 2020. Why can we remember the past but not the future? And why do objects persist? I discuss how folk metaphysics draws attention to genuine puzzles about the nature of time, and outline some desiderata for a physical explanation.

Brain states and metaphysics

In a previous post, I discussed presentism, the view that only the present exists. I argued that, though compelling at the level of folk psychology, presentism is ultimately unable to explain change, and our sense data are telling us about brain states rather than metaphysics. But perhaps this is a bit too quick. Our brain states might tell us something deep about the universe after all! In particular, it seems odd that we can remember the past but not the future. As Terry Pratchett puts it in Reaper Man:

Alone of all the creatures in the world, trolls believe that all living things go through Time backwards. ‘If the past is visible and the future is hidden,’ they say, ‘then it means you must be facing the wrong way.’

Why do we face the wrong way?

At the level of folk epistemology, being lodged in the present moment gives rise to presentism, and being “uninfluenced” by future events gives rise to the doctrine of free will. At a less folky level, it explains the appeal of “growing block” ontologies for spacetime, where the future does not yet exist. I think none of these conclusions is licensed by the properties of our brain states. But being lodged in the present seems like a trivially explicable thing, while our inability to remember the future is not. This is related to an even deeper puzzle, namely that objects persist, which we will elaborate below.

Temporal solipsism

Let’s pause for a moment and untangle a common thread winding through these ideas. Presentism, free will, and growing blocks all represent a type of solipsism. A solipsist proper treats the fact that they cannot experience other minds as conclusive evidence that other minds do not exist. A presentist treats the fact that they only experience the present moment as evidence only this moment exists. Similarly, an enthusiast of growing blocks or free will imagines that future events (or future decisions) do not exist since they have yet to encounter (or make) them. To be sure, a blocker is more liberal than a presentist, since they believe in the past, but this is like a “friendly” solipsist who believes only in the existence of the people they have met.

Solipsism would not be crazy if you were the only sentient being in a world of amoebae, since you would not need a theory of mind to explain their behaviour. But in a world of beings whose behavioural complexity matches your own, mental states you cannot access remain the best explanation for the behaviour of others. Solipsists may be good Cartesians, retaining only those ontological commitments that cannot be spoofed by a malicious Cartesian demon, but they are terrible scientists. They can explain nothing! I think the appeal of solipsism is not that it is explanatory, but that it survives the scorched-earth epistemic program of Cartesian doubt.

Temporally speaking, we do not live in a universe of amoebae. We live in a spacetime continuum where different temporal slices richly obey the same laws of physics, namely, Einstein’s general relativity, at least at large enough scales. As with human behaviour, these slices look the same from the outside. A paranoid Cartesian might say: things look different from in here, so they are different out there. A realist replies: they look the same from the outside, and the best explanation is that they look the same from the inside too. But like certain jokes, to see the inside, I guess you need to be there.

Thisness and thatness

Let’s return to our original question, namely, to what extent brain states license metaphysical conclusions. Solipsists and presentists notice that there is a quiddity, a thisness, to being in a mind and being in a moment. But from “thisness”, they leap to the remarkable inference that “thatness” is the same as non-existence! A growing blocker or free willer is, I think, fundamentally making the same inference, but they are prepared to let existence spread like a contaminant from present effects to their causes.

To me, these conclusions make no sense, and are almost deliberately non-explanatory. But the fact there is a “thisness” at all is unavoidable. For instance, the quiddity of having a mind is the experience of mental sensations, also called qualia. I don’t think it’s plausible to deny qualia, though efforts to explain them away, or comfortably ensconce them in a physicalist framework, are heroic and often amusing. I would be very surprised if someone could one day extract my subjective experience of the colour red from the standard model Lagrangian, but good luck to them all the same.

In the temporal case, the quiddity of being lodged in the present moment is trivially explicable: the “thisness” of the present and “thatness” of the future and past are indexicals in the same spirit as “hereness” and “thereness”. (See the prequel for more details.) But while the spirit is similar, there is an asymmetry between future and past which does not exist between up and down, or left and right. This asymmetry is what makes free will and the growing block plausible. And that is really the point I want to make: while the folk Cartesian may draw the wrong conclusions, the premises are sound. There is something strange about being in a mind. There is something strange about being in time.

The bow and the arrow

The problem can be clearly stated as follows: why change? The presentist or blocker might answer: because existence. In other words, what exists is changing, and changes become in the world. If we dismiss this as temporal solipsism, and adopt an even-handed four-dimensionalist ontology, the question becomes: why cause and effect? Put differently, why can we remember the past but not the future?

At this point, physicists step in and claim to offer a solution. The relativist says: because spacetime signature. In other words, the spacetime manifold comes equipped with a timelike direction, locally, everywhere. This is evidently so, but it does not explain the asymmetry between time and space; it simply bakes it into the geometry. Is there a more fundamental way of explaining the asymmetry? The statistical mechanic says: because entropy. Roughly speaking, a system with many parts changes in an effectively random way, and it will tend towards the most likely outcomes, particularly when the odds for the unlikely outcomes are roughly one in $2^{10^{23}}$. The second law of thermodynamics states that such odds are well-approximated by zero.

The claim is that the irreversible, macroscopic arrow of time arises from a system exploring ways to be. Let’s examine this claim a little more closely. The entropy $S$ is just the logarithm of the number of ways $N$ the system can be while looking the same at a macroscopic level, $S = \log N$. There can be some maximally likely way for a system to be, which corresponds to maximum entropy, $S_\text{max}$. But if the universe (or a box of gas, or a shiny new pair of sneakers, or whatever) is for some reason in a sub-maximal, or low entropy state (LES), then it will explore ways to be in an effectively irreversible fashion, even though the laws of physics are reversible, simply because it is fantastically unlikely to find its way back to the LES. Although the universe might not know about cause and effect at a fundamental level, it would be madness to bet against them! In the language of physics, the LES “spontaneously breaks” the invariance of the laws of physics under time translation. The laws may not change with time, but the objects do, and cause and effect are born.

This point of view has a curious consequence, and a curious premise, neither of which is usually stated. The odd consequence is that if I have an LES, then causes should flow away from that event in both directions. Time not only has a translation symmetry, but a reflection symmetry, and the residuum after introducing the LES is reflection around this special point in time when it occurs. In the same fashion, the residuum of time translation symmetry is that the LES can occur at any point in time. (Technically, if the symmetry group is $\mathbb{R} \times \mathbb{Z}_2$, we simply break it to $\mathbb{Z}_2$ with a real line’s worth of “degenerate” places to put the LES.) In a sense, the LES is a bow which launches the arrow of time, but in fact it launches two arrows, one in either direction.

The curious premise is actually very subtle. Essentially, it is the notion that objects persist. In other words, slightly different copies of the system are arranged along some special dimension, and there is enough correlation between these copies that they can explore phase space. These are evidently very different, and much stronger, than the correlations that exist between physical objects along the spatial dimensions. So, the question “why change” becomes: why persistence?

Emergent time

(This section is both technical and rather preliminary.) What would a satisfying answer look like? Here are a few preliminary thoughts. Start off with some highly symmetric mathematical object $\mathcal{M}$ which does not possess any notion of time. Introduce patterns or structures or fields, collectively labelled $\Psi$, and some laws $L$ governing them, perhaps written as $L(\Psi) = 0$. These laws $L$ should not make any reference to time. Finally, there might be boundary conditions for $\Psi$ on $\partial\mathcal{M}$, which once again should know nothing about time. Here, $\mathcal{M}$ might be something rather different from a manifold, and $\partial$ something rather different from a boundary operator. I am being schematic.

I would say this theory provides an emergent theory of time if the solutions $L(\Psi) = 0$ spontaneously break some symmetry of both $L$ and $\mathcal{M}$, and develop one-dimensional “timelike defects” along which correlations between local values $\Psi$ are parametrically stronger. These strong, unidimensional correlations would be persisting objects. To get an arrow of time, entropy perhaps is the key, and one could get phase space by taking slices transverse to this one-dimensional defect, i.e. time slices of the persisting objects. Ideally, these should be described by some emergent Lorentzian metric, but just figuring out why objects persist would be important progress in my books.

Conclusion

Presentists, growing blockers, and other temporal solipsists are probably wrong about ontology, but right about epistemology: there is something strange about time. The usual physical explanations presuppose change along a distinguished timelike direction. Really, the only satisfying explanation, from a four-dimensionalist perspective, would be to define physical laws which know nothing about time, on a mathematical space which knows nothing about time, and have time — i.e. one-dimensional defects with highly constrained correlations — emerge via spontaneously broken symmetry. But it’s amusing that the collision between folk metaphysics and four-dimensionalism might, if approached with suitable humility, give us clues about fundamental theories of physics.

Written on July 8, 2020
Physics   Philosophy