Reversing Time’s Arrow: Two Thought Experiments to Ponder

Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.
— Pierre-Simon Laplace, A Philosophical Essay on Probabilities

This evocative passage of the French astronomer Pierre-Simon Laplace rests on two crucial assumptions. The first, obviously, is determinism. The laws of nature, in Laplace’s view, do not give probabilities, but certainties: given an exact knowledge of the events of a certain moment, a sufficiently vast intelligence could use the laws of physics to deduce exactly what would happen next. With the advent of quantum mechanics, determinism is no longer as fashionable as it once was—though there is a well-known interpretation of quantum mechanics, sometimes dubbed “pilot-wave theory,” that manages to salvage it. I accept that determinism is probably false, but in what follows, I am going to assume a deterministic view of the world on purely practical grounds. It will make my thought experiments simpler, without making them less interesting. Everything I say could be recast in probabilistic terms without undermining the main point.

Laplace’s second assumption is that the laws of nature are time-reversible. Let us take two moments in time, one earlier and one later. We’ll call the earlier M1 and the later M2. The time-reversibility of physical law means that just as we can use the laws of nature to deduce the events of M2 from the events of M1, we can also use them to deduce the events of M1 from the events of M2. That the laws of nature are, in this sense, time-reversible is widely believed, with the million-dollar qualification that quantum mechanics raises some thorny issues.

But the time-reversibility of physical laws may prompt some bewildering reflections.


Suppose that the universe were exactly as it is now, with just one exception: there are no living creatures. In this parallel universe of our imagining, the atoms that make up our bodies simply have no existence. Everything else is precisely as it is now. Books—the supposed products of human genius—sit on bookshelves across the world. A hypothetical visitor to the Bodleian library could pull down and peruse the works of Shakespeare, just as in our universe. Pictures of human beings, Mount Rushmore, iPhones, computers: these things exist in our parallel universe, just as in the one we know. Our imaginary world lacks life, but nothing else.

There is nothing impossible about such a world. It describes a perfectly coherent arrangement of matter and energy, just as ours does. And just as our world has a perfectly defined history, so must this world. If we reverse time’s arrow, so to speak, the laws of physics will immediately take over, and play back the history of this alternative universe as far into the distant past as we would like. It is very hard for us to imagine just what that history would look like—might it contain some kind of extinct intelligence?—but it must exist. Since this hypothetical universe is so similar to our own, it seems reasonable to guess that its past events would all lead back to a “Big Bang,” but it is hard to say much.


In the laboratory of the mind, we are all mad scientists at heart, so let us make the thought experiment stranger still. Let us take the present moment M. We shall now convert it into the imaginary moment M* by leaving everything exactly as it is, save for one particular: instead of a White House in Washington, D.C., there is a massive Egyptian-style pyramid. Notice that, at M*, no one believes there is a massive pyramid in Washington: our brain states, and hence our memories, are exactly as they are in M! There is nothing, moreover, incoherent or physically suspect about this situation: it describes an arrangement of matter and energy that is perfectly consistent with the laws of physics.

Allowing time to move forward, we will all awake and be shocked to discover a pyramid on the “White House lawn.”

But instead of running the laws of physics forward, let us run them backward. The great mystery will be how we all came to have, at M*, our radically false belief that there is a White House rather than a giant pyramid in Washington, D.C.

Clearly, our imaginary universe has a physically coherent past. Yet the path from days of yore to M* must seem deeply mysterious. Surely, running the laws of physics in reverse, the pyramid was there not just at M*, but at M* – 1 second, and so on back a great stretch of time. But until M* there is a huge mismatch between our psychological states and the real world. This is unproblematic in physical terms, but it is bewildering all the same.


Do these thought experiments tell us anything fundamentally interesting about nature? Maybe. I think there are a couple of things worth considering:

1. The possibility of running complexity backward in time points to a flaw in the naive intelligent-design argument that the first cell must have been specially created by God at a certain point in time. In fact, a disposition toward the development of cellular life may have been present ab initio, from the foundation of the cosmos.

2. It is as consistent with the laws of physics to have, at any given moment, a world full of creatures with radically unrealistic beliefs as it is to have a world full of creatures with roughly sound views of the world. Indeed, the arrangements of matter/energy that yield the former would seem to be more plentiful than those that yield the latter. It is interesting to reflect that each of these hypothetical worlds has an equally plausible “naturalistic” history.

2 comments on “Reversing Time’s Arrow: Two Thought Experiments to Ponder

  1. “There is nothing impossible about such a world. It describes a perfectly coherent arrangement of matter and energy, just as ours does.”

    No idealist philosopher would agree with this, I think.

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