The question is sometimes referred to as the "psychological arrow of time" (Hawking, 1985). Here the past is understood as a moment or time when the entropy of the universe was lower, and contrarily for the future. So it is generally thought that PAOT is a consequence of the thermodynamic arrow of time of our universe. If so (maybe not?), how do the two relate?

Some explanations in the literature:

  1. Practical memory systems work in a way that the formation of new memories entails an overall increase of total entropy of the system and the environment. For example, to create a memory, i.e. to cause our neurons to orient in a particular fashion, requires energy which results in our body heating up a little bit, increasing the total entropy (Hawking, 1985 and 1994); The initialization of memory to make it reusable is an irreversible process that increases total entropy (Landauer, 1961. Wolpert, 1992).
  2. More recently, People have argued that even reversible and non-dissipative memory systems are subject to PAOT (Mlodinow and Brun, 2014). The conclusion is arrived by imposing some constraints on what a memory system should be like. Specifically, they argue that a memory should be somehow robust to small microscopic changes in states of the system it records (what they call "generality" requirement). But the smallest changes in the future state destroy the thermodynamic arrow of time between now and the future. So any memory of the future of the system "could remember only one possible configuration of that system". This fine-tuning disqualifies it as a bona fide memory.

My problem with explanation (1) is that even if it's correct, it doesn't seem to be a complete answer in itself. Yes, increase of (new) memory happens only as total entropy of the universe increases. So what? It doesn't have anything to say on the nature of that memory. Why couldn't it occasionally be a memory of the future for that matter? Explanation (2) leaves no such ambiguity. But the generality requirement seems artificial: surely a memory that records the only future configuration of the system remembers the future in a deterministic world, there being no "what ifs" regarding that state?

Of course, my understanding of the problem is only preliminary. I'd like to know whether there is not some generally accepted explanation, or any other thoughts you have on it.

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    $\begingroup$ As you may recall, I've already explained this to you next week. $\endgroup$ – rob Jul 6 '14 at 13:17
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    $\begingroup$ The Laplace demon probably has no problem remembering both past and future. So maybe PAOT isn't a necessary consequence of TAOT, but the result of how our particular memory system adapts to TAOT? $\endgroup$ – Eric Jul 6 '14 at 13:32
  • $\begingroup$ Down voters please explain why. $\endgroup$ – Eric Jul 6 '14 at 13:34
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    $\begingroup$ I didn't downvote, but I was thinking of it. In physical terms, your question is not clear. Can you provide a physical definition of memory? (Not only of its storage, but how memory of the past and memory of the future are physically distinguishable) I do not see how your question could ever generate an answer that is firmly grounded in physics instead of the answerer's personal philosophy. $\endgroup$ – ACuriousMind Jul 6 '14 at 13:39
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    $\begingroup$ I don't see how you could have stored something in your head that hasn't actually happened yet. $\endgroup$ – Kyle Kanos Jul 6 '14 at 14:23

It is a reasonable question at the elementary particle physics level , since the mathematical formulae of all the models we have are reversible as to time. It is in the thermodynamic manifestation of the laws that an arrow of time appears, and in special relativity which separates observations in timelike and spacelike regions.

So it is one of those questions of "why" addressed to physics that really have the only answer "because". Macroscopically , where we live and die, there exists the arrow of time described by the laws of thermodynamics, and that is that.

The theory of special relativity has been validated with innumerable measurements and therefor again the answer is "because this is what we observe. A future event cannot register in the present because of the velocity of light which is the limit in the transfer of information.

  • $\begingroup$ I do not believe that special relativity is relevant here. There is nothing in special relativity that makes it any harder (or easier) to infer things about the future than it is to infer things about the past. All I have access to at the moment is the current (macro) state of my brain. Running the laws of physics backward and forward, I can draw inferences about what sort of events might be present inside my brain's past and future light cones. SR provides no reason for me to trust one set of inferences more than the other. $\endgroup$ – WillO Mar 10 '16 at 1:10
  • $\begingroup$ To put this another way: All SR says is that, from the information available to me, I can draw no inferences about events outside my (past and future) light cones. But it draws no distinction between the sort of inferences I can draw about my past and the sort I can draw about my future. $\endgroup$ – WillO Mar 10 '16 at 1:13
  • $\begingroup$ @w en.wikipedia.org/wiki/Light_cone the future light cone goes with the velocity of light. for a signal/information to come backwards from the future one would have to break the limit of c backwards too. $\endgroup$ – anna v Mar 10 '16 at 5:41
  • $\begingroup$ But I am not talking about anything coming backwards from the future. I am talking about predicting the future based on what we know of the present, which is exactly the same procedure as "predicting" the past based on what we know of the present --- which in turn is exactly what memory is. $\endgroup$ – WillO Mar 10 '16 at 5:45
  • $\begingroup$ To add to that --- Memories do not involve signals arriving from the past. When a photon from the sun hits my eye, it does not trigger a memory; it triggers a sensation. Instead, memories involve drawing inferences about the past from what we know of the present. ("The fact that my neurons are in such and such a configuration strongly suggests that I had eggs for breakfast this morning"). As far as SR goes, drawing inferences about the future is no more difficult than drawing inferences about the past, so SR cannot be the right story here. $\endgroup$ – WillO Mar 10 '16 at 5:49

All you have direct access to at any moment is the macrostate of your brain at that moment. A (backward) memory is an inference from that state to what the macrostate of the world was at some time in the past and a (forward) memory is an inference from that state to what the macrostate of the world will be at some time in the future.

A given macrostate is compatible with a great many microstates, each of which yields inferences about the past and inferences about the future, all by running the same laws of physics both backward and forward. This gives you a range of possibilities (and a probability distribution) for what the past was like and a range of possibilities (and a probability distribution) for what the future will be like.

So I think your question should be rephrased this way: Why are we so much more confident about our backward inferences than about our forward inferences? The answer must be twofold:

  1. The inferred probability distribution over past states is much more concentrated than the probability distribution over future states. (That is, our memories of the past are more accurate than our memories of the future.)
  2. At some level, we are aware of this. (That is, we give far greater credence to our memories of the past than our memories of the future.)

The first follows from increasing entropy, which in turn follows from the fact that the Universe was once in a state of very low entropy. The second follows, perhaps, from the first together with natural selection, which rewards true beliefs and punishes false ones.

So I think the answer to your question is something like this: Our ability to remember the past but not the future (or more precisely, our much greater faith in our backward predictions than in our forward predictions) results from Darwinian evolution in a universe that started with a Big Bang.


If you think of the future as a probabilistic distribution of events, for the far future there are an infinite number of possible events. As you approach those events in time, past (and present) actions force the future to collapse to a single event (assuming two can't happen simultaneously). You could think (and even predict) one event would happen over another, but you can't have a memory of one because it hasn't happened until it happens.

In this respect, you could almost think of events in time as being a larger version of Schrödinger's cat

  • $\begingroup$ Great answer. Makes me realize an implication of remembering the future is there is no freewill. $\endgroup$ – User314159 Nov 3 '17 at 16:55

protected by Qmechanic Dec 13 '17 at 17:51

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