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

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) prediction 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.

  • $\begingroup$ Thanks, you've put this really clearly. (I came here after reading Sean Carroll's excellent The Big Picture and feeling confused.) $\endgroup$
    – Eli Rose
    Oct 31 '19 at 0:00
  • $\begingroup$ Dear WillO, I think this type of argument is deeply flawed, because local entropy can certainly decrease. But in those scenarios you don't observe the local time arrow (or your inferences therein) contradict the global arrow. Put a man in some sealed chamber and steadily decrease the temperature inside, in which case entropy decreases for the system (chamber-man) and future probability distribution will be more concentrated than past. According to your argument he should be remembering the low entropy future inside the chamber, which we know isn't the case. What happens [to be continued ] $\endgroup$
    – Eric
    Nov 16 '19 at 4:16
  • $\begingroup$ outside the chamber can't effect his inference because he can't sense them. However, his inferences accords to the outside global arrow which he can't sense, instead of the inside entropy decreasing local environment which he does sense. $\endgroup$
    – Eric
    Nov 16 '19 at 4:23
  • $\begingroup$ @Eric: Has this experiment been done? What justifies the phrase "which we know isn't the case"? $\endgroup$
    – WillO
    Nov 16 '19 at 5:16
  • $\begingroup$ Because similar situations occur everyday everywhere. Turn on the air conditioning and the room cools and entropy decreases. Do you remember the future in such a room? $\endgroup$
    – Eric
    Nov 16 '19 at 6:17

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.

Edit for clarification:

There are theories for particle physics extending the standard model, and there tachyons can exist. Tachyons in these theories can travel backwards in time and could interact with the electromagnetic structure of our brain if the theory allows it. Thus it could affect the memory banks and leave a record that could be interpreted as a future memory. There is no experimental sign for such particles.

So future memories belong to science fiction and metaphysics (precognition and such).

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    $\begingroup$ 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
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    $\begingroup$ 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
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    $\begingroup$ 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

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
  • $\begingroup$ Nothing in this answer explains the asymmetry between past and future. $\endgroup$
    – user4552
    Nov 13 '19 at 6:00

The answer to your question is that we don't remember the future because we haven't yet stored any memory of it.

Your memories arise from connections wired in your brain as a consequence of experience. You have not yet experienced the future, so the configuration of your brain has not been affected by it.

You can, of course anticipate and imagine the future. Indeed, the sensation of imagining, say, a walk in the woods tomorrow, can be as vivid as recalling a walk in the woods a year ago.

The phenomenon is not in the least confined to the human mind. The history file associated with my browser contains only the sites I have already visited. It does not contain information about the sites I am going to visit, because I haven't yet done so.

The one way direction of time arises naturally if you consider time to be a counter of change (as it is in the case of SI units). If I increment a counter every time there is a transition between the states of a given caesium atom the counter will inexorably rise. If the transitions were to somehow reverse themselves they would still count as changes, and the total on the counter would still increase. The count can never decrease.

To take another example, the number of transactions on your bank account can never decrease, because, unlike the balance of the account, it does not differentiate between positive payments in and negative payments out- it is counts both as an increase regardless of their sign. Past transactions are those that have been counted- future transaction have yet to be counted.

There should be no mystery to the arrow of time. Change happens. Time is simply a count of it.

  • $\begingroup$ If it has nothing to do with entropy, why do our memories increase as the entropy of the universe increases (I remember yesterday but not tommorow, and yesterday's entropy of the universe is lower than that of tommorow)? Why does the count increase in the direction of the 2nd law of thermodynamics? Coincidence? Correlation? Or Causation? $\endgroup$
    – Eric
    Jan 22 at 3:19
  • $\begingroup$ It seems to me that your argument is a bit circular. Because you essentially DEFINED the past as the sum total of our memories. But the very same definition is equally valid if time runs backwards! You have the same number of changes, microscopically, because physically laws are reversible at that scale. So why don't we remember the other way around? $\endgroup$
    – Eric
    Jan 22 at 11:43
  • $\begingroup$ You are over-thinking this, Eric. Memory is simply a record of events that have happened. Future events by definition have not happened, ergo they do not form part of any memory. $\endgroup$ Mar 28 at 15:59

Here's an answer that should be taken with a grain of salt.

I believe there is an explanation of the arrow of time. I think the explanation is not the second law of thermodynamics because I don't actually believe that law myself. I think there is another explanation for it but I won't get into that here. I believe that the short answer is that a certain property of the state of the universe at the beginning of time held and if the state of the universe at any time satisfies that property, it's state at a tiny bit later time must also satisfy that property. I'll give one example. According to general relativity and the big bang theory, a white hole can never exist because none existed at the beginning of time and a black hole can never get destroyed once it has been created.

The brain follows the arrow of time. Environmental factors run in an unpredictable way. Once you see something, a memory of it gets stored in the brain but the memory doesn't form until after you see it.


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