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:
- 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).
- 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.
Best Answer
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:
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.