If the entropy of the universe were to suddenly go in reverse would we be able to detect it or would our memory formation and perceptions being reversed make it indistinguishable from what we experience now?
Yes, time reversal would also reverse the process of our perception and memory, so we would experience time "moving forward" even if time were "moving" backward. We would experience entropy increasing even if entropy were "decreasing with time". (And it's perfectly valid to call the past "+t" and the future "-t"; the laws of physics don't care; if you do that, you'll see that entropy decreases as "t" increases, but despite changing definitions you'll still only have memories of a universe with lower entropy than the present).
This is one reason why it might be more correct to say that time doesn't move at all. We just perceive a direction of time wherever the universe has an entropy gradient along "the time axis".
Entropy decreasing is not equivalent to time reversal.
[Edit: to expand a bit: time reversal requires that some previous macrostate is achieved again. Entropy decreasing merely requires that the system enters any macrostate represented by less microstates than the current one.
Put in more simple terms, the ice cube could reform but in a different shape. Entropy would have decreased, but it would not "look like" time reversal - it would just look like something very strange had happened. ]
This is true! I oversimplified a bit, because it's much easier to concretely discuss that scenario and its consequences, and it's more important from a philosophical perspective. Just like it's much easier to catch ice cubes forming on film by rewinding a tape than to run the camera waiting for spontaneous entropy decrease.
Nonetheless, if the entropy of the whole universe were to consistently decrease for a sufficient time, even along a different route than time reversal, you should gradually start to notice that it's easier to form predictions or "memories" of the future than to remember the past, due to Landauer's principle. Before long, you should go back to considering the future to be the state of higher entropy.
I think you're priviledging microstates. There are plenty of entropy decreases that are possible without the ice cube reforming. They're (extremely) unlikely of course, but somewhat less unlikely than the new, singular microstate you're asserting is somehow "less of a coincidence". It's vastly more likely (for example) that 1% of the particle velocities reverse than all of them doing so, and that could (depending ...) still lead to a decrease in the entropy of the system (but not a reformed ice cube).
I don't see how a long term entropy decrease that does not follow the time reversal route could be easier to form predictions in. There are many possible higher entropy states for the water than the water sitting in the glass, and if the universe enjoyed random entropy decreases, I see no reason why it would tend to pick certain macrostates over others.
Ah, I think we're just miscommunicating. I'm not saying that local time-reversal is more likely to happen than other kinds of entropy decrease; I'm not saying that a system is more likely to retrace its past than to enter a different state of low-entropy. Spontaneous local entropy decreases happen all the time, of course (but are overpowered by entropy increases), and the majority of those won't be exact reversals.
And I'm not saying that locking yourself in a refrigerator will allow you to predict the future!
I'm mainly picking on time reversal because it's easier to concretely communicate and reason about as an example of how a system behaves under entropy decrease, and is philosophically important because depending on one's definition of the sign of 't', you could actually view our universe as undergoing entropy decrease right now. But redefining the arrow of time won't let you form memories of the future -- you'll have memories of the lower entropy universe, regardless of which way you call "the future".
The deeper point is, that's not a coincidence and doesn't depend on entropy decreases specifically being tied to time reversal. If we lived in a universe where the second law were somehow different and entropy "statistically always" decreased with time the way it "statistically always" increases now, then... well, it's hard to reason about such a universe because either it has very different laws than our own, or it's just our own universe with exactly that arbitrary t <--> -t transformation. But in most logically-consistent interpretations of that scenario, that universe's version of Landauer's principle would also flip the arrow of time perceived by its local inhabitants, and they'd end up with only memories of their "future".
If I'm not quite making my point clear, try asking yourself why, if the laws of the universe are time reversible, why can't you remember the future the way you can remember the past? This gets into the mechanics of how memory works (as a general concept, not human memory specifically; it's easier to think about computer memory).
(Edit): Why isn't this a trivial point? Well, if you imagine a universe composed of a chain of of "linked states" that goes from (low entropy) - (high entropy) - (low entropy), you'd find that any inhabitants of that universe would perceive a universe with directional time that progresses in the entropy gradient, even though that universe has no consistent directional time.
> why can't you remember the future the way you remember the past
Memory of a finite brain isn't -- and cannot be -- a perfect record, so to some extent human memory retrodicts personally experienced past events extrapolatively. That human memory is better than human prediction of future events might not be closely coupled to cosmic thermodynamics.
For example, our ancestors with good memories producing more viable offspring than their contemporaries with poor memories but better predictive skills. You might not want to play certain competitive sports against the better predictors but worse rememberers, since they are likely to know where to be to catch the ball or whatnot; but you also might not want to eat the food they prepare because they don't reliably remember crucial food-safety practice.
The relative entropy inside the braincase of a living Australopithecus or H. erectus versus inside a living modern human's braincase has little to do with the change in total entropy of the universe over the past couple million years. It is perfectly plausible under modern physics that humans a couple million years in the future may end up with simpler and smaller brains, rather than larger or more complex ones. And the improving scientific knowledge of the evolutionary changes in human skull dimensions was not helpful in resolving the 20th century question of whether the universe was collapsing, expanding, or static.
Finally we aren't very good at communicating with the other intelligent species on our planet. Maybe orcas or octopuses have terrific memory and don't feel a significant difference between remembering a recent previous hunt and predicting the one they are just about to embark upon. It'd be fun to find out that our distinction between memory and prediction is just another part of human vestigiality, like our inability to produce L-ascorbic acid internally. Colloquially, maybe "future memory" was one of the things that were too metabolically expensive for our starving distant ancestors to live with, and so it fell off like tails.
>why can't you remember the future the way you can remember the past
this is getting a bit meta, maybe even off-topic. But I think this is fairly simple to explain: you can't remember states you haven't been in. Generalized memory implies some record of a state that has occured - states that have not occured cannot be remembered. The problem is that memory of types that we are familiar with (human, written, computer) all involve macrostates, not microstates. And increasing entropy (aka "more probable things are more likely to happen") mean that there is asymmetry at the macrostate level, and thus in memory.
A memory system that only recorded microstates would, I suggest, have no concept of time, and a much reduced notion of causality. There may be some statistical patterns that could be observed and could perhaps be "strong" enough to infer that "after state N we frequently end up in state P", but the sheer number of states would likely interfere with this.
There's also the timescale problem. A memory system that operates on the timescales of typical human experience will notice relatively constant change in much of the world, as macrostates come and go. But a memory system that operates at, say, geological timescales won't record many macrostate changes at all, and will tend to indicate that almost nothing happens in the world. All those macrostates ("tables", "chairs", "houses", "books") that came and went without being noticed form no part of this system's memory of the world. Of course, there are processes still taking place (new macrostates made up of even more vast microstates), but these going to be even more directional/asymmetric.
The one part of this view that leaves me a little confused is that at very short timescales, the unchanging nature of many macrostates is echoed in relatively unchanging microstates for most solids. The piece of metal that makes your <whatever> isn't changing macrostates at any appreciable pace (which is why its eventual wearing out forms an asymmetric experience of time for us), but it also isn't changing microstates in any notable way either. I find this confusing.
False memories are commonplace. Where exactly did you put your keys? Even if you give the right location, is that a true memory of the state you and the keys were in when you separated, or is it a retrodiction ("I probably put them in their usual storage place")?
> A memory system that operates on the timescales of ...
You mean one that measures parts of the world periodically?
ISTR we discussed this some exp(10^120) years ago[1] but I forget whether we reached any conclusions.
Sorry for the late reply. Don't know if you'll still be reading this, but...
> This is getting a bit meta, maybe even off-topic. But I think this is fairly simple to explain: you can't remember states you haven't been in. Generalized memory implies some record of a state that has occured - states that have not occured cannot be remembered.
In a discussion about the arrow of time, this is somewhat begging the question! The difference between a state that you've "been in" and a state that you "will be in" is exactly the subject that we're discussing. How do you precisely define "been in" or "occurred" in a way that doesn't reverse under a transformation from t <---> -t?
The answer I've provided elsewhere in this thread is along the lines of: Other than melting icecubes and scrambling eggs, the only other difference you can notice between the past and the future is that you can remember the past, but you cannot remember the future. If you could remember the future just as well as you remember the past, you probably wouldn't have strong opinions about which way time goes (or which direction is "clockwise"). If you, Merlin-like, could only remember the future then you'd probably be here asking why you always observe entropy decreasing in closed systems, and complaining that they got the second law of thermodynamics backwards.
On a fine-grained scale causality works just as well in a rewound video, although it is full of spontaneous-seeming coincidences with surprising macroscopic effects. There are only two things that establish an arrow of time:
* The universe has an entropy gradient along the "time axis", with one direction (which we can call 'P') having lower entropy and the other ('F') having higher entropy.
* We (and other physical systems) are able to form memories in one direction, but not the other. Because of this, we perceive a sense that time progresses "from" the direction that we can remember. This happens to be the direction of increasing entropy. Because of this ability to remember only along one direction of the entropy gradient, we call 'P' the past and 'F' the future.
This is not a coincidence. Memory operates on systems of increasing entropy, so you'll always only remember the past having less entropy than the present. [1]
>In a discussion about the arrow of time, this is somewhat begging the question!
Not really. "Been in" isn't meant to imply a temporal relationship. If a system has been in microstates A, B and C, then it can potentially remember states A, B and C. It cannot remember state D. That doesn't stay anything about whether or not A preceeded B, or C preceeded A.
I agree with your last two paragraphs, but not the formulation in the middle para. "you cannot remember the future" ... this just seems like an non-useful observation to me. I think the problem comes from this line:
>We (and other physical systems) are able to form memories in one direction, but not the other.
I think this is wrong. The issue is that our memories are of macrostates, and macrostates are subject to the entropy gradient. If we could form memories of microstates, we'd effectively be able to remember events that had no arrow of time associated with them. But then you say this yourself in your final line. And Maccone's concept seems fine to me (as if that matters :)
