While the notion of “entropy” seems to make a lot more sense when considered as observer-dependent, what continues to confuse me about this is what happens when you have time-reversed observers. If phase space volume is simply conserved, then the same principles apply to time-reversed observers, i.e., they also see entropy increasing. But this would imply that any time-reversed observer would have to draw boundaries very differently from us, and it’s not at all clear how simply negating the ‘t’ coordinate causes you to draw your boundaries in such a way that you know more about two gases when mixed rather than when unmixed. I feel I must be making some fundamental mistake here but I can’t tell what.
That question does strike at the very basic assumptions that try to make sense of these phenomena. I read some more about this issue in Drescher’s Good and Real, chapter 3.
The key issue with your question is, what exactly is a time-reversed observer? If you mean to flip the universal “time counter” and ask what the observers observe, well, there are some problems off the bat (no universal space of simultaneity, time not being an independent variable but a kind of measure of the other variables). But let’s assume those away.
With time reversed, if you look at each time-slice, the observer perceives the exact same history that they would if time had been going the other way. This is because their makeup contains the same evidence telling them that they had the same past experience. In other words, their memories are the same. So they wouldn’t have to draw boundaries any differently from us.
More generally, you shouldn’t look at time as going positive or negative along some timeline; you should think of it as going futureward (toward higher observer-perceived entropy) or pastward (toward lower). As an analogy, think of the shift from modeling the earth as flat, to modeling it as a sphere with gravity: you realize that your “up” and “down” are not two unique, constant vectors, but rather, refer to whether you are going towards or away from the center of the earth. Just the same, futureward and pastward are determined, not by an increasing or decreasing time variable, but whether entropy increases or decreases from that point, so there can be negative time directions that go futureward.
To simplify a bit, it’s not that “Hey, time increases, entropy increases—gosh, they always seem to happen together!” Rather, it’s that it’s not possible for us to perceive (have a set of memories consistent with) entropy decreasing.
(I had been writing up a summary of Drescher’s chapter 3 as an article but never got to finishing it. This comment draws from both Drescher, and from Barbour’s “timeless universe” ideas.)
I don’t mean reversing time on the whole universe; that is not really meaningful, for the reasons you specify. What I mean is, since the laws of physics are (nearly) time-symmetric, it seems that it should be possible to have, in our own universe alongside us, some sort of creature that is has a brain that really does remember what we would consider the future, and attempts to anticipate what we would consider the past. How would such a thing arise? Well, presumably by a time-reversed evolution, with mutation and natural selection occuring on a “replicator” that propagates itself backwards in time; that is, after all, what it would have to optimize for (well, given the right environment).
Yes, if you take us out of the picture, you can just negate the t-coordinate and say I’m not proposing anything weird. But the (near) time-reversibility of the laws of physics means that it should possible for us to both occur in the same universe.
Admittedly, if we saw such a thing, we would probably never recognize its “genes” as replicators of any sort—if we saw the pattern at all, they would appear as some sort of anti-replicators. And could we even recognize such creatures as containing decision engines at all?
...OK, having written that out I now can’t help but suspect the problem is in posing the existence of these things in the first place. After all, the anti-replicators that formed their genes, would have to have some causal origin from our point of view, and that seems highly improbable. Anti-replicators become less common, not more common, meaning, but there shouldn’t be any at the start of the universe—or in other words, they should all be extinct by then. What does a time-reversed extinction event look like? Probably not just one thing. But of course, if, for example, we were to hypothetically nuke the whole planet and destroy all life, they’d see the sudden appearance of a whole bunch of anti-replicators, which then slowly annihilate each other over 4 billion years, and have a good causal explanation for the whole thing! If they recognized the pattern at all, that is.
This forces me to wonder if, yes, it really is correct that a time-reversed observer necessarily would have to have such a different point of view that it would be natural to draw the boundaries in a way such that they still saw entropy as increasing.
I don’t actually understand this very well, so I don’t think I’m close to an actual answer, but I think here’s my best attempt: While such things are theoretically possible, if they existed, we could never recognize them (or vice versa), as that would violate the second law of thermodynamics from our (their) point of view? I think? Though that still is not answering the original question.
While the notion of “entropy” seems to make a lot more sense when considered as observer-dependent, what continues to confuse me about this is what happens when you have time-reversed observers. If phase space volume is simply conserved, then the same principles apply to time-reversed observers, i.e., they also see entropy increasing. But this would imply that any time-reversed observer would have to draw boundaries very differently from us, and it’s not at all clear how simply negating the ‘t’ coordinate causes you to draw your boundaries in such a way that you know more about two gases when mixed rather than when unmixed. I feel I must be making some fundamental mistake here but I can’t tell what.
That question does strike at the very basic assumptions that try to make sense of these phenomena. I read some more about this issue in Drescher’s Good and Real, chapter 3.
The key issue with your question is, what exactly is a time-reversed observer? If you mean to flip the universal “time counter” and ask what the observers observe, well, there are some problems off the bat (no universal space of simultaneity, time not being an independent variable but a kind of measure of the other variables). But let’s assume those away.
With time reversed, if you look at each time-slice, the observer perceives the exact same history that they would if time had been going the other way. This is because their makeup contains the same evidence telling them that they had the same past experience. In other words, their memories are the same. So they wouldn’t have to draw boundaries any differently from us.
More generally, you shouldn’t look at time as going positive or negative along some timeline; you should think of it as going futureward (toward higher observer-perceived entropy) or pastward (toward lower). As an analogy, think of the shift from modeling the earth as flat, to modeling it as a sphere with gravity: you realize that your “up” and “down” are not two unique, constant vectors, but rather, refer to whether you are going towards or away from the center of the earth. Just the same, futureward and pastward are determined, not by an increasing or decreasing time variable, but whether entropy increases or decreases from that point, so there can be negative time directions that go futureward.
To simplify a bit, it’s not that “Hey, time increases, entropy increases—gosh, they always seem to happen together!” Rather, it’s that it’s not possible for us to perceive (have a set of memories consistent with) entropy decreasing.
(I had been writing up a summary of Drescher’s chapter 3 as an article but never got to finishing it. This comment draws from both Drescher, and from Barbour’s “timeless universe” ideas.)
I don’t mean reversing time on the whole universe; that is not really meaningful, for the reasons you specify. What I mean is, since the laws of physics are (nearly) time-symmetric, it seems that it should be possible to have, in our own universe alongside us, some sort of creature that is has a brain that really does remember what we would consider the future, and attempts to anticipate what we would consider the past. How would such a thing arise? Well, presumably by a time-reversed evolution, with mutation and natural selection occuring on a “replicator” that propagates itself backwards in time; that is, after all, what it would have to optimize for (well, given the right environment).
Yes, if you take us out of the picture, you can just negate the t-coordinate and say I’m not proposing anything weird. But the (near) time-reversibility of the laws of physics means that it should possible for us to both occur in the same universe.
Admittedly, if we saw such a thing, we would probably never recognize its “genes” as replicators of any sort—if we saw the pattern at all, they would appear as some sort of anti-replicators. And could we even recognize such creatures as containing decision engines at all?
...OK, having written that out I now can’t help but suspect the problem is in posing the existence of these things in the first place. After all, the anti-replicators that formed their genes, would have to have some causal origin from our point of view, and that seems highly improbable. Anti-replicators become less common, not more common, meaning, but there shouldn’t be any at the start of the universe—or in other words, they should all be extinct by then. What does a time-reversed extinction event look like? Probably not just one thing. But of course, if, for example, we were to hypothetically nuke the whole planet and destroy all life, they’d see the sudden appearance of a whole bunch of anti-replicators, which then slowly annihilate each other over 4 billion years, and have a good causal explanation for the whole thing! If they recognized the pattern at all, that is.
This forces me to wonder if, yes, it really is correct that a time-reversed observer necessarily would have to have such a different point of view that it would be natural to draw the boundaries in a way such that they still saw entropy as increasing.
I don’t actually understand this very well, so I don’t think I’m close to an actual answer, but I think here’s my best attempt: While such things are theoretically possible, if they existed, we could never recognize them (or vice versa), as that would violate the second law of thermodynamics from our (their) point of view? I think? Though that still is not answering the original question.