> you don't need any additional assumptions
What you wrote after that is such an assumption. You can't derive asymmetry from nothing, logic or mechanics. The only way to have it, is to assume it in addition to those.
What you wrote after that is such an assumption. You can't derive asymmetry from nothing, logic or mechanics. The only way to have it, is to assume it in addition to those.
Not quite. There is an underlying assumption, but that's not it. I can demonstrate the asymmetry between the past and future. For example:
Suppose I flip a fair coin, and I make a video of the coin flip. Let's say the coin comes up heads. I can predict with near 100% certainty (modulo shenanigans) that if I watch the video I will see a coin being flipped and coming up heads. By way of very stark contrast, I cannot predict the outcome of actually flipping the coin again with better than 50% odds.
I claim that this asymmetry in my prophetic abilities (100% ability to predict what will be seen on the video vs 50% for re-flipping the actual coin) is a result of the asymmetry between the past and future.
Note that this is not a circular argument; this demonstration would work equally well in a universe where it is possible to unscramble an egg. All it requires is for there be some experiment whose outcome I can record but not predict, even with arbitrarily advanced technology. The existence of such an experiment is an assumption, but it is a very weak assumption, much weaker than the second law itself. Indeed, it is a necessary assumption for doing thermodynamics at all, indeed, for doing anything. If I can reliably predict the outcome of any experiment, that means I know everything that is going to happen before it happens, including my own actions.
So yes, I have to assume that I cannot be omniscient. Or maybe a better word here would be "hope" because being omniscient would render my entire existence meaningless.
No, this and other similar memory-induced asymmetries have much more prosaic reason. It is more successful to predict systems we have enough knowledge and control of (video playback) than those we don't (coin flip).
Predicting and retrodicting systems we understand and have memory of is successful, and predicting and retrodicting systems we don't understand and don't have memory of is not. This has nothing to do with universal asymmetry of past vs future.
Your memory of what has happened (e.g. some system had lower entropy in past) does not explain why your original argument does not apply now to retrodiction of past macrostates; the memory only contradicts the result of that argument.
> If I can reliably predict the outcome of any experiment, that means I know everything that is going to happen before it happens, including my own actions.
That would in no way prevent validity of 2nd law.
Nope. Consider this variation on the experiment: I flip a coin, I make a video recording, but I do not look at the coin, I only reveal it to the video camera.
Now I cannot predict the result of watching the video despite the fact that my "knowledge and control" of my video recorder is exactly the same as before.
And, BTW, my ability to make a reliable prediction in the first case is in no way contingent on my knowledge of how video recorders work, nor is it contingent on my having control of the camera. I could be completely ignorant of the inner workings of video recorders, and the camera could be completely outside of my control, and I could still make an accurate prediction, but only if I saw the coin after if was flipped.
> That would in no way prevent validity of 2nd law.
I never said otherwise, but that is neither here nor there.
Yes, knowledge of details of how the recorder works is indeed largely irrelevant, but that was obvious. The point was that being successful with predictions or retrodictions of some system is correlated with having enough information on its state and the laws it obeys. This difference of success for predicting playback vs predicting result of a future experiment sensitive to unknown conditions is due to sufficient information vs insufficient information. I don't see anything in your responses that shows some universal asymmetry between past and future that would explain why your original argument does not work for past macrostates, but does work for future ones.
No, I lack information about the state of the coin. All of my observations and knowledge of the operation of the recorder are exactly the same as before. I can still see the camera, see that it is pointing at the location of the coin (even though the coin itself is hidden from me). Nothing has changed in that regard.
> I don't see anything in your responses that shows some universal asymmetry between past and future
Maybe it would be clearer if I change the scenario slightly: instead of one camera, I'll use N>>1 cameras, all pointing at the same coin. I flip the coin in view of all the N cameras, but hidden from my view, and then I put the coin in my pocket without ever looking at it.
At this point I can make no reliable predictions. But if I wach the playback on one of the N cameras, I can then reliably predict the outcome of viewing the playback on any and all of the other cameras. But under no circumstances can I ever accurately predict the outcome of flipping the coin again.
Why? Because there is a fundamental asymmetry between the past and future. It is possible to make reliable records of the past, and if you make multiple records of the same event, all of those records will agree on what the outcome was (that's what "reliable record" means). By way of very stark contrast, it is not possible to make reliable records of the future.
And that implies you lack information on the record, which is decisive for predicting successfully its playback.
> But under no circumstances can I ever accurately predict the outcome of flipping the coin again.
Because you lack the necessary information, because you assume those experiments are that way. If you set them up so that you don't look at the coin flip result, but in the next coin flip you measure the initial conditions and the flipping process accurately enough, the conclusion would be the opposite - you would accurately predict the new coin flip, and would not be able to predict the playback.
> Why? Because there is a fundamental asymmetry between the past and future.
Not at all. The asymmetry is due to how you defined constraints on the experiments.
> It is possible to make reliable records of the past, ... it is not possible to make reliable records of the future.
Record is, by definition, a pattern that has been created in the past, and this is likely to correlate more with the past states than with the future states. This is a property of the concept, not of some universal asymmetry between past and future. We may introduce analogous concept of a future record, which will be created in the future, and which will correlate with the future states.
We can talk instead about prediction and retrodiction. And then this is more of an easy/hard thing, not possible/impossible thing, and the distribution of success on this axis depends on details. Predicting Moon's position on sky 2 years into future is easier than retrodicting it 20 000 years into past.
None of this explains why your original argument does not apply to past macrostates.
Yeah, that's gonna be a long row to hoe if I can't even get you to acknowledge that there's a difference between the past and the future independent of the second law itself.
Maybe I should just ask: do you think there is any difference between the past and future (independent of the 2nd law)? If so, what is it?
But in the meantime:
> that implies you lack information on the record
This turns on what it means to have information "about" something. All of the data I have first hand access to comes to me through my senses, mainly my eyesight. When I say a coin is heads-up it's because I can see the coin, i.e. there are photons emitted from the coin (presumably) that end up on my retina and create electrical impulses that go to my brain and leave me with the subjective sensation of seeing a heads-up coin. There are all kinds of background assumptions about how light works, how coins work, how my retina works, and how my brain works, but for the most part one chooses to sweep those under the rug and accept as a working hypothesis that the reason I have the subjective sensation of seeing a heads-up coin is that there is in point of actual fact a coin "out there" and that it is, again in point of actual fact, heads-up.
But the camera is a very different story. I get direct input from the camera in the same way that I get direct input from the coin. I can see the camera just as I can see the coin. But unlike the coin, the camera's state with respect to what it has recorded is not directly apparent to me. That state is part of the internal state of the camera. It is hidden from me. I cannot directly observe it simply by looking passively at the camera the way I can with the coin while my visual cortex of my brain does the heavy lifting. I cannot even tell that there is hidden internal state based on anything that I can see about the camera while it is recording.
Making a prediction about what will happen during "playback" (indeed, even predicting that there will be something interesting to observe at all!) requires a much more complicated model of the world and chain of inference than it took for me to conclude that the coin was heads-up.
I introduced multiple cameras so that the structure of the example eliminated all that complexity and everything was symmetric. All the cameras are the same, and my knowledge of them is all the same -- until I start looking at the playback, at which point things start to diverge. When I look at the playback on one camera, I now have direct information about the (previously hidden) state of that camera, but not of any of the others.
So here again the question is: why should (direct) information about the state of one camera tell me anything about the state of any of the other cameras? It is because of a very complex chain of inference, part of which includes the hypothesis that there are, in point of actual fact, events which have occurred in the past (and which now cannot be changed) and that there are things in the present (like cameras) whose states correspond to those past events, and for that reason correlate with each other in the present.
I've lived a long time and I've engaged in a lot of philosophical discussions, but you are the first person with whom I've ever had to go into that level of detail on such a foundational matter. Not that there's anything wrong with that, you're keeping me on my toes. But my point is just that if you're going to insist that I be excruciatingly precise about something this elementary, it's going to be a very long time before we can come back to talking about thermodynamics.
This lack of skill is the same towards the future as towards the past, at least in the context of reversible theories of motion like classical mechanics or evolution governed purely by Schroedinger's equation.
Flip a coin, do not look at it, and make a short video of the coin from above when it is at the top position. This video provides us with details of state of the coin.
Assuming a fair coin and a strong enough flip, from this state of things we can't predict the resulting face, and also can't predict the starting face on the thumb. This problem is symmetric towards the future and towards the past.
The same argument holds for knowledge of one microstate of gas at single time instant. Past and future are equally undetermined, and all probabilities are the same towards the future as towards the past.
To get 2nd law, we need to assume the asymmetry in addition, and it's best if it is explicit. E.g a process connecting two equilibrium macrostates, where the two states aren't defined in a symmetric way. For example, as Jaynes does, we define B as the reliable result of autonomous evolution after manual intervention in A. This makes A,B asymmetric, because it is not stated in the assumptions (and usually not considered possible) that also A is the reliable result of autonomous evolution after intervention in B. This asymmetry is what allows us to derive 2nd law.
See e.g. this Jaynes' paper, Section IV The 2nd Law. https://github.com/lawrennd/jaynes/blob/main/gibbs-vs-boltzm...
It is interesting that this derives asymmetric 2nd law from symmetric (reversible) underlying microscopic model. The asymmetry comes in exclusively due to the assumption of B being the reliable result of intervention in A.
We cannot have complete knowledge of the state of a gas. We cannot even have complete knowledge of the state of a single particle because the positions and velocities of classical particles are real numbers but our knowledge is constrained to be finite, so there will always be some measurement error, and so chaos theory applies. (And physical reality is actually quantum, so we have the uncertainty principle at work as well.)
> This problem is symmetric towards the future and towards the past.
Only because you've carefully crafted this example to have this property; it is not true in general. You have constrained your knowledge of the present to exclude that which is needed to reliably extrapolate into the past. But it is possible to change your scenario and collect data that allows reliable extrapolation into the past, for example, by looking at the coin before it is flipped and remembering (or writing down) what you saw. But for the future this is not possible. That is the essential asymmetry.
> See e.g. this Jaynes' paper
I have a lot of respect for Jaynes so I'll take a look but it may be a while before I have the time to give it the attention it deserves.
One thing I see right away that he gets right (well, mostly): in section 6 he observes that there is no such thing as "the entropy" of a system, which is correct. Entropy can only be measured relative to a state of incomplete knowledge. But calling it "anthropomorphic" is not right. It's not a function of human ignorance specifically, it's a function of ignorance in general.
Agreed. But it is true for your original argument applied to a non-equilibrium state at any single time instant, while not assuming any more on the past or the future states.
If we adopt further assumptions about the past states, but not about the future states, then we agree this problem of prediction/retrodiction is asymmetric between past and future and this may be the reason why the multiplicity argument does not have to result in past entropy being higher. In particular, there may be other facts on record about the past states and that would override/modify the multiplicity argument for the past.
> it is possible to change your scenario and collect data that allows reliable extrapolation into the past, for example, by looking at the coin before it is flipped and remembering (or writing down) what you saw. But for the future this is not possible. That is the essential asymmetry.
Yes, in any realistic scenario involving prediction and retrodiction at any time, we have some data on the past states (in some lucky cases, enough data for having certainty), but never data on the future states (we may have predictions, but those are not of the same quality as data). I agree.
But in addition, you seem to argue that this asymmetry of availability of data is an essential fact to derivations of the 2nd law.
Consider a scenario where we have an isolated system that is a mixture of miscible liquids that exists for ages but we have data on its state only for the last 2 years, and that data says its entropy was steadily rising the whole time.
Now, given this data, was entropy increasing before the collection of data started, or was it decreasing? For short enough times around the edges, we can extrapolate the entropy curve based on collected data, but for long enough times, we can't. Using the multiplicity argument, including the data, we get that entropy of very distant past states was much larger than entropy of the first recorded state. Which contradicts 2nd law.
Effect of that "essential asymmetry" has a time span that is not universal, but limited to times where collection of data was happening. Outside it vanishes, and using only that data and the multiplicity argument, the distant past becomes as cloudy(highly entropic) as the distant future is.
No, it isn't. But we need to take this one step at a time. (And, I should also point out, this is not my argument. It's Boltzmann's and Shannon's.)
> further assumptions about the past states
They are not assumptions, they are observations. There is actual evidence that it is possible to remember the past but not the future. (I can't believe I'm actually having to persuade you of that. This is a pretty basic fact about reality.)
> in some lucky cases, enough data for having certainty
Nope, you can never be certain. Even the best measurements have error bounds, and our brains and recording devices have finite storage capacity. Our knowledge of the past can never be perfect. But -- and this is the important part -- our knowledge of the past can be vastly better than our knowledge of the future.
> you seem to argue that this asymmetry of availability of data is an essential fact to derivations of the 2nd law
I don't know if it's essential. I'm just saying that 1) it is a fact supported by evidence, not an assumption and 2) the second law follows from it (plus a few other things). It might be possible to derive the second law without it, I don't know, and I don't care because the actual fact of the matter is that this asymmetry between past and future does exist in point of actual fact. I don't care about hypothetical universes that behave differently from the one I inhabit.
> Using the multiplicity argument
Sorry, what is "the multiplicity argument"?
> Effect of that "essential asymmetry" has a time span that is not universal, but limited to times where collection of data was happening.
No, it doesn't matter whether data is actually being collected. What matters is that it is possible to collect data (about the past) because the past actually happened. Whether or not anyone actually bothered to make a record is irrelevant. If a tree falls in the forest, it actually falls even if no one makes a video of it.
You certainly don't have to waste time convincing me of that, but it seems you should try to explain why this general asymmetry of concept pairs record-past, record-future is relevant to your original argument. We're at this for days and you did not write any coherent argument where this evidence (which I don't contest) would play obvious role.
When I talk about some statement as an assumption, this does not mean I contest its factual evidence or validity. I am interested in the structure of your argument, and all assumptions need to be illuminated, even if they are based in factual evidence.
> what is "the multiplicity argument"?
It's your original argument: given the system is evolving without external influences, and we know its macrostate and its entropy at some time, then most likely the future macrostates will be such that they do not have lower entropy, but higher or same, and this is so because there is immensely more microstates corresponding to macrostates of higher entropy (macrostates of high multiplicity) than there is microstates corresponding to macrostates with lower entropy (macrostates of low multiplicity).
I don't see how asymmetry of memories or records made plays role in this argument. I can see how they play role in my example with collecting data for 2years. But then my argument stands: the data becomes more irrelevant the farther into the past we retrodict, and for very distant past it can be discarded, and the multiplicity argument wins, and fails to be consistent with 2nd law.
To me, this is due to fact one cannot derive 2nd law in general, as probable behaviour for all processes. There is as many phase space trajectories increasing entropy as there is decreasing it. One has to select those macroprocesses that we consistently observe to have the same result (Jaynes ' states A -> B) and then one can derived 2nd law for those processes, only.
> Whether or not anyone actually bothered to make a record is irrelevant.
It is relevant in that it changes data based on which predictions (or retrodictions) are made. I'm sure in science, different data means possibly different predictions.
Try to formulate your whole argument (which I understand as being based on the multiplicity argument), including how "it is possible to remember the past" makes its application to distant past which nobody remembers invalid, while keeping its application to distant future valid.
No. The universe has kept a record of the very distant past. We can directly observe the past all the way back to the cosmic microwave background, which gets us >99% of the way to the big bang.
So yes, I agree with you that it is possible to have a universe where the second law does not apply. It just happens that the universe we live in is not such a universe, not because of any assumptions, but because of what we can directly observe today, and how we can explain those observations in terms of a past that actually existed.
"The reason entropy was lower in the past is that the universe started out in a low-entropy state. The reason for that is still a mystery."
And my answer to this is the same. Unsubstantiated assumption that universe started out, and that its entropy at this start was low. In addition, it is not at all clear how this assumption helps us to explain that an isolated system could not have higher entropy in the past long before we observed it.
You have elided something very important here. I did not say that the universe started out, full stop. I said it started out in a low-entropy state. It is the "in a low entropy state" part that matters, not the "started out" part. If you don't like the idea that the universe "started out" then you can replace this with "the universe was, at some point in the past (specifically, about 13 billion years ago) in a low-entropy state. We don't know how it got there, or what, if anything, happened before that."
And this is not an "unsubstantiated assumption." There is evidence that the universe was in a low-entropy state in the past. In fact, the evidence is overwhelming. Disputing it is akin to disputing that the earth is round.
> it is not at all clear how this assumption helps us to explain that an isolated system could not have higher entropy in the past long before we observed it.
That's because it isn't true. An isolated system can have a high-entropy past, e.g. https://en.wikipedia.org/wiki/Spin_echo
But any system that we actually observe is not isolated, and that is part of the reason why we never observe decreasing entropy despite the fact that decreasing entropy is not only possible, it actually does occur under the right circumstances.
In fact, we can invoke the anthropic principle to explain why we do not observe decreasing entropy: creating a record of the past is not possible in a universe where entropy decreases. There are, by definition, fewer low-entropy states than high-entropy states, and so transitioning from a high entropy state to a low entropy state requires the destruction of information by the pigeonhole principle. And so the reason such universes are not observed is that such universes cannot contain records of the past, and so they cannot contain observers.