Why Ethan Siegel is Wrong About the Arrow of Time

One of the most widely read physics blogs here on Medium is Ethan Siegel’s Starts With a Bang. This is pulled over from his column at Forbes magazine where he is a science contributor. Its focus is primarily on his area of expertise (astrophysics), and from what I’ve seen, the entries on that subject are pretty well done. In general, I’d recommend it as a good blog and a useful, well written, source of information for most people.

But occasionally I find myself disagreeing with the things Siegel writes, especially when they get into issues that depend on other areas of physics outside his expertise.

For example, last month he wrote a piece hyping the supposed possibility of a Star Trek style faster-than-light warp drive. Something I’m pretty convinced will never be possible. (I would agree with him that its impossibility has never been fully and adequately proven, however I do think there are some pretty compelling reasons to believe that eventually it will be proven — we just need to understand more about quantum gravity to prove it). I left a brief comment on his Forbes article mentioning some of those reasons.

This month, he has an entry on the arrow of time where he says things I disagree with even more strongly. In fact, some of the claims he makes about thermodynamics and the arrow of time I consider just flat out wrong. I don’t doubt that there are other physicists who might take his point of view, but I don’t think his point of view is in line with how most experts on statistical mechanics and thermodynamics look at it. Perhaps this is not a coincidence, as one of the main reasons I don’t believe warp drives will ever be possible is that I think, like traversable wormholes (both of which allow for closed-timelike-curves) they are inconsistent with the 2nd law of thermodynamics. Most of the professional research I’ve published has been in high energy theoretical physics (aka, particle physics), but I’ve also published on statistical mechanics, in a journal specializing in the subject, so I do know a thing or 2 about thermodynamics (the early name for the field of statistical mechanics, now mostly interchangeable with it).

The first thing I notice about Ethan Siegel’s article that strikes me as odd is that, he doesn’t seem to accept that the 2nd law of thermodynamics (entropy either increases or remains the same) is responsible for the arrow of time (a very noticeable asymmetry between how physics looks when run forward versus how it looks when it is run backwards). He writes:

We know from experience that time only flows one way: forwards. So where does the arrow of time come from? Many people believe there might be a connection between the arrow of time and a quantity called entropy.

and

So, does that mean that we only experience time the way we do because of the second law of thermodynamics? That there’s a fundamentally deep connection between the arrow of time and entropy? Some physicists think so, and it’s certainly a possibility.

He even refers to Sean Carroll, author of one of the most widely used textbooks on General Relativity, and someone who has published both research and popular books on the subject of the arrow of time, as an “entropy/time’s arrow fan” as if the connection between entropy and the arrow of time is just a case of a starry eyed fanboy falling for a fashionable trend, as opposed to an undeniable and widely accepted fact about physics. You could argue that there may be more to the story than just entropy, but to suggest that perhaps entropy has nothing to do with the arrow of time sounds pretty absurd to me. Entropy is without question the central thing discussed in most peer reviewed discussions of the arrow of time. I have a challenge for Ethan: if he can find a single peer reviewed publication on the arrow of time (in all of history) which does not mention the word “entropy”, then I will gladly accept that associating entropy with the arrow of time is just a case of being a “fan” rather than an established fact.

Now, it’s true that there are many arrows of time. Sometimes it’s useful to distinguish between them. The most important arrow of time, I’m sure most physicists would agree, has to do with the fact that eggs don’t spontaneously assemble themselves from a broken state into an unbroken state, that creamed coffee doesn’t spontaneously unmix itself from a fully mixed state into a state where the cream is all in one blob and the coffee surrounding it. And this is usually the arrow time I would think people would mean when they say “the” arrow of time. This arrow of time is undeniably due to the 2nd law of thermodynamics, so it is not simply a matter of opinion that this is connected with entropy. To Siegel’s credit, he does appear to admit this is true at some point. Although inferring from other things he writes in the piece, it seems like he doesn’t view this as the most important arrow of time for some reason.

What are the other arrows of time? There is the radiative arrow of time (having to do with the question of why ripples in a pond tend to move outward from a point but never inward towards a point). There is also a built in time asymmetry in the microscopic laws of physics called CP-violation. (The laws of particle physics are almost, but not quite, time symmetric.) There is the cosmological arrow of time (the universe is expanding, rather than contracting). And there is also the psychological arrow of time (why do we remember the past, but not the future?) There may be more, but these are the ones I’m most familiar with. I plan to discuss all of them and their interrelation in my book, although I haven’t written this chapter yet.

Much of the discussion over the course of the history of physics has been about whether the various other arrows of time which have been identified are related to or can be reduced to the main arrow of time which has been in the physics literature for the longest, namely the thermodynamic arrow of time. So if you say “an arrow of time” it could mean any, but if you say “the arrow of time” it usually means the thermodynamic arrow of time.

Next, he makes a common mistake I’ve seen all over the internet, which is a personal pet peeve of mine — he repeats the widespread myth that the 2nd law of thermodynamics only applies to closed systems!

Except, it isn’t irreversible completely. You see, there’s a caveat that most people forget when it comes to the second law of thermodynamics and entropy increase: it only refers to the entropy of a closed system, or a system where no external energy or changes in entropy are added or taken away.

It’s true in a sense that “entropy only increases in a closed system”, but this is a pretty misleading and vacuous statement as you can say that about nearly any law of physics. An open system is one where there is a system interacting with an environment. The 2nd law applies to all open systems, just as it does to all closed systems. It’s just that the form the 2nd law takes in the case of open systems is slightly different. It says that any decrease in entropy in the system has to be compensated by a greater increase in the entropy of the environment (in the form of heat escaping the system). I think this is something Siegel knows, but my experience has been that most people, when they hear popularizers of science say that, then conclude that this represents some kind of loophole in the 2nd law. But it’s not any different from saying that conservation of energy only applies to closed systems and for some reason I never hear people making that point. A better way of saying it is “any time you keep track of energy, it is always conserved” and “any time you keep track of entropy, it always increases or remains the same”. If you allow either to leak out into the environment without keeping track of it, then of course you can’t state the law in quite the same way. Yet another way to say this is that locally, energy is always conserved. And locally, entropy always increases. But globally, this is only true for closed systems as the new entropy produced in any physical process doesn’t have to stay where it was produced — it can leave the system if it is open. Similarly, the only system in which you can say energy is globally conserved is a closed system, as otherwise it can move in or out. The important point of the second law is that all physical processes increase entropy — period. It doesn’t matter whether they are in some kind of closed container or not.

The statement “the 2nd law only applies to closed systems” is a prime example of what I mean when I talk about bad translations of physics. Interpreted in just the right way, “entropy only increases in a closed system” could be viewed as correct, but it’s so misleading as to be a useless thing to say when explaining thermodynamics. And it doesn’t get at anything deep or important about how the 2nd law works and what it means. Personally I think it should always be avoided. There are perfectly good formulations of the 2nd law which apply to open systems, and these are taught just as frequently in the classroom as the versions that apply to closed systems.

And now, we come to the third and arguably most important disagreement I have with Siegel about thermodynamics and the arrow of time. Near the end of his piece, he comes to the false conclusion:

Here’s the kicker: even if you lived in the box and failed to detect the existence of the demon — in other words, if all you did was live in a pocket of the Universe that saw its entropy decrease — time would still run forward for you. The thermodynamic arrow of time does not determine the direction in which we perceive time’s passage.

This follows a fairly standard discussion of Maxwell’s demon — also something I plan to discuss in my book. I have no disagreements with his description of Maxwell’s demon, aside from the misleading open systems comment. But I completely disagree with what’s quoted above. He claims that the thermodynamic arrow of time does not determine what’s usually referred to as the psychological arrow of time — the direction which we perceive time’s passage. And yet, there is a pretty solid argument that the psychological arrow of time is in fact always determined by the thermodynamic arrow. My opinion is that they are ultimately one and the same. The argument has been published in peer reviewed journals in many different forms. As far as I’m aware nobody has succeeded in refuting this argument, and many people (including myself) still passionately agree with it.

He even doubles down on his rejection of the possibility that the thermodynamic arrow is always correlated with the arrow of perception further saying:

So where does the arrow of time that correlates with our perception come from? We don’t know. What we do know, however, is that the thermodynamic arrow of time isn’t it.

It may be true that we don’t know for certain that the psychological arrow of time correlates with the thermodynamic arrow of time, but as I mention there is a pretty solid argument that it does (backed up by lots of math and physics). Personally, I think the statement “we know that the thermodynamic arrow of time is responsible for our perception of the arrow of time” is much closer to the truth than his exact opposite statement “we know that it isn’t”. Although I will admit that it would be good if people wrote more on this topic, helping to make more clear exactly how the psychological arrow of time reduces to the thermodynamic arrow.

A recent paper which lays out the argument in detail was published in May 2014 by Leonard Mlodinow and Todd Brun titled The Relation between the Psychological and Thermodynamic Arrows of Time. (The free preprint for it can be found here: https://arxiv.org/abs/1310.1095). But the argument for the equivalence of the psychological and thermodynamic arrow of time goes back to the 80’s and 90’s. Stephen Hawking was among the first to suggest such an equivalence, and to the best of my knowledge he has never changed his mind on his gut feeling that such an equivalence must hold.

David Wolpert made the case rather well for why the psychological perception of time for humans aligns with the thermodynamic arrow in his 1992 paper Memory Systems, Computation, and the Second Law of Thermodynamics, by pointing out that human memory works very much the same as photographic memory (how an image gets imprinted onto a photograph using a camera). However, he left the door open that perhaps there could exist some kind of non-human sentience which has a reversed psychological arrow of time (like an AI whose memory is based on a fully reversible computer). This loophole has now been closed, as Mlodinow and Brun have now proven (under a pretty reasonable set of assumptions) that no matter what kind of sentient being you have, as long as it has some kind of memory which makes it capable of remembering anything, those memories will always be of the thermodynamic past, not the thermodynamic future. Perhaps someone might find further loopholes in the argument, or perhaps one of the assumptions might be flawed or need clarification. The door may not be completely shut yet. But the burden of proof is on people like Ethan Siegel (who refuse to believe that the psychological arrow is determined by the thermodynamic arrow) that there is a flaw somewhere in the argument.

The early form of these arguments were motivated by Landauer’s principle (from the 1980’s) that in order to erase 1 bit of information in any computational system, it necessarily requires dissipation of kT ln(2) of heat and will always result in an increase in entropy by at least k ln(2) (k is Boltzmann’s constant here, and T is the temperature.) Landauer’s principle is a law of physics which was discovered directly via thinking through the Maxwell’s demon thought experiment, and is now usually accepted as an important part of the resolution to the Maxwell’s demon paradox (of why a tiny microscopic sentient being who obeys the laws of physics can appear to violate the 2nd law of thermodynamics, but can’t actually violate it). By now there is ample evidence for Landauer’s principle, and it rests of very solid theoretical ground. In fact, if it weren’t true, I think it’s safe to say that Maxwell’s demon would still be an unresolved paradox — although Siegel’s piece gives the impression that he accepts it is resolved (ie, the demon does not actually violate the 2nd law).

The most up to date argument I’m aware of, from Mlodinow and Brun, outlines the conditions for what could possibly constitute a functioning memory. Importantly, it must be general enough to record any type of information it encounters, not a contrived special purpose device specifically designed to remember certain things (this would mean essentially, planting false memories, rather than allowing it to have new experiences, and store new memories naturally). And another important condition is that it must be robust to small perturbations of either the system or the sentient being / recording device. This means that if there is a very slight change in the brain of the entity recording the memories, it can’t suddenly completely change those memories. And similarly, if there is a slight change in the system being observed, it’s not going to completely change the recorded observation. These both seem like reasonable criteria, and it’s hard to imagine how one could build a sentient being of any kind (whether silicon-based, carbon based, or extra-terrestrial) which doesn’t adhere to these basic criteria.

As mentioned above, an important criteria which was thought necessary by many in the 1990’s — that the memories be irreversible, as they are in humans — has now been shown to be inessential. The argument based on irreversibility is still relevant, and covers nearly all cases one could imagine — it’s just not the most general argument one can make.

So what went wrong with Siegel’s claim that “if all you did was live in a pocket of the Universe that saw its entropy decrease — time would still run forward for you”? The assumption is flawed. One way to say it is this: you cannot find yourself in a “pocket of the universe” where entropy is decreasing, because entropy always increases. I think this mistake is exactly the kind of mistake that gets made when people start to say misleading things like “entropy only increases in closed systems”. Despite the Internet lore, the 2nd law applies to any system, whether open or closed.

It’s true that you could find yourself in a room where the total entropy in the room 1 hour before was greater than the total entropy in the room right now. But that’s not because the laws of thermodynamics are working backwards. It just means that whatever processes happened in the room within the past hour must have produced a lot of heat, and that this heat was allowed to escape the room during that hour. You still see the heat (and associated increase in entropy) being generated. If the door to the room is open, then yes there is a possibility that this heat will escape the room, which lowers the “total entropy in the room”, an irrelevant artificial quantity. But in either case, you are seeing the laws of thermodynamics work in the same direction as usual. Opening a door to let some heat out does not in any way reverse the thermodynamic arrow of time. Nor does it reverse your psychological arrow of time, as it is simply not possible to see the laws of thermodynamics work in reverse.

But what if, for the sake of argument, we assume that somehow there is some pocket of the universe where for some reason, the laws of thermodynamics really are running in reverse? (Contrary to the way our universe works.) In other words, the decrease in the total entropy in the room is not just because some heat escaped out the door. It’s because entropy in the room is spontaneously decreasing. If that were the case, then the thermodynamic arrow of time in that room has truly been reversed. And in that case, I believe he’s wrong that the psychological arrow of time could just continue to go forward — it would also have to reverse. What you would think of as the past would still be the low-entropy direction, and what you would think of as the future would still be the high-entropy direction. That’s because our psychological perception of time is always correlated with the thermodynamic arrow of time. Indeed, what we usually mean by the word “past” is “the lower entropy direction of time”. And what we mean by the word “future” is “the higher entropy direction of time”. There may be other things, such as the radiative arrow of time, which are not quite equivalent to the thermodynamic arrow, but those are also correlated with the thermodynamic arrow for similar reasons. By analogy, they function in the same way the second law does.

To wrap up, I’ll just briefly comment on the other arrows of time that have gone mostly unmentioned. There are 2 arrows of time which really have nothing to do with the thermodynamic arrow: the cosmological arrow of time (universe is presently increasing) and the particle physics arrow of time (CP-violation). Both of those represent asymmetric parameters in the fundamental laws of physics. But either of them could easily be reversed without affecting the thermodynamic, radiative, or psychological arrows. The particle physics arrow is so unnoticeable on the macroscopic scale that it wasn’t even known about until 1964, and only showed up in the decays of rare particles produced artificially in a lab. If it hadn’t been for that, nobody would have ever even noticed this time asymmetry. (Contrast this with the thermodynamic arrow, which has been argued about since the 1800's). The cosmological arrow is similar to the particle physics arrow. It was a bit more noticeable (first discovered/conjectured in the 1920’s, eventually confirmed in — coincidentally, also 1964), but still doesn’t make much of a difference in our every day lives. It has nothing to do with the question of why we see eggs breaking but not spontaneously healing themselves. If the universe began contracting, there is no reason to think that the thermodynamic arrow (or the psychological arrow) would reverse. The laws of thermodynamics would proceed as usual. And we would still view the low entropy direction in time as the past, and the high entropy direction as the future.