Monday, November 14, 2011

The Fabric of the Cosmos II

The Illusion of Time

A few weeks ago, I discussed the first episode of The Fabric of the Cosmos on PBS (see the full episode here), one about space.

This is the second episode:

The last six minutes are here: sorry.

Again, it's a perfectionist piece of acting and video trickery. Also, there are many nicely done explanations of the science of time in this episode – atomic clocks, slicing the relativistic spacetime bread under different angles, and so on. However, there's also lots of bizarre pop philosophy in this episode that I consider incorrect.

In fact, this episode is probably the most problematic one among all the episodes of The Elegant Universe or The Fabric of the Cosmos that I have watched (most likely, even among those that will arrive later). This observation is also correlated with a significant decrease of the witnesses who are top physicists and a significant increase of philosophers and pop-science-level physicists.

First of all, the meme that "no one knows what time is" is repeated at least a dozen of times. This is probably a cheap way to make the show exciting for the lay audiences (look, scientists have no clue what they're talking about, that's great!) but I don't think that such a statement may be justified by the scientific evidence; and I don't think that it helps the public to understand science.

As the story about the atomic clocks shows, we know what time is with the accuracy of one part per quadrillion; and as the relativistic stories indicate, we have refined our conceptual ideas of how time works in various profound ways, too. Time is what we may measure with clocks (ideally, with the most accurate clocks we may get at this point). That's it: the physics attitude really is to give an operational definition to concepts we want to use and avoid talking about concepts that can't be given such a definition. Much of the "mystery worshiping" based on our "complete ignorance what time is" is nothing else than a vacuous philosophical or terminological babbling. If you don't have any idea what it is, why are you using the word "time" at all, Brian?

There are logically flawed conclusions in the show made out of various careless arguments, too. For example, it's being said that one must adopt "eternalism" – all of the spacetime, whether it is in the past or in the future – is equally real. But such a conclusion is once again sloppy. Nothing like that follows from relativity. And in fact, relativity combined with quantum mechanics implies things like the "free will theorem" which pretty much refutes eternalism.

What the possibility to cut the bread in different directions means is that for a distant extraterrestrial cyclist, all spacelike-separated regions of spacetime are equally real from his perspective and they may include events on Earth which belong to our past, present, as well as future. But that doesn't mean that the reality of the past, present, and future on Earth has to enjoy the same "reality status" from our perspective.

If I translate this comment into a slightly more technical language, Brian Greene is effectively saying that the question "what is real [now and here]" must have an absolute answer that all observers in any region of spacetime must agree upon. But this assumption contains "eternalism" in it so it is not surprising that one may derive "eternalism" out of it, by adding extra assumptions and ideas (which are really not needed).

However, relativity allows many things to be relative. In particular, what is the "past" and what is the "future" depends on the event in spacetime that you use as a benchmark. The spacetime may be divided to the past light cone, future light cone, and the ambiguous "spacelike-separated region" from the viewpoint of any event in spacetime. And the past light cone, the spacelike-separated region, and the future light cone have vastly different "degrees of reality" from our viewpoint. For example, the free will theorem guarantees that in a quantum theory, the future "cannot exist at this point yet", namely that it can't be determined by anything that belongs to the past. The (random, probabilistically predictable) outcomes of events we care about are only decided once we live through them.

So it's just not true that relativity prohibits the laws of physics and arguments that impose a difference between the future, the past, and the spacelike-separated region. And indeed, we know that these two realms have a very different relationship to our "present era here". Relativity, despite its name, implies the existence of many new absolute things. The difference between the past and future light cones is one of these absolute differences: for a given point in spacetime, these cones don't depend on the velocity of the observer.

Peter Galison promotes his idea that Einstein discovered the special theory of relativity because he had to work with time-synchronization railway patents. That may be a tangible or likable story except that it's historically (and logically) untrue: Einstein really thought about these matters long before he worked in the patent office. Moreover, thinking about trains doesn't really help you to find relativity in any way because, as many people know, it's perfectly legitimate to think about a high-precision synchronization of trains in the context of classical physics, too. Nothing would ever tell you that something about the Newtonian physics is wrong if you just thought about engineering railway questions. Newton's physics was a self-consistent theory at this level.

It's probably mandatory on such shows on time to hear that time traveling into the past may be possible, too. It may be possible because of Einstein and wormholes, Brian Greene says. Well, the reality is that nothing like time machines follows from relativity. Any kind of traveling into the past creates a logical paradox of the same degree of severity as it does in the Newtonian physics. The new thing about relativity is that the required absence of such paradoxes allows us to derive stronger constraints on the detailed laws of physics (and perhaps on the allowed configurations of matter) than those in the Newtonian physics. For example, the information is not only prohibited to travel back into the past; it is also prohibited to travel faster than light because the superluminal propagation looks like "back into the past" propagation according to other reference frames. There's no absolute, qualitative difference between them.

When I was giving an interview on the OPERA experiment recently, I liked a reaction of a reader to my thought experiment about killing your grandfather before his first sex with your grandma. The reader said it was brutal: wouldn't it be enough to castrate him? ;-)

Brian Greene wants to keep the possibility of time traveling into the past open. Well, I think such an open-mindedness only comes from a sloppy evaluation of the possibilities and impossibilities. But OK, one could at least get a "mixed" verdict: it could be impossible, they say. Thank God.

Denying the arrow of time: a stream of nonsense

Needless to say, the most irritating portion of the program are the comments about the arrow of time. Again, we are told that we don't understand the arrow of time. Why don't they say "I don't understand the arrow of time"? It's just dishonest because those physicists who have mastered at least undergraduate statistical physics and thermodynamics do understand the arrow of time. Ludwig Boltzmann was the first one who did and the refusal of others to appreciate his profound discoveries contributed to his decision to commit suicide. We're living 100+ years later and his discoveries are still being obfuscated and refused by the ignorant people.

Brian Greene says "the laws of physics don't allow something like this to happen" and an arrow suddenly anti-dissipates energy from the target and returns to the hunter in a time-reversed fashion. So far, so good. However, Brian Greene says that "they actually do". This is just plain incorrect. In the video-loaded sentence, the term "something like this" is clearly meant to be a time-reversed macroscopic process. However, the laws of physics don't allow time-reversed macroscopic processes to happen.

More quantitatively, we may rigorously show that the probability of the evolution from CPT(B) to CPT(A) isn't the same as the probability of the evolution from A to B where A,B are macroscopic states (ensembles of microstates) and CPT refers to the CPT conjugation (essentially time reversal: velocities are flipped). Instead, the former probability is smaller because of an extra multiplicative factor of \(\exp[-(S_B-S_A)]\). If the entropy difference (the exponent) is macroscopic, like \(10^{26}\), the probability is suppressed not just by \(10^{-26}\): it is suppressed by \(\exp(-10^{26})\) and is zero for all practical (and even almost all impractical) purposes.

The vanishing of a probability means that a process isn't allowed.

The laws of physics don't allow the time-reversal of macroscopic processes to take place. Note that in the video segment, Brian Greene doesn't say this sentence explicitly: he doesn't say that the laws of physics allow the entropy to decrease etc. because he would probably know that they don't allow it. Especially the second law of thermodynamics prohibits it. So instead of saying this lie explicitly, he says it with the help of some video trickery. The subject in the sentence that is allowed is "something like this" while the nature of this something is given by the video. But because the content of the video means "time reversal of a macroscopic process involving a hunter and an arrow" and Brian Greene ordered this to be a part of the video, his sentence is still a straight lie. It may be easier to say the lie in this way but it is still a lie.

This lie is repeated many and many times; it is really annoying. There's nothing in the laws of physics that has a preferred arrow of time, we're informed again. Except that it's not true. Whenever we deduce the predictions of the laws of physics for any system with many degrees of freedom, we get time-reversal-asymmetric equations and predictions. That's also why effective laws for these systems always explicitly contain time-reversal-asymmetric terms such as terms with the first time derivatives: friction forces, diffusion terms, heat conduction, viscosity, all other kinds of energy dissipation, decoherence, and so on. All these processes are all about terms that break the time-reversal symmetry "maximally" and all these processes may be deduced from the fundamental laws of the Universe that we understand.

Almost everything that Brian Greene and others say about these matters is just a plain misconception, an utter stupidity. The microscopic laws of physics may be shown to have a simple action of the time reversal (or CPT) but science is ultimately about the prediction of probabilities of various things (of general enough statements) and all such predictions – with the extremely special exception of predicting the exact microstate from another exact microstate at a different time – are completely violating the time reversal symmetry simply because the mathematical logic has to be used and any logical or probabilistic calculation applied to questions involving the real time have to respect the logical arrow of time which is the primary source of the asymmetry. The logical arrow of time says that the properties of future events and configurations may be derivable consequences of the properties in the past (because the future evolves from the past); but it can't be the other way around. The past may only be deduced from the future indirectly (and the conclusions will always depend on arbitrary, partly psychological priors) because the past doesn't evolve from the future.

Brian Greene "unshatters" a glass of wine. It's trivial, he says: we just flip the signs of all velocities. Except that the laws of physics don't allow you to reverse all the velocities in a system of a high number of degrees of freedom. The probability that you succeed in any such a maneuver, regardless of the quality of your planning, will still contain the tiny factor of \(\exp(-10^{26})\) or so.

OK, at least Boltzmann and his profound discoveries on the entropy get heard as the "second alternative" description of the arrow of time: a minute or so is dedicated to the proper physical viewpoint on these questions. Probably no one else except for me cares that only this part of the program is right.

However, even this part isn't completely right. "Maybe it's the answer: things are moving towards a greater disorder." Except that even the second law, however far-reaching and universal it is, isn't really the "fundamental" source of the arrow of time. It is a derived one. We don't really need to talk about the entropy to show why the world is past-future-asymmetric. The second law may be mathematically proven (as the H-theorem and its generalizations); however, the truly "primordial" assumption that makes the proof possible isn't the thermodynamic arrow of time. It's the logical arrow of time, something that Brian Greene and apparently everyone else in this business of babblers about the mysteries on the arrow of time completely denies.

After a minute, Brian Greene returns to pure crackpottery. Entropy should increase in the direction of the future as well as the past. Holy cow. He also adds that it makes no sense but he must clearly misunderstand why it makes no sense, otherwise he wouldn't be repeating this nonsense for so many years. If we're determining the past from the present, we're retrodicting the past and if we do it right, retrodiction follows totally different rules than the predictions of the future. Whenever we use the rules for "predicting the evolution from A to B" that are known from predictions, then we say – by definition – that B is in the future of A.

Let me mention one thing, an example of a guest. Sylvester Jim Gates is saying various things and in isolation, everything he says is perfectly valid. (Maybe the same thing is true for a few others.) Unfortunately for him, he is included to a broader scheme of "explanations" that is almost perfectly invalid.

Brian Greene continues with all the delusions and delusions, infrequently spiced with a correct proposition. The Big Bang created the arrow of time (the latter has nothing to do with the laws of physics), holy cow. "We don't know why the Universe started in a low-entropy state," holy cow. We perfectly know why it did. If it started with a state of a high entropy, we could always ask "what was before that". The only thing that prevents us from going before a moment is that the moment has the minimal mathematically possible value of the entropy, namely zero.


To summarize, about 50% of this episode is composed of misconceptions and the overall contribution of the episode to the public's understanding of time as understood by physics may be close to zero. That's not that bad – that isn't too good, either. But I don't really care about the laymen's opinions too much: generic viewers of PBS will never really understand relativity or statistical physics and they will always view physics as a shaky confused discipline. What I find more troubling is that these layers of confusions and myths define the actual scientific community. 100+ years after Boltzmann's key realizations, his explanation of the irreversibility of the natural phenomena is still being widely denied. It's just sad. The same thing holds for the postulates of quantum mechanics and many other things (and I don't even have to get to string theory).

Chances are that the mankind (and maybe even the scientific community) will collectively never overcome these childhood diseases.

And that's the memo.


  1. If the clock were turned back to before I was born, I wouldn't be there to maim an ancester, would I?

  2. I once had dinner with a cable producer who had been put in charge of a popular science type program because it was getting lousy ratings. She was proud of the fact that the ratings improved under her control which was essentially a change in subjects like ghosts and flying saucers.

  3. Dear k, I've had somewhat similar experiences. Making things dumb and popular among morons – a very large segment of the population – is a source of immense pride for many people. ;-)

    Just to be sure, even if all Brian Greene's episodes were like this one, it would still be vastly above ghosts, reincarnation, and telepathy when it comes to the scientific credibility.