Is cosmology behind the second law?

Previous articles about the same topic:

Boltzmann's brains
Predicting the past

A newer article that will be written in the future:

Myths about the arrow of time

Sean Carroll gave a talk in Santa Cruz promoting the idea that cosmology is the cause of the second law of thermodynamics. I happen to fully agree with one of the commentators who happens to be more senior than UCSC graduate students:

Finally, the magnitude of the entropy of the universe as a function of time is a very interesting problem for cosmology, but to suggest that a law of physics depends on it is sheer nonsense. Carroll’s statement that the second law owes its existence to cosmology is one of the [dumbest] remarks I heard in any of our physics colloquia, apart from [Rosenblum & Kuttner]’s earlier remarks about consciousness in quantum mechanics. I am astounded that physicists in the audience always listen politely to such nonsense. Afterwards, I had dinner with some graduate students who readily understood my objections, but Carroll remained adamant.

Why do I agree? Well, indeed, it is interesting to study what entropy is doing during the cosmological evolution. But the second law of thermodynamics is a local law that applies to any macroscopic process even if it takes a very short time in any small but macroscopic region of space. The law shows its muscles instantly. The slow cosmological evolution has virtually no detectable influence on such local processes.




The second law of thermodynamics trivially implies that the initial state of the Universe in the past had to have a smaller entropy than its current value. But it is incorrect to revert this implication. A low entropy at the beginning is not a sufficient assumption to fully replace the second law of thermodynamics in the context of all physical questions.

In physics, we usually ask the question what is the probability of different outcomes at time "T" given some initial conditions at an earlier time "t". It is important to realize that the initial time "t" is almost never the Big Bang. While we could argue that the entropy at time "t" is probably smaller than the entropy at time "T" because of a low entropy at the very beginning of the Universe, this observation is not sufficient to guarantee that we only define the initial conditions at "t" and predict the outcomes at time "T", not the other way around.

This logical arrow of time has to be inserted into quantum mechanics by hand. It is a key part of the interpretation of quantum mechanics. It doesn't contradict other, dynamical laws of physics - on the contrary, it peacefully co-exists - and it implies that the thermodynamical arrow of time has inevitably the same direction as the logical arrow of time used by the interpretation of quantum mechanics. The dynamical laws are time-reversal symmetric but the interpretation of quantum mechanics is not. But one can't derive these conclusions just from "cosmology".

In some sense, I agree with the UCSC physicist that the error in Carroll's reasoning is analogous to the errors encountered by the authors who propose links between quantum mechanics and consciousness. For example, Roger Penrose has blamed the collapse of the wavefunction in the brain on the gravitational force, or something along these lines. But the gravitational force between small particles is negligible while the features of quantum mechanics such as the time evolution of the wavefunction or the localization of the particle after the measurement is an extremely accurate, reliable fact about Nature.

It simply follows that gravity can't be responsible for that because of its immense weakness. Analogously, cosmological evolution can't influence the validity of any robust, local laws of physics such as the second law of thermodynamics today. And saying that the cosmological evolution in the past is the primary culprit either violates locality or it contradicts other dynamical laws of physics.

More generally, Carroll's thesis contradicts very basic facts about the relationships between laws of physics. In physics, the short-distance laws are fundamental and the long-distance effective laws are their consequence. The second law of thermodynamics is a law that applies to very small systems, and it thus can't be a consequence of some properties of the Universe at the cosmological scale. The relations between short and long distances may be modified by various kinds of UV/IR mixings in string theory but you only expect those to be relevant when you study physics at the Planck scale, not Carnot engines.

Concerning the sociological portion of the UCSC statement, I also agree. It is just weird whenever physicists silently and politely listen to some complete crap even though their often complex work guarantees that they should be able to spot the errors within picoseconds.

This extreme politeness may have been a good thing sometime in the past. But in the current world controlled by all kinds of media campaigns, it is dangerous. Whenever you don't criticize a nonsensical talk or book about physics, you make it much more likely that tomorrow, this nonsense will be proudly spread to thousands if not millions of other people who are just not able to spot the errors. You should think twice before you decide to be polite.

And that's the memo.