## Wednesday, July 18, 2012

### Entropy: The unsolved problem

This post is part of "A few things wrong about the cosmological argument", a series using the cosmological argument as an excuse to talk about other stuff.

On a side note, I recently discovered that Chris Hallquist has a book review of William Lane Craig's Reasonable Faith, and is talking about his cosmological argument right now.  I recommend his William Lane Craig tag.

I previously talked about William Lane Craig (WLC) and his scientific argument that the universe must have had a beginning.  I think this is, in principle, a good argument, but WLC exaggerates his case by misrepresenting Big Bang cosmology.  Today I will discuss another scientific argument involving entropy.

The entropy argument

I've explained the definition of entropy elsewhere, but the short version is that entropy is disorder.  The idea is that physics gets really complicated when we have billions of billions of objects bouncing around, and we can't really keep track of it all.  So we describe the system with aggregate properties, even though we're really piling together many microscopic states by ignoring the details.  The entropy tells you the number of microscopic states we've piled together.

A disordered desk has higher entropy than an ordered desk because there are lots of different ways to arrange things on your desk such that it looks disordered, but only a few ways to arrange them such that it looks ordered.

But note that the amount of entropy involved in arranging a desk is actually very trivial.  I have a moderately messy desk with two dozen different objects in it, but this doesn't hold a candle to the billions of billions of molecules in a single mote of dust on my keyboard.  Likewise, arranging atoms into life-forms actually trivial in comparison to the amount of ordering involved in sunlight.

The Second Law of thermodynamics states that entropy increases over time in a closed system. The idea is that all those complicated processes involving billions of billions of objects are more or less random.  Therefore, each accessible microscopic state is equally likely.  High entropy states contain a far greater number of possible microscopic states, thus higher entropy states are more likely.  So if we have a system in an ordered state, it is likely that its entropy will increase.

Of course, for this argument to make sense, we have to have an ordered state to begin with.  Otherwise, the system would be in a state of maximum entropy, and continue to be in this state indefinitely.  And then that ordered state has to come from an even more ordered state, which had to come from an even more more ordered state.  This chain can't continue forever, since it's thought that entropy has a lower bound.  (Think of the lower entropy bound as a system which is so orderly, that it corresponds to exactly one microscopic state.)  And so we argue that the universe must have had a beginning with very low entropy.

WLC stops there, but one could go on to argue, by analogy, that the universe is like my desk.  Just as the desk required a sentient being to rearrange it so it has some semblance of order, so the universe must require some sentient being to carefully place it in an ordered state at the beginning.

This argument fails because I don't really reduce entropy by rearranging my desk.  Rather, I am simply reducing the entropy of my desk arrangement at the cost of greatly increasing other entropy.  Furthermore, the vast majority of processes which reduce entropy (at the cost of increasing entropy elsewhere) do not involve any sentience.  Take, for example, the fact that the poles are colder than the equator.  Such a temperature difference implies a far greater amount of order than could possibly exist on my desk.  But this order was created by completely mechanical processes like sunlight.  So even if the universe is analogous to smaller ordered systems within the universe (which is itself highly questionable), then this does not suggest that sentience is involved.

An unsolved problem in physics

The Second Law of thermodynamics really does present a problem in physics, and WLC deserves credit for getting that much right.  Allow me to re-frame the problem as a physicist sees it.  Imagine that we use our knowledge of physics to predict what happened further and further into the past.  On the microscopic level, this is no different from predicting the future.  Just as there is exactly one* path it can follow into the future, there is exactly one path it can follow into the past.  But because we can't keep track of the motion of every particle, we use statistics and thermodynamics, including the Second Law.

*I'm temporarily using the MW interpretation of quantum mechanics, which is deterministic forwards and backwards in time.

Assuming the Second Law holds true forever into the past, it seems that at some point in the past there is nowhere for our prediction to go.  We'll find the universe in a state which cannot have come from any lower entropy state.  Mind you, this does not mean that the universe cannot have come from anywhere at all.  Remember, on a microscopic level, there exists exactly one path the universe can follow into the past.  It's just that this path can no longer obey the Second Law.

It's possible that the Second Law of thermodynamics does not hold forever into the past, in which case, our universe is presently in a statistical fluctuation to a low entropy state.  However, there's a powerful argument to suggest this is not the case: if humans are only formed by statistical fluctuations, then the vast majority of humans would find themselves in much smaller statistical fluctuations than the one we see presently.  (I've discussed this "Boltzmann Brain" argument before, so I won't dwell on it further.)

So yes, it is a problem.  But a "problem in physics" does not mean "We can't think of any solution".  In fact, it usually means that there are many solutions, and we can't figure out which one is right, if any.  Unfortunately, there's a major obstacle to figuring out the correct answer here: quantum gravity.  As explained before, we don't have the theory required to predict past a certain point in the past.

I do not know what solutions people have advanced and argued for this problem.  There are probably many solutions involving loopholes in the Boltzmann Brain argument, loopholes in the lower bound of entropy, quantum mechanics, or a beginning to the universe.  I do not wish to opine on this matter, since as a physicist my answer would be taken seriously even though cosmology is not my field.

In my field, superconductivity, one of the great unsolved problems is the mechanism for high temperature superconductivity.  But in fact countless mechanisms have been and are being proposed.  So if someone suggests that our inability to find a solution means we should look to the supernatural, they've fundamentally misunderstood the problem.  We don't just need solutions, we need data to determine which, if any, of our existing solutions are correct.

(ETA: also see "Why I'm agnostic on cosmology")

"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite
6. Forming Infinity, one by one
7. Uncertain beginnings
8. Entropy: The unsolved problem
9. Kalam as an inductive argument
10. Getting from First Cause to God

Anonymous said...

The entropy of the universe may not be a well-defined property if the universe is actually infinite in extent. It is an extensive property, after all. Perhaps the most we can say is that some finite region of the universe, insofar as it is closed, must obey the second law of thermodynamics.

However, the universe is expanding, and it doesn't make much sense to talk about a finite region of the universe as closed unless we consider this region to expand, too. So its entropy must increase---but the average entropy per unit volume, depending on how quickly the region expands, may actually decrease.

I'm afraid I'm not very well-versed in cosmology, but it seems plausible to me, considering the above, that some region of the universe may have a low entropy, even after much time has passed. And it's my understanding that the observable universe is proposed by some models, such as one where we're in a bubble of low-cosmological-constant space that nucleated within a high-cosmological-constant space, to be only a small region of the total universe. But then, it's also my understanding that the whole universe must still have a finite age in such models, for technical reasons I don't really grasp.

miller said...

I had some similar speculations when writing this post, but I didn't want to commit them to blog because my speculations are not very authoritative.