- P(the universe has low entropy | naturalism) is extremely tiny.
- P(the universe has low entropy | theism) is not very small.
- The universe has low entropy.
- Therefore, the low entropy of the universe strongly confirms theism over naturalism.

Low-entropy states have low probability. So, (1) is true. The universe, at the Big Bang, had a very surprisingly low entropy. It still has a low entropy, though the entropy has gone up. So, (3) is true. What about (2)? This follows from the fact that there is significant *value* in a world that has low entropy and given theism God is not unlikely to produce what is significantly valuable. At least locally low entropy is needed for the existence of life, and we need uniformity between our local area and the rest of the universe if we are to have scientific knowledge of the universe, and such knowledge is valuable. So (2) is true. The rest is Bayes.

When I gave him the argument, Dan Johnson made the point to me that this appears to be a species of fine-tuning argument and that a good way to explore the argument is to see how standard objections to standard fine-tuning arguments fare against this one. So let's do that.

I. "There is a multiverse, and because it's so big, it's likely that in one of its universes there is life. That kind of a universe is going to be fine-tuned, and we only observe universes like that, since only universes like that have an observer." This doesn't apply to the entropy argument, however, because globally low entropy isn't needed for the existence of an observer like me. All that's needed is locally low entropy. What we'd expect to see, on the multiverse hypothesis, is a locally low entropy universe with a big mess outside a very small area--like the size of my brain. (This is the Boltzmann brain problem>)

II. "You can't use as evidence anything that is entailed by the existence of observers." While this sort of a principle has been argued for, surely it's false. If we're choosing between two evolutionary theories, both of them fitting the data, both equally simple, but one of them making it likely that observers would evolve and the other making it unlikely, we should choose the one that makes it likely. But I can grant the principle, because my evidence--the low entropy of the universe--is not entailed by the existence of observers. All that the existence of observers implies (and even that isn't perhaps an entailment) is locally low entropy. Notice that my responses to Objections I and II show a way in which the argument differs from typical fine-tuning arguments, because while we expect constants in the laws of nature to stay, well, constant throughout a universe, not so for entropy.

III. "It's a law of nature that the value of the constants--or in this case of the universe's entropy--is exactly as it is." The law of nature suggestion is more plausible in the case of some fundamental constant like the mass of the electron than it is in the case of a continually changing non-fundamental quantity like total entropy which is a function of more fundamental microphysical properties. Nonetheless, the suggestion that the initial low entropy of the universe is a law of nature has been made in the philosophy of sceince literature. Suppose the suggestion is true. Now consider this point. There is a large number--indeed, an infinite number--of possible laws about the initial values of non-fundamental quantities, many of which are incompatible with the low initial entropy. The law that the initial entropy is low is only one among many competing incompatible laws. The probability given naturalism of initially low entropy being the law is going to be low, too. (Note that this response can also be given in the case of standard fine-tuning arguments.)

IV. "The values of the constant--or the initially low entropy--does not require an explanation." That suggestion has also been made in the philosophy of science literature in the entropy case. But the suggestion is irrelevant to the argument, since none of the premises in the argument say anything about explanation. The point is purely Bayesian.

## 18 comments:

If we're choosing between two evolutionary theories, both of them fitting the data, both equally simple, but one of them making it likely that observers would evolve and the other making it unlikely, we should choose the one that makes it likely.I know it was just an example, but I think many people would fight that suggestion. Theories that "make observers more likely" to evolve would seem to suggest that we should always prefer the more teleologically suggestive views of evolution (God/an intelligent agent fixes the results of evolution, evolution is directed/rigged towards certain outcomes, etc) that Darwinism is often viewed as opposing.

(Mind you, I wouldn't fight it. But others would seem to.)

Also, what about arguments that claim the universe always starts out with low entropy, but is rigged up to do this perpetually in cycles? (Penrose's cyclic cosmology idea comes to mind.)

This argument seems to be based on a misunderstanding of thermodynamics. Admittedly, I am only an undergraduate engineering student, so I am far from an expert. But the flaws with this argument seem to be rather fundamental.

I'll offer some thoughts and questions.

First, consider what “low entropy” means. What is the entropy low compared against? The second law (in one version) states that entropy tends to increase until the system is in equilibrium. At that point entropy can no longer increase; it is at its maximum.

Naturalism does not necessarily predict high entropy. If naturalism predicts anything, it predicts that the total entropy is overwhelmingly likely to increase if the universe starts with low total entropy. But how quickly entropy increases is not specified.

Second, how do you propose entropy is kept low in a theistic universe without violating the second law? Would God directly intervene in the universe to keep entropy low if necessary? That violates the second law (which I suppose a God could do). It also has not been observed (though that does not exclude it from possibility). Did God rig the universe such that it would have low entropy? How would that situation be distinguishable from naturalism?

Third, the probability (under naturalism) that some parts of the universe some of the time will have low entropy at any time is almost certainly not “extremely tiny.” I don’t have the knowledge to calculate this probability, but I am very certain it is not low, especially given the size of the known universe. Someone fairly knowledgeable about statistical physics could calculate this probability.

Fourth, premise one should read “P(the universe has low local entropy and life | naturalism) is extremely tiny”. The problem is, this probability is not extremely tiny as low local entropy is a necessary condition for life. You seem to understand this based on what you said in II. Perhaps I am misunderstanding what you wrote. Could you explain II again in different words?

"What is the entropy low compared against?"

Against the equilibrium entropy. :-) And the probabilities are then measured in some analogue of the classical microcanonical ensemble measure.

"Naturalism does not necessarily predict high entropy. If naturalism predicts anything, it predicts that the total entropy is overwhelmingly likely to increase if the universe starts with low total entropy."

Given naturalism, we should not expect a low initial total entropy. And given an initial high entropy, we should expect that the entropy will remain high, except for rare downward forays.

"Second, how do you propose entropy is kept low in a theistic universe without violating the second law?"

One option is for God to start the entropy at a very low level, and then if it appears to be reaching an unacceptably high level, intervene miraculously. This is consistent with our observations so far: since it hasn't yet reached an unacceptably high level, there has been no need for such miraculous intervention. Another possibility, suggested by Jewish, Christian and Islamic revelation, is that eventually the universe will be radically transformed, and that may include a new set of laws.

Furthermore, the second law of thermodynamics talks of closed systems. But if God exists, the universe isn't a closed system.

'Third, the probability (under naturalism) that some parts of the universe some of the time will have low entropy at any time is almost certainly not “extremely tiny.”'

Sure. In an ergodic system, given an infinite amount of time, we're almost certain to have periodic excursions to low local entropy.

But I am running the argument based on global entropy, not local entropy.

Now, given ergodicity, we're also almost certain to get periodic excursions to low global entropy. But we have no reason to think that

now--about 13-14 billion years after the beginning of the universe--there would be such an excursion to low global entropy. (You can make a reasonable anthropic case that we can only observe the universes where there is an excursion to low local entropy. But the question is about low global entropy.)"Fourth, premise one should read 'P(the universe has low local entropy and life | naturalism) is extremely tiny'"

Why should I change a premise that is true to a premise that may well be false? :-)

Besides, we should use all our available evidence rather than a subset of it. Our available evidence is not just that our universe has low local entropy. Rather, our available evidence is that it has low global entropy, and indeed that it started out in that state.

Thanks for the quick reply!

“Against the equilibrium entropy. :-) And the probabilities are then measured in some analogue of the classical microcanonical ensemble measure.”

Of course. But what is the equilibrium entropy of the universe, the current entropy of the universe, and the entropy of the young universe? I think estimates of those entropies are necessary to justify this argument.

(As a side note, involving these estimates could make this a very complicated design argument. But I digress. :-)

“Given naturalism, we should not expect a low initial total entropy."

This is an interesting assertion, but how is it justified?

My understanding of cosmogony is very limited, but it seems to be easy to justify a low entropy at the beginning of the universe. Assuming supernatural reductions in entropy have not occurred (as naturalism does), the entropy in the past was surely lower than the present entropy by the second law. Also, small volumes have less places for particles to go, and consequently the entropy is lower.

In justifying premise one, you said “Low-entropy states have low probability. So, (1) is true.” But as far as I know (and please correct me if I’m wrong as I have no idea whether you are more knowledgeable than I am in this area), those probabilities are for systems in equilibrium. The universe obviously has not reached equilibrium yet. I don’t know anything about non-equilibrium thermodynamics, so I could be wrong here.

“One option is for God to start the entropy at a very low level, and then if it appears to be reaching an unacceptably high level, intervene miraculously. This is consistent with our observations so far: since it hasn't yet reached an unacceptably high level, there has been no need for such miraculous intervention.”

Yes, but is this not indistinguishable from what a naturalist might expect if the initial total entropy was low? I’m unsure how to argue for or against God’s existence given that.

“Furthermore, the second law of thermodynamics talks of closed systems. But if God exists, the universe isn't a closed system.”

Ah, yes, I had not considered that. That’s one way to look at it.

“But I am running the argument based on global entropy, not local entropy.”

I reread your post and I think I get this now. The argument is referring to things that should be largely independent of the existence of observers.

Might the evidence for dark matter, energy and flow be evidence for antimatter standing waves? Were that the way in which matter and antimatter come into existence in a Big Bang (like protons surrounded by electron shells), then we would expect expanding antimatter standing waves to fill space initially, and they would force matter to occupy states that would seem to be of very low entropy were the standing waves ignored. And of course, there might be other ways in which Naturalism would expect states that you would take to support (3).

Apart from time travel and the like, explanation doesn't go from future to past. So, to explain the low entropy at the beginning in terms of the present entropy is a non-starter. (Another problem is that the laws are time-reversible.)

Small volume is compatible with high entropy if the particles occupying the small volume have a wide variety of momenta. Entropy involves positions and momenta.

Low entropy IS improbable in the microcanonical ensemble measure. In fact, on the best account of why the 2nd law holds, it holds because the universe happens to start in an improbably low entropy starting state, and this improbably low entropy is unlikely to continue.

It is widely thought by non-theistic philosophers of science and cosmologists that the initially low entropy of the universe is remarkable and puzzling. The post-big bang state exhibits surprising uniformity.

Here's another way to put the point. If the system is ergodic, the fraction of time it spends in a macrostate is proportional to the microcanonical measure of the macrostate. Therefore, given naturalism, most of the times at which there are observers should be times at which the observers are in a merely local patch of low entropy. But that's not what we observe.

"I think estimates of those entropies are necessary to justify this argument."

Penrose estimates the probability of the initial state at 1/10^(10^123). See this paper by Callender for some background on the issue. Callender himself takes the tack that I labeled "IV"--he argues that no explanation is needed.

enigMan:

Maybe. But do we have any

priorreason to think such a theory is true given naturalism? The point is this: Suppose only naturalism. What kind of a world should you expect? I say--one without any kind of special arrangement. Is naturalism compatible with laws and etiologies that produce special arrangements? Certainly. But if all we knew was that naturalism is true, we wouldn't expect such.If Naturalism is true then probably the world began with a Big Bang. We would expect such special arrangements as the energy of which our mass is made would naturally have, none others (although they might occur). So there are two problems. The first is that we have no idea of the probability of my antimatter idea, whether it is high or low. What was the probability that space was Newtonian at the time of the ancient Greeks? Insofar as it was low, that probability was so subjective that it could not do the job you want it to do.

The second problem is (3), the initial entropy being low.The Big Bang begins with a singularity, but is its entropy therefore high or low or not well defined? What is the entropy of a point-sized particle in a 0-dimensional box? That seems to have low entropy, but the Big Bang was like a breaking particle in an exploding box; what does that do to entropy? I’m not sure, but consider a gas of particles in a finite space, for simplicity:

The gas is spread out, so it looks like it has low entropy. But the space has a centre, the centre of mass of the gas, to which the particles collapse. As they do so, their entropy increases. And when they are clumped together, their internal forces may become apposite, so that they explode. Again, as they do so, their entropy increases. And when they are spread out, their internal forces become irrelevant, and they may return to their original state. So entropy has increased and then increased again and yet we are back where we started. What happened was that entropy decreased (and not improbably, even in this isolated system) as the internal forces became apposite. (The internal forces were always there, of course; and energy is conserved.)

Probably the best way to understand the "initial" entropy is by a limiting process. Shortly after the big bang, the entropy is well-defined and, I understand, extremely low. Take the limit as time goes to "the time of the Big Bang" then.

Even so, there's the

prima facieproblem that entropy seems to decrease as internal forces become apposite (as above), and that shortly after the Big Bang, the fundamental forces of the Big Bang were breaking out of symmetry (in response to the expanding spacetime, presumably)...The following is from your Prosblogion post:

If we're going to have any hope of doing science, we need to privilege simpler hypotheses and give them higher priors.We also need to privilege more complex hypotheses, similarly. This is often over-looked, and I don't know why. Recall doing science at school, or your reading of the history of science. Scientists look at the world and discover what it's like. They don't add unnecessary complications to their theories. But that isn't to say that they make them as simple as possible. Similarly, they don't unnecessarily simplify their theories (except for introductory pedagologic reasons).

A complex curve will go through all the observation-points, but be unlikely. It's likely that there were some mistakes. But a straight line is not always the right sort of curve. The scientist looks at the dots and sees what sort of shape they are. However complicated it is, that's what she sees. (There is of course a limit to humanly perceptible complexity, but that's not a deliberate privileging.)

Similarly, chemistry is quite simple, with the patterns of the Periodic Table and such, but that was a discovery. Natural philosophers were quite happy with complex alchemy to begin with. Indeed, had they preferred a simple alchemical theory to a more accurate theory, they would have been less likely to get to chemistry. And as it is now, scientists are quite happy with the conceptual complexities of Bohr's quantum mechanics. Most scientists are unimpressed with the simpler theories that simply ignore the complexities that nature seems to them to be showing them.

One might do some physics research. Many physicsts are indeed interested in the notion that the universe had a low entropy beginning. And they've worked on naturalistic explanations. A good place to start is the work of Laura Mersini-Houghton.

This argument fails, because the entropy of the universe HAD to start out low, given that it started out small. The same thing would happen if you started out with a box of gas and expanded it: it would not be in equilibrium (at least once the relevant degrees of freedom decoupled). Study up on your cosmology before you try to make this kind of argument, will ya?

Let me clarify my previous argument.

A gas of single species expanded adiabatically will not undergo an entropy change. However, if we have massless particles (E=pc) and massive ones

(E=sqrt((pc)^2+(mc^2)^2)) that start off at equilibrium (that is, maximum entropy given the boundary conditions) and then decouple, after the expansion they will no longer be in equilibrium with each other, hence the thermodynamic free energy available.

Penrose assumed a phase-space conservation , which applies only to systems with time-translation-invariant boundary condition, inapplicable for an expanding cosmos (regardless of exactly how and if it began).

Hence the nonequilibrium state of the present universe is precisely what would be expected from the laws of physics, and thus cannot be used as evidence of anything supernatural.

Penrose is talking about the initial state, not the present state. I am not sure that it matters for the initial state that we've got inflation afterwards.

Pruss,

Isn't the biggest problem with this argument actually with premise 1? The probability of a low-entropy universe given naturalism is currently unknown and would be difficult to calculate

John:

People have tried to give bounds on it. Penrose gave a bound of 10^(-10^123) assuming some things about the laws of physics.

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