I've been trying for a while now to understand Sean Carroll's explanation of time and how it fits into his model of the universe. I think I have a better understanding of what he's saying now than I used to, but there are still some gaps. And I may still have a misunderstanding. But I thought I'd explain it as best I can in hopes that maybe somebody else will leave a comment correcting what needs to be corrected or telling me I'm on the right track or something.
If time is static, in other words, if eternalism is true, it raises the question of why it seems like time has a direction. After all, on a spacetime block, moments of time are analoguous to places in space. Space doesn't have a direction in which we can only travel one way. But it does seem like time has a direction since we can only go in the future direction. Why is this the case if time is not dynamic?
Carroll's answer is that the arrow of time is determined by the direction of increasing entropy. The problem I have with this answer is that it strikes me as being backward. It isn't increasing entropy that determines the arrow of time; rather, it's the arrow of time that determines increasing entropy. Let me explain that.
For any configuration of stuff (matter, energy, legos, or whatever) there are far more random or chaotic configurations than there are ordered configurations. For example, if you have a bowl of Alphabet cereal, there are far more possible arrangements of individual pieces of cereal that don't spell any words or sentences than there are configurations that spell words or sentences. So if you were to shake the bowl, it's far more probable that you'd end up with a random ordering of letters than an ordering that spells words and makes sentences. Since disorder is more probable than order, we should expect that as a system changes, it will tend toward less order, more homogeneity, etc.
There are endless examples of this in our experience. If you have a hot cup of coffee in a cold box, heat will flow from the cup to the rest of the box until it's evenly spread out, but you wouldn't expect the process to reverse. If you put folded clothes in a dryer and turn it on, you'd expect the clothes to become a jumbled mess, but you wouldn't expect them to end up folded again. If you drop a wine glass, you'd expect it to shatter into a bunch of random pieces on the floor, but you wouldn't expect those pieces to randomly come together in the form of a wine glass again.
And that's basically the second law of thermodynamics. Heat and energy tend to spread out. Nature tends toward equilibrium. While the total energy in a system may remain constant, energy can only be used as it is converted from an ordered state to a disordered state. The amount of energy that is no longer available to do work is called entropy. So entropy can be thought of as the amount of disorder, or randomness, or homogeneity, or equilibrium, or whatever. It always increases in a closed system where energy is not added to or taken away from the system.
It seems to me that it is because time has a direction that entropy increases. In the next moment of time, it is far more probable that we will end up with a more random configuration of stuff than that we will end up with a more ordered configuration of stuff. So I don't understand why Carroll thinks it's the other way around. If we assume time has a certain direction, it's easy to see why entropy will increase in that direction. But if, as Carroll thinks, time is static, there's no explanation for why entropy increases in any particular direction. He appears to simply define the arrow of time as pointing in the direction that entropy just happens to be increasing. Somebody please correct me if I've got this wrong.
Carroll's definition of the arrow of time leads to another mistake that I think William Lane Craig misunderstood in their debate. Since the second law of thermodynamics is based on statistics (disordered states are vastly more probable than ordered states), it is not an absolute law. It is possible for entropy to spontaneously decrease in a closed system.
Let me digress for a minute. Of course we see it decrease in open systems all the time. When water freezes, it forms crystals which have a lower entropy than liquid water. But this happens because it gives off heat. So while the entropy of the water decreases, the total entropy of the universe still increases since the increase of entropy surrounding the ice is always greater than the decrease in the entropy of the ice.
Okay, so it is possible, though unlikely, that in a closed system, the total entropy of that system will spontaneously decrease. This improbability can be overcome with enough time. Currently, the entropy of our universe is increasing. Eventually, the universe will undergo "heat death" or "thermodynamic equilibrium," which both amount to the same thing. But given enough time, it should spontaneously become ordered again, resulting in another big bang.
In some models of the universe, space is infinite, and there's an infinite amount of stuff out there. It's all in thermodynamic equilibrium, and always has been. But statistics being what they are, there are localized areas of low entropy that spontaneously emerge, and our big bang was just one of them.
In Carroll's model of the universe, entropy had to have decreased from a disordered state prior to the big bang. Since he defines the arrow of time in terms of the direction of increasing entropy, the fact that entropy was decreasing immediately prior to the big bang means that time was running backward prior to the big bang. This is the part that seemed to confuse William Lane Craig in their debate. Craig looked at Carroll's diagram which had an arrow of time drawn in opposite directions on either side of the big bang, and this lead him to think Carroll's model implied an absolute beginning at the big bang. But that was a mistake.
But Caroll's position still strikes me as being nonsense. The only reason he says time was moving backward prior to the big bang is because that's how he has defined the direction of time. In reality, time was moving forward like it always does, and it just happened, by a statistical fluke, that entropy was spontaneously decreasing. This is inevitable given infinite time and an infinite universe.
This can be seen just by looking at how entropy decreases in local areas of our own space. Entropy decreases whenever crystals form, but we don't say time is moving forward in the space surrounding the crystals while moving backward inside the space where the crystals are forming. In the same way, we shouldn't say time is moving backwards in a localized region of space that's getting ready for a big bang while moving forward in the rest of the infinite ocean of space. And this shouldn't change if we suppose that there is no infinite ocean of space and that our local universe is all the universe there is. The fact that entropy decreases prior to the big bang does not entail that time is literally moving backwards.
It strikes me as being nonsense to say that time is moving backwards in the first place. The direction of time is the same thing as the way time is flowing. So to say time is flowing backward is to state what seems to me to be a contradiction.
So it strikes me as being mere semantics for Carroll to say that time is flowing backward prior to the big bang since he only says that because he's defining the arrow of time in terms of the direction of increasing entropy. What's really and literally going on is that entropy happens to be decreasing as time moves forward, and this isn't impossible since there is a tiny but non-zero probability of that happening. If time always flows in the direction of increasing entropy, then it would be impossible for entropy to ever decrease.
I think all Carroll's model does as far as undermining the Kalam Cosmological Argument, is that it weakens the argument for an absolute beginning of the universe from the second law of thermodynamics. The argument for an absolute beginning of the universe from the second law of thermodynamics is that if the past is infinite, then the universe should've already reached thermodynamic equilibrium, but since it hasn't, then the past is not infinite. But since the second law of thermodynamics is statistical, and it's possible, though unlikely, for entropy to spontaneously decrease, then it's possible the universe has reached thermodynamic equilibrium, but then given an infinite amount of time, it spontaneously reached a state of low entropy again, resulting in the big bang. (Of course Carroll's model runs up against the Boltzmann Brain problem, but that's beyond the scope of this post.)
The argument from the second law of thermodynamics still carries some weight, though, since Carroll's model is a mere possibility. Not everybody agrees with the statistical explanation of the second law of thermodynamics either. Consider a situation in which you've got a pipe with high pressure air on one end and low pressure air on the other end. We should expect air to flow from the high pressure end to the low pressure end until the pressure in the pipe is evenly distributed. The statistical model tells us that it improbable but not impossible for all the molecules of the air to randomly accumulate on one end of the pipe again, creating a high pressure region at one end and a low pressure region on the other end. But this may not be possible since to do so would require the air molecules to move against the pressure they create as they get closer together. It's the pressure that keeps them spread out. In the same way, the tendency of energy to spread out in the universe and become homogeneous may not be reversible.
It could be that the statistical model of the second law applies to some situations but not to others.
Anywho, I thought I'd leaves some links to some videos on one of my favourite YouTube channels, PBS Space Time, about the second law of thermodynamics for your edification.
The Misunderstood Nature of Entropy
Reversing Entropy with Maxwell's Demon
