A system that you have contrived such that it will change over time to a “low entropy” state must itself be very highly ordered. It’s not “typical”. It’s just that the very special ordering is not as obvious as it is when all your particles are bunched up in one place.

To me this seems to be a way of deceiving yourself that you’ve created something different. All you’ve done is to create a system that shows the weakness of our method of calculating the macroscopic property we call entropy.

Sean: “It’s more likely that both entropies will remain high for most of the evolution, and one will suddenly go down at the end.”

It’s not a statistical thermodynamics measure of entropy that will “suddenly go down”. It’s a sloppy macroscopic measure of entropy that you’re deceiving yourself with.

Concepts like the Arrow of Time only work as a macroscopic approximation when you don’t have a deceptive intelligence contriving your starting conditions. As soon as you introduce a deliberate deceiver, you’re not talking physics, you’re talking parlor tricks.

And you’re right that interactions with other systems will break the illusion. A system designed to evolve so that it simulates a reversed Arrow of Time is so fragile that any interaction from outside the system will wreck the illusion.

Slightly off-topic: I suddenly realised, from reading this, that I don’t understand the “Horizon Problem” which inflation supposedly solves.

Think of it this way. Go out with your handy horn antenna and measure the cosmic microwave background (CMB) background temperature in a random direction. Now measure the temperature in the exact opposite direction. You are seeing photons, greatly redshifted, from the last scattering surface of the so called recombination. If you make some simple assumptions about the topology of the universe (e.g., that spacetime isn’t a torus or a Klein bottle or some other tricky topology), then those photons come from regions of spacetime that had no causal connection with each other at the time of recombination – i.e., there is no way for a star or a nova or a intelligent being in one of those regions to communicate with or influence the other, at least using light or matter to send signals. These two regions only “came through the horizon” and became causally connected with you now, when you got their photons, and are still not causally connected with each other. (You are closer to them than they are to each other.)

This leads to the Horizon Problem : if these two regions have never been in contact, then how do they “know” to have the same temperature ? You could have weird topologies for the entire universe (where looking in opposite directions means that you are really looking at the same distant objects), but I am not aware of any interesting theories that require or assume weird topologies. A related problem is the smoothness of the universe – gravity will make small initial perturbation grow, and it is hard to see how an initial big bang would give us the smoothness of the microwave background we observe. Note that having weird topologies really don’t do anything to solve this problem.

In inflation, a small piece of very early space time greatly expanded, at much faster than the speed of light, making everything we see (even the entire cosmic microwave background) to have come from one tiny original patch of spacetime, which was causally connected (and quite smooth, because it was tiny). So, in a sense you have pushed the Horizon problem “up a step” to the theory of inflation (there is no need to postulate faster light travel now, but you have to postulate a rapidly expanding spacetime then), but the theory of inflation seems to hang together well, and it does solve the horizon and smoothness problems.

> In fact, there is no relationship between the second law of thermodynamics and the fact that most animals senesce.

> In fact, there is no theoretical reason why an animal could not get more robust, more fertile, and stronger with each passing year.

> In fact, there are some animals and many more plants that fit the definition of “negative senescence”. Mortality rates decline over time, rather than rising exponentially as in the usual process of senescence.

There is a review paper on this subject, “The Case for Negative Senescence”, from the laboratory of James Vaupel, who is probably the world’s most prominent demographer:
http://tinyurl.com/9vegsu
Theor Popul Biol. 2004 Jun;65(4):339-51.

“The different parts of the universe are all rapidly evolving, but they are evolving in perfect synchrony, despite never having been in causal contact.”

That may not be as bad as it sounds. After all, we have no problem accepting that laws of nature are valid all over spacetime, but there is no suggestion that this was established “causally”. If there is some law of nature that dictates initial smoothness everywhere in space, then that would solve the problem without any violation of causality. So I still find the “horizon problem” rather fishy. Anyway thanks again.

But beyond that, the horizon problem is really an issue of causality, not just entropy. The different parts of the universe are all rapidly evolving, but they are evolving in perfect synchrony, despite never having been in causal contact.

You say: “Having everything at the same temperature is certainly not the most probable state in this particular kind of background (an expanding universe). There are many more ways for conditions to be very different from place to place.”

I thought that what counts is: how many ways can you re-arrange things *so that the macroscopic states are indistinguishable*. I would have thought that uniformity would have *more* ways of re-arranging things without changing macroscopic conditions than non-uniformity, no?

I guess in General Relativity, a very uniform matter distribution would correspond to very smooth geometry, which is a low-entropy state, so a uniform initial state becomes very unlikely when you take that into account — is that what you mean?

” (Think of it this way: if you had several *disconnected* boxes of gas, with randomly chosen densities and energies, you would indeed be very surprised to find them all at the same temperature, even if that would be the eventual high-entropy state once they were all brought into contact.)”

I guess the point here is contained in “randomly chosen”. Suppose God creates a room full of gas and does it in a completely “random” manner. Won’t the room *immediately* be full of gas, uniformly distributed, in equilibrium? After all, that is the most probable state, right? [Again, I'm ignoring gravity here; if God takes that into account, the result will probably be a black hole I guess....]