Is it ever physically possible for a broken egg to reassemble into an unbroken one?

[polymath257]

The conventional answer is that it would never happen. But couldn't it be the case that, while it would be extremely unlikely for a broken egg to be spontaneously reassembled into an unbroken egg, there's still nevertheless this very tiny tinge of possibility that this can happen (maybe a 1 out of a googolplex probability)?

The overall entropy may be increasing, but I don't see why the atoms that constitute a broken egg couldn't, by sheer coincidence, collect together in a way that the arrangement now constitutes an unbroken egg?

Let's see what our local physicists here have to say.

The notion of entropy is a *statistical* one. In a sense, the second law says that things go from less probable to more probable over time.

But we know of violations of the second law for small systems. The smallness of the system is what makes the probability of violation large enough to expect to be observable.

Let's do a little calculation. Suppose we have a mole of some gas And a container. There are 6*10^23 molecules of that gas. So, what is the probability that they will ALL end up on the left side of the container? it isn't too difficult to determine the odds are about 1 in 2^(6*10^23). This is around 10^(1.8*10^23), which is far less than a googleplex.

A similar calculation would apply to the broken egg, although there are additional dynamical constraints. But, we would be considering the probability that the molecules in the countertop will all direct to launching the egg pieces and the egg into the air in such a way that the egg spontaneously reassembles.

There is more than a mole involved here, but that honestly doesn't affect much in the above calculation. You would have to raise this number to something like the 10^76 power to get to a googleplex.

So, yes, at that level of probability you can expect to see things like eggs reforming, people gasping for air in a room suddenly, etc.