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If I break an egg, how broken it is depends on "when" I am not "where" I am. Why is the time dimension special?

JohnnyD
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  • how broken it is doesn't depend on "when" you are. The only thing that the second principle of thermodynamics says is that if your egg gets broken (whenever you want to break it), it won't repair itself spontaneously as time goes on. – gatsu Aug 05 '14 at 12:26

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First off, there are a couple of reasons why we don't have complete symmetry between space and time:

  1. We have 3 spatial dimensions and only one timelike one.

  2. The particles in the standard model have timelike or lightlike world-lines; as far as we know, there are no tachyons.

For these reasons, it only makes sense to talk about laws of physics that take initial conditions on one spacelike surface and predict the evolution of the system from there. We don't have laws of physics that can take data on a timelike surface and evolve that outward in space.

The other issue is that to get the second law, you need two ingredients: (1) some sort of state-counting that says there are more way to make some macrostates than others; (2) something that breaks time-reversal symmetry. (See this answer.) What breaks time-reversal symmetry in our universe is that, for reasons unknown to us, we had a low-entropy Big Bang. This necessary fact about cosmology also breaks the symmetry between space and time. The Big Bang was something that happened at a certain point in the past, everywhere; it's not something that happened at a certain point in space, at all times.

Community
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  • I know the argument about the entropy at the Big Bang being low but it always kind of confuses me...I mean, the only thing we know is that it was, according to our current wisdom, less or much less than today. Why is that a mystery, it is a fact no? Boltzmann explained why this kind of stuff should be the exception and not the rule. Also, I am a bit dubious when it comes to relating the second law of thermodynamics for a broken egg with its application to cosmology, the two descriptions involved seem very different and may relate to two different entropies. – gatsu Aug 05 '14 at 20:19
  • Pick any measure of entropy. Where it increases, it does so only over time, never one of the spatial dimensions. Why is the time dimension special? Is it a necessary property of the geometry of the universe and do we know why our universe has the geometry it does (rather than, say, a purely euclidean one). I think that the idea that big bang started at one point in time everywhere rather than at all times in one point is a starting point. – JohnnyD Aug 06 '14 at 07:14