The Biggest Ideas in the Universe | 20. Entropy and Information 

More like entropy gets to us, sooner or later...

How do you have gas presure without the necessary antecedent of a container if entropy is still a thing?! Space is fake!!!!

@@TheOne10525 Might be funny if you were trolling... this is a long way from your flat-earth, conspiracy theory, biblical literalist content that you normally consume. What are you doing here? Seriously: if you came to learn, don't heckle with your FE nonsense. If you came to ask serious questions from a different crowd than you normally hang with, then ask on a post for that purpose rather than non-sequitor replies to other questions, and be receptive to actually getting (and understanding) the answer rather than just babbling the same stupid thing over and over no matter how many times it's been explained. Go pick on Thunderf00t: you'll ether learn or be destroyed. Either outcome is fine as far as the rest of us are concerned.

1. Yeah... the universe does that a lot. ;) As in most cases when questions start with "But the universe does X, doesn't that violate Y?" the answer is likely "Because the universe is expanding, so NOT Y". For example, as light redshifts as it travels across vast distances, it loses energy. But that energy doesn't _go_ anywhere, so doesn't that violate Conservation of Energy? Well, the universe is expanding, and that means it is a non-inertial reference frame, so energy is not conserved. In this case, I suspect that something similar could be said, along the lines of that because the universe is expanding, it _acts as if_ it were not a closed system, _even though_ it may not have anything outside of itself with which to interact and thus is definitionally a closed system. Even worse, the _observable_ universe's expansion is accelerating, which means that _it_ is _definitely not_ a closed system; the cosmic horizon generated by that expansion has stuff flowing across it, "exiting" the observable universe all the time. Whole galaxies disappear beyond it, in fact, so the observable universe is _certainly_ not a closed system. 2. I think this is a result of Dr. Carroll taking some shortcuts since he didn't want to go into too much detail. I suspect it isn't _just_ the anthropic principle that refutes the recurrence objection, but rather the combination of the anthropic principle and the Copernican principle, which together say that we must necessarily be not only in a phase of the universe in which we can exist, but with overwhelming probability we must also be in a _typical example_ of such a phase. Since the overwhelmingly large probability for such phases is that you are a Boltzmann Brain that just popped into existence as you are reading this, with the memories of what came before already in place, and will perish immediately after reading this, yet that is clearly not the case, then the anthropic principle alone doesn't completely defeat the recurrence objection.

fantastic. It seems so simple...

Good question, I would also like to know the answer.

Also your videos are amazing

that's the reason that inflation was necessary

Well, thermodynamic beta has units if reciprocal of energy, which if you look back at Sean's earlier lecture explaining natural units, is the same as space and time. I'm not sure how they equate "bytes per joule" with just "per joule" in two different measurement systems. But having done so, you can solve for bytes and make the similar correspondence for space and time.

Yes, that's what he said. When the universe is cooler and more rarefied, being spread out increases entropy again. Hard to believe? Well, think about that big black holes won't decay until the universe is much older, as their temp is lower than the CMB. They actually are growing by absorbing CMB photons. It's not _until_ the outside is lower entropy that the BH starts to evaporate.

In the microcanonical ensemble, a macrostate is defined by a value for the total energy, so the subset is defined by the equation H (p, q) = E, for some fixed energy E.

@@Majoen1998: Okay, so it's more like a foliation. So the "discontinuity" of S that prof. Sean Carrol hinted at some point in the video probably isn't a thing, in this case.