0

So I don't understand why it's surprising that the universe in an extraordinarily low-entropy state right after the big bang?

The way I see it the second law of thermodynamics forbids almost anything else. The second law and continuity give time a direction. The second law is:

$$ \Delta S_{universe} \geq 0 $$

The $y$- axis is entropy and the $x$- axis is time. Now one may argue why not analytically continue the line for all eternity?

enter image description here

Consider the below figure where we extend the line and when the entropy meets the $x$ - axis we label it $S(T) = 0$. Take $2$ events such that $t_1$ and $t_2$ where:

enter image description here

$$t_2 < t_1 \leq T $$

What is the change in entropy?

$$S(t_1) - S(t_2) < 0$$

This is forbidden as the second law recommends. For a non-caricature version of the real thing see below:

enter image description here

Now the only another alternative where $S$ remains constant $$S_{universe} = \text{constant}$$ (again in such universes the constant could be of low entropy).

So the question isn't why is the initial condition of low entropy but rather why don't we observe a heat death as the initial condition? And then we would if we could exist we might argue well why didn't the universe begin with low entropy? (and I'm not sure why at this point this isn't a silly question)

Qmechanic
  • 201,751
More Anonymous
  • 1,309
  • 1
    You have to realize that the point of Boltzmann's argument for a start of the universe in a low entropy state is to explain the second law of thermodynamics in terms of statistical mechanics. You can't assume the second law when that's what you try to explain. – Raskolnikov Apr 09 '23 at 04:31
  • Also, this question is a duplicate and I think the accepted answer should be satisfactory to you. But if not, you can modify your question here to ask about it. – Raskolnikov Apr 09 '23 at 04:35
  • I will edit the question but I'm on my phone but heres my contention. Even in GR there are processes which are time irreversible like formation of a blackhole, etc. Further this whole problem only comes when one assumes mechanics is fundamental and there are no continuity issues. If one were to assume thermodynamics was fundamental there is no problem: for example in bbgky hierarchy the assumption of molecular chaos or uncorrelated velocities leads to the increase in entropy. – More Anonymous Apr 09 '23 at 05:35
  • I guess if you make those assumptions, there is no problem. But this is an unorthodox view. The mainstream accepted view is that the second law is a law of statistical nature. – Raskolnikov Apr 09 '23 at 06:06
  • The universe wasn't in a low entropy state. It was in a thermal state at the beginning, i.e. in almost perfect equilibrium. The problem with your argument is that it assumes that the universe is a closed system under the terms of classical TD. It isn't because it keeps creating new space all the time. – FlatterMann Apr 09 '23 at 09:54
  • @FlatterMann https://www.mso.anu.edu.au/~charley/papers/Chapter22Lineweaver.pdf Page 417 : Expansion of the universe is Isentropic – More Anonymous Apr 09 '23 at 13:25
  • @MoreAnonymous How are you even going to do entropy without energy conservation and with most of the universe decoupling all the time? That doesn't make any physical sense whatsoever. – FlatterMann Apr 09 '23 at 18:03

0 Answers0