This post is a continuation of my previous post on the reason for the direction of the arrow of time. I also placed a post like this on the Physics Forum because this is, in my opinion, one of the most fascinating open questions for science. So, I'm going to continue this discussion here because somebody on the Physic Forum placed a link to a 1-hr long presentation by Sean M Carroll on the Big Bang and the Arrow of Time. The video is quite interesting to watch, and I think that the lecture does a really good job of raising the question: where does the directionality of the arrow of time come from? My problem is not with his talk per se, but Sean M Carroll seems to be missing something really important. I'll quote a few of his statements below and then discuss the problems with the statements.
--"But the arrow of time is no where to be found in the fundamental laws of physics."
--"The laws of physics do not point in any direction...they are reversible...
play a movie backwards or forwards, and you won't know which way it goes."
The problem with these statements is that they are not correct. Not all of the equations of physics are reversible. For example, the weak nuclear force does not have a time reflection symmetry operator, and because of this, it is not reversible. A movie run backwards or forwards will look very different when the weak nuclear force is involved.
It appears in fact that the weak nuclear force is the cause of the arrow of time. Knowledge of the exact microstate of the universe decreases with time...i.e. the entropy increases because the weak nuclear force adds in a source of randomization because this force of nature is not time reversible.
When talking about dark energy and the accelerating expansion of space-time itself, he also states
--"The origin of the arrow of time is fundamentally due to cosmology."
--"Everything can be traced back to the big bang...(paraphrasing here) Aging, biological life & death, as well as memory, can be traced back to the origin of the universe."
or yet again:
--"Entropy has been increasing because it was low at the beginning."
These statements are completely incorrect. The reason for the increase in entropy is not that it was low at earlier times. If the laws of physics were reversible, then low entropy stays low entropy. The fact that the entropy was low does not imply that it must be higher at a later time. Carroll is making a logical mistake here that I've seen a lot of cosmologists make before.
Here's the analogy: The boundary points of a differential equation do not tell you anything about the equation itself. How would the boundary conditions of a differential equation tell you about what type of differential equation is governing the dynamics of systems inside of the boundary conditions?
While I disagree with the main point he's trying to make. I think that it's an interesting talk because he at least raises interesting questions and admits that he doesn't know everything.
I do agree with his statement, "We do not know why the entropy was low at the beginning of the universe."
And I also agree with these statements, "We are no where near equilibrium."
"It's a story that fits together...but is it right? I don't know."
The story, as told by Sean M Carroll, is not correct because he fails to even mention the weak nuclear force. But that's okay. We're stilling learning a lot about the universe, and we're still learning a lot about the weak nuclear force. We know a lot, but we have a lot more to learn.
What I'd like to reiterate is that the boundary conditions at the start of the universe do not by themselves tell us anything about why entropy increases in the universe.
If the entropy at the beginning of the universe were the number 100, then that does not tell us whether the entropy will remain 100, or whether it is decrease to 0 or increase towards much higher numbers.
Knowing the starting boundary conditions, by themselves, do not tell us about how matter will behave. We also need to know the laws of physics. And as far as we know, the laws of physics are not time reversible because the weak nuclear force is not time reversible. This is a quite interestingly phenomena; one that we are just starting to learn. The hard work will be figuring out the connection between the time irreversibility of the weak nuclear force and the second law of thermodynamics.