Tuesday, May 28, 2013

The "Past Hypothesis" and the Arrow of Time

I've been watching Sean Carroll's lecture series Mysteries of Modern Physics: Time. In general, I would say that it's a good lecture series. I'm a big fan of the Great Courses lecture series concept. Sean Carroll is a great lecturer, and the Great Courses lecture series does a good job of adding in photos and videos to help explain the material. Some of my favorite lectures were the neuroscience lectures, probably because I've never taken a class in neuroscience. However, as a former physicist, it's easy to pick up on the physics mistakes in the lectures. In any lecture series to a general audience, there are going to be mistakes that wouldn't be there if the actually equations were used. I'll point out a few of the mistakes at the end of this post, but the main point of this post is to highlight the general problem I see across the whole set of lectures. The problem is that the "Past Hypothesis" and reversible laws of physics can not alone explain why entropy increases with time. So, I'll try to explain (a) why Sean Carroll thinks that the "Past Hypothesis" is enough to explain the arrow of time, (b) why the "Past Hypothesis" is not enough to explain the arrow of time, and (c) why we actually need a time-irreversible force of nature (such as the weak nuclear force) to explain the arrow of time.

Carroll knows that the weak nuclear force is the only force of nature that is space-time asymmetric. However, in Lecture 7, Carroll unfortunately dismisses the weak nuclear force. "The weak nuclear force has almost no effect on our everyday lives. In fact, it is really weak." 
But the fact that weak nuclear force is weak does not mean that it's not the cause of the arrow of time. There are lots of particles interacting in the universe. The arrow of time can be smaller (i.e. weaker) than the gravitational or E&M forces without causing any concern. In fact, if the gravitational or E&M forces were the cause of the arrow of time, we would have a lot of explaining to do because these fields exist everywhere.
The other reason why Carroll doesn't think that the weak nuclear force is the actual cause of the arrow of time that we perceive is that weak nuclear force (according to him) "is just an arrow in which the rates are higher in one direction than another?" (According to Carroll, the weak nuclear force is not the cause of the arrow of time because asymmetric part of the weak nuclear force is only a small component of the force and very small in general.)

While it is true that the time-asymmetric part of weak nuclear force (i.e. the component of the CKM matrix that is time-asymmetric) is a small component of the weak nuclear force (i.e. of all of the components in the matrix), this doesn't mean that the asymmetric component isn't the cause of the arrow of time. Note that this 1 component in the CKM matrix is the only part of a force of nature that is time asymmetric. There are no components in gravity or E&M that are time-asymmetric. There are components in the strong nuclear force that hypothetically could be time-asymmetric, but experimentally have been determined to be near-zero. And all of the time-asymmetric components of the weak nuclear force boil down to the same time-asymmetric component of the CKM matrix. I do not think that it is a coincidence that there is one arrow of time, that the universe is expanding, and that there is only one component of the forces of the nature that is time-asymmetric.

So, let me rephrase this because it's important to highlight. The time-asymmetric part of the weak  nuclear force is small compared with the time-reversible parts of the weak nuclear force. Think of this as a small drift velocity sitting on top of a symmetric distribution of velocities in a gas. The drift velocity is small compared with the root-mean-square velocity, but this can cause a large macroscopic effect over time as all of particles eventually move in one direction. So, to be precise, it is one of the (relatively small) components of the weak nuclear force that is the cause of the arrow of time. Unfortunately, Prof Carroll focuses on the whole CKM matrix rather than focusing on the 1 component of the CKM matrix that is time asymmetric.

Monday, May 27, 2013

Leonard Susskind: Holograms and Indestructible bits

For those of you who haven't watched this video by Leonard Susskind on Holograms and Black Holes, I suggest watching it (a few times.)
Below are some of my favorite lines from the lecture, as well as some comments on the ideas.



(1) Dr. Susskind has created what he calls the Negative First Law of Physics:
"Bits are indestructible"

By this, he means that information can't be destroyed. To paraphrase how he puts it, "Can you erase a bit?"   Answer: "From the computer..yes. But you eject it out of the computer into the environment, the bit does not get destroyed." This means that information can be spread out or brought together, but it can't be destroyed.

While I completely agree with Susskind's statement that information can't be destroyed, I think that this is just a partial restatement of the 2nd Law of Thermodynamics (as stated by Joe Rosen.) Dr. Rosen stated that "The symmetry group of the cause is a subgroup of the symmetry group of the effect. Or less precisely: The effect is at least as symmetric as the cause." According to Dr. Rosen, the symmetry group of the universe increases or remains the same. In fact, the symmetry group of the past is embedded into the symmetry group of the future, and hence you can't destroy information. This is why I think that Susskind's Negative First Law is just part of the Second Law of Thermodynamics...which is really just the Symmetry Principle, as stated by Joe Rosen.

But there's more to the 2nd Law of Thermodynamics than what is stated in Susskind's "Negative First Law." The 2nd Law states that the symmetry state of the universe can increase. This means that we can increase the amount of information. Second Law of Thermodynamics is saying that the information in the universe is non-decreasing with time. The negative first law states that information can't be destroyed, so when you combine the two (as in Joe Rosen's formulation of the 2nd Law), you get the following: "Information in the universe can't decrease with time and can't be destroyed." New information can be generated, but old information can't be destroyed. Information might be hidden from us (such as inside of a Black Hole.) But the black hole eventually will evaporate. When it evaporates, it releases the information it grabbed when it "ate my homework" plus it also releases more information about what happened inside of the black holes during its irreversible lifetime. Just like the information in the thermal energy ejected from your computer screen into the environment when you go to a new website, the information ejected from a black hole is in a form such that it is virtually impossible for us to "recreate our homework after the black hole eats it."