Is the Conservation of Information a Valid Principle in Physics?

[Sandor]

I have heard many times in those PBS or BBC dumbed-down-science-for-ordinary-dolts shows (unfortunately they're the only sources of this sort of information I have) that there was a black hole paradox at one point, wherein some people were deeply concerned over whether black holes destroy information, and eventually they decided that they don't because a black hole is actually not really quite a black hole and can't be distinguished from a bunch of mass that hasn't quite fallen in through the depth that would be its event horizon and so after the black hole expires due to the Hawking radiation effect, the information is freed back into the universe. Or at least that's what I thought of when I first heard about the paradox and then when it was resolved, it sounded like the explanation was consistent with what I thought of, but it involved multiple universes or something, so maybe not.

Anyway, the thing is, I never understood why this was supposedly a problem, since when I took physics, long, long ago, no one ever said anything about the universe requiring that information be conserved. Energy is conserved. Momentum is conserved. Information, no one ever talked about. Well, they DID talk about information, of course, but they called it entropy. And entropy, meaning the disorder of a system and requiring a certain amount of information to describe (it takes few words to describe a perfect crystal, namely, but many to describe the location of atoms randomly strewn about), always increases. That's the second law of thermodynamics. So my question is, did someone connect the dots wrong here? Just because the entropy of the universe never decreases, that doesn't mean information is never destroyed. You can replace 1 bit of important information with 2 bits of trash that say nothing about what was contained in that one bit of information before it was lost. Just like I can overwrite a 1-kilobyte file with a 2-kilobyte file which had absolutely nothing to do with the 1-kilobyte file. So who decided that information was never destroyed? Does anyone actually have any observations to back up this ridiculously massive assertion, or is it just wishful thinking? And if it is the former, why wasn't I taught this back when I was in school? Or is this something they only decided on in the 80s or 90s?

Another question, now that I'm thinking about it. These same dumbed-down physics shows I've seen have said that time travel wouldn't violate the laws of physics, which is why it is supposedly an open question as to whether or not it is possible to go back in time. But if all reference frames are valid, then in the reference frame of the time traveler, whose clock ticks ever forward and simply ends up in the universe at an earlier time according to some other observer, the universe has, as HIS clock ticked forward, regressed to a more ordered state. Thus this violates the second law of thermodynamics, as according to at least one observer, the time traveler or someone who stayed in the normal flow of time, the universe was less ordered at one point in time and more ordered later. How can they say it doesn't violate the laws of physics when it obviously violates the second law of thermodynamics? Is the second law of thermodynamics not considered to be a law of physics?

 

[mikeph]

My argument for this would be that since the laws of physics are time-reversal invariant, any piece of information in the past can be retrieved with knowledge of everything in the present, just as information in the future can theoretically be retrieved. If you have a mechanism which truly destroys information, then I think this would imply the laws of physics are not time-reversal invariant.
"if all reference frames are valid"

More precisely, all reference frames where the magnitude of the relative velocity |v| < c in constant are inertial frames, and the laws of physics in them are identical. There is no frame of the time-traveller that I know about.

PS. I wrote a load about the 2nd law, then realized it was not really relevant, but I didn't want to get rid of it so here's my interpretation of it based on statistical physics:

And I am not 100% on this but the second law is basically a statistical law governing the macrostate of a system of (for example, in a gram of metal) 10^22 microstates. The simplest is the paramagnet, if the magnetic moment of every 10^22 atom is aligned in the same direction, this system has minimum entropy, if about half are aligned up and half down, then this is maximum entropy. It is much more likely that the system has about 50% up than 100% up, however, it is exactly as likely that the system has 100% up, as it has" up,down,up,down,..." in that exact configuration. The entropy is higher only because there are many more microstate configurations of individual atoms which all correspond to the macrostate: "half up", whereas there is only one which corresponds to "all up".

Basically, if the entropy decreases it is not a disaster, just incredibly unlikely event. You are going to win the lottery one time in 10^12, but the chance of your numbers coming up are identical to that of the person who does win, so it's not a disaster to the laws of physics if you do actually win.

 

[Sandor]

Ummmmm... so your argument that information about the past is preserved is based on the assumption that information from the future can be retrieved? But whoever said that? That's an even bolder statement! That's kind of like being handed the task of proving aliens exist and going about it by trying to prove that they're abducting people and probing them. True, that WOULD prove it. But you're trying to prove something that might be true by using it as a consequence of something that definitely isn't true. You're claiming that this is a deterministic universe then! Or to quote someone else, you are saying that god does not play dice with the universe. So I guess Einstein said that. But it was his most famous mistake. This argument would work great in saying that the future can be predicted if the past can be reconstructed. And then you can further make the argument that since the entropy is higher in the future, it requires more information to describe it than there exists in the universe today and therefore the universe cannot be fully predicted (not to mention there's all that stuff about quantum mechanics saying that the future CAN'T be predicted) - thus if things are perfectly symmetric to time reversal, then information about the past can't be retrieved (postdicted?) either since it's easy to see why the future can't be predicted. Of course this falls apart if you don't assume that all the laws of physics are the same in time reversal. Obviously the second law of thermodynamics isn't the same in time reversal. The inequality points the other way. And I was under the impression that the second law of thermodynamics was not merely a statistical thing but only appears to be so superficially. Well, if the entropy of the universe can go down, then information can DEFINITELY be destroyed. Because then you're talking about overwriting a 2 kilobyte file with a 1 kilobyte file. Overwriting a 1k file with a 2k file, the 1k file might be contained in the 2k file, but with the other way around, you can be sure information was lost. Unless you're about to suggest a cosmic version of winrar. That's a joke. Talking about true entropy, that measures how much information there would be after the best compression. And that's where your magnet example fails, by the way. All up or all down or alternating up or down, these are highly compressible states. True, flipping a coin and getting heads 100 times has odds of 1 in 2 to the -100th power. Just as flipping a coin and having the result be any particular random sequence, or the first 100 digits of pi in binary. The difference, however, is the kolmogorov complexity. The entropy is highest when it is random because nothing can compress that information down in any way. At any rate, I certainly don't see how both of these statements could be true: 1. time travel doesn't defy the laws of physics 2. information is preserved as time passes. If time travel is possible than there is no universal agreement of "before" and "after" and therefore no universal agreement of "as time passes" and so information must be preserved in both temporal directions, but since entropy is the total quantity of information, that would imply that the entropy of the universe never increases OR decreases, but it DOES.

Well, I never said that the time traveler occupies an inertial reference frame. He's sitting in a closed timelike curve. That means he leaves his friend behind (say his friend is a girl so I don't confuse things by overusing the pronoun "he"), his clock ticks forward, and then he meets up with his friend, and while his clock shows a later time than in their first meeting, hers shows an earlier time. To her, the first meeting happened second and the second meeting happened first. And if they were both making observations, surely one of them would see that the universe has become more ordered with the passing of time.

 

[Sandor]

Would someone smarter and wiser than me answer my question already?

Why do I keep hearing about information never being destroyed? Why do these people say time travel wouldn't violate the laws of physics when it would definitely violate the 2nd law of thermodynamics? As sketchy as these ideas are on their own, they certainly are at odds pretty strongly against each other. In other words, in a universe in which time travel is possible, information very definitely can be destroyed. So someone's wrong about something here.