I’ve often heard this said in a physics context (most recently I heard it on an astronomy podcast which discussed the concept in relation to black holes). However, I’ve never quite understood it.
What, exactly, is meant by “information” in this context?
http://en.wikipedia.org/wiki/Physical_information
Which seems to be another example of using a common English word to refer to a concept something in quantum physics which can actually only be described mathematically, but that whole article is a bit above my head.
This previous thread: ‘Can “Information” be destroyed?’ has quite a nice discussion of the subject, I think.
If you take a can of 1000 balls in a known original configuration, and spill it on the floor, entropy will increase and the balls will become disordered but all the information explaining how they got that way, which could be reversed to put them back in the original order, still exists. It may not be written down - it may be impossible to record or to even know it, but it still exists. That info can be reversed, and energy can be applied to put the 1000 balls back into their original configuration.
Information exists (may be 10,000,000 variables) to calculate what the weather was like on earth 3 million years ago. That info may be impossible for us to know, may be “lost” to us in that sense, but it still exists. It’s never destroyed.
Hmmm. Still not getting it, I’m afraid. If it’s impossible to record or know, where does it exist?
In the microscopic description of a system – typically, there are many possible microstates that lead to the same macrostate, i.e. that ‘look the same’ to us. Take the atoms in a volume gas – you can exchange atoms with one another in a great many ways, while it still looks like the same volume of gas to us – possessing the same volume, temperature, and pressure. Essentially, in quantum mechanics, the description of this microstate is always preserved, such that given the microstate at some time always allows reconstructing the microstate at some prior time – in this sense is the information stored within it never lost. There’s more detail in this post, if you like.
Ahh. Yeah. That post just makes things worse, not better!
I really am an ignoramus here - but even terms like “miscrostates” and “macrostates” mean nothing to me. Is it possible to explain it in real layman’s terms?
I work in biology and computer science, not physics, but my friend’s physicist dad explained it to me once as: if you burn a page of a book, the information is lost as far as humans are concerned, but it isn’t really destroyed – it’s just scattered in the form of ash particles, gas molecules, etc. If you had access to all the information that was occurring at the time the page was burning – where each atom was going, what photons were being created or interacting with the paper and ink as it was burning, gravitational waves (maybe?) that were passing through, etc., you could reconstruct the content of the page.
But in practical terms, that’s impossible because a good chunk of the information is traveling away from us at light speed and can never be retrieved (barring inventions that might as well be magic as far as we’re concerned now).
I meant to post this in that last thread, mentioned above in post 3 by Half Man Half Wit, but I never got around to it; anyway, I wanted to ask, how accurate was his summary (or at least my memory of it)?
IIRC, isn’t there a considerable group of physicists who disagree with that postulate?
I think so. I seem to remember that idea from one of Greene’s popular books. I may be misremembering, since I read way more “popular” science books than a layman should (and they start to blur together), but I’ve read at least a couple that I think remember arguing that information is destroyed in a black hole. If pressed, I guess I’ll have to go to my kindle history to piece it all together.
/Doesn’t pretend to understand it all, but enjoys it.
Yes, since the only thing that leaves a black hole is randomized Hawking radiation.
And this is the apparent problem that’s lead to the theory that the event horizon of a black hole is coated with a 2D representation of all the information that enters, preserving the information but in an inaccessible way.
Which, inexplicably, annoys me to no end.
Also, here’s a really, really bad metaphor but which kinda illustrates the point.
Imagine the entire universe is one of those zen sand gardens, with a single rock. When you push the rock around, the little trails left indicate the direction and speed the rock is pushed.
Using that “information,” the details of the original position of the rock can be inferred. Even if you push it around a whole bunch, if you perfectly understand the physics of the system, the trails could always be reconstructed.
On a very, very tiny scale, all the matter in the real universe has aspects similar to those sand trails that could, in theory, be used to reconstruct the original positions of the particle. It’s infinitely tiny and infinitely subtle, but it’s there.
Another approach (that I think is even less accurate) is this: if you could “freeze” the entire universe as an EXACT snapshot and have an understanding of the states of every tiny particle, you could “rewind” the world to any prior point because every interaction is ultimately determined by predictable systems. In this analogy, the problem with black holes is that a true theoretical singularity can’t be “rewound” since, even with a perfect snapshot, there’s no information to indicate the direction or size of captured particles.
OK, let’s say you’ve got a container of gas. The macrostate of the gas would be something like “Two liters of helium in a spherical container, at a pressure of ten atmospheres, and a temperature of 297 Kelvin”. Pretty much anything about the gas that you could measure with human-scale instruments, you could derive from that fairly small amount of information. There are some things I didn’t give explicitly, like the total mass of the gas, but you could calculate that from the things I did give.
But of course, that’s not a complete description of the gas. In principle (though of course, not in practice), I could tell you the position and velocity of each atom within that container. That would take an awfully long space to describe-- In fact, it’d take more information to even give the position of a single atom than it did for the whole macrostate, and there are over 10[sup]23[/sup] atoms in there. This full, detailed description is the microstate. Of course, if I did actually give you the full description of all of the atoms’ motions, you could determine the macrostate from that. But there are a very great many different microstates that would all give you the same total pressure and temperature-- In other words, any single macrostate corresponds to a very large number of microstates.
Incidentally, you’ve heard of entropy, I imagine? It’s often described in layman’s terms as a measure of the amount of disorder in a system. But what it really is, ultimately, is just a count of how many different microstates correspond to any given macrostate. The number is pretty much always going to be huge, but it’s huger for states we’d consider “disordered”.
So why doesn’t the randomness of quantum physics play into this? You can only make calculations on events that happen in a predictable manner, but according to quantum physics, nothing is completely predictable.
This is what I was just about to ask. The above only seems to work in a completely deterministic universe, if I’m understanding it correctly. But if God does indeed play dice with the universe, which seems to be the case on at least some level, so far as it’s always been explained to me, doesn’t that negate this idea that information cannot be lost?
Aha! Thanks, guys! I think I’ve got it!
This is a question about the interpretation of quantum mechanics. Fundamentally, if there is a wave-function collapse, then this collapse is indeed a mechanism that destroys information, ‘forgetting’ about the superposition the wave function was in prior to measurement. But quantum mechanics can be interpreted in such a way that information is always preserved, too – if the wave function collapse is only apparent, due to a decoherence process, or in something like the many worlds interpretation. One can make an argument that such interpretations are more parsimonious, and thus should be preferred, as no ‘extra’ mechanism to make the wave function collapse needs to be introduced – you need nothing but the ordinary evolution of quantum mechanics, which always preserves information.