[phn]

So, layman's question about black holes, almost 100% sci-fi derived.

Starting from the time mechanics shown in, e.g., Interstellar. If when you're near a massive black hole time passes differently (more time passes away form the hole, so to speak), couldn't it be said that the regions near and far the black hole are drifting apart in the "time dimension"?

If we take the black hole to be an extreme case of that, isn't the black hole a region that is drifting away so "fast" that light isn't fast enough to reach "us" on the outside?

In that case, there would be no paradox, right? Whatever is inside the black hole is still there, but with no way to communicate.

[philipov]

> isn't the black hole a region that is drifting away so "fast" that light isn't fast enough to reach "us" on the outside?

I've seen some models of black holes that are similar to this. Specifically, what is happening in those models is that the space inside the event horizon is growing faster than the speed of light, so more space is created than light can traverse.

This is the inverse of how cosmological horizons work. The reason we can only observe a limited portion of the universe is because objects are uniformly moving away from all other non-gravitationally bound objects. Space is being created between them. The farther you look, the faster galaxies are moving away from us because space is being created at every point in between. If you try to look far enough, the speed that objects are moving away from us becomes faster than the speed of light: space is being created faster than light can traverse it.

This sort of faster-than-light travel doesn't break the relativistic speed limit because these objects aren't inertially accelerating inside their frame of reference, the frame of reference itself is expanding.

[hinkley]

> space is being created faster than light can traverse it.

Which is precisely the sort of behavior one might expect if they lived inside of a black hole.

[alasdair_]

Isn’t this what is happening in our universe as well? Space is expanding faster than light can traverse it?

[hinkley]

I am at this point waiting to see someone prove that we aren't.

Though ultimately I don't know if it matters. What we have is so vast that we can't really fathom it ending except in the abstract. No matter how big a ripple I make in the pond it's not going to matter in a couple billion years. I content myself by thinking in centuries.

[defrex]

This is a reasonable conceptualization, IMO. However, the problem isn't that we can't access the information in a black hole (there are other places in the universe where information becomes inaccessible).

The problem is that black holes evaporate. If the particles released via evaporation don't contain the information about the particles that entered, information is lost when the black hole is completely gone.

The proposed solution is that the information is encoded onto the surface of the black hole and thus into the hawking radiation being released from that surface.

[eloff]

This idea in physics that information is conserved, neither created nor destroyed, just transformed seems awfully similar to a computer to me. A classical computer is not the right metaphor really when you think of the universe as a possible computational process, but the parallels are striking to me.

[simonh]

I suspect it may be just necessarily true that information is preserved in a consistent universe. I don't know though, maybe someone could come up with a model for a consistent universe with information loss, but it seems to me that would lead to physically possible states that are not derivable from consistent laws of physics.

[causasui]

Physics layman, but I agree as a computer scientist. It also sometimes feels like there are "optimizations", e.g., delayed-choice quantum erasure (https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser)

I'm open to the idea that it's just me projecting what I understand onto what I don't.

[macrolocal]

Nb. wave function collapse messes with this, and a computer would use something like lazy evaluation to avoid generating the Everettian multiverse.

[pygy_]

I'm tying loose ends in my head that probably have long been tied in other ones...

Reading this next to the comment making a parallel between the black hole event horizon and the cosmological horizon...

Wouldn't this give credence to holographic model of the universe?

Could the so-called heat death of the universe and black hole evaporation be identical phenomena seen from either the inside or the outside of the boundary?

[marcyb5st]

The problem is that black hole evaporates due to Hawking radiation, which is a special case of Unruh radiation. This radiation is independent of what falls into the black hole, but just its size (and hence mass). This is the paradox. Two black holes of the same mass can be created with completely different matter and they would radiate exactly the same way and in so doing destroying the quantum information of matter they are made of.

Your point of view/theory would hold if black holes were eternal, but they probably are not if our understanding of physics is correct. In fact, if black holes "die" then the quantum information has to be released back into the universe somehow. This paper proposes a mechanism for that to happen.

[kstrauser]

Why does that information have to be released? To my naive layman's thinking, if you told me that a black hole permanently destroys that information, I'd think "sure, it destroys lots of other things, so that makes sense". What problem does it cause if we believe that the information is gone forever?

[amluto]

Because quantum mechanics _really_ does not like destroying information. Mangling information beyond recognition is just fine, but the laws of quantum mechanics are very insistent that, if you have a complete description of the state of the universe, you can solve the equations backwards and figure out what happened in the last. When you throw in a black hole following Hawking’s rules, or any other device that irretrievably chews things up and spits them out in a way that can’t, even in theory, be undone, quantum mechanics breaks.

[kstrauser]

Got it, thanks! That seems unintuitive to me (which is pretty much the summary of QM as far as I can tell), but I trust that some pretty clever people are convinced of this.

[hollerith]

The problem is that black-hole evaporation is a high-level description of many "fundamental" events, and at the level of fundamental physics, there is no known process that destroys information.

Or so popular-science articles tell me.

[naasking]

All information is physical. The information you're reading right now could conceivably be stored in electron charge, or spin, or polarization on optical storage, etc. Information simply must have some physical form.

Accepting the destruction of any information means that none of the physical symmetries we observe actually hold up, like conservation of momentum and energy. That would change literally everything.

[drdeca]

I believe the idea is that in quantum mechanics, time evolution is described by a unitary operator, and because it is unitary, it must have an inverse, and, therefore, the state after must determine the state before.

Which, of course, reduces the question to "why does time evolution have to be unitary?"

And, one definition of what it means for an operator U to be unitary, is that it preserves inner products, and is surjective.

Why should it preserve inner products?

Well, a state should have norm 1, i.e. the inner product of it with itself should be 1, and the state in the future should also have norm 1. (this 1 can be thought of representing the probability that "something/anything happens", which should always be 1.) And also, the time evolution should be linear (that things are done with linear operators is nearly the core assumption of QM ime ), so therefore it should also preserve the norm of other vectors. And, the polarization identity allows one to recover the inner product operation from a norm which came from an inner product,

In what follows, "<" and ">" are angle brackets, not less than or greater than signs. also, by ||x||^2 I mean the norm squared of x, i.e. the inner product of x with x, i.e. <x | x> . The polarization identity (a theorem of math, not specific to physics) states that

<x | y> = (1/4)( ||x + y||^2 - ||x - y||^2 - i||x + i y||^2 + i||x - iy||^2)

So, in particular, for some linear operator A,

<A x | A y> = (1/4)( ||A x + A y||^2 - ||A x - A y||^2 - i||A x + A i y||^2 + i||A x - A iy||^2) = <A x | A y> = (1/4)( ||A (x + y)||^2 - ||A (x - y)||^2 - i||A(x + i y)||^2 + i||A(x - iy)||^2)

And, if A preserves norms, i.e. if for all x, ||A x|| = ||x|| , then therefore

<A x | A y> = (1/4)( ||A (x + y)||^2 - ||A (x - y)||^2 - i||A(x + i y)||^2 + i||A(x - iy)||^2) = (1/4)( ||x + y||^2 - ||x - y||^2 - i||x + i y||^2 + i||x - iy||^2) = <x | y> .

So, by the polarization identity, if a linear operator preserves norms, it preserves inner products.

So, if you accept the "time evolution is linear, and the state should always be a unit vector in a Hilbert space", then it follows that time evolution should preserve inner products.

The only thing remaining is, I guess, the assumption that time evolution is surjective. I.e. for any state, there is some state which should be able to lead to it.

I suppose one could question this assumption?

But I don't think giving this up would result in allowing the loss of information, because these requirements still imply that time evolution should be injective. If two states x and y were both sent by time evolution to the same state z, then, if x and y are not equal to each-other, then x-y is not zero, and it can be re-scaled to have norm 1, (specifically, giving us (x-y)/||x-y|| ) and be a valid state,

and the time evolution would send (x-y)/||x-y|| to (z-z)/||x-y|| = 0. Which would mean, it would send a valid state to, uh, nothing. This contradicts our assumption that it preserves a norm of 1. To interpret this a bit, if it did fail to be injective in this way, sending both x and y to z, then if the current state were (x-y)/||x-y|| , then in the future, after applying the time evolution operator, the probability that "anything" would be 0, which is absurd (and also contradicts our assumption of preserving the norm).

So, if [the state is represented by a vector in a Hilbert space, and the Born rule applies for probabilities, and time evolution is linear], then time evolution has to preserve the inner product and therefore also be injective.

This I think basically justifies the "information is preserved" idea.

You might ask "ok, how would you modify quantum mechanics in a way that did allow time evolution to not be injective?" and, I'm not sure what the appropriate way to do that would be.

Hm, I suppose maybe you could like, use states which are technically different, but not in ways that any observable could ever (even theoretically) distinguish between?

(are selection sectors relevant to that? I'm not sure.)

[kstrauser]

Awesome, thank you for that!

And in my nightmares tonight, I shall be required to write that from memory on a chalkboard in front of the class.

[macrolocal]

Well, objects falling into a black hole can reach the singularity in a finite amount of time. So you're going to have to enrich these singular spacetime points with a lot of extra structure if you want whatever passes through them to still exist. ¯\_(ツ)_/¯

To wit, you can imagine classical black holes as pulling whatever's near them into the future. The effect is so severe when you pass the event horizon that escaping the black hole amounts to traveling backwards in time. The effect is so severe when you reach the singularity that the entire timeline of the universe is in your past. So the singularity itself is more like an infinitely distant future than a point in space, with the caveat that the black hole slings you toward it with enough acceleration that you either actually reach it or something about this classical picture breaks down.

[saalweachter]

I feel like there's something so scary about falling into a black hole, literally unable to escape, that we just really, really want it to be "survivable", somehow.

Which is kind of funny when you consider that no one would expect to survive falling into a star, but we don't grasp at straws the same way to say, "Oh, you wouldn't actually be immolated, the solar wind would blow you back into space first."

[macrolocal]

To be fair, virtually any place in the universe, except where you happen to be right now, is probably not survivable.