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How do black holes destroy information and why is that a problem?

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Re: How do black holes destroy information and why is that a problem?

#81

Post by DiogenesKynikos »

openasocket wrote: post #69

The other major example of a time-irreversible operation/object is much more mundane: the collapse of a wave function. I've never been able to find a decent layperson's explanation of what the wave function collapse really means, and why physicists seem to have no issue with it being time irreversible but seem quite concerned with black holes

It is a problem. Quantum mechanics, as it's normally taught, basically has two components:

1. Schrödinger's equation, which governs how the wavefunction (or quantum state) evolves in time. This equation is time-reversible: given a state at time t, you can calculate what the state was at time t-T. Technically, that means that the "time evolution operator" is invertible. All the information about the history of how system's state is contained in the present state. No information is ever destroyed.

2. Observation. A quantum state looks like a_1 * psi_1 + a_2 * psi_2 + ... + a_n * psi_n, where psi_i are all the possible states of the system and a_i are complex numbers called "amplitudes." When you observe a state (I'm obviously leaving out some mathematical details here, so anyone with physics knowledge please forgive me), you observe it to be in one of the possible states, psi_i, with i between 1 and n. The probability of observing it to be in state i is proportional to |a_i|^2. This operation destroys information, because the state collapses to psi_i, and all the amplitudes, a_j, j≠i, are lost. You can no longer reconstruct the previous state of the system.

I think most physicists who "seriously" think about quantum mechanics do not believe that step 2 above actually happens. It is a simplification of a much more complicated process called "decoherence." In order to understand decoherence, you have to change your perspective on what observation means. If you treat the observer as a system governed by Schrödinger's equation, which interacts with the system that's being measured, you find that the observer becomes entangled with the system under observation. The observer ends up in a superposition of states, each of which has observed a different outcome. It appears to each state of the observer as if there has been wavefunction collapse, but there actually is a larger quantum system containing both the observer and thing being observed, in which no information has been lost.

The theory of decoherence and the "many-worlds interpretation" began to be developed in the 1950s by one of Wheeler's students, Everett. Somehow, it hasn't really made it into undergraduate physics yet, and most physicists can get by without thinking too deeply about what observation means. You can do most calculations assuming wavefunction collapse happens.

Re: How do black holes destroy information and why is that a problem?

#82

Post by aeternum »

maffydub wrote: post #68

(I am not a physicist.) One thing I've struggled with around black holes is what it means for anything to fall into a black hole. From a reference frame outside the black hole, observing an object falling into the black hole, don't we observe time slowing down as the object approaches the event horizon? In this reference frame, does it ever cross the event horizon, or does it just asymptotically approach it? If it do…

There is a somewhat recent theory that supports this idea. It is unclear whether or not things actually fall-in, but the idea is that the entire surface is a hologram, and the surface alone is sufficient to describe the entire contents. (Thus preventing any information loss).

Much better described here:

https://www.youtube.com/watch?v=2DIl3Hfh9tY

Re: How do black holes destroy information and why is that a problem?

#83

Post by maffydub »

jadams5 wrote: post #70
maffydub wrote: post #68

(I am not a physicist.) One thing I've struggled with around black holes is what it means for anything to fall into a black hole. From a reference frame outside the black hole, observing an object falling into the black hole, don't we observe time slowing down as the object approaches the event horizon? In this reference frame, does it ever cross the event horizon, or does it just asymptotically approach it? If it do…

(also not a physicist) I think you're correct that objects falling into a black hole never cross the event horizon from our reference frame, but at the same time the light from the object red shifts towards zero energy as it approaches the event horizon as well.

Thanks!

Does the fact that the light red shifts towards zero energy mean that the information has been lost, or just that you can't observe it _at_the_moment_?

If the black hole then shrinks due to Hawking radiation, what happens to the object that _never_quite_fell_into_ the black hole?

If it hasn't yet fallen into the black hole, presumably its light becomes slightly-less-red-shifted once more, meaning that you can observe its information again?

Re: How do black holes destroy information and why is that a problem?

#84

Post by maffydub »

aeternum wrote: post #82
maffydub wrote: post #68

(I am not a physicist.) One thing I've struggled with around black holes is what it means for anything to fall into a black hole. From a reference frame outside the black hole, observing an object falling into the black hole, don't we observe time slowing down as the object approaches the event horizon? In this reference frame, does it ever cross the event horizon, or does it just asymptotically approach it? If it do…

There is a somewhat recent theory that supports this idea. It is unclear whether or not things actually fall-in, but the idea is that the entire surface is a hologram, and the surface alone is sufficient to describe the entire contents. (Thus preventing any information loss). Much better described here: https://www.youtube.com/watch?v=2DIl3Hfh9tY

Good video - thanks!

I didn't quite follow how information came back out of the black hole as it shrank - is it "encoded" on the Hawking radiation?

Re: How do black holes destroy information and why is that a problem?

#85

Post by mannykannot »

aserafini wrote: post #80
mannykannot wrote: post #40

Earlier quoted context omitted.

Ha! I had not looked at it that way before. Insofar as addition is an abstract representation of merging two collections, we are abstracting away the information that links each element of the resulting collection to the one it came from.

Isn’t this exactly the same for subtraction, multiplication and division?

Considering integer operators specifically: in subtraction, you partition a collection and then discard one part. Multiplication is more abstract, as one of the operands denotes the number of applications of an operator (addition), and in division, the result is a count of the number of applications of a subtraction. I'm not sure if that can be called the same as addition in this regard, but they all lead back to that case.

Re: How do black holes destroy information and why is that a problem?

#86

Post by aeternum »

maffydub wrote: post #84
aeternum wrote: post #82

Earlier quoted context omitted.

There is a somewhat recent theory that supports this idea. It is unclear whether or not things actually fall-in, but the idea is that the entire surface is a hologram, and the surface alone is sufficient to describe the entire contents. (Thus preventing any information loss). Much better described here: https://www.youtube.com/watch?v=2DIl3Hfh9tY

Good video - thanks! I didn't quite follow how information came back out of the black hole as it shrank - is it "encoded" on the Hawking radiation?

I believe Hawking thought so, but that's just one possible explanation. Others think it all escapes at the very end.

Re: How do black holes destroy information and why is that a problem?

#87

Post by perl4ever »

TheOtherHobbes wrote: post #28
TeMPOraL wrote: post #18

Earlier quoted context omitted.

IANAPhysicist, but couldn't information be radiated away? When you have a particle and antiparticle annihilating, the information about what collided and when is carried away by the radiation from that annihilation event; nothing remains at ground zero to be inspected. As matter traverses the accretion disk and falls towards the event horizon, couldn't information about it be radiated away? As an observer, you could…

When it comes to black holes, no one is a physicist. The problems appear when you try to apply GR and the rest of classical physics - which all assume spacetime is continuous and analytically smooth - to a situation it can't handle. It's a good tool for normal spacetime, it's fine for making predictions all the way up to an event horizon, but it's absolutely unable to say anything useful about what happens at an even…

I know nothing, but from reading Wikipedia, I ran across something that really appealed to me - the idea that "black holes" are really fuzzy balls of strings (or whatever lies within the particles we know) where you would otherwise expect an event horizon. Anything falling into them comes apart into that stuff when it gets there.

To me, that feels right, even though I can't say anything about the math.

Re: How do black holes destroy information and why is that a problem?

#88

Post by improv32 »

hyperpallium wrote: post #5

> The important thing is that all evolution equations that we know of are time-reversible. I've heard this before, but it's so surprising to me, when one of the simplest mathematical operations - addition - is not reversible. e.g. if a+b=4 , you can't infer the values of a and b (beyond their linear relationship). This non-injectivity is a kind of summarising, with less information, where more than one state maps to…

A closer mathematical operation would be unitary matrix multiplication

Re: How do black holes destroy information and why is that a problem?

#89

Post by SamReidHughes »

Strilanc wrote: post #58
hyperpallium wrote: post #5

> The important thing is that all evolution equations that we know of are time-reversible. I've heard this before, but it's so surprising to me, when one of the simplest mathematical operations - addition - is not reversible. e.g. if a+b=4 , you can't infer the values of a and b (beyond their linear relationship). This non-injectivity is a kind of summarising, with less information, where more than one state maps to…

Actually addition is reversible, as long as you do it inline. The inverse of `a += b` is `a -= b`. An example of an action that's not reversible is masking: `a &= b`. But if you dig deep enough into the physics, you find that these kinds of irreversible actions are actually always implemented in a way analogous to the following: // a &= b acquire zero'd register z from environment z ^= a & b z ^= a a ^= z z ^= a disc…

The function (a,b) -> a+b is not reversible. The function a -> a+b is reversible, and so is (a,b) -> (a+b, b).

Re: How do black holes destroy information and why is that a problem?

#90

Post by hyperpallium »

hyperpallium wrote: post #56
OscarCunningham wrote: post #9

Earlier quoted context omitted.

The difference between them is that physical evolution takes one state to another state, whereas addition takes two numbers to another number.

|a| = 2 a^2 = 4

Most functions are not invertible.

In modulo arithmetic (numbers wrap around like days of the week, months, hours in a day, or the units column, e.g. mod 10 has numbers 0 to 9, and 9+1=0) we can count them.

There are n^n possible functions (each of the n inputs could map to any n values), but only n! invertible functions (the first input can be to any of n, the second can be to any but the first's, etc (n)(n-1)(n-2)...(1)).

n!/n^n for all n>2

Does this converge to a fraction as n->infinity (i.e. for the naturals)? As a recurrence relation, we have:

n!/n^n = (n-1)!/(n-1)^(n-1) x n(n-1)^(n-1)/n^n

We could change variables to rewrite the factor as (n+1)n^n/(n+1)^(n+1) = n^n/(n+1)^n

Since n+1 converges to n, I think this converges to 1. Meaning that the whole thing converges to something - but working out what it converges to is beyond my abiility.

EDIT Wolfram says the limit is actually 0 https://www.wolframalpha.com/input/?i=n%21%2Fn%5En

  lim_(n->∞) n^(-n) n! = 0
Reversibility is very rare indeed! At least, with the prior pr density implied from this comception of functions.
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