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

backreaction.blogspot.com

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

#11

Post by graycat »

Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a different energy level.

Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover the state at time t1 or even know just when t1 was. That is, the reversible time evolution equation of state at time t2 can't tell us the random time t2 - t1 or t1 so cannot recover the state at time t1 -- at time t2, we just do not know just when or how we got to the state at time t2.

So, the time evolution equation is time reversible but the event of the emission of the photon is not time reversible.

This thought experiment seems to conflict with the OP. Where am I going wrong?

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

#12

Post by sohkamyung »

ailideex wrote: post #10
ben_w wrote: post #8

Earlier quoted context omitted.

That’s why it’s a problem — the two best tested laws of physics contradict each other.

Which law of physics say information must be lost in a black hole? AFAIK if information is lost in a black hole it will also violate the second law of thermodynamics - so really you have many many laws saying it cannot be lost - and Hawking temporarily claimed it will be lost in black holes before recanting and saying it won't. So ... I don't quite follow. I mean this title is as concerning to me as something that cl…

I believe the 'No-hair theorem' is closest to a 'law' that says Black holes destroy information [1]. If it is true, then when you throw anything into a black hole, information about what you threw in (whether it is a chair, a star, a planet, etc.) is 'lost' as to the outside world they all yield the same observable parameters of the black hole.

[1] https://en.wikipedia.org/wiki/No-hair_theorem

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

#13

Post by evanb »

graycat wrote: post #11

Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a different energy level. Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover th…

The final state wavefunction, which you need to recover the initial state, contains an exponentially decaying distribution of different t2s. The final state wavefunction is not "here's a definite t2"---that requires measurement.

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

#14

Post by someguy12342 »

graycat wrote: post #11

Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a different energy level. Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover th…

It is a bit more difficult to see this because you are describing a continuous time process, however, the answer is that yes you would be able to to figure out the time t1 given you knew had a snapshot of the whole system through the time evolution equation.

Perhaps your confusion stems from the fact that the time t2 is observed, and it seems like you can't go back after that. An easier to grasp manifestation of this problem is that if you find Schrodinger's cat dead you can't tell if was always dead or if was dead only after your experiment. The reason is because that's only with the narrow knowledge of that cat being dead (maybe the would call this the cat state subsystem). It might be unsatisfactory to you, but in the theory of quantum mechanics, if you knew the state of everything (say the room, measurement apparatus, and so on), then you would be able to trace back to whether the cat was alive or dead. The moral is that the measurement looks irreversible if you look only at the system you are observing, but overall, people accept that there is a overarching greater space (the "environment, universe" where everything is just a unitary operation in motion according to the time evolution equation [1]). To be clear, the time evolution equation only admits reversible solutions. So with full knowledge, of say, the room and measurement apparatus, it would be possible to deduce the original state of the cat.

https://www.quantiki.org/wiki/church-larger-hilbert-space

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

#15

Post by JDEW »

maxheadroom wrote: post #4

To save you the read, the summation is in the second-to-last paragraph: > As you have probably noticed, I didn’t say anything about information. That’s because really the reference to information in “black hole information loss” is entirely unnecessary and just causes confusion. The problem of black hole “information loss” really has nothing to do with just exactly what you mean by information. It’s just a term that…

I think the article is already quite concise. Moreover it is nicely written and explains a current open problem in physics from first principles.

A summary like this is useful if the underlying article is bloated and clickbait-y but in this case potentially detracts a reader from a good article.

As featured on the front page a few days ago [1]: knowledge without understanding is meaningless.

[1] https://www.theguardian.com/commentisfree/2019/aug/24/dougla...

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

#16

Post by kmm »

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…

Your state changes from two numbers to one number, such a transition is of course not going to be bijective unless carefully designed. In physics most states stay the same "shape", making invertibility easier to achieve.

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

#17

Post by yk »

graycat wrote: post #11

Q. At time t1 = 0, we know the state of our system. Then we send a photon into an atom. Assume the atom absorbs the photon by having an electron move to a different energy level. Some time later, at time t2, the electron returns to where it was and emits a photon. As I understand, t2 - t1 is random, with exponential distribution, and independent of everything else in the universe. So, at time t2, we cannot recover th…

You are collapsing the wave function at t1 and t2. At t1 explicitly by stating that the state is known, and by t2 implicitly by defining that you have a defined distance t2- t1.

The emission of an photon at an explicit time t2 is not reversible, the emission of an photon according to the wave function of the atom leads to an photon entangled with the atom and the total has a reversible wave function. (For illustrative purposes, when you measure and you find the photon at a distance (t- t2)*c from the atom, then you will also find the atom in a state that has emitted a photon at t2, no Idea if that is especially illustrative.)

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

#18

Post by TeMPOraL »

sohkamyung wrote: post #12
ailideex wrote: post #10

Earlier quoted context omitted.

Which law of physics say information must be lost in a black hole? AFAIK if information is lost in a black hole it will also violate the second law of thermodynamics - so really you have many many laws saying it cannot be lost - and Hawking temporarily claimed it will be lost in black holes before recanting and saying it won't. So ... I don't quite follow. I mean this title is as concerning to me as something that cl…

I believe the 'No-hair theorem' is closest to a 'law' that says Black holes destroy information [1]. If it is true, then when you throw anything into a black hole, information about what you threw in (whether it is a chair, a star, a planet, etc.) is 'lost' as to the outside world they all yield the same observable parameters of the black hole. [1] https://en.wikipedia.org/wiki/No-hair_theorem

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 definitely tell whether somebody threw a planet or a planet-sized bunch of paperclips into a black hole by observing the accretion disk as it happened.

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

#19

Post by codernyc16 »

myaccount80 wrote: post #6
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…

It is not reversible because you’re ereasing information. If you want to have a reversible addition you are not allowed to destroy the information. The same happens if you apply the standard AND operator to two bits because the output is only one bit, therefore it is impossible to figure out the two input bits. To have a reversible AND operator you can define it like this: f(x1, x2, b) = (x1, x2, b XOR (x1 AND x2)).…

You’d have to do that for all results, not just one. This is basically what an event sourced system does: you store all the events and fold your state, so you can “play back” to any point in time. You could theoretically reverse from the end, but I haven’t seen it done.
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