B Unitarity and Entanglement: Examining the Fate of Information in Black Holes

[Will K]

What happens to the information about the objects falling into the black hole? Are their states somehow contained in the Hawking Radiation, and if so, how? Or is the information scrambled as it passes the EH?

 

[mfb]

That is one of the big open questions about black holes. See No-hair theorem for an introduction.

 

[Will K]

That is one of the big open questions about black holes. See No-hair theorem for an introduction.

ok, thanks

 

[Chronos]

Nature abhors waste. Whatever goes in comes out, irrespective of how mangled it may become.

 

[K. Doc Holiday]

Dear Chronos.
Great answers but I don't understand your final answer.
I was under the impression that anything crossing the event horizon of a black hole was lost to our universe forever.
Is that no longer currently accepted theory?

 

[mfb]

It is unknown.

 

[phinds]

Dear Chronos.
Great answers but I don't understand your final answer.
I was under the impression that anything crossing the event horizon of a black hole was lost to our universe forever.
Is that no longer currently accepted theory?

Suskind and Hawking had a 30 year running battle about exactly that. Suskind said that information about the stuff going in a black hole could not be lost and Hawking said it had to be. Suskind won and wrote a book about it.

https://www.amazon.com/dp/0316016411/?tag=pfamazon01-20

Overview
Hawking proposed that information is lost in black holes, and not preserved in Hawking radiation.[2] Susskind disagreed, arguing that Hawking's conclusions violated one of the most basic scientific laws of the universe, the conservation of information. As Susskind depicts in his book, The Black Hole War was a "genuine scientific controversy" between scientists favoring an emphasis on the principles of relativity against those in favor of quantum mechanics.[1] The debate led to the holographic principle, proposed by Gerard 't Hooft and refined by Susskind, which suggested that the information is in fact preserved, stored on the boundary of a system.[3]

 

[Chronos]

There are any number of ways quantum information could eventually be liberated by the time a black hole evaporates. I see no need resort to quantum mechanics to forbid quantum information from surviving indefinitely.

 

[Marquael Sartor]

What's beyond the "Event Horizon" of a Black Hole?

 

[Greta]

Nature abhors waste. Whatever goes in comes out, irrespective of how mangled it may become.

I've wondered about this. If an organism fell into a black hole, presuming they didn't burn up en route, I can see how the information regarding the organism's atoms might be preserved. However, wouldn't the information pertaining to the conditioned processes of life be lost, as seems to occur with any death?

Sorry if it's a dumb question.

 

[Comeback City]

What's beyond the "Event Horizon" of a Black Hole?

http://nautil.us/issue/35/boundaries/where-nature-hides-the-darkest-mystery-of-all

 

[mfb]

I've wondered about this. If an organism fell into a black hole, presuming they didn't burn up en route, I can see how the information regarding the organism's atoms might be preserved. However, wouldn't the information pertaining to the conditioned processes of life be lost, as seems to occur with any death?

Sorry if it's a dumb question.

Every object gets destroyed - that is sure.

The question about information loss is different. Let a nuclear weapon explode next to some object: the object gets completely destroyed. The information survives: if you could track all atoms after the explosion and extrapolate back, you could figure out how the object looked before the explosion. In theory - there is no way to actually do this.

 

[Greta]

Every object gets destroyed - that is sure.

The question about information loss is different. Let a nuclear weapon explode next to some object: the object gets completely destroyed. The information survives: if you could track all atoms after the explosion and extrapolate back, you could figure out how the object looked before the explosion. In theory - there is no way to actually do this.

Thaks for your reply.

So basically the information about atoms' prior spin, location and type is contained within the chaotic information store that is in the BH's event horizon and a more advanced species could theoretically recreate all the things that fell in? So, on a practical basis, the quality of the information is not preserved, but the quantity is.

Would a black hole's absorption of a complex object add more to its mass and generate more heat than an equally massive simple object?

 

[BillTre]

Let a nuclear weapon explode next to some object: the object gets completely destroyed. The information survives: if you could track all atoms after the explosion and extrapolate back, you could figure out how the object looked before the explosion. In theory - there is no way to actually do this.

I have thought about this scenario for the same reason: could larger scale information be lost?

I am not trained in quantum mechanics, so perhaps I'm missing something, but:

It seems to me that something blown up in a nuclear explosion would be destroyed by (among other things) by interacting with many particles and photons.
Each photon and particle would exist in the form of probability distributions until they interact with something (the object being blown up) and collapse into a single (randomly chosen) state derived from that probability distribution.

How, in theory, could this be followed backwards to reconstruct the original object (deconstructed in the explosion)?
Does not, going through the probability state collapse make exact predictions (of the results on the other side of the collapse) impossible?
Would not causal actions proceeding through randomly chosen results of a probability function collapse not be predictable in theory?
Would it not also be impossible to get all the needed information (position and movement) for each particle due to uncertainty issues?

These seem to be theoretical blocks to recovering the initial states of the blown up object.

 

[shihab-kol]

When some thing gets into a black hole it gets destroyed,yeah.But due to that there is an increase in the energy and thus the temperature which accounts for the hawking radiation. Basically, we would get destroyed but that will not matter as the energy IS conserved.

 

[mfb]

So basically the information about atoms' prior spin, location and type is contained within the chaotic information store that is in the BH's event horizon and a more advanced species could theoretically recreate all the things that fell in? So, on a practical basis, the quality of the information is not preserved, but the quantity is.

We don't know this. See post 2. Maybe, maybe not.

Would a black hole's absorption of a complex object add more to its mass and generate more heat than an equally massive simple object?

No.

Does not, going through the probability state collapse make exact predictions (of the results on the other side of the collapse) impossible?

There are interpretations without collapses. It is impossible to reconstruct the quantum-mechanical state exactly in every interpretation, that makes such a reconstruction impossible, yes. But if you would know the precise quantum state (in interpretations without collapses), you could do the reconstruction by simply letting time evolve backwards according to the laws of quantum mechanics.
One more reason to avoid interpretations that introduce arbitrary, non-unitary, non-local, and generally weird collapses.

When some thing gets into a black hole it gets destroyed,yeah.But due to that there is an increase in the energy and thus the temperature which accounts for the hawking radiation.

If the black hole mass increases, the temperature decreases.

 

[anorlunda]

These seem to be theoretical blocks to recovering the initial states of the blown up object.

It is very tricky discussing these things with natural language rather than mathematics, because of overloaded definitions of common words.

For purposes of this post, let me define information as the number of possible states, and knowledge as knowing something about which of those states are most probable. An electron has two spin states; that's information. Observation may tell us which state it is in; that's knowledge.

The conservation law discussed here is that the quantity of information is conserved (and look to Von Neumann entropy for a definition of that quantity). Your deconstruction example, shows that you are trying to interpret that as knowledge being conserved. They are not the same thing.

Take an event, (a simple collision of two particles or a nuclear blast), it may destroy all knowledge of the pre-event statesk and chances for deconstruction, but the post-event quantity of information must match the pre-event quantity of information.

Said another way, a system with N possible states can not have a time evolution into a future with other than exactly N possible states. That's called unitarity. That says nothing at all about knowledge of what the actual state is or was or will be.

In everyday language, we often use the word information to be synonymous with knowledge. For example, what information do we have on that man? That is what makes these conservation laws so difficult to discuss. There is no natural language word that corresponds to Von Neumann entropy.

 

[BillTre]

It sounds to me like you mean:
The information is still there in the complexity of the states of resulting post-blast particles (or whatever), but the knowledge of their pre-blast arrangement will be (most likely) lost.

So, when I am thinking of the information encoded as a written message on a piece of paper taped to an A-bomb:
That information (in the diversity of post-blast states) is maintained numerically (due to unitarity), but the knowledge of the the message would rapidly become non-retrievable as the explosion progressed, due to the increasing number of state collapses over time.
This seems to be than a theoretical limit to knowledge recovery then, if not information recovery. Yes? No?

Does the knowledge of the original arrangement (the "information" in the message) then just become fuzzier as more time elapses (although the information (as counted by number of states) remains the unchanged)?

That aside, if one requires complete knowledge of all the particles etc. coming out of the explosion in order to be able to back-calculate the initial state, does that require being able to get more information about the current states of things than uncertainty says is possible?
This still seems like a theoretical limit to me, but maybe I'm not getting something.

 

[mfb]

If the explosion happens in a perfect vacuum, and you build a gigantic quantum computer around the explosion to process the explosion products in a suitable way, you should find some operation that allows to retrieve the original letter. Purely theoretical of course, but within the laws of physics.

You don't have to measure the precise state of everything. Just apply suitable operations to get as observable what you are interested in, e.g. the contents of the letter.

 

[anorlunda]

This seems to be than a theoretical limit to knowledge recovery then, if not information recovery. Yes? No?

I think the word that describes that is reversibility. Irreversible processes loose knowledge. Some processes are reversible, others irreversible.

Simple mechanics of particles colliding is reversible. In theory, you can play time forwards and backwards all the way back to the pre-big-bang if you have perfect knowledge and huge computing capacity.

If I take an electron with unknown spin and observe that it is up, then there is no chance of ever knowing what it's pre-observation state was. That is an irreversible process. I do not need to subscribe to wave function collapse interpretations of QM to make that irreversible.

You should look up coarse grain entropy on Wikipedia. That gives you a classical picture of how knowledge can be systematically and irreversibly destroyed, while information is conserved. It is closely associated with entropy, and the second law of thermodynamics. As knowledge is destroyed, entropy increases.

 

[x_engineer]

That you can always work backwards is true only if the mathematics describing an interaction between particles is continuous and two different prior states can never produce the same following state.

Inelastic collisions are not described by such math. (But one could argue that there is no such thing as an inelastic collision...!)

Perfectly elastic collisions can be described by such math only if you disallow point particles.
Allowing point particles allows for infinite prior states to result in the same following state
(the angle of line of approach to the line of separation is unconstrained)

Doesn't quantum mechanics allow multiple prior states to map to the same following state?
(Any system that employs math that does not allow infinite precision will have the problem that multiple prior states could result in the same following state)

On the flip side - this is the same argument as determinism vs existence of free will.

Niket Patwardhan

 

[mfb]

Doesn't quantum mechanics allow multiple prior states to map to the same following state?

It doesn't. Unitary evolution in quantum field theory is time-symmetric (or CPT symmetric to be precise).

 

[x_engineer]

Yes, there is that. But to go backwards (in terms of engineering some method to do it) you have to be able to observe enough state information. The act of observation causes(?) one or more collapses of the evolution, which is the same as saying multiple states map to the same observable state.

By the way, I thought unitary evolution was an assumption. Am I wrong? Is it not the same as (or very close to) the assumption that "physics is deterministic"?
(Einstein's hangup re:"God does not play dice")

Also, when you "entangle" two systems - does "unitarity" span the "entanglement" or does it apply only to the "space" "between" the "entanglements"?

Niket Patwardhan

 

[x_engineer]

Re "unitarity" I like Anorlunda's #17, and the way he distinguishes between quantity of information and actual knowledge.

Said another way, a system with N possible states can not have a time evolution into a future with other than exactly N possible states. That's called unitarity. That says nothing at all about knowledge of what the actual state is or was or will be

But I don't agree with this part from his note #20

Simple mechanics of particles colliding is reversible. In theory, you can play time forwards and backwards all the way back to the pre-big-bang if you have perfect knowledge and huge computing capacity.

For example, if we have two equal point masses colliding, conservation of momentum and energy laws give us math that allows infinite prior states and after states (with the same "size" of infinity), thus preserving unitarity; but the mapping between a particular prior state and a particular after state is not defined. That is, the angle between the line of approach and the line of separation is not defined. So this system both has unitarity and can map multiple prior states to a single after state.

When we constrain the separation line with an observation (or constrain the approach line with the preparation), we break the unitarity of the math.
If we want to keep it we have to throw some additional assumptions into the physics.

1) Point masses can NEVER collide (! - a reasonable assumption since they will always miss!) or cannot exist (!)
or
2) The line of separation is aligned with the line of approach (in the limit of the above missing by a small amount and the particles are indistinguishable)
2a) If the particles are distinguishable(e.g. have spin), some assumption about which direction the vector from one to the other is oriented before and after.
or
3) Assume unitarity does not get broken, and use it to get interesting results. This gets complicated if the masses can be connected by a "long range" force like that due to a charge (one could argue they are no longer "point" masses, and we are back at 1).

Our physics breaks down below the Schwarzschild radius of every particle (including a black hole), and only works in between the particles, because below that the very concept of before and after are gone.

See this paper for a discussion of avenues to maintain unitarity across observation or entanglement:-

https://arxiv.org/abs/1601.02598

Of note:-
1) photons confined to a point or even just a compact space break unitarity.
2) Maintaining unitarity seems to require including future observations and the setup as part of the "initial" conditions of the wave function.

 

[anorlunda]

If you would like to learn more about conservation of information, and about the time reversibility of fundamental laws, I highly recommend the first hour of the video below. Leonard Susskind is a highly respected physicist and a superb teacher.

 

[x_engineer]

Thx.

 

[mfb]

But to go backwards (in terms of engineering some method to do it) you have to be able to observe enough state information.

If you go forward you need that as well. Same thing.

The act of observation causes(?) one or more collapses of the evolution,

Only in some interpretations of quantum mechanics.

which is the same as saying multiple states map to the same observable state.

It is not.

By the way, I thought unitary evolution was an assumption.

It is an assumption as much as the assumption "gravity exists". It is backed by countless experiments.
Unitary evolution is deterministic, sure.

Also, when you "entangle" two systems - does "unitarity" span the "entanglement" or does it apply only to the "space" "between" the "entanglements"?

I don't think that question makes sense. The combined state evolves unitarily.

For example, if we have two equal point masses colliding, conservation of momentum and energy laws give us math that allows infinite prior states and after states (with the same "size" of infinity), thus preserving unitarity; but the mapping between a particular prior state and a particular after state is not defined.

That is not what unitarity means, and no one said classical mechanics with point particles would be deterministic. Our world is not classical.

 

[x_engineer]

In response to:
Also, when you "entangle" two systems - does "unitarity" span the "entanglement" or does it apply only to the "space" "between" the "entanglements"?

I don't think that question makes sense. The combined state evolves unitarily.

The referred to paper seems to imply that unitary evolution is not generally assumed across the entanglement process. He is trying to show how it could be.