# B Black Holes and Information

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1. Nov 26, 2017

### 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

2. Nov 26, 2017

### Staff: Mentor

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

3. Nov 29, 2017

### 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

4. Nov 29, 2017

### x_engineer

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

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

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.

Last edited: Nov 29, 2017
5. Nov 29, 2017

### Staff: Mentor

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.

6. Nov 29, 2017

### x_engineer

Thx.

7. Nov 30, 2017

### Staff: Mentor

If you go forward you need that as well. Same thing.
Only in some interpretations of quantum mechanics.
It is not.
It is an assumption as much as the assumption "gravity exists". It is backed by countless experiments.
Unitary evolution is deterministic, sure.
I don't think that question makes sense. The combined state evolves unitarily.
That is not what unitarity means, and no one said classical mechanics with point particles would be deterministic. Our world is not classical.

8. Dec 14, 2017

### 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"?
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.