B Would Laplace's Demon work?

[sayetsu]

TL;DR Summary

Hypothetically, of course. If you could get all information on the particles in the universe, OR in a certain region of it, could you recover everything in the past about those particles?

I've heard about quantum information, how information can't be created or destroyed, etc. I don't know a lot about this stuff. Would the demon work in theory?

 

[pines-demon]

TL;DR Summary: Hypothetically, of course. If you could get all information on the particles in the universe, OR in a certain region of it, could you recover everything in the past about those particles?

I've heard about quantum information, how information can't be created or destroyed, etc. I don't know a lot about this stuff. Would the demon work in theory?

Generally the answer is no, but it kind of depends on the assumptions.

Assuming we allow for

• the demon to know all possible variables that he is physically allowed in a given instant in a given foliation of spacetime
• the demon can retain that information and calculate what is going to happen (or what has already happened) as precisely as he can without converting himself into a black hole
• current quantum mechanics is true, meaning that the demon does not have access to hidden variables that could bypass uncertainty relations

Then the demon is only allowed to predict (postdict) the future (past) probabilistically because due to uncertainty relations he cannot know all possible variables. Some mutual measurements are incompatible due to quantum mechanics. Add to that chaos, then some trajectories will diverge rapidly so the demon's prediction is going to be sparse and not very useful.

 

[sayetsu]

Oh, my question was specifically about the past. With presently available quantum information, could he reconstruct the history of the universe, basically?

 

[phinds]

Oh, my question was specifically about the past. With presently available quantum information, could he reconstruct the history of the universe, basically?

No, the universe is not deterministic, it is statistical.

 

[sayetsu]

No, the universe is not deterministic, it is statistical.

But the past is set, yes?

 

[phinds]

But the past is set, yes?

Well, sure, what has happened has happened, but so what? What's your point?

 

[sayetsu]

Well, sure, what has happened has happened, but so what? What's your point?

I'm wondering if the information of those past events would be enough for someone in the present with hypothetical omnipotence to wind the clock backwards, as it were, and know the entire history of the universe up to this point.

 

[PeterDonis]

I'm wondering if the information of those past events would be enough for someone in the present with hypothetical omnipotence to wind the clock backwards, as it were, and know the entire history of the universe up to this point.

Only if you had all the information. But it's impossible for anyone, even someone with "hypothetical omniscience" (I'm assuming you meant "omniscience" instead of "omnipotence"), to have all the information; even an omniscient being in a relativistic universe can only have the information that's in their past light cone, and that's not all the information.

 

[pines-demon]

Oh, my question was specifically about the past. With presently available quantum information, could he reconstruct the history of the universe, basically?

My response works also in the other direction. You cannot know everything when quantum mechanics is involved.

 

[sayetsu]

My response works also in the other direction. You cannot know everything when quantum mechanics is involved.

Would you please elaborate? Even if there are probabilities for different outcomes, once the wave function collapses, I'd ithink it'd be possible to see how it "got there." This is in principle, of course; I'm far from a QM expert.

 

[sayetsu]

Only if you had all the information. But it's impossible for anyone, even someone with "hypothetical omniscience" (I'm assuming you meant "omniscience" instead of "omnipotence"), to have all the information; even an omniscient being in a relativistic universe can only have the information that's in their past light cone, and that's not all the information.

Yes, I did mean "omniscience." Autocomplete your with my glasses off. Thanks. I forget what a "light cone" is. Would you please explain?

 

[PeterDonis]

I forget what a "light cone" is.

The past light cone of an observer, at a given event on that observer's worldline (say you sitting at your computer as you read this) is the set of all events that can send light signals to that observer at that event. That is always just a finite-sized subset of the universe as a whole.

 

[PeterDonis]

once the wave function collapses

If wave function collapse is an actual, physical event, then it destroys information: the dynamics is no longer unitary. So no, in such a case knowing the state after collapse does not tell you the state before the collapse.

If you use a no collapse interpretation of QM, like Many Worlds, then the dynamics is unitary, but you never know the full state, so although information is preserved by the dynamics, even Laplace's Demon could never have enough of it to back predict everything (or forward predict everything).