Question about the principle that information is never lost

Robin

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Robin
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One thing I have trouble understanding in physics is the principle that information is never lost. Sean Carroll explains the principle like this:

If you take an encyclopedia and toss it into a fire, you might think the information contained inside is lost forever. But according to the laws of quantum mechanics, it isn’t really lost at all; if you were able to capture every bit of light and ash that emerged from the fire, in principle you could exactly reconstruct everything that went into it, even the print on the book pages.
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But as far as I can see you couldn't do this even in principle. If you could capture all the information every bit of light and ash and then work backwards, in principle, to reconstruct the encyclopedia it would imply that you could get that information, in principle, to an arbitrarily high precision.

But isn't it also a principle of physics that you can't, even in principle, get all of that information to an arbitrarily high precision?

So you can't take the remnants of the encyclopedia and reconstruct the encyclopedia, even in principle.

Carroll addresses the point by saying that the state is not given by a set of little bits of information, but by a single wave function, the evolution of which is completely reversible.

But I don't see how this helps you go from all the bits of ash and light back to the original encyclopedia. If you (or some supercharged version of Laplace's Demon) could know the wave function for the system and evolve it backwards they still wouldn't be able to pick out an individual encyclopedia which was the prior state of those bits of light and ash.
 
Robin said:
But isn't it also a principle of physics that you can't, even in principle, get all of that information to an arbitrarily high precision?
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Whether or not you can get it is a separate question from whether or not it exists.

But I don't see how this helps you go from all the bits of ash and light back to the original encyclopedia.
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All the time evolution equations in physics can be run forwards or backwards. If you know the end state of the system, plug that into the equations and run them backwards to get the starting state.

Nothing deeper than that is being expressed here. As a practical matter you can't get the full end state of the system, so your backwards projections will be limited in accuracy because of that, but again, whether information exists is a separate question from whether or not you can get it. It obviously needs to exist in order to get it, but existing doesn't suffice to be able to get it.
 
Ziggurat said:
Whether or not you can get it is a separate question from whether or not it exists.



All the time evolution equations in physics can be run forwards or backwards. If you know the end state of the system, plug that into the equations and run them backwards to get the starting state.

Nothing deeper than that is being expressed here. As a practical matter you can't get the full end state of the system, so your backwards projections will be limited in accuracy because of that, but again, whether information exists is a separate question from whether or not you can get it. It obviously needs to exist in order to get it, but existing doesn't suffice to be able to get it.
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But the isn't the Uncertainty Principle part of the theory? Not just a limitation on what is practically possible?
 
And, again, rolling the wave function back will get you a prior version of the wave function, it won't give you an individual encyclopedia.
 
Can you in principle know both the momentum and position of a particle to an arbitrarily high precision?

It was my understanding that this was not possible even in principle.
 
Robin said:
Can you in principle know both the momentum and position of a particle to an arbitrarily high precision?

It was my understanding that this was not possible even in principle.
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Heisenberg gets stopped for speeding. "Do you know how fast you were going?" says the cop. "Nope," Heisenberg replies, "but I know exactly where I am."
 
I think this is going at it all backwards. You're asking how information works in quantum physics.

You probably need to just learn quantum physics, and then you'll understand the workings of the thing that quantum physics calls "information".

You're trying to apply a layman's definition to a specialized and esoteric body of knowledge. Terms of art and technical jargon behave very differently than everyday speech.

You think of "information" as "stuff I know that has meaning" or some similar connotation.

But in quantum physics, "information" is something more like "any theoretically possible process state".
 
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I read a book on this recently and I can't recall a damn thing about it other than hairy holes.

I think that was the same book...
 
Robin said:
But the isn't the Uncertainty Principle part of the theory? Not just a limitation on what is practically possible?
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Correctly understood, the uncertainty principle is not a limit on what you can measure, but a limit on what can even exist. A wave function with a narrow distribution of possible locations must necessarily have a wide distribution of possible momenta. This is intrinsic to the property of the wave function itself, and it holds regardless of whether you do any measurement. Furthermore, the reason it applies to measurements is because the results of a measurement must still be a wave function, and thus constrained by that same limit.
 
Robin said:
Can you in principle know both the momentum and position of a particle to an arbitrarily high precision?

It was my understanding that this was not possible even in principle.
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That's correct, but the reason isn't because of a limitation on our measurement process, but because of a limitation on reality itself.
 
Robin said:
Can you in principle know both the momentum and position of a particle to an arbitrarily high precision?

It was my understanding that this was not possible even in principle.
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As a layman if it isn't possible to know something in principle then I struggle to see how the information could be lost, you wouldn't have it to begin with.
 
Leonard Susskind borrows an encyclopedia from Stephen Hawking. A few weeks later, Hawking asks if Susskind can return it. Susskind says, "Sorry, I lost it." Hawking replies "AHA! I win!"

A week later, Susskind shows up at Hawking's office with a box of ashes. Hawking asks, "What's this?" Susskind says, "I discovered that I had dropped your encyclopedia in the fireplace and it burned up. I win!"
 
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theprestige said:
I think this is going at it all backwards. You're asking how information works in quantum physics.

You probably need to just learn quantum physics, and then you'll understand the workings of the thing that quantum physics calls "information".

You're trying to apply a layman's definition to a specialized and esoteric body of knowledge. Terms of art and technical jargon behave very differently than everyday speech.

You think of "information" as "stuff I know that has meaning" or some similar connotation.

But in quantum physics, "information" is something more like "any theoretically possible process state".
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In which case I wonder why people like Carroll even bother, if we could not possibly understand the point he was making unless we already knew what the point was.
 
In any case, I don't think that asking about the claim that you could, in principle, reconstruct an encyclopedia that was burned from the remnants requires any special insight into how a physicist understands the concept of information.

I am asking is it really possible, in principle, to reconstruct a burned book from the remnants as Carroll (and others) say?

And I am asking, wouldn't that require that we could know things like the position and momentum to an arbitrarily high precision?
 
Ziggurat said:
That's correct, but the reason isn't because of a limitation on our measurement process, but because of a limitation on reality itself.
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Which suggests to me that you could not, even in principle, reconstruct the burned book from the remnants.
 
It's not about information available to us, it's about information encoded in the state of the universe. There is nothing that says it has to be recoverable by us.
 
Classical physics is predictable, you throw a ball and in theory you can calculate exactly where it goes if you know the starting state. Relativity is classical physics, relativistic motion is still predictable. Quantum mechanics is unpredictable, I throw a photon at the double slit and I cannot predict what will happen. I cannot predict when a nucleus will decay.

Quantum information is not the same as what is written in a book. An example is quantum entanglement. In theory the entanglement is eternal until the quantum state is collapsed; until it is read. The quantum state of the entangled particles is indeterminate until you read one which then 'forces' a state on the other. That is the information. The analogy given of burning a book and being able to reconstruct it is not what is meant; it is a terrible analogy. Even in classic physics you have one way systems; I am pretty certain that stirring the ashes will create a chaotic system which is not reversible; the usual example given is you cannot unstir the sugar out of your coffee.

I am aware this is an awful explanation but I can't think of a better way of explaining it at present.
 
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