Question about the principle that information is never lost

Planigale said:
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.
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In the classical case it is the case that the state of the universe at time t+1 contains all the information present in the universe at time t=0.

This means that the state of the book before it's burnt is encoded in the ashes + the radiation + the motion of the air +etc. (the entire system that interacted with the book).

This is made obvious by the time reversal symmetry of the laws of physics.

The system however is, as you say, chaotic, and as such we will never be able to gather that information. This is related to the increase in entropy (and in fact quantified by it).

The same is actually true of quantum mechanics as well, but it's more subtle. For instance, the variables that make up what can be known about a system (the information content) are not the same variables as in classical physics.
 
Robin said:
Which suggests to me that you could not, even in principle, reconstruct the burned book from the remnants.
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The information content of the book before it's burned isn't those unknowable variables, but it's quantum state. You can't reconstruct the location and momentum of each particle in the book because those things don't exist, but you can reconstruct the state of the wavefunction at t=0 from the state of the wavefunction at t=1.

(When I say "you can", I don't mean you, only that the information is there, obviously you'll never have the means to access that information, and it becomes harder and harder to do so as the system continues to interact due to the rise in entropy)
 
Planigale said:
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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In a classical system you could not compute a past from a present because the positions of effectively everything will be uncomputable.

But in a classical system any state would be associated with one and only one past. So Laplace's Demon with a hyper-computer could in principle take any state and compute one past from it and one future and so could both reconstruct the burned encyclopedia and unstir the coffee.

But with a quantum system, as I gather, there is not one past associated with any particular observed state, so even Laplace's Demon with a hyper-computer could not unstir the coffee, nor reconstruct the encyclopedia from the embers.

(NB of course both stirring coffee and burning an encyclopedia involve chemical reactions for which there is probably no classical analog in any case).
 
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Roboramma said:
The information content of the book before it's burned isn't those unknowable variables, but it's quantum state. You can't reconstruct the location and momentum of each particle in the book because those things don't exist, but you can reconstruct the state of the wavefunction at t=0 from the state of the wavefunction at t=1.
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Yes, but that can't help you reconstruct an encyclopedia from all the bits of information about the remnants.

Having a superposition of every possible state and saying "the original encyclopedia is one of these states" is pretty much equivalent to not having the information at all.

If someone asks if I have the licence plate of the car that hit me and I have generated a list of all the possible licence plates and say "yes I have it here", I am technically correct, but actually I don't have the licence plate.
(When I say "you can", I don't mean you, only that the information is there, obviously you'll never have the means to access that information, and it becomes harder and harder to do so as the system continues to interact due to the rise in entropy)
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But could it be done even in principle? I mean if Laplace's Demon could freeze the system and feed the data to her hyper-computer could she access the information?

Is there even a theoretical path from the embers back to the encyclopedia?
 
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Robin said:
Yes, but that can't help you reconstruct an encyclopedia from all the bits of information about the remnants.

Having a superposition of every possible state and saying "the original encyclopedia is one of these states" is pretty much equivalent to not having the information at all.
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I think you misunderstood: the original encyclopedia was a superposition of states. The problem is simply to bring it back to that superposition.

But maybe you do understand and the issue comes down interpretations of QM. I think that under Copenhagen you would actually turn out to be correct, that the collapse of the wavefunction actually does induce a loss of information. The problem is that Copenhagen is ridiculous.
 
Copenhagen is a way of stopping using quantum mechanics. It works, but it isn't really quantum mechanics itself.
 
Roboramma said:
I think that under Copenhagen you would actually turn out to be correct, that the collapse of the wavefunction actually does induce a loss of information. The problem is that Copenhagen is ridiculous.
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The Copenhagen interpretation is ridiculous but remains a useful fiction* in many situations, in much the same way that it can be useful to assume signal voltages within a digital electronic circuit are restricted to the values used to represent the bits 0 and 1. It takes some care to justify that approximation in a digital circuit, just as it takes some care to check that some experimental setup or quantum device can be analyzed properly while assuming the Copenhagen interpretation, but these fictions, when properly employed, are useful because they simplify design and analysis at higher levels of abstraction.

*The fictions used in science, often called abstractions or models, are useful when they simplify reality in ways that don't affect the matters of interest. In this thread, the Copenhagen fiction is not useful because, as you say, it immediately implies loss of information, which is the question being discussed.
 
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W.D.Clinger said:
The Copenhagen interpretation is ridiculous but remains a useful fiction* in many situations, in much the same way that it can be useful to assume signal voltages within a digital electronic circuit are restricted to the values used to represent the bits 0 and 1. It takes some care to justify that approximation in a digital circuit, just as it takes some care to check that some experimental setup or quantum device can be analyzed properly while assuming the Copenhagen interpretation, but these fictions, when properly employed, are useful because they simplify design and analysis at higher levels of abstraction.

*The fictions used in science, often called abstractions or models, are useful when they simplify reality in ways that don't affect the matters of interest. In this thread, the Copenhagen fiction is not useful because, as you say, it immediately implies loss of information, which is the question being discussed.
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Thanks, that's a good point, I agree completely.
 
Roboramma said:
I think you misunderstood: the original encyclopedia was a superposition of states. The problem is simply to bring it back to that superposition.

But maybe you do understand and the issue comes down interpretations of QM. I think that under Copenhagen you would actually turn out to be correct, that the collapse of the wavefunction actually does induce a loss of information. The problem is that Copenhagen is ridiculous.
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No, and I still misunderstand.

What I am doubting is that there is any way at all to get back from the remnants of the burned encyclopedia to the encyclopedia.

For any set of burned remnants there are countless prior states that would result in those remnants.

It does not matter whether the waveform collapses or not, there is no way of matching up any set of burned remnants with a particular book, not even in principle. Even in Everettian QM.

If I am wrong about this I would be interested in the 'in principle' method that could be used to get back from a particular set of remnants to a book.

What information would be used and how would it be used to reconstruct the book?
 
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Robin said:
For any set of burned remnants there are countless prior states that would result in those remnants.
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What makes you say that?

Keep in mind, the relevant "remnants" aren't just the ashes. The light emitted (and whatever it ends up doing) is part of it too, for example. So the remnants will quickly mix in with the rest of the universe, but that doesn't mean that that information is gone.
 
Ziggurat said:
What makes you say that?

Keep in mind, the relevant "remnants" aren't just the ashes. The light emitted (and whatever it ends up doing) is part of it too, for example. So the remnants will quickly mix in with the rest of the universe, but that doesn't mean that that information is gone.
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But are you saying that the information exists at a sufficiently high precision to be able to reconstruct prior stages, even in principle?

Remember, in order to reconstruct prior states from an arbitrarily long period then the information would have to exist at an arbitrarily high precision.
 
Sideroxylon said:
Can you work back from generations of Wolfram’s rule 30 to recover earlier states?
https://en.m.wikipedia.org/wiki/Rule_30
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Perhaps in some specific cases, but I don't think in general. Consider one row of only 1's. What's the next row going to be? Only 0's. Now consider a row of only 0's. What's the next row going to be? Only 0's. So if you have a row of only 0's, you can't tell what the proceeding row was.

Is this a relevant comparison?
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Probably not.
 
Robin said:
But are you saying that the information exists at a sufficiently high precision to be able to reconstruct prior stages, even in principle?
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Only in principle. There is no method to extract that information, but yes, it still exists.
 
Robin said:
But the information is in principle accessible at an arbitrarily high precision?
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It exists to an arbitrary precision, but it was never accessible to that precision, not even before it burned.
 
Ziggurat said:
It exists to an arbitrary precision, but it was never accessible to that precision, not even before it burned.
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If it isn't even in principle accessible then it is not even in principle possible to reconstruct those past states.

Further, how do you know it exists to an arbitrary precision if it is not even, in principle, accessible?
 
Also, what is the difference between "not even in principle accessible" and "lost"? Is there a definition?
 
Maybe this framing will help:

The information about the encyclopaedia exists in the ashes (and radiation, etc.) in exactly the sense that the information about the ashes exists in the encyclopaedia.

That information isn't accessible in either case, but you certainly agree that the information must be present in the system that leads from that state [Encyclopaedia] to the state [ashes, etc.], even if we can't access or analyse that information to get from A to B. That information is there in principle, but only in principle. The reverse is also true.

If any objection you make to the case of going from ashes to encyclopaedia also applies to the reverse case of going from encyclopaedia to ashes, you might see that there's clearly a problem with that objection.

The final point here is that the laws of physics obey a time reversal symmetry.
 
Robin said:
Also, what is the difference between "not even in principle accessible" and "lost"? Is there a definition?
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I mean that if I give you, say, a book, you cannot get the whole quantum state of that book. The information obviously must exist because the book exists, but there’s no way to extract it all from the book.

If you could get all that information, then you could create an exact copy of the book. But quantum mechanics prohibits that. Look up the no cloning theorem.
 
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