Question about the principle that information is never lost

[P.J. Denyer]

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 prefer-:


Heisenberg gets stopped for speeding. "Sir, I've stopped because you were doing 80mph" says the cop. "Damn it!" Heisenberg replies, "Now I'm lost!"

 

[Robin]

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.

I know something about the no cloning theorem. It is not really relevant, because what we are talking about is not necessarily an exact copy of the book.

If I have the unburned copy of the book in front of me then I could produce a word for word copy of the book.

If I have the remnants, ashes, light, heat etc, then there is no way even in principal ( as I understand it) that I could produce that word for word copy of the book.

So that information - the words and the order they were in - was accessible when the book was unburned and thus represents information that is lost when the book is burned.

 

[Robin]

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.

Not really. I don't buy that the encyclopedia contains information about its eventual fate. An encyclopedia might be burned, rot away or be pulped. A burned encyclopedia might end up in all sorts of configurations of ashes light and heat.

OK, you might say that the information resides, not just in the encyclopedia, but also in a sufficiently large portion of its surrounding environment.

But again, if you could, in principle, predict the eventual fate of the encyclopedia from information about the book (and enough of its surrounding environment) it would also imply that you could, in principle, get that information at an arbitrarily high precision.

 

[Robin]

I don't think people here get what confuses me.

We have three statements:

1. It is possible in principle to do A
2. It is not possible, even in principle, to do B
3. In order to do A it is necessary to do B

At least one of these statements must be wrong.

 

[Robin]

Anyway, I think I understand better now. It is best to think of it in terms of a single particle in a single dimension.

If I have the quantum state of a single particle in one dimension and the expectation value for position then I could evolve it forward and get the quantum state at a future date with the expectation value of where the particle would be then.

Then I could start with the future quantum state and evolve it backwards and get my original quantum state with the same expectation value.

So Laplace's Demon doesn't need information about a particular momentum and position, rather he needs the quantum state - the probability distribution.

Similarly, in order to get back to the encyclopedia Laplace's Demon would not need a particular state of ashes and light, but rather a probability distribution of all the ways that the ashes and light could be as a result of the encyclopedia burning.

 

[theprestige]

It's possible to have a fully-assembled jigsaw puzzle. It's possible to know it's fully assembled, even if the exact shape of all the puzzle pieces is somehow not known. It's also possible to have the same puzzle, disassembled, in any number of configurations of pieces. But even though you may not be able to reassemble it, the principle of conservation of information tells you that all the pieces are still there.

 

[RecoveringYuppy]

Not really. I don't buy that the encyclopedia contains information about its eventual fate. An encyclopedia might be burned, rot away or be pulped. A burned encyclopedia might end up in all sorts of configurations of ashes light and heat.

Yes, correct. To demonstrate the time reversal in the cases you are bringing up here you would also have to incorporate all the things that the encyclopedia interacted with during it's life. But the point remains.

 

[Ziggurat]

I know something about the no cloning theorem. It is not really relevant, because what we are talking about is not necessarily an exact copy of the book.

But we're talking about an exact copy of all the information in the book. The same math still applies.

If I have the unburned copy of the book in front of me then I could produce a word for word copy of the book.

Quantum mechanically, that's a trivial portion of the information contained within the book. There's a hell of a lot more information which is mostly not relevant to readers of the book, but it's still there.

The difficulty is that the relevant information (the words) and the irrelevant information gets scrambled together when it burns. You can't pick out just the relevant information like you can when you read the book, you need ALL of it in order to untangle it.

And it all exists, but you can't get it all.

 

[Robin]

It's possible to have a fully-assembled jigsaw puzzle. It's possible to know it's fully assembled, even if the exact shape of all the puzzle pieces is somehow not known. It's also possible to have the same puzzle, disassembled, in any number of configurations of pieces. But even though you may not be able to reassemble it, the principle of conservation of information tells you that all the pieces are still there.

But if you have a jigsaw puzzle that can be put together more than one way then you don't have the information about the way it was put together before it was taken apart.

 

[theprestige]

But if you have a jigsaw puzzle that can be put together more than one way then you don't have the information about the way it was put together before it was taken apart.

The point is that all the pieces are still there. That's what is meant.

 

[Robin]

The point is that all the pieces are still there. That's what is meant.

But so what?

I am not doubting that all the pieces of the burned book are still there, I am doubting that their prior arrangement could, in principle, be retrieved from the remains because that would imply that we could, in principle, access information about the remains to an arbitratily high precision.

Sent from my Moto C using Tapatalk

 

[theprestige]

I am doubting that their prior arrangement could, in principle, be retrieved from the remains because that would imply that we could, in principle, access information about the remains to an arbitratily high precision.

Good thing that's not what the principle of conservation of information means, then.

 

[Robin]

Yes, correct. To demonstrate the time reversal in the cases you are bringing up here you would also have to incorporate all the things that the encyclopedia interacted with during it's life. But the point remains.

How much or how little is not the point.

The point that remains is that unless you could, in principle, access that information to an arbitrarily high precision, you could not reconstruct prior states, even in principle.

Sent from my Moto C using Tapatalk

 

[Robin]

But we're talking about an exact copy of all the information in the book. The same math still applies.

We are talking about a claim often made by physicists that if you burned a book " 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."

For the purposes of the current discussion we only need to know if you can reconstruct any information that you could have observed when the book was intact.

Something we couldn't observe in principle when the book was intact is beside the point.

Some information like "What this encyclopedia says Albert Einstein's birthday is" is something that we can easily observe when the encyclopedia is intact. After it is burned, it is not so easy. But physicists say that it is, in principle, still possible to reconstruct what this encyclopedia says Albert Einstein's birthday is even after it is burned.

I say that this appears to contradict the Heisenberg Uncertainty Principle, ie that if you could, in principle, get back that data from the remains it would imply that you could, in principle, get at information about the remains like momentum and position to an arbitrarily high precision.

But, as I understand it, it is not even in principle possible to know the position and momentum of a particle to an arbitrarily high precision.

 

[Robin]

Good thing that's not what the principle of conservation of information means, then.

I misread your statement. See my below question.

 

[Robin]

Again:

I don't think people here get what confuses me.

We have three statements:

1. It is possible in principle to do A
2. It is not possible, even in principle, to do B
3. In order to do A it is necessary to do B

At least one of these statements must be wrong.

A="Gain any information about prior physical states from information about present states"
B="Access information about a physical state to an arbitrarily high precision"

So I am unclear on anyone's position on this which means I am still at the question I asked in my OP.

Is it "There is no contradiction between those statements"?

Or is it "Yes there is a contradiction between those statement, one or more is wrong"?

If the latter case then which statement is wrong?

 

[Robin]

Good thing that's not what the principle of conservation of information means, then.

OK, lets get this clear. Here is the statement from Sean Carroll again that I referenced in the OP:

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.

So do I understand you to be saying that the conservation of information principle does not imply what Carroll is saying?

Then what principle is he referencing here, if any?

 

[Puppycow]

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.

Can we use that as a kind of "time machine" to learn exactly what happened at any time in the past from the laws of physics? E.g., I'd like to go back and see what the world was like in the age of the dinosaurs. Or am I just talking about the science of palaeontology.

 

[Ziggurat]

We are talking about a claim often made by physicists that if you burned a book " 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."

Note the conditional. If that condition isn't satisfied, then nothing else follows.

Something we couldn't observe in principle when the book was intact is beside the point.

I disagree. It's absolutely essential to understanding the problem.

Some information like "What this encyclopedia says Albert Einstein's birthday is" is something that we can easily observe when the encyclopedia is intact. After it is burned, it is not so easy. But physicists say that it is, in principle, still possible to reconstruct what this encyclopedia says Albert Einstein's birthday is even after it is burned.

If you could satisfy that conditional. But you can't. The reason you can't, however, is not because of the uncertainty principle.

I say that this appears to contradict the Heisenberg Uncertainty Principle, ie that if you could, in principle, get back that data from the remains it would imply that you could, in principle, get at information about the remains like momentum and position to an arbitrarily high precision.

No. That isn't the problem. Properly understood, the Heisenberg uncertainty principle is not a limit on measurement precision, but a description of the properties of the wave function itself. The exact wave function has the property of having a spread of momenta and positions, with the product of the two always having a lower bound. A measurement which tells you the wave function exactly will not violate the Heisenberg uncertainty principle. Any particle you measure must end up in some wave function as a result of the measurement, which means those limits will manifest themselves in your measurement "error", but they exist independently of any measurement.

But, as I understand it, it is not even in principle possible to know the position and momentum of a particle to an arbitrarily high precision.

No. Rather, particles do not even have exact positions or momenta. But they can have exact wave functions.

 

[Ziggurat]

Can we use that as a kind of "time machine" to learn exactly what happened at any time in the past from the laws of physics?

Yes. We do that all the time. That's how we model, for example, the creation of the solar system, and the big bang itself. But since our knowledge of the present is incomplete, reconstructions of the past in this manner have constrained accuracy.