Question about the principle that information is never lost

[Sideroxylon]

Appreciating your posts here, Ziggurat.

 

[Ziggurat]

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.

But the jigsaw can't be put together more than one way. Time reversal symmetry (or more specifically, CPT symmetry) means that for the present to have more than one possible past, it would also need to have more than one possible future. And that would require that the laws of physics are not deterministic. But as far as we can tell, they are deterministic.

Quantum mechanics measurements look random (wave function collapse), but that only happens when you stop doing quantum mechanics. Wave function collapse is a heuristic for getting from your quantum mechanical description to a non-quantum description, there's no reason to think that there's an actual collapse process.

 

[Robin]

Here is how I understand the HUP:

"He also famously enunciated the uncertainty principle, which states that the more accurately one were to measure, say, the position of a quantum particle, the more uncertain becomes one’s knowledge of its momentum, and vice versa."

That is from Feynman.



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[Robin]

A measurement which tells you the wave function exactly will not violate the Heisenberg uncertainty principle.

OK back up a moment there. You say "A measurement which tells you the wave function exactly".

Is there such a thing? Even in principle?




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[Robin]

If our particles behaved like classical objects you might have something like the following:

https://photos.app.goo.gl/qZRZE4r1u1FsbdbN6

And if so you could measure information about the later states and work back and find the original:

https://photos.app.goo.gl/DnFyXT7vEA2kS57z6

However if there was a limit to the precision to which you could measure these then you could not get back the original, not even close.

So this is what you cannot do in a quantum system.

So what is the information about the later states that would allow you to get back and read the original word? Certainly no kind of measurement would allow you to do this.

I suggested earlier that if you knew the quantum state at the end you could evolve it backwards and get the quantum state at the start.

Is that what Carroll means?

 

[Ziggurat]

OK back up a moment there. You say "A measurement which tells you the wave function exactly".

Is there such a thing? Even in principle?

We can get pretty close. For example, you can measure if an electron is in the ground state of a hydrogen atom. We know that wave function with incredibly high precision.

But we can’t solve any quantum 3 body problems exactly (true in many classical cases as well), and even some 2 body problems have to be approximated, so we can’t get to exact. But there’s no theoretical limit on how close we can get.

 

[Robin]

We can get pretty close. For example, you can measure if an electron is in the ground state of a hydrogen atom. We know that wave function with incredibly high precision.

But we can’t solve any quantum 3 body problems exactly (true in many classical cases as well), and even some 2 body problems have to be approximated, so we can’t get to exact. But there’s no theoretical limit on how close we can get.

So you are saying that if you have, say, three particles in a closed system then theoretically you could do a measurement on them and infer the quantum state so that you could evolve it back arbitrarily far back in time and find the prior quantum state of those three particles?

 

[RecoveringYuppy]

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.

Someone may have made this point already. Ziggurat mentioned "knowing the end state of a system". The current complete end state of the age of the dinosaurs would involve knowing about photons that are currently millions of light years away and we have no hope of ever "catching up" to.

 

[Ziggurat]

So you are saying that if you have, say, three particles in a closed system then theoretically you could do a measurement on them and infer the quantum state so that you could evolve it back arbitrarily far back in time and find the prior quantum state of those three particles?

You would need to know quite a lot about the system to begin with in order to arrange an appropriate measurement. The accuracy of your solution would be constrained by your calculation methods, which would have to be numerical approximations since there aren't analytic solutions to 3-body quantum problems. Furthermore, many quantum systems are chaotic, so that linear growth in extrapolated time would require exponential growth in required computation. But otherwise, sure.

All that really means though is that quantum mechanics is deterministic.

 

[Robin]

Say Alice models three particles moving in a confined space and starts with expectation values for the momenta and position of each particle and then evolves this system forward, say an hour or two, there would be for each particle one momentum and one position that was the expectation value for that particle?

So that Bob, without knowing the details of Alice's calculation, could get those expectation values and infer the calculation Alice was doing and evolve the system back to get to Alice's original values at significantly better accuracy than a random guess?

That would surprise me. Alice would have the information to evolve the system back to it's original state, but I am surprised that Bob, knowing only the results of a measurement on the system, could do so.

 

[Robin]

Again, it my previous understanding that it was the evolution of the wave function in time that was deterministic and reversible, not individual observations made of that system.

Indeed there is a whole description of when to sum probabilities as interfering probabilities and when to sum them as non-interfering probabilities that would not make sense if this were not the case.

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[Ziggurat]

Again, it my previous understanding that it was the evolution of the wave function in time that was deterministic and reversible, not individual observations made of that system.

Why should that be so, if the laws of quantum mechanics are deterministic?

Well, in order to do any measurement, you need an interaction. Which means that if you want to model what happens during a measurement, you can't only model the system you're measuring, you have to model your measurement apparatus too, because the interaction affects the time evolution. So in order to trace what happens from after a measurement to before a measurement, you have to know not only what the system is doing, but what the measurement apparatus is doing.

And how do you determine the quantum state of your measurement apparatus? You can't. You have to stop using quantum mechanics. Which is how the artifact of "wave function collapse" gets introduced as if it's a non-deterministic process, even though quantum mechanics is deterministic.

 

[Robin]

Why should that be so, if the laws of quantum mechanics are deterministic?

Because, as I said, the thing that is deterministic is the evolution of the wave function in time and not the individual observation.

For example I have something that can emit an electron and a backplane that can detect an electron then there is one and one only probability distribution about where the electron will land on the backplane.

There is not one and one only position on the backplane on which the electron will land.

If this is not the case then I have seriously misunderstood quantum physics.

 

[Ziggurat]

Because, as I said, the thing that is deterministic is the evolution of the wave function in time and not the individual observation.

For example I have something that can emit an electron and a backplane that can detect an electron then there is one and one only probability distribution about where the electron will land on the backplane.

There is not one and one only position on the backplane on which the electron will land.

If this is not the case then I have seriously misunderstood quantum physics.

How do you get from one quantum mechanical distribution to multiple possible positions?

Hint:

You stop using quantum mechanics.

 

[Robin]

Someone may have made this point already. Ziggurat mentioned "knowing the end state of a system". The current complete end state of the age of the dinosaurs would involve knowing about photons that are currently millions of light years away and we have no hope of ever "catching up" to.

But what I am saying is that it would involve much more than that, it would involve knowing about every possible place where those photons could have ended up and the probability that they would have ended up there.

 

[Robin]

How do you get from one quantum mechanical distribution to multiple possible positions?



Hint:

You stop using quantum mechanics.

This does not seem to relate to what I said in the part you quoted.

Also - a hint? Am I supposed to guess what you mean? Why not just say what you mean?

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[Robin]

How do you get from one quantum mechanical distribution to multiple possible positions?



Hint:

You stop using quantum mechanics.

Also, you missed a step, you need to get from your observation to your QM distribution first.

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[Robin]

We could start with something easy.

Say we have a wave packet for a single particle moving through free space.

As it evolves through time the wave packet spreads (as I understand it).

You can take a measurement of this and then from the measurement infer the shape of the wave packet and evolve it back to get the original wave packet.

So how do you go about it? How do you get a measure of how spread out the wave packet is, for example, from the measurement?

 

[Ziggurat]

This does not seem to relate to what I said in the part you quoted.

It does. You talked about measurements. But measurements, in the sense you mean them, are not quantum mechanical. Their non-deterministic appearance may be an artifact and not any actual randomness. The Everett many-worlds interpretation, for example, involves no real randomness or non-determinism.

Also - a hint? Am I supposed to guess what you mean? Why not just say what you mean?

I’m trying to get you to put some of the pieces together yourself. Doesn’t always work, oh well.

 

[Robin]

It does. You talked about measurements. But measurements, in the sense you mean them, are not quantum mechanical.

Did I suggest they are?

It seems to me that the problem I am outlining is precisely because they are not quantum mechanical and therefore cannot be considered to be part of a deterministic, reversible system.

Whether or not they are actually deterministic is neither here nor there since the problem is with reversibility as I have said.