Question about the principle that information is never lost

[Robin]

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

Oh well, forgive me for thinking it was a way of avoiding direct answers.

 

[steenkh]

It is news to me that quantum mechanics is deterministic. Does that mean that the decay of particles can be determined in advance - in principle?

 

[Robin]

It is news to me that quantum mechanics is deterministic. Does that mean that the decay of particles can be determined in advance - in principle?

As far as I know it can't, but I am not a physicist.

My understanding, as I said before, is that the evolution of the wave packet in time was deterministic and reversible, but that this does not apply once you start making measurements.

 

[Robin]

To simplify the question even further, suppose you detect a particle at point B. At point A there are a number of things which may have emitted the particle but you don't know which.

Doing some calculations you can see that there is no possible even theoretical measurement of the momentum and position of the particle could be done to distinguish which source emitted it.

That seems, on the face of it, to represent information loss.

If you knew the wave function of the particle you could evolve it back in time and find the source but as far as I can see the observation would be consistent with many, possibly infinitely many, wave functions.

 

[Robin]

Back to Carroll's encyclopedia, suppose we burn this in a small hermetically sealed furnace to save us the trouble of chasing bits of light, matter and heat across the universe, the thing that is reversible is the final quantum state, that is (roughly speaking and, again,as I understand it) a set of all the possible states in which the encyclopedia could have ended up (including the tiny possibility that it could have rearranged itself into a dictionary) along with the probabilities for each.

That is not anything that could, even in principle, be "captured", and certainly not anything that could be gleaned from an examination of the contents of the furnace.

 

[Ziggurat]

It is news to me that quantum mechanics is deterministic. Does that mean that the decay of particles can be determined in advance - in principle?

The quantum mechanical decay of a particle is not a discrete event. It is a continuous leaking of the wave function through tunneling, which can be determined in advance. To get to a discrete decay event, you need a measurement that collapses this leaking wave function. But that brings us back to stopping using quantum mechanics.

 

[Ziggurat]

Back to Carroll's encyclopedia, suppose we burn this in a small hermetically sealed furnace to save us the trouble of chasing bits of light, matter and heat across the universe, the thing that is reversible is the final quantum state, that is (roughly speaking and, again,as I understand it) a set of all the possible states in which the encyclopedia could have ended up (including the tiny possibility that it could have rearranged itself into a dictionary) along with the probabilities for each.

That is not anything that could, even in principle, be "captured", and certainly not anything that could be gleaned from an examination of the contents of the furnace.

Sure. But the fact that the information is still there matters. It has physical consequences.

Consider, for example, a computer. We've got some inputs that we put in the computer's memory, we do some calculations on that information, and then we want to wipe the memory in order to do some new calculation.

But we can't actually get rid of that information. It has to go somewhere. In particular, there's going to be an entropy cost to removing it from the computer's memory to dump somewhere else. And that means that there's going to be an energy cost to erasing computer memory. If information could disappear, then we could erase that memory without paying any energy cost. But we can't.

 

[caveman1917]

Consider, for example, a computer. We've got some inputs that we put in the computer's memory, we do some calculations on that information, and then we want to wipe the memory in order to do some new calculation.

But we can't actually get rid of that information. It has to go somewhere. In particular, there's going to be an entropy cost to removing it from the computer's memory to dump somewhere else. And that means that there's going to be an energy cost to erasing computer memory. If information could disappear, then we could erase that memory without paying any energy cost. But we can't.

I was going to comment on this with reference to Landauer's principle but couldn't remember the name of the principle, and looking it up I stumbled on this:

Sub-kBT micro-electromechanical irreversible logic gate

In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR and XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates, where the sole knowledge of the output logic value is not sufficient to infer the logic value of the two inputs. Such gates are usually believed to be bounded to dissipate a finite minimum amount of energy determined by the input–output information difference. Here we show that this is not necessarily the case, by presenting an experiment where a OR logic gate, realized with a micro-electromechanical cantilever, is operated with energy well below the expected limit, provided the operation is slow enough and frictional phenomena are properly addressed.

They claim they operated an irreversible OR gate well under the expected minimum energy bound, and given that operation of such gate is equivalent to your description of "erasing computer memory" (which is what I was originally planning to comment on) I was wondering whether you could comment on it.

 

[Robin]

Oh well, forgive me for thinking it was a way of avoiding direct answers.

Incidentally, this horribly worded sentence sounds like a sneer, but wasn't meant to be. It was supposed to be an acceptance that you had no such motives. I apologise if it was taken any other way.

 

[Robin]

I was going to comment on this with reference to Landauer's principle but couldn't remember the name of the principle, and looking it up I stumbled on this:



They claim they operated an irreversible OR gate well under the expected minimum energy bound, and given that operation of such gate is equivalent to your description of "erasing computer memory" (which is what I was originally planning to comment on) I was wondering whether you could comment on it.

Let me take a guess and say that, since the erasing is being done by the stored kinetic energy in an out-of-equilibrium spring that this energy is then dissipated into the mountings of the cantilever and presumably dissipated into the environment, ie it is using its environment like the cold sink in a heat engine.

If it was running any quicker this would not happen and there would be a requirement to cool down the system in general.

 

[Steve]

Incidentally, this horribly worded sentence sounds like a sneer, but wasn't meant to be. It was supposed to be an acceptance that you had no such motives. I apologise if it was taken any other way.

I thought your sentence could read two different ways, but I assumed it was an acceptance as you say. Classy clarification anyway. I am enjoying the discussion between you and Zig, and learning a little on a topic that is mostly way over my head.

 

[Ziggurat]

Incidentally, this horribly worded sentence sounds like a sneer, but wasn't meant to be. It was supposed to be an acceptance that you had no such motives. I apologise if it was taken any other way.

I wasn't really sure, but decided to assume the latter and not the former. Now I'm glad I did, I would have felt like a heel if I had jumped on you over that.

 

[phunk]

To simplify the question even further, suppose you detect a particle at point B. At point A there are a number of things which may have emitted the particle but you don't know which.

Doing some calculations you can see that there is no possible even theoretical measurement of the momentum and position of the particle could be done to distinguish which source emitted it.

That seems, on the face of it, to represent information loss.

If you knew the wave function of the particle you could evolve it back in time and find the source but as far as I can see the observation would be consistent with many, possibly infinitely many, wave functions.

The problem is you're only looking at one particle. Information on what event emitted that particle isn't just encoded in the particle, it's encoded in all of the output of said event and anything that output has interacted with in any way. In essence, it's encoded in the entire light cone of that event.