That cat: not dead and alive

post by DavidPlumpton · 2011-08-30T08:23:22.578Z · score: 3 (10 votes) · LW · GW · Legacy · 10 comments

I've read through the Quantum Physics sequence and feel that I managed to understand most of it. But now it seems to me that the Double Slit and Schrodinger's cat experiments are not described quite correctly. So I'd like to try to re-state them and see if anybody can correct any misunderstandings I likely have.

With the Double Slit experiment we usually hear it said the particle travels through both slits and then we see interference bands. The more precise explanation is that there is an complex valued amplitude flow corresponding to the particle moving through the left slit and another for the right slit. But if we could manage to magically "freeze time" then we would find ourselves in one position in configuration space where the particle is unambiguously in one position (let's say the left slit). Now any observer will have no way of knowing this at the time, and if they did detect the particle's position in any way it would change the configuration and there would be no interference banding.

But the particle really is going through the left slit right now (as far as we are concerned), simply because that is what it means to be at some point in configuration space. The particle is going through the right slit for other versions of ourselves nearby in configuration space.

The amplitude flow then continues to the point in configuration space where it arrives at the back screen, and it is joined by the amplitude flow via the right slit to the same region of configuration space, causing an interference pattern. So this present moment in time now has more than one past, now we can genuinely say that it did go through both. Both pasts are equally valid. The branching tree of amplitude flow has turned into a graph.

So far so good I hope (or perhaps I'm about to find out I'm completely wrong). Now for the cat.

I read recently that experimenters have managed to keep two clouds of caesium atoms in a coherent state for a hour. So what would this look like if we could scale it up to a cat?

The problem with this experiment is that a cat is a very complex system and the two particular types of states we are interested in (i.e. dead or alive) are very far apart in configuration space. It may help to imagine that we could rearrange configuration space a little to put all the points labelled "alive" on the left and all the dead points on the right of some line. If we want to make the gross simplification that we can treat the cat as a very simple system then this means that "alive" points are very close to the "dead" points in configuration space. In particular it means that there are significant amplitude flows between the two sets of points, that is significant flows across the line in both directions. Of course such flows happen all the time, but the key point is here the direction of the complex flow vectors would be aligned so as to cause a significant change in the magnitude of the final values in configuration space instead of tending to cancel out.

This means that as time proceeds the cat can move from alive to dead to alive to dead again, in the sense that in any point of configuration space that we find ourselves will contain an amplitude contribution both from alive states and from dead states. In other words two different pasts are contributing to the present.

So sometime after the experiment starts we magically stop the clock on the wall of the universe. Since we are at a particular point the cat is either alive or dead, let's say dead. So the cat is not alive and dead at the same time because we find ourselves at a single point in configuration space. There are also other points in the configuration space containing another instance of ourselves along with an alive cat. But since we have not entangled anything else in the universe with the cat/box system as time ticks along the cat would be buzzing around from dead to alive and back to dead again. When we open the box things entangle and we diverge far apart in configuration space, and now the cat remains completely dead or alive, at least for the point in configuration space we find ourselves in.

How to sum up? Cats and photons are never dead or alive or going left or right at the same moment from the point of view of one observer somewhere in configuration space, but the present has an amplitude contribution from multiple pasts.

If you're still reading this then thanks for hanging in there. I know there's some more detail about observations only being from a set of eigenvalues and so forth, but can I get some comments about whether I'm on the right track or way off base?

10 comments

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comment by mwengler · 2011-08-30T12:18:25.401Z · score: 6 (8 votes) · LW · GW

My background is as a PhD physicist whos main association with quantum mechanics wave particle duality was in 1) solid state physics: electrons and 'cooper pairs' of electrons in superconductors and crossing barriers by tunneling 2) figuring out the noise properties of amplifiers treating high frequency radio waves as both waves and particles.

The diffracted electron does not go through one slit or the other. To see if it goes through one slit or another you have to, for example, turn a light on to look at the electron. You see the electron by bouncing photons off the electron. When you turn a light on of sufficiently short wavelength to see which slit the electron goes through two things happen: 1) you see the electron go through one slit or the other 2) the diffraction pattern formed by electrons disappears! Bouncing photons off the electrons in order to see them with sufficient resolution to determine which slit they go through also screws up the correlation required to get two-slit diffraction patterns.

So now you turn the light back off, you can't see which slit the electrons are going through, and you see the banded diffraction pattern past the slits building up again.

This is the uncertainty principle. In order to localize the electron sufficiently to restrict it to one slit or the other, you have to randomize its momentum to the point that two-slit diffraction effects are blurred out. In order to "localize" the electrons momenta to the point that you see diffraction patterns, you have to randomize its location to the point that you cannot actually, even in principle, say it went through one slit or the other.

I may be giving you one QM "interpretation" here. But I have not seen any "Many Worlds" interpretations that overcome the uncertainty principle and can also be used to calculate the results of experiments. I admit these descriptions may not exist, but the way I describe the electrons and slits absolutely can be used to make quantitative predictions that fit experiments.

comment by jhuffman · 2011-08-30T18:48:05.229Z · score: 2 (2 votes) · LW · GW

I don't think any interpretation provides a novel set of tools for measurement or prediction.

comment by prase · 2011-08-30T11:17:33.376Z · score: 5 (5 votes) · LW · GW

The problem with this experiment is that a cat is a very complex system and the two particular types of states we are interested in (i.e. dead or alive) are very far apart in configuration space. It may help to imagine that we could rearrange configuration space a little to put all the points labelled "alive" on the left and all the dead points on the right of some line. If we want to make the gross simplification that we can treat the cat as a very simple system then this means that "alive" points are very close to the "dead" points in configuration space. In particular it means that there are significant amplitude flows between the two sets of points, that is significant flows across the line in both directions. Of course such flows happen all the time, but the key point is here the direction of the complex flow vectors would be aligned so as to cause a significant change in the magnitude of the final values in configuration space instead of tending to cancel out.

This paragraph doesn't sound as a correct approach. The main objection is that you don't need to classify all classical states as alive or dead to think about the cat experiment. It is sufficient to take one arbitrary alive state as the initial condition. Ideally, after coupling the cat to the poisoning mechanism, the system evolves to a superposition of two classical states whose labels are unambiguously "alive" and "dead". Speaking about flow crossing the line in both directions doesn't help understanding and even doesn't add realism: the distribution of states in complex systems is never uniform and the flow usually goes overwhelmingly in one direction across such macroscopic boundaries, as we know from thermodynamics. (By the way, it would help if you specified what do you mean by "amplitude flows between the two sets of points" more technically.)

In the original setting when the poison is triggered by a decaying nucleus, the cat doesn't oscillate between dead and alive in any meaningful sense. It is in an eigenstate of the alive operator initially and over time the projection to the alive subspace monotonously exponentially decreases in magnitude.

(If I can make a general suggestion for any arguments about quantum physics: Do it in mathematical notation first and then interpret the symbols. Quantum theory is perhaps the hardest discipline if one wishes to perform correct reasoning without math.)

Edit: An additional, although possibly not much relevant, problem is that you assume that alive and dead are properties that can be given to points in the configuration space. But that is not true: dead or alive are certainly sensitive to momenta of the cat's constituent particles, not only positions that are specified by the location in the configuration space. In other words, the "alive operator" doesn't commute with the configuration space labeling observables, unless you have selected a very special set of observables to begin with.

comment by lessdazed · 2011-08-30T09:14:04.529Z · score: 1 (1 votes) · LW · GW

So sometime after the experiment starts we magically stop the clock on the wall of the universe.

Upvoted for using the word "magically" as a label for "in a way such that I don't understand how such a thing would even be possible".

but the present has an amplitude contribution from multiple pasts.

I think it's the other way around, and the past was set up for multiple futures.

the particle is unambiguously in one position (let's say the left slit). Now any observer will have no way of knowing this at the time, and if they did detect the particle's position in any way it would change the configuration and there would be no interference banding.

If there's a particle, there's no banding in the future. If there's banding, there wasn't a particle in the past.

I think. This is less to instruct or discuss and more to make a record so I won't be able to avoid the fact I was wrong.

comment by Oscar_Cunningham · 2011-08-30T10:01:31.713Z · score: 1 (1 votes) · LW · GW

If there's a particle, there's no banding in the future. If there's banding, there wasn't a particle in the past.

At any given point in the configuration space there is a particle, but since we're not looking at it (and it's not interacting with anything else) no decoherence occurs, and so we still get an interference pattern.

comment by hairyfigment · 2011-08-30T20:54:48.865Z · score: 0 (0 votes) · LW · GW

But if we could manage to magically "freeze time" then we would find ourselves in one position in configuration space where the particle is unambiguously in one position

I would say that at a given time there exist complex numbers or arrows attached to different points or positions. But I take it you want to identify yourself with a single point in configuration space at time t, or a timeline connecting such points?

Then your account seems correct for the Double Slit -- though vague, as prase says -- but probably wrong for the cat. It might "move from alive to dead", but it shouldn't go the other way. No definite "dead" configuration, assuming that phrase makes sense at all, should contribute to the amplitude of "alive" configurations in a meaningful way. (So, what prase said.)

comment by Manfred · 2011-08-30T16:36:54.486Z · score: 0 (0 votes) · LW · GW

Off base - in MWI, "observer" means "thing that gets entangled with the system." Before it gets entangled with the system, the system is really truly not observed. Before being observed, things really are indeterminate from the perspective of the observer (see Bell's inequality), and so representing them as if they were determined doesn't work.

comment by __Emil__ · 2011-08-30T13:55:51.286Z · score: 0 (2 votes) · LW · GW

So sometime after the experiment starts we magically stop the clock on the wall of the universe. Since we are at a particular point the cat is either alive or dead, let's say dead.

If we stop time, we do not find ourselves at a "a particular point [where] the cat is either alive or dead". If we stop time, we find ourselves at a point in the configuration space. At this point in configuration space, the different possible configurations have different amplitudes. Some of these configurations include the cat being alive, and some include the cat being dead.

comment by Logos01 · 2011-08-30T13:19:43.623Z · score: 0 (0 votes) · LW · GW

But if we could manage to magically "freeze time" then we would find ourselves in one position in configuration space where the particle is unambiguously in one position (let's say the left slit).

It is not my understanding (I am a layman) that this is an appropriate statement to make: I don't think that even the frozen-time point would show the particle to be in a discrete position. I tend to the belief that the 'wave' portion of quantum wave/particle duality represents the many probabilities co-existing within our physical universe. I'm aware this disagrees with the basic Bayesian assumption of non-frequentism, but I'm not prepared to get into that argument at this time. (I tend towards Bayesian thinking in all other ways, just not on this point.)

Anyhow -- the point is, while when discussing the exact manners in which a given particle can interact with others, it is only relevant to discuss its particle-nature; when discussing its opportunities to interact, it is only relevant to discuss its probability-spaces. As multiple probabilities tend to interact by forming subsets of available probabilities, and as 'larger scale' physics is composed definitionally of complex systems, this would tend to 'factor out' towards the blissfully deterministic-appearing world we see in the "Middle World".

The consequence of this notion, however, is that as the Cat/box system has a radioisotope whose decay triggers the release of the toxin; the presence of both possibilities means that the system at the Newtonian scale will behave as though the isotope had decayed. In which case, you've got yourself one dead cat.

I am quite certain that someone of greater expertise would rip this comment to shreds, and I invite the opportunity to be educated. :)

comment by Oscar_Cunningham · 2011-08-30T09:58:59.951Z · score: -1 (3 votes) · LW · GW

can I get some comments about whether I'm on the right track or way off base?

You're dead right.

EDIT: The standard LessWrong view (and that given in Good and Real) is that the idea of freezing time and finding yourself at a particular point is a Mind Projection Fallacy. The wave function is defined for each time and each point in configuration space, and just sits there as a "fixed" crystal. Then the illusion of a single universe is created by the fact that at each point in configuration space we have consistent memories of just one universe.