That cat: not dead and alive

by DavidPlumpton 2 min read30th Aug 201110 comments

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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?

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