That cat: not dead and alive

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?