I Schrodinger's cat state

1. Feb 20, 2016

durant35

Hey guys, this is my new thread regarding the problem of decoherence combined with the Schrodinger's cat experiment. If somebody has the patience and isn't annoyed (which is perfectly understandable) I hope that I will get an appropriate answer.

So basically I've read Lindley's where does the weirdnesss go book and I want to analyze some parts. He said that after decoherence there is still a chance that the two cat states will interfere and if the cat survives that it may spontaneously end up in a superposition of dead and alive again. I understand this part because the interference terms are non zero and that's fine even though it's weird.

Then he asks is it possible that something that is alive, let's say anyone of us, ends spontaneously in a superposition of dead and alive. He said that there is a small chance even for that. Now I don't understand this because in the cat case there was a trigger event that caused all of this (decay of the atom) and in ours case there is no such case, while decohering the only thing that is really decohering is the position while all other properties remain stable through time (as I've concluded from previous posts). So how is it theoretically possible for this to happen? Or to ask it better what is happening during everyday decoherence of objects that are already in definite states and theoretically there are no superpositions to destroy, like the cat that was alive before entering the box. I want to conceptualize this better.

2. Feb 20, 2016

stevendaryl

Staff Emeritus
Given just about any two configurations of matter, if they have the same values for all conserved quantities (total charge, total energy, total momentum, total angular momentum, etc.) then there will likely be a nonzero chance that a system initially in the first configuration will later be found in the second configuration. So just about any weird thing you can imagine has a nonzero probability: cats spontaneously coming to life, shards of glass reforming into an unbroken mirror, etc. But typically, we treat extremely small probabilities as if they are zero.

3. Feb 20, 2016

durant35

Okay, thanks, great post. So this is based on probability not on actual decoherence and leaking of information into environment?

4. Feb 20, 2016

stevendaryl

Staff Emeritus
Decoherence makes transitions that might have a 1 in $10^{10}$ chance into transitions that have a 1 in $10^{10^{10}}$ (where I'm just making up those numbers).

5. Feb 20, 2016

bhobba

The Linley book is good but it is written at the lay level.

Remember I mentioned there are a number of ways to resolve Schroedinger's Cat? The best way IMHO is to realise due to decoherence everything has an actual position. That is what I explained in other threads. Once that is done all your issues are non issues. The only issue is theoretically there are interference terms - but they are so small they are effectively zero. If such worries you, and it does worry some, then the decoherence program is kaput. But the vast majority of those exposed to it recognise it as a non issue.

Thanks
Bill

Last edited: Feb 21, 2016
6. Feb 21, 2016

durant35

For the sake of the argument, can you explain what is really meant when it is said that interference terms aren't exactly zero? That the position of the object isn't 100 percent defined, but we can treat it as it is and the objects are exactly there in a particular position? And if we do that everything else is classical including the behavior of everyday objects.

7. Feb 21, 2016

bhobba

In decoherence models it very very quickly goes to a very very small number. Its like exponential decay:
https://en.wikipedia.org/wiki/Exponential_decay

No one in their right mind, for time periods much greater than the life-time, would say its not zero even though it strictly speaking isn't. That's all there is to it - nothing more to be said. If you believe that a theoretical very small value is an issue then decoherence is kaput for you and you will need to look into something else. I wont be going there - you are on your own.

Thanks
Bill

8. Feb 21, 2016

durant35

Thanks Bill, I believe it will become a non-issue but my question is interference between what? You said that it has something to do with the position theoretically not being 100%, so is it that the whole issue we are talking about when discussing 'theoretical interference terms'

9. Feb 21, 2016

bhobba

The off diagonal terms in the density matrix. If that makes no sense then the jig is up- it cant be explained at the lay level - at least I cant do it.

Thanks
Bill

10. Feb 21, 2016

durant35

I know that mathematically the off diagonal terms are what is meant. But you also mentioned that here in the macroscopic world what is meant by decoherence is the position/location of the object. So practically is that what is meant by interference terms are not zero, that we shouldn't worry that the position isn't 100% certain and behave as if the objects have definite position?

11. Feb 21, 2016

eloheim

Can't you just say that the macro objects are in spatial superposition but over super tiny distances so it's like the object is just smeared an imperceptibly miniscule amount?

12. Feb 21, 2016

bhobba

Sorry - it's mathematical and cant be explained at the lay level.

Thanks
Bill

13. Feb 21, 2016

bhobba

No.

Its simple. Nothing complicated. Here in the macro world decoherence leads to mixed states of definite position. Superposition, meaning superposition of position, is precisely what is NOT going on. A mixed state of definite position has the form ∑pi |bi><bi|. The |bi><bi| are states of definite position - the pi give the probability of it being in state |bi><bi|.

At the lay level there is a lot of confusion about what exactly a superposition is. Every state is in a superposition of many different states in many different ways. Technically its simply the states form a vector space - its not what many who throw the term about think it is.

Thanks
Bill

Last edited: Feb 21, 2016
14. Feb 21, 2016

durant35

Ok, that's clear. But when you mention that interference terms are not exactly zero do you mean that at some tiny instant the object spreads in position and then decoherence kicks in and brings it back to mixed state? I know you say it is hard to explain it on the lay level but all I seek is an explanation of 'theoretically interference is not zero'. Interference of what? Of the object in one position and the same object in a slightly different position? It's not all about maths if you get a pretty direct question to answer.

15. Feb 21, 2016

bhobba

Thanks
Bill

16. Apr 23, 2016

A. Neumaier

http://xkcd.com/45/