Can Decoherence Create a Superposition of Life and Death?

[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.

Thanks in advance.

 

[stevendaryl]

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?

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.

 

[durant35]

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.

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

 

[stevendaryl]

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

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).

 

[bhobba]

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..

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 realize 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

 

[durant35]

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 realize 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 decoherene program is kaput. But the vast majority of those exposed to it recognise it as a non issue.

Thanks
Bill

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.

 

[bhobba]

For the sake of the argument, can you explain what is really meant when it is said that interference terms aren't exactly zero?

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 won't be going there - you are on your own.

Thanks
Bill

 

[durant35]

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 won't be going there - you are on your own.

Thanks
Bill

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'

 

[bhobba]

Thanks Bill, I believe it will become a non-issue but my question is interference between what?

The off diagonal terms in the density matrix. If that makes no sense then the jig is up- it can't be explained at the lay level - at least I can't do it.

Thanks
Bill

 

[durant35]

The off diagonal terms in the density matrix. If that makes no sense then the jig is up- it can't be explained at the lay level - at least I can't do it.

Thanks
Bill

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?

 

[eloheim]

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 won't be going there - you are on your own

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?

 

[bhobba]

I know that mathematically the off diagonal terms are what is meant.

Sorry - it's mathematical and can't be explained at the lay level.

Thanks
Bill

 

[bhobba]

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?

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

 

[durant35]

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

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.

 

[bhobba]

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?

The off diagonal terms in the density matrix. If that makes no sense then the jig is up- it can't be explained at the lay level - at least I can't do it.

Thanks
Bill

 

[A. Neumaier]

if the cat survives that it may spontaneously end up in a superposition of dead and alive again

http://xkcd.com/45/