Can All Particles of a Cat Be in Superposition Simultaneously?

[durant35]

Hi guys,

just a quick question. This is an idea that came up to my mind while thinking about decoherence and stability of macroscopic objects in the world. As we know all superpositions and interference effects are destroyed in a enormously tiny timescale, and as Mfb mentioned it is meaningless to talk about a quantity that is in superposition in that short time interval. Now this may or may not imply bizzareness, but is it possible that all particles of a cat or a table can be in a superposition of different composition in that tiny instant, for instance a cat that is in a state of being in a normal state with its particles constitued as we see it and a state of let's say its neurons being in its legs, or whatever, just that those particles that make up her body are differently ordered. I hope somebody can clear up this bizzareness and explain. Thank you

 

[alw34]

If macroscopic objects are in such a state for 10^{-bazillionths of a second} or whatever
why worry? Once things get to the Planck scale, nobody knows what's happening anyway.

 

[durant35]

It is bizzare, just that

 

[bhobba]

and as Mfb mentioned it is meaningless to talk about a quantity that is in superposition in that short time interval.

Of course not. Macro objects do not come into existence instantaneously then decohere. They are there all the time constantly being decohered. As the object with localised position spreads it interacts with the environment and that stops the spreading keeping it in a definite position.

Thanks
Bill

 

[durant35]

I don't understand it, simply I don't. Logic says this - if decoherence is such a fast process any superposition that occurs is destroyed in a range of a smallest fragment of time. What it means to constantly decohere? Do superpositions of properties occur or not?

 

[StevieTNZ]

I don't understand it, simply I don't. Logic says this - if decoherence is such a fast process any superposition that occurs is destroyed in a range of a smallest fragment of time. What it means to constantly decohere? Do superpositions of properties occur or not?

Dear durant35

Decoherence only causes apparent collapse. In principle, the superposition (macroscopic object entangled with the environment) still exists.

 

[durant35]

Dear durant35

Decoherence only causes apparent collapse. In principle, the superposition (macroscopic object entangled with the environment) still exists.

Yes, I know that. The thing I don't understand is the consequence of this for everyday objects. When we see or measure an object we always find in a definite state, so if we focus solely on that object and its properties does or does not the object have a definite state at each instant? Thats what I don't understand regarding decoherence.

 

[bhobba]

does or does not the object have a definite state at each instant? Thats what I don't understand regarding decoherence.

Yes - but it isn't not a pure state. Its a mixed state. Mixed states can be interpreted as being in a certain state with some probability. This is written as ∑pi |bi><bi| which says its in state |bi><bi| with probability p1. Trouble is that's not how it was necessarily prepared ie it was not necessarily done by some process randomly selecting some state |b1><ibi| with probability pi. If it was done that way its called a proper mixed state. But that not what happens in decoherence - it mathematically exactly the same - you can't tell the difference - but it wasn't prepared as a proper mixed state. That's why its only called apparent collapse. Can we assume it is a proper mixed state and actual collapse occurred. Of course you can - and if you do all problems in QM gone. Its called the ignorance ensemble interpretation (ensemble comes from the frequentest probability interpretation of the pi - its a slight variation on the ensemble interpretation). The thing is it an interpretive assumption - how does it become a proper one - blank out. There are all sorts of ways it could, BM, MW, Nelson Stochastics, primary state diffusion. It may even be nature is simply like that - nothing deeper going on at all. That's where ignorance comes in.

Thanks
Bill

 

[StevieTNZ]

Yes, I know that. The thing I don't understand is the consequence of this for everyday objects. When we see or measure an object we always find in a definite state, so if we focus solely on that object and its properties does or does not the object have a definite state at each instant? Thats what I don't understand regarding decoherence.

To us we see it in a definite state; it's description by Quantum Mechanics has it being in a superposition. This is where we meet the measurement problem.

 

[bhobba]

it's description by Quantum Mechanics has it being in a superposition.

That's not true. After decoherence its not in a superposition - its in a mixed state. Note every pure state is a superposition of many other states and in many different ways. When referring to decoherence here in the macro world we are referring to superpositions of position because the usual radial symmetry of interactions decoheres into a mixed state of position ie the |bi><bi| of ∑pi |bi><bi| are position eigenstates. 100% for sure it is not in a superposition of position.

Thanks
Bill

 

[durant35]

ut according to the MWI, it *is* a superposition (the mixed state is just an approximation). According to the MWI, unitary evolution is the only kind of evolution there is, and a unitary transformation can't turn a pure state into a mixed state.

(Bear in mind that I'm not necessarily agreeing with the MWI; I'm just trying to be clear about what it says.)

What about this old post from PeterDonis?

 

[bhobba]

ut according to the MWI, it *is* a superposition (the mixed state is just an approximation).

That's wrong.

The off diagonal elements are not quite zero - but so low to be undetectable - but that does not mean its in a superposition. In fact since its entangled so it can't be in a pure state hence can't be in a superposition.

Before drawing conclusions like the above you need to study the detail so you have the background to make correct ones.

Thanks
Bill

 

[durant35]

It wasn't my conclusion of course, I'm not competent enough to type down something like that. It was from another forum member and I just wanted your opinion about it because everything you say makes sense pretty much. So if we assume the ignorance ensemble approach combined with decoherence, can we conclude that each macroscopic object has a definite property at each instant on the timescale (but a mixed state ofc), nature doesn't really care and collapse has actually happened (there are no macroscopic superpositions in conditions we live in) ?

 

[bhobba]

can we conclude that each macroscopic object has a definite property at each instant on the timescale (but a mixed state ofc), nature doesn't really care and collapse has actually happened (there are no macroscopic superpositions in conditions we live in) ?

Of course we can.

But again I stress we are dealing with the property of position.

As I have said don't get worried about the fact theoretically its not zero. It's the type of thing that happens in applied subjects all the time.

Thanks
Bill

 

[durant35]

Of course we can.

But again I stress we are dealing with the property of position.

As I have said don't get worried about the fact theoretically its not zero. It's the type of thing that happens in applied subjects all the time.

Thanks
Bill

I understood the thing about. So other properties are basically derived and the same as in classical world because the object is really-well localized?
The main thing I was stressing about (and you know it) are the Schrodinger cat-like properties (like dead or alive, or the shape of the object). So all objects are constantly decohering and the position basis or location is well defined at any instant, and from follows that the other properties of the object are definite (or classical) at any instant. Why does the decoherence time get mentioned so much then in textbooks so it leaves an impression that the objects properties in fact are in a superposition but then decoherence destroys the superposition?

 

[stevendaryl]

Hi guys,

just a quick question. This is an idea that came up to my mind while thinking about decoherence and stability of macroscopic objects in the world. As we know all superpositions and interference effects are destroyed in a enormously tiny timescale, and as Mfb mentioned it is meaningless to talk about a quantity that is in superposition in that short time interval.

Just to clarify something: Every quantum state can be interpreted as a superposition of other quantum states. So it doesn't really make sense to say that decoherence gets rid of superpositions. What it does is prevent interference effects among macroscopically distinguishable states. So you can never observe interference effects between a dead cat and a live cat. But there are still superpositions involved.

 

[durant35]

Just to clarify something: Every quantum state can be interpreted as a superposition of other quantum states. So it doesn't really make sense to say that decoherence gets rid of superpositions. What it does is prevent interference effects among macroscopically distinguishable states. So you can never observe interference effects between a dead cat and a live cat. But there are still superpositions involved.

If we understand decoherence as a collapse, no as an apparent collapse, (like Bill mentioned), the superpositions go away, right? How would you describe the superpositions that are not macroscopically distinguishable, can you give me an example?

 

[bhobba]

Why does the decoherence time get mentioned so much then in textbooks so it leaves an impression that the objects properties in fact are in a superposition but then decoherence destroys the superposition?

Decoherence isn't just for the quantum classical transition - it has practical applications as well. Now don't ask me about those because I am not into it, but its important for that, in particular they want to prevent it in quantum computing.

Thanks
Bill

 

[stevendaryl]

ut according to the MWI, it *is* a superposition (the mixed state is just an approximation). According to the MWI, unitary evolution is the only kind of evolution there is, and a unitary transformation can't turn a pure state into a mixed state.

(Bear in mind that I'm not necessarily agreeing with the MWI; I'm just trying to be clear about what it says.)

What about this old post from PeterDonis?

Another point of clarification: When you ask whether some subsystem--such as an electron, or a molecule, or a cat--is in a superposition of states, that's a little ambiguous. In MWI, there is a single wave function for the entire universe, and that wave function is in a superposition of possibilities. But subsystems don't have a wave function, in general. If two subsystems are entangled, there can be a wave function for the composite system, but not for each subsystem.

 

[stevendaryl]

If we understand decoherence as a collapse, no as an apparent collapse, (like Bill mentioned), the superpositions go away, right?

I don't know if "go away" is the right phrase. The way I understand decoherence as applied to Schrodinger's cat is this: Originally, you have a uranium atom that is in a superposition of decayed/undecayed states. The superposition quickly "infects" the rest of the universe. You don't have a cat that is in a superposition of live and dead, instead, you quickly have the entire world in a superposition of a world with a dead cat and a world with a live cat. The implications of the uranium decay spread out at the speed of light. In one "branch", there is a decayed uranium atom, and there is a dead cat, and there is me, crying over my dead cat, and there is Schrodinger patting me on the back and telling me that my cat died for the good of science, etc. In another cat, the atom is undecayed and the cat is alive, and I'm not sad, and Schrodinger isn't patting me on the back.

Once a superposition has "infected" the whole world, the various macroscopically distinguishable branches no longer have any effect on each other. At this point, you may as well assume that the branch you're observing is the only one. Or you can go MWI and assume that the other branches exist, as well. It doesn't make any practical difference.

How would you describe the superpositions that are not macroscopically distinguishable, can you give me an example?

Sure. A molecule can be in two different configurations of the same atoms, or it can be in a superposition of those configurations. Such a superposition is not of macroscopically distinguishable states.

 

[durant35]

Sure. A molecule can be in two different configurations of the same atoms, or it can be in a superposition of those configurations. Such a superposition is not of macroscopically distinguishable states.

I thought so, but I was reffering to small time intervals combined with macroscopic objects. So at any instant of time can we assign a definite macroscopically distinguishable state to an object?

 

[durant35]

Decoherence isn't just for the quantum classical transition - it has practical applications as well. Now don't ask me about those because I am not into it, but its important for that, in particular they want to prevent it in quantum computing.

Thanks
Bill

Zurek mentions it for neurons in our brain, so he leaves the impression that they are constantly jumping in and out of superposition.

 

[durant35]

The thing that I still conceptualy grasp rightly is the 'evolution' of decoherence in time. So let's consider the example of my car and a period of half an hour of its existence. It is valid to say that it is undergoing process of decoherence, but my car existed before this interval, it wasn't brought to existence and than decohered for let's say 5 miliseconds and started behaving classically. During this period of an half an hour, what happens with the car? Is it decohered for the full interval (no presence of interference effects at any moment) due to constant interaction? The concept of 'decoherence time' is basically my biggest obstacle since it implies that an object jumps from a superposition to a definite state then again to a superposition and then again to a definite state, but that superpositions last shortly. So what is achieved by constant monitoring of an system like car, in everyday world, that wasn't in a superposition before focusing on the specific interval (unlike the Schordinger cat setup).

 

[Nugatory]

The concept of 'decoherence time' is basically my biggest obstacle since it implies that an object jumps from a superposition to a definite state then again to a superposition and then again to a definite state, but that superpositions last shortly.

Part of the problem here is that we're using this term "definite state" which doesn't have a clear definition. It sounds as if you're thinking that a "definite state" is one that is not a superposition, and that our definite measurement results indicate that we must have such a state after the measurement. However, "not a superposition" makes no sense because all states are superpositions (or mixtures of superpositions) in some basis - the question is whether the observables corresponding to this basis are macroscopically interesting. @stevendaryl posted a good example above: A chemically bonded molecule is just about always described by a superposition of states of the valence electrons, but a position measurement of the molecule doesn't care.

 

[durant35]

Part of the problem here is that we're using this term "definite state" which doesn't have a clear definition. It sounds as if you're thinking that a "definite state" is one that is not a superposition, and that our definite measurement results indicate that we must have such a state after the measurement. However, "not a superposition" makes no sense because all states are superpositions (or mixtures of superpositions) in some basis - the question is whether the observables corresponding to this basis are macroscopically interesting. @stevendaryl posted a good example above: A chemically bonded molecule is just about always described by a superposition of states of the valence electrons, but a position measurement of the molecule doesn't care.

You're right, the terminology is the problem, I'm not an expert and by my terminology I use common-sense phases.
By a definite state I mean a macroscopic property, like being dead or alive. In the Schrodinger's cat experiment the cat settles into a definite state before observation (for instance it survives and it's alive). We observe definite properties on everyday basis, my computer is white, rectangular and so on.. That's what I mean by definite state. Now you may understand it better.

 

[durant35]

Part of the problem here is that we're using this term "definite state" which doesn't have a clear definition. It sounds as if you're thinking that a "definite state" is one that is not a superposition, and that our definite measurement results indicate that we must have such a state after the measurement. However, "not a superposition" makes no sense because all states are superpositions (or mixtures of superpositions) in some basis - the question is whether the observables corresponding to this basis are macroscopically interesting. @stevendaryl posted a good example above: A chemically bonded molecule is just about always described by a superposition of states of the valence electrons, but a position measurement of the molecule doesn't care.

Can you explain what do you mean when you say that all states are superpositions in some basis, with an example?

 

[StevieTNZ]

Can you explain what do you mean when you say that all states are superpositions in some basis, with an example?

E.g. the photon polarization |H> being a superposition of |45> - |135>, polarization |V> being |45> + |135>

 

[StevieTNZ]

and a unitary transformation can't turn a pure state into a mixed state.

That is correct.

 

[durant35]

E.g. the photon polarization |H> being a superposition of |45> - |135>, polarization |V> being |45> + |135>

Okay, I get that. I was referring to the fact that let's say my computer is *rectangular*, that is not a superposition, we don't observe a superposition. That's what I mean when I say definite state.

 

[Nugatory]

Can you explain what do you mean when you say that all states are superpositions in some basis, with an example?

Try posts #9 and #11 of this thread: https://www.physicsforums.com/threads/nature-of-quantum-mechanics.823160/

 

[durant35]

That is correct.

Bill said it isn't correct.

Try posts #9 and #11 of this thread: https://www.physicsforums.com/threads/nature-of-quantum-mechanics.823160/

Now I understand what you meant, thank you. I still don't understand how does the macroscopic world emerge from quantum physics and how do all these states that seem definite occur. I can precisely describe the objects around me right now but I never get a simplification of anything and a common-sense description of the process.

 

[StevieTNZ]

Bill said it isn't correct.

bhobba was responding to a different part of the sentence that I responded with that comment to.

EDIT: here are some posts of mine in other threads -- https://www.physicsforums.com/threa...ependent-outcome-problem.825657/#post-5184705 and https://www.physicsforums.com/threa...e-double-slit-experiment.765350/#post-4819722

 

[durant35]

So basically we would need a collapse to avoid bizzarity in macroscopic interferences, or a better quantum theory which explains the objective evolution of 'classical' objects?

 

[bhobba]

Can you explain what do you mean when you say that all states are superpositions in some basis, with an example?

I am sorry but the jig is up here. You need to delve into the technicalities. One can only go so far in explaining this linguistically. Feynman commented on this. It doesn't matter how good you are at lay explaining you will always run into the difficulty the laws of physics are written in the language of math. You must learn that for any real understanding.

All you have to accept however is due to the nature of interactions here in the macro world we generally don't see superpositions of position.

Thanks
Bill

 

[bhobba]

So basically we would need a collapse to avoid bizzarity in macroscopic interferences, or a better quantum theory which explains the objective evolution of 'classical' objects?

No. It is generally accepted that decoherence explains why we generally do not see interference effects.

Again if you want to go beyond simply accepting what we say and actually draw inferences you must learn the detail. Start here:
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

Bill said it isn't correct.

Just to be clear what I am saying. When objects are entangled with other objects and you observe one of those objects and not the other it is found to be in a mixed state. If the system as a whole is isolated they evolve by unitary evolution.

Suppose you have system 1 that can be in state |a> or |b> and system 2 can be in state |a> or |b>. If system 1 is in state |a> and system 2 is in state |b> that is written as |a>|b> and similarly if system 1 is in state |b> and system 2 in state |a> that is written as state |b>|a>. Now according to the principle of superposition you can have a superposition of these ie c1|a>|b> +c2|b>|a>. The systems are entangled. Each system is no longer in a pure state - they have lost their individuality. The interesting thing however is if you observe system 1 it acts as though its now in a mixed state. The entanglement has broken the unitary evolution. The two systems as a whole evolve unitarily - but the systems when observed behave differently. This is the origin of decoherence and since everything here in the macro world is entangled why we have classical properties.

Thanks
Bill

 

[StevieTNZ]

[Mentor's note: edited to remove quoted text from deleted posts]

As bhobba has (at least the way I've interpreted it) stated if you have system 1 + system 2 entangled, and you only look at system 1, then the Mathematics of system 1 is a mixed state. But the true reality is system 1 is still entangled with system 2, thus system 1 and 2 are in a superposition (Bill can correct me if I am wrong in summarising his point. I am unsure whether he is using the word 'observe' as theoretically looking at system 1, or experimentally measuring system 1).

 

[bhobba]

As bhobba has (at least the way I've interpreted it) stated if you have system 1 + system 2 entangled, and you only look at system 1, then the Mathematics of system 1 is a mixed state. But the true reality is system 1 is still entangled with system 2, thus system 1 and 2 are in a superposition (Bill can correct me if I am wrong in summarising his point. I am unsure whether he is using the word 'observe' as theoretically looking at system 1, or experimentally measuring system 1).

That's it. The modern view of observation is to place the Von Neumann cut just after the systems become entangled which is equivalent to taking the mixed state as proper mixed state. Of course out there everything is always entangled so there is no pure state that evolves. Even in deep interstellar space objects are entangled with the CBMR and the quantum vacuum which is responsible for spontaneous emission.

Thanks
Bill

 

[durant35]

Just to be clear what I am saying. When objects are entangled with other objects and you observe one of those objects and not the other it is found to be in a mixed state. If the system as a whole is isolated they evolve by unitary evolution.

Suppose you have system 1 that can be in state |a> or |b> and system 2 can be in state |a> or |b>. If system 1 is in state |a> and system 2 is in state |b> that is written as |a>|b> and similarly if system 1 is in state |b> and system 2 in state |a> that is written as state |b>|a>. Now according to the principle of superposition you can have a superposition of these ie c1|a>|b> +c2|b>|a>. The systems are entangled. Each system is no longer in a pure state - they have lost their individuality. The interesting thing however is if you observe system 1 it acts as though its now in a mixed state. The entanglement has broken the unitary evolution. The two systems as a whole evolve unitarily - but the systems when observed behave differently. This is the origin of decoherence and since everything here in the macro world is entangled why we have classical properties.

Thanks
Bill

But what about other macroscopic properies and their interference? Can you say, reasonably, and for sure that you aren't both dead and alive in any fragment of time, that those two properties do not interfere like in the case of Schrodinger's cat?

 

[durant35]

I think I understood it, when we talk about macroscopic objects we are talking about position basis and interference effects between different positions. In Schrodinger's cat the interference effects were created from a subatomic effect and that's why the interference properies were alive and dead. Since no microscopic/macroscopic sequence of events occurs in the real world we can safely assume that the only properties that are interfering are location properties, everything else is stable. Right?

 

[bhobba]

Can you say, reasonably, and for sure that you aren't both dead and alive in any fragment of time,

I have answered that before - it never is - ever ever. Its impossible ie a live cat breaths, has a heart pumping - its constituent parts with definite position behave in a different way

Thanks
Bill

 

[durant35]

I have answered that before - it never is - ever ever. Its impossible ie a live cat breaths, has a heart bumping - its constituent parts with definite position behave in a different way

Thanks
Bill

Ok. You said that decoherence leads to macroscopic position basis, so the only uncertainties or small undetectable interference effects are related to the position of the object, everything else evolves classicaly without interferences. So when we are sure that the object is well located the classical behavior emerges and there is no bizzareness.

 

[durant35]

I have answered that before - it never is - ever ever. Its impossible ie a live cat breaths, has a heart bumping - its constituent parts with definite position behave in a different way

Thanks
Bill

This was one of your older posts:
We know 100% for sure the cat is not in any kind of superposition that is detectable. In fact decoherence shows it decays to way way below our ability to detect very very quickly.

Thanks
Bill

So in the experiment is there a possibility for an undectetable interference?

 

[bhobba]

So in the experiment is there a possibility for an undectetable interference?

I have already said theoretically its not actually zero. The other issue is the components of a cat were decoherted way way back even before the cat was born. The cat never ever ever is in a superpoition of position.

Thanks
Bill

 

[durant35]

I have already said theoretically its not actually zero.

Thanks
Bill

But that state can't be qualified as a relevant superposition, right?

 

[stevendaryl]

But what about other macroscopic properies and their interference? Can you say, reasonably, and for sure that you aren't both dead and alive in any fragment of time, that those two properties do not interfere like in the case of Schrodinger's cat?

Yes, that's the whole point of decoherence is that there is no superposition of a live cat and a dead cat. Or rather, getting a superposition of a dead cat and a live cat is about as likely as getting a melted ice cube to reform on a hot day.

 

[durant35]

Yes, that's the whole point of decoherence is that there is no superposition of a live cat and a dead cat. Or rather, getting a superposition of a dead cat and a live cat is about as likely as getting a melted ice cube to reform on a hot day.

And of course, you would have to induce it with a microscopic event like in the experiment with the atom decay or like they induced an excited state with the photon in the diamonds experiment.

 

[durant35]

I have already said theoretically its not actually zero. The other issue is the components of a cat were decoherted way way back even before the cat was born. The cat never ever ever is in a superpoition of position.

Thanks
Bill

So let me get this straight, in the experiment there was a cause for the potential death of the cat (the nucleus decaying) and even though the decoherence happens at the particle detector when it reaches the cat there is still undetectable interference?

But without a cause like the nuclear decay, in everyday life, anything that is alive is decohered to the position basis and interference properties don't exist?

 

[durant35]

It seems that if interference again occurs, that nature is forced to select again.

Consider this example, let'say the decoherence happened at the particle detector and the cat survived and it is alive. If the beyond detectable interference between alive and dead again occurs, the cat may die without a reason simply because nature chose a different outcome based on that moment of time. The same thing applies to any human if there occur interference terms between alive and dead at any instant. I know this sounds crazy, so please correct me when I'm wrong, if it's possible in common-sense terms.

 

[bhobba]

The same thing applies to any human if there occur interference terms between alive and dead at any instant.

That's not possible as I have explained. I have zero idea why you want to pursue it.

You need to study the actual theory - you will never understand it the way you are trying to.

Thanks
Bill