Quantum Coherence: Macroscopic Superpositions Explained

[durant35]

Hi guys,

as it has been said many times on the forum and outside of it the ability to achieve and maintain coherence is the biggest reason why macroscopic superpositions cannot be measured. The typical examples of macroscopic coherence are superconductors where atoms all behave in a similar fashion, therefore bringing coherence from the micro level to the macro level. So my question is, do the atoms in macro objects, or should I say it better - in systems of many, many particles have to behave in a similar way, non-independently to achieve coherence of the system as a whole and therefore creating a superposition of two distinct quantum states of the system as a whole? In the fictive and so oftenly mentioned Schrodinger's cat, would all the atoms inside of the cat's body act coherently like in the case of a superconductor while 'giving us' the alive and dead states?

I appreciate your help. Regards.

 

[bhobba]

is the biggest reason why macroscopic superpositions cannot be measured.

Regardless of state any system is in a superposition in many different ways.

You need to be clearer exactly what you are asking.

Systems of many particles in superposition - superposition of what? And why exactly is such a concern?

You misunderstand Schroedinger's cat completely. The cat is in a state of definite position at all times via interaction with the environment - just like you are. While this is obvious for a cat exactly were to put the cut is the issue and is the point Schroedinger was trying to make. Nowadays its put just after decoherence.

Thanks
Bill

 

[durant35]

Regardless of state any system is in a superposition in many different ways.

You need to be clearer exactly what you are asking.

Systems of many particles in superposition - superposition of what? And why exactly is such a concern?

You misunderstand Schroedinger's cat completely. The cat is in a state of definite position at all times via interaction with the environment - just like you are. While this is obvious for a cat exactly were to put the cut is the issue and is the point Schroedinger was trying to make. Nowadays its put just after decoherence.

Thanks
Bill

Can you give me an example how any system is in a superposition of something in many ways?

Thanks.

 

[Nugatory]

Can you give me an example how any system is in a superposition of something in many ways?

Consider one of the cat's hairs. Not any random hair, but a particular one: the one that is is sprouting from the follicle that is exactly 9387.4 millimeters back from the left corner of the right ear of this cat. Now look closely at that hair; there's a keratin molecule near its tip, in that keratin molecule there's a carbon molecule, that carbon molecule has seven orbital electrons. Let's focus our attention on the outermost of those electrons, which is just one of the $10^{25}$ or so particles that make up the cat. That electron is in a superposition of spin-up and spin-down because it's chemically bonded into the keratin molecule and that's part of how chemical bonds work.

Therefore, the wave function of the cat is a superposition of "this particular electron is spin up and the other particles making up the cat are what they are" and "this particular electron is spin down and the other particles making up the cat are what they are". Of course the cat is alive either way.

 

[stevendaryl]

You misunderstand Schroedinger's cat completely. The cat is in a state of definite position at all times via interaction with the environment - just like you are. While this is obvious for a cat exactly were to put the cut is the issue and is the point Schroedinger was trying to make. Nowadays its put just after decoherence.

I have pointed out this distinction before, but just for clarity, I would like to say it again. The way I understand it, decoherence makes it where there is no such thing as "the cat's quantum state", so there is no such thing as the cat being in a superposition of states. But presumably, there could be a state for the entire universe, and the entire universe could be in a superposition of two states, one of which has a dead cat and one of which has a live cat. Because there is, for all practical purposes, no possibility of observing interference effects between these two states, we can then treat it as if it were a classical mixture--that one or the other is "real", we just don't know which until we make an observation.

The way that you put it seems to imply that decoherence collapses the wave function of the cat, but decoherence is just unitary evolution, but of a larger system than just the cat: it's the cat plus potentially the whole rest of the universe.

 

[bhobba]

The way that you put it seems to imply that decoherence collapses the wave function of the cat, but decoherence is just unitary evolution, but of a larger system than just the cat: it's the cat plus potentially the whole rest of the universe.

It causes APPARENT collapse meaning there is no way to tell the difference.

Thanks
Bill

 

[f95toli]

Can you give me an example how any system is in a superposition of something in many ways?

Thanks.

You need to decide what you want to put into a superposition. Using macroscopic states in a superconducting device you could for example create a superposition of flux, phase of charge; all of these have been demonstrated and are in fact different types of qubits. The flux qubit is perhaps the one that is the most "macroscopic" in that the two flux states corresponds two directions of current flowing in a superconducting ring "at the same time". However, in all these examples everything else about the device would be "classical"..

 

[bhobba]

Can you give me an example how any system is in a superposition of something in many ways?

Its from the definition of superposition.

The principle of superposition is if |a> is a state and |b> is a state then c1 |a> + c2|b> is another state ie the states form a vector space. This means given any state we can find many other states whose superpoition is that state.

Its basic QM.

Thanks
Bill

 

[A. Neumaier]

That electron is in a superposition of spin-up and spin-down

No. One cannot assign a meaningful pure state to this electron, because it is part of a multielectron state. If anything, this electron is in a mixed state. Already the notion of ''the outermost electron'' makes sense only in Hartree-Fock type approximations, and becomes completely dubious in a chemical bond, where one only has delocalized electron clouds with indistinguishable electrons.

 

[durant35]

Consider one of the cat's hairs. Not any random hair, but a particular one: the one that is is sprouting from the follicle that is exactly 9387.4 millimeters back from the left corner of the right ear of this cat. Now look closely at that hair; there's a keratin molecule near its tip, in that keratin molecule there's a carbon molecule, that carbon molecule has seven orbital electrons. Let's focus our attention on the outermost of those electrons, which is just one of the $10^{25}$ or so particles that make up the cat. That electron is in a superposition of spin-up and spin-down because it's chemically bonded into the keratin molecule and that's part of how chemical bonds work.

Therefore, the wave function of the cat is a superposition of "this particular electron is spin up and the other particles making up the cat are what they are" and "this particular electron is spin down and the other particles making up the cat are what they are". Of course the cat is alive either way.

Thank you very much Nugatory.

The reason that I am asking this is because I am trying to compare the case of coherence in the superconductor where all atoms in a similar way and by that principle the coherence is achieved at a macro scale, with the case of other objects which are quite messy, like the cat which has all its atoms jiggling around. So in a hypotethical state of the dead and alive cat would all the atoms behave like in the superconductor, in a similar way, so the coherence can be achieved.

 

[bhobba]

So in a hypotethical state of the dead and alive cat

Its impossible. Cats, alive or dead, have a definite position. Break it up into a large number of small parts all with definite position. The behaviour of those small parts are different for an alive cat or a dead cat ie the alive one has a heart that beats - the dead at doesn't. They are in mutually exclusive states so it can never ever be in a superposition. That's because here in the macro world, and cats are macro objects, they have definite position. If it was a superposition it would not have a definite position - ergo its impossible.

Now please will you stop with this alive and dead cat nonsense. Its pop-sci rubbish.

Thanks
Bill