Does measuring an atom collapse the wavefunction of its parts?

[friend]

Suppose you have an experiment that measures the property of an atom as a whole, maybe you can put it through a double-slit or measure its spin, whatever. Presumably that will collapse the wavefunction that you used to describe the atom in that experiment. Would this entail that in the process you collapsed the wavefunction of all the subatomic particles that made up the atom? Could you know the overall spin, for example, and not know the spin of all of the parts?

 

[DrChinese]

Suppose you have an experiment that measures the property of an atom as a whole, maybe you can put it through a double-slit or measure its spin, whatever. Presumably that will collapse the wavefunction that you used to describe the atom in that experiment. Would this entail that in the process you collapsed the wavefunction of all the subatomic particles that made up the atom? Could you know the overall spin, for example, and not know the spin of all of the parts?

Yes, that's correct. Other observables might remain in a superposition even as a particular observable takes on a well defined value.

 

[friend]

Thinking further on this. Would it be the case in measuring the spin of the atom, for example, that the spins of all the subatomic particles would have to at least add up to the value measured of the atom, but this would allow some freedom for various combinations of how those spins were distributed among the subatomic particles? So in effect does measuring the atom then put the subatomic particles into entanglement with each other, when perhaps before they were not? Or were they always entangled with each other? Thanks.

 

[DrChinese]

Thinking further on this. Would it be the case in measuring the spin of the atom, for example, that the spins of all the subatomic particles would have to at least add up to the value measured of the atom, but this would allow some freedom for various combinations of how those spins were distributed among the subatomic particles? So in effect does measuring the atom then put the subatomic particles into entanglement with each other, when perhaps before they were not? Or were they always entangled with each other? Thanks.

Your basic idea is correct, that there is freedom for the component particles of the system to have various combinations that sum to the observed value.

A good basic rule is that ground state electrons (say in helium), being indistinguishable, are entangled. You know their total spin is 0, for example, but there is no way to say which is +1/2 and which is -1/2. That is a recipe for entanglement.

 

[friend]

When we talk about how many ways to get the same measured value, then that's the definition of entropy (and perhaps information). So it sounds like what we seem to be saying is that there is some entropy associated with measurement, at least in measurements of composite particles. And it sounds like we are also talking about entanglement. Do these considerations give us a mathematical connection between a measure of entropy and a measure of entanglement? Does this suggest they are both different ways of describing the same thing? Thanks.

 

[atyy]

@friend, I have not thought about your OP carefully, but quickly reading your posts, you might be interested in reading about the entanglement entropy: http://www-bcf.usc.edu/~tbrun/Course/lecture17.pdf (slide 32).

 

[Khashishi]

Yes, subatomic particles are within atoms are usually if not always entangled. Entanglement is some constraint on two or more objects that can't be written as a constraint on each object individually. Since each constraint reduces the number of possibilities, it reduces the entropy. But you can have other kinds of constraints that reduce the entropy, so I wouldn't think too much about the connection between entanglement and entropy.

Perhaps it is time to learn about LS coupling (and jj coupling). We label the state of an atom or molecule using "term symbols" which include information about the magnitude of the total spin S, magnitude of the total orbital angular momentum L, and magnitude of the total angular momentum J. We can determine this information with spectroscopy. We don't know the direction of the total spin or the direction of the total angular momentum, but we do know that they add up to J. Since we don't know all the information, there are multiple microstates with the same term symbol.