Does an electron's position collapse when measuring g factor?

[joegibs]

https://link.springer.com/chapter/10.1007/978-3-540-39664-2_1

http://iopscience.iop.org/article/10.1088/0031-8949/1988/T22/016/pdf
In these two experiments done back in the 80's, electrons were trapped inside a penning trap for long periods of time. They were measuring the ratio of the magnetic moment and the angular momentum of the electron (the "g factor"). My question is, when measuring the magnetic moment and angular momentum, did they collapse the electron's positional wave function when doing it? Or was the positional wave function of the electron still uncertain/spread out?

 

[John Park]

was the positional wave function of the electron still uncertain/spread out?

It sounds as though they were doing cyclotron resonance and measuring resonant absorption of radiation. in that case, the position of the electron would be unimportant and hence largely unconstrained.

Also:

The classical notion of an atomic particle at rest in free space is discussed, and shown to be approximable by zero-point confinement of the particle in a laboratory trap.

If the electron was approximately at rest it implies the trap is large and again the position would be uncertain. In the zero-point state, the position is certainly not localised.

 

[joegibs]

It sounds as though they were doing cyclotron resonance and measuring resonant absorption of radiation. in that case, the position of the electron would be unimportant and hence largely unconstrained.

Also:If the electron was approximately at rest it implies the trap is large and again the position would be uncertain. In the zero-point state, the position is certainly not localised.

Is that the case in both of these experiments?

 

[John Park]

Is that the case in both of these experiments?

As far as I can see, the main topic in both the links you give is the same work, out of Seattle.

 

[joegibs]

As far as I can see, the main topic in both the links you give is the same work, out of Seattle.

Oh ok. How does one measure the magnetic moment of the electron tho? And what is the magnetic moment?

 

[John Park]

In one way or another by measuring the strength of its interaction with a magnetic field. What is it you really want to know?

 

[joegibs]

In one way or another by measuring the strength of its interaction with a magnetic field. What is it you really want to know?

What do you mean?

 

[John Park]

You started by asking whether the electron was localised, and now you're asking about measuring magnetic moments. Is there a connection?

 

[joegibs]

You started by asking whether the electron was localised, and now you're asking about measuring magnetic moments. Is there a connection?

No just curious

 

[John Park]

Okay. An electron can take one of two states in a magnetic field; the energy difference between these states is proportional to the magnetic moment and the field. In one type of experiment, you get the electron in the lower state to absorb electromagnetic energy and flip to the upper state,. The frequency of the radiation absorbed is proportional to the energy difference of the two states, from which you can calculate the magnetic moment.

 

[joegibs]

Okay. An electron can take one of two states in a magnetic field; the energy difference between these states is proportional to the magnetic moment and the field. In one type of experiment, you get the electron in the lower state to absorb electromagnetic energy and flip to the upper state,. The frequency of the radiation absorbed is proportional to the energy difference of the two states, from which you can calculate the magnetic moment.

Oh ok. But how do they use the information about the magnetic moment to calculate the size of the electron in these two experiments? It would seem as if they have no connection.

 

[PeterDonis]

did they collapse the electron's positional wave function

This depends on which interpretation of QM you adopt. If you adopt a collapse interpretation like Copenhagen, then yes. If you adopt a no collapse interpretation like the MWI, then no.

If you are asking whether these experiments providea actual evidence that wave function collapse happens, independent of QM interpretation, the answer is no. The results of these experiments can be explained using standard QM (indeed, I believe the papers you linked to do that), which is compatible with both collapse and no collapse interpretations.

 

[John Park]

I think that's to do with quantum electrodynamics--relativistic quantum theory--which I don't claim to understand, but it seems there are subtle effects on the energies involved if the electron has a finite size. (This is not the same as talking about uncertainties in its position--different experiments measure different things; in some the electron is spread out like a wave in others it behaves more like a particle.)

 

[joegibs]

This depends on which interpretation of QM you adopt. If you adopt a collapse interpretation like Copenhagen, then yes. If you adopt a no collapse interpretation like the MWI, then no.

If you are asking whether these experiments providea actual evidence that wave function collapse happens, independent of QM interpretation, the answer is no. The results of these experiments can be explained using standard QM (indeed, I believe the papers you linked to do that), which is compatible with both collapse and no collapse interpretations.

In these experiments, were they just determining the size of internal structure (if there is one)? In that case, the wave function would've never collapse regardless of which interpretation you take. Since all interpretations hold that the internal structure is zero

 

[John Park]

In these experiments, were they just determining the size of internal structure (if there is one)? In that case, the wave function would've never collapse regardless of which interpretation you take. Since all interpretations hold that the internal structure is zero

Peter Donis is better equipped to answer this than I am, but I'll offer my thoughts. As I understand it, "collapse of the wavefunction" doesn't refer to the wavefunction somehow shrinking in physical space so that a particle becomes located at point. It means that the quantum mechanical description of the particle has become less ambiguous (as simple as possible, roughly speaking). Before the "collapse" occurs a particle or other system is in an indefinite state, called a superposition, made up of all possible states. In the case of an electron spin, for any given direction it can be pointing in the same direction or the opposite. The collapse means that the system has entered a single one of the possible states. This description requires that the states have distinct quantum numbe; in many cases identifying the final "collapsed" state and its quantum number still leaves other quantities imprecise: the Seattle authors talk about an electron in its zero-point state. This is an energy state with quantum number zero; it means the energy is precise, but other quantities such as position are still described by distributions. Position in space is not quantised (in conventional quantum mechanics), so there are no pure states corresponding to a particular location of a particle.

The question of the size or internal structure of the electron is a prediction of theories, but the aim of experimental science is to test theories.

 

[PeterDonis]

As I understand it, "collapse of the wavefunction" doesn't refer to the wavefunction somehow shrinking in physical space so that a particle becomes located at point. It means that the quantum mechanical description of the particle has become less ambiguous

More or less, yes. A more technical (and precise) statement would be that collapse means the wave function changes from a superposition of eigenstates of the observable being measured, to one of those eigenstates. If position is being measured, the collapse would be to a position eigenstate. But if some other observable is being measured, the collapse (on a collapse interpretation) would be to an eigenstate of that observable; and the resulting spread in position of the particle's state would depend on the eigenstate that it ended up in (more precisely, on its position representation).

(Strictly speaking, position eigenstates--Dirac delta functions--are not valid states, because they are not normalizable. So an even more precise statement would be that the observable actually being measured when we say we are measuring "position" is not the position operator as it is usually given in idealized QM, but an operator whose eigenstates are something like Gaussians with a narrow spread in position--how narrow depends on the accuracy of the measuring device.)

Before the "collapse" occurs a particle or other system is in an indefinite state, called a superposition, made up of all possible states.

A superposition does not have to contain "all possible states". Which states it contains will depend on how the particle was prepared prior to measurement.

 

[PeterDonis]

were they just determining the size of internal structure

I don't think any of the models being used to analyze these experiments attribute any internal structure to the electron; they all use the standard QM assumption that the electron (like all other fundamental particles) is a point particle. Heuristically, I would say that the measurements being made were to try and determine the spatial "spread" of the electron's wave function--the size of the region of space in which the amplitude, in the position representation, was significantly different from zero.

 

[John Park]

A superposition does not have to contain "all possible states". Which states it contains will depend on how the particle was prepared prior to measurement.

Reference https://www.physicsforums.com/threa...-when-measuring-g-factor.908221/#post-5720600

Thanks for the correction. (I was also trying to explain without using the term "eigenstate".)