# Permenance of Collapsed Wave Function Spin State

1. Apr 9, 2014

### ChiralWaltz

Hello Everyone,

General curiosity question.

We start with a particle who is in superposition.

We observe it and collapse its wave function. This is how the particle's spin is determined. Two states can exist, spin up or spin down.

My question is, once we observe the spin state, is the particle locked into that specific spin state forever or can it revert back into superposition?

Assuming the latter may be true, is there a specific amount of time we have to wait for before it re-assumes superposition?

Thank you,
Chiral

2. Apr 9, 2014

### WannabeNewton

As an aside, unless I'm misinterpreting what you're saying, you seem to be under the impression that a measurement of the spin of a particle in a superposition of spin states yields the spin the particle possessed before measurement-this is not how superposition is usually interpreted in QM. Rather, when the particle is in such a superposition, it cannot be said to possess any value of spin at all; the classical notion of particles possessing values for an observable is usually seen as inapplicable in QM for particles in superpositions of eigenstates of an observable. In other words, it is not the case that it possesses a spin that we are ignorant of before measurement.

This depends entirely on the interactions within the system. If we have an electron at rest in a magnetic field (meaning we have the electron be in a momentum eigenstate and boost to the frame in which the associated momentum eigenvalue vanishes) initially in a definite spin state, the spin of the electron will precess as per the time evolution under the Schrodinger equation with the interaction Hamiltonian being given by the coupling of the electron magnetic moment to the external magnetic field. If we then make a measurement of the spin of the electron at an arbitrary instant of its precession and take the resulting spin eigenstate and feed it back into the Schrodinger equation as a new initial condition then it will again precess. The precession will in general have the electron be in a superposition of spin states.

In theory it happens immediately after but in practical terms it depends on the characteristic time scale of the interactions in the system.

3. Apr 9, 2014

### kith

You seem to have a misconception about the concept of superposition. Being "in superposition" is not a property of the system. Every system in a definite quantum state is in a superposition state with respect to some observables and in an eigenstate with respect to some other observables. ("eigenstate" is the opposite of superposition; if the system is in an eigenstate of a certain observable, the value of this observable is definite)

After a spin measurement in direction z, your system will be in an eigenstate of the corresponding spin observable. But at the same time, this state is a superposition of spin direction x eigenstates.

Every state is an eigenstate of the spin observable in some direction and every state is a superposition of eigenstates of the spin observable in many other directions.

So your question seems not very meaningful to me.

4. Apr 10, 2014

### ChiralWaltz

WannabeNewton and kith,

Thank you so much for answering my question. Obviously, I need to be hanging out with Newton more before I play in this forum.

I apologize for incorrectly wording my question and costing you valuable time.

Also, thank you for going into the depth that you did. I am a little unclear on it but that will require reading and math on my part to understand it before I come back to this.

Chiral

5. Apr 10, 2014

### WannabeNewton

6. Apr 10, 2014

### kith

There's nothing to apologize. If one doesn't understand something, the first step is to find good questions. Understanding why a certain question doesn't make sense may improve the overall understanding greatly.

7. Apr 10, 2014

### ChiralWaltz

This is helping greatly.

I'll work on developing my questions more thoroughly.

Round 2:

I'm confused about the statement made by WannabeNewton and the one made by Geoffrey.

What I am seeing here is two conflicting ideas. Does the interpretation of QM vary from user to user and allow for both of these ideas to be correct?

Please let me know if I am starting to get what is going on here:
I have a particle in superposition.

I can take a measurement of position, momentum or energy. Does this mean I can only take one measurement at a time on a single particle? I would assume so due to the Heisenberg uncertainty principle in regards to measuring position and momentum.

Since my name is Chiral and I want to find the chirality of the particle. I do so by measuring (observing?) the momentum, correct?

Doing so collapses the wavefunction into "a Dirac delta function in the eigenbasis" (no idea what this is but I will when I get there in the math) in momentum space.

Either the particle has to wait to go back into superposition or it happens instantly.

Then I take a measurement, of which I have three choices, and the whole thing starts all over again?

Thank you for helping me understand this better.

Last edited by a moderator: May 6, 2017