Permenance of Collapsed Wave Function Spin State

In summary: If you make a measurement of the spin state very quickly after observing the spin state, the particle may be in a superposition of spin states but it will be in a specific spin state after the measurement.
  • #1
ChiralWaltz
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5
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
 
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  • #2
ChiralWaltz said:
This is how the particle's spin is determined.

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 possesses 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.

ChiralWaltz said:
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?

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.

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

In theory it happens immediately after but in practical terms it depends on the characteristic time scale of the interactions in the system.
 
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  • #3
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
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
 
  • #6
ChiralWaltz said:
I apologize for incorrectly wording my question and costing you valuable time.
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
WannabeNewton said:

This is helping greatly.

kith said:
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.

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.

WannabeNewton said:
ChiralWaltz said:
can it revert back into superposition? how long does it take?
In theory it happens immediately after but in practical terms it depends on the characteristic time scale of the interactions in the system.

[PLAIN said:
http://physics.stackexchange.com/que...surement-stops[/PLAIN] [Broken] (Geoffrey)]
"if you make another measurement of the same observable very quickly after making the first measurement (and I mean VERY quickly), you will get back the same result because the wave-function has not had time to evolve away from that state yet"

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:

1. What is the collapsed wave function spin state?

The collapsed wave function spin state refers to the state of a particle's spin after it has been observed or measured. In quantum mechanics, particles can exist in a superposition of multiple spin states until they are observed, at which point the wave function collapses and the particle's spin is determined to be in a specific state.

2. How does the collapsed wave function spin state affect the behavior of particles?

The collapsed wave function spin state can affect the behavior of particles in different ways. It can determine how the particle will interact with other particles or fields, and it can also influence the outcome of future measurements on the particle.

3. Is the collapsed wave function spin state a permanent state?

No, the collapsed wave function spin state is not a permanent state. It is only a temporary state that occurs when the particle is observed or measured. As soon as the particle interacts with its environment, its spin state can change and the wave function will expand again.

4. Can the collapsed wave function spin state be predicted?

No, the collapsed wave function spin state cannot be predicted with certainty. According to quantum mechanics, it is impossible to know both the position and momentum of a particle at the same time. Therefore, the exact spin state of a particle cannot be predicted, but only the probability of it being in a certain state.

5. Are there any real-world applications of the collapsed wave function spin state?

Yes, the collapsed wave function spin state has many real-world applications in technologies such as quantum computing and cryptography. It is also crucial in understanding the behavior of subatomic particles and can lead to advancements in fields such as material science and medicine.

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