What constitutes as a measurement?

[Qentanglement]

I was talking to my professor about what constitutes as a measurement and the topic of the Stern-Gerlach experiment arised.

*Please don't discuss about schrodinger's cat and that funny business, I've heard it many times and I am very bored of that discussion. Please no metaphysics BS, I want to discuss explicitly about measuring spin of a charged particle.

So my professor told me that when you send charged particles, electrons, through the SG machine it will separate out spin up particles and spin down particles because of a varying magnetic field. Then what he says constitutes as a measurement is that "the electrons say hit a screen and makes two marks"

I don't understand this. So if you didn't have a screen, then no measurement is made? Won't the electron's spin be measured already because we know that spin up electrons are going a different path from the spin down electrons? Or do can we not know the path or trajectories of electrons? What I constitute as a measurement is "Whenever an interaction occurs" In this case the interaction is the magnetic field with the electrons.

Why does there have to be a recording of this interaction for there to be a measurement?

From my definition, won't electrons measure each other's spin's all the time? Charged particles create a varying magnetic field because they are moving and thus electrons go through each other's magnetic field and constantly measure each other's spins?

My professor says that my example with electrons are just interacting with each other and not really measuring their spins!

What is the answer to this?

 

[alxm]

Whenever an interaction with the environment-at-large occurs.

For instance, if a spin-up electron scatters off a spin-down electron, you end up with two entangled electrons, one of which is spin-up and one of which is spin-down, but you don't know which is which. So you're correct: That interaction didn't cause any 'collapse of the wave function' (from the Copenhagen POV). And does not constitute a 'measurement' of the spin of either electron, even though a related interaction occurred.

Yet, a measurement with a Stern-Gerlach apparatus clearly does, even though everything in the SG-apparatus is clearly operating on the same fundamental interactions! That's the crux of the issue (illustrated by "Schrödinger's Cat") right there: Interactions at the quantum level don't cause a 'collapse', yet interactions at the macroscopic level do. Why? Moreover, the QM level interactions are time-reversible, but the 'collapse' isn't, why?

To begin with the latter, when you perform a measurement on a quantum-mechanical particle then your macroscopic system is in some labile state (e.g. a PMT in the Geiger counter in the Schrödinger's Cat example), when 'magnifying' your state from the quantum to the macro level, you're moving to a less energetic state, causing entropy. This explains how one gets from a microscopic, reversible system to a macroscopic, irreversible one. Basically, the 'arrow of time' is thermodynamic. (There's a nice http://www.youtube.com/watch?v=_Kab9dkDZJY" on it)

The answer to the first question is now usually regarded as decoherence. The way it works (part simplified and part because there's still a lot about it we don't know), is that as you go to a macroscopic system, the number of constituent quantum states increases enormously. A "live" or "dead" cat or a SG-apparatus giving a result, is after all not a single state of matter but comprises a gigantic number of quantum-mechanical states of all the constituent atoms and so on. As your quantum-mechanical state is becoming magnified to this greater number of states, information is being lost to the environment due to entropy. The end result of this is that the quantum-mechanical superpositions get 'washed out', and you are left with real probabilities. The cat was either alive or dead, the electron was either spin up or down.

So an environmental interaction that would allow you to determine, in principle, a particular state of a quantum-mechanical system will lead to decoherence and a 'measurement'. The more strongly it interacts with the environment, the greater the likelihood of the 'measurement' occurring. (e.g. we can keep the spins of the nuclei in molecules in a coherent state for quite some time, because they only interact very weakly with the 'outside') It doesn't matter if you're recording the result of the measurement or not, only whether or not the 'measuring interaction' is there or not.

 

[Qentanglement]

I just learned in QM class today that decoherence is due to the fact that the superposition of different basis wave functions that make up the total wave function are each affected differently because of the time phase factor. The example we did in class is with a varying magnetic field.

The time phase factor, exp(-i*E*t/h) is multiplied by the time independent spin wave function.

The time independent spin wave function is, Phi = 1/sqrt(2) * [ up + down ].

My professor points out that the time phase factor depends on energy and when it is multiplied with Phi, then it has a different effect on the up vs the down.

E = gamma*B*(h_bar/2) for the up case, and E = -gamma*B*(h_bar/2) for the down case.

What you end up getting is a phase difference between the states once B was introduced, Phase factor = gamma*B*t

Since B fluctuates, then the Phase factor fluctuates as well making the expectation value of the spin wave function completely random. I see that the spin wave function did not collapse but measurements on the spin wave function yield results that are exactly like a mixture of states. Thus this effect is known as decoherence.

So the difference between a decohered spin wavefunction vs a mixture of spin wavefunctions is that the mixture are collapsed wave functions whereas the decohered spin wavefunction are not. And experiments cannot find out the difference! Because the expectation value of a mixture of spin states is 50% up and 50% down, and the expectation value of a decohered spin wave function is also 50% up and 50% down.

My professor showed decoherence on one particle! showing it with how a varying magnetic field can cause the spin wave function to decohere.

So what you are saying with a general large wave function is that there are more than two basis states and that the time phase factor will act differently on each of those basis states? I don't see how decoherence has anything to do with answering the question of what constitutes as a measurement

As I understand entropy, It is the number of states a system can be in. A system with a lot of energy would mean more different states that it could be in, thus high entropy. A system with low energy would mean less states and thus low entropy. I don't see how entropy has anything to do with what constitutes as a measurement

In the end, you do agree with my definition. You say that it doesn't matter if the measurement is recorded or not, only if there is an interaction.

You agreed with me but I don't understand your reasoning from your answer

 

[ThomasT]

So if you didn't have a screen, then no measurement is made?

Yes, that's my understanding.

Won't the electron's spin be measured already because we know that spin up electrons are going a different path from the spin down electrons?

No. You don't 'know' anything wrt any specific trial until you get a qualitative, ie. classical, instrumental response.

Or do can we not know the path or trajectories of electrons?

That's my understanding.

What I constitute as a measurement is "Whenever an interaction occurs" In this case the interaction is the magnetic field with the electrons.

Magnetic fields and electrons are theoretical constructions. The level of correspondence between these constructions and a reality underlying instrumental behavior is unknown. Anyway, this isn't, conventionally, what the term 'measurement' refers to. 'Measurement' refers to instrumental behavior.

Why does there have to be a recording of this interaction for there to be a measurement?

Because that's what the term, 'measurement', refers to.

From my definition, won't electrons measure each other's spin's all the time?

Your definition of 'measurement' isn't the conventional one. You can say, wrt the formalism, that electrons are 'interacting'.

It's just a semantic consideration.

'Interaction' refers to the formalism. 'Measurement' refers to recorded detection attributes.

 

[alxm]

I just learned in QM class today that decoherence is due to the fact that the superposition of different basis wave functions that make up the total wave function are each affected differently because of the time phase factor.

And your professor said that decoherence is due to this fact? Sorry but either you or him are wrong on that, and I'm leaning towards the former.

Since B fluctuates, then the Phase factor fluctuates as well making the expectation value of the spin wave function completely random. I see that the spin wave function did not collapse but measurements on the spin wave function yield results that are exactly like a mixture of states.

That is completely wrong. A superposition is not 'exactly like' a mixed state at all. The two yield observably different results.

Thus this effect is known as decoherence.

That's not it at all, no. Read the http://en.wikipedia.org/wiki/Quantum_decoherence" article or whatever, or any number of threads on this forum on the topic.

So the difference between a decohered spin wavefunction vs a mixture of spin wavefunctions is that the mixture are collapsed wave functions whereas the decohered spin wavefunction are not.

Again, you're not understanding the difference between a mixed state and a superposition. A decohered wave function is a mixed state, not a superposition.

And experiments cannot find out the difference! Because the expectation value of a [superposition] of spin states is 50% up and 50% down, and the expectation value of a [mixture of] spin wave function is also 50% up and 50% down.

So you see no observable difference in the double-slit experiment regardless of whether or not you measure which slit the particle passed through? In one case it's a 50-50 superposition, in the other a 50-50 mixed state.

My professor showed decoherence on one particle! showing it with how a varying magnetic field can cause the spin wave function to decohere.

How is that 'one particle'?

So what you are saying with a general large wave function is that there are more than two basis states and that the time phase factor will act differently on each of those basis states?

No, what I'm saying is that the off-diagonal elements of the density matrix cancel out as you move towards a macroscopic system.

I don't see how decoherence has anything to do with answering the question of what constitutes as a measurement

Well, I suggest you make an effort to understand the concept next time instead of redefining it to be about the time-evolution operator just because your previous lecture happened to be about that.

As I understand entropy, It is the number of states a system can be in. A system with a lot of energy would mean more different states that it could be in, thus high entropy. A system with low energy would mean less states and thus low entropy.

Well, then your understanding of basic thermo is pretty bad too. The number of states and energy have no direct relation to each other or to entropy. Entropy is essentially a description of the distribution of energy among the available states.

I don't see how entropy has anything to do with what constitutes as a measurement

I didn't say it did have anything to do with "what constitutes a measurement", but it's intimately related to the measurement process, i.e. decoherence.

In the end, you do agree with my definition.

Not the definitions you gave above, no.

 

[Fredrik]

So my professor told me that when you send charged particles, electrons, through the SG machine it will separate out spin up particles and spin down particles because of a varying magnetic field.

They don't need to be charged. The original SG experiment used silver atoms, which are electrically neutral. The particles do however need to be magnetic dipoles.

So if you didn't have a screen, then no measurement is made?

Correct.

Won't the electron's spin be measured already because we know that spin up electrons are going a different path from the spin down electrons?

No, the interaction with the magnet just creates a correlation between position states and spin states, so that we can measure the spin state by detecting the presence of the particle in a specific region of space.

Or do can we not know the path or trajectories of electrons?

Until the position measurement has been performed, it's wrong to say that the particle took "either the left path or the right path". It's in a superposition of the two options, which is a different thing than "either/or".

What I constitute as a measurement is "Whenever an interaction occurs" In this case the interaction is the magnetic field with the electrons.

Why does there have to be a recording of this interaction for there to be a measurement?

If an interaction doesn't create a stable record of the result, you wouldn't be able to use the result for anything, because you don't have a memory of what just happened. (Your memory is by definition a stable record of the result). What I said about you specifically actually holds for all "information gathering and utilizing systems". This includes all conscious physical systems, since we wouldn't consider a physical system that can't store any information "conscious". And this clearly includes all physicists, since physicists are conscious by definition.

Since physicists can't use the results of interactions that don't produce stable records, it's extremely natural to define a "measurement" to be an interaction that does produce a stable record of the result.

In the SG experiment, the magnet that creates a correlation between position states and spin states doesn't produce a stable record of the result, but the screen that creates correlations between particle positions and dark spot positions does, because the spot's interaction with its environment (the rest of the screen and the air around it) will move the quantum weirdness into the microscopic degrees of freedom of that environment.

 

[zonde]

So my professor told me that when you send charged particles, electrons, through the SG machine it will separate out spin up particles and spin down particles because of a varying magnetic field. Then what he says constitutes as a measurement is that "the electrons say hit a screen and makes two marks"

I don't understand this. So if you didn't have a screen, then no measurement is made? Won't the electron's spin be measured already because we know that spin up electrons are going a different path from the spin down electrons? Or do can we not know the path or trajectories of electrons? What I constitute as a measurement is "Whenever an interaction occurs" In this case the interaction is the magnetic field with the electrons.

Charged particles will stuck in SG machine. So it's uncharged particles with magnetic dipole.

Anyways it seems quite straight forward to assume that SG machine changes (not measures) spin of the particles to one of the two stable states - up or down.

 

[DrChinese]

Anyways it seems quite straight forward to assume that SG machine changes (not measures) spin of the particles to one of the two stable states - up or down.

That implies that the magnet imparts something onto the particle which changes it. That is not experimentally verifiable (i.e. is not supported). I think it is better to say that the act of measurement brings out a property by reducing the number of possible outcomes.

 

[zonde]

That implies that the magnet imparts something onto the particle which changes it. That is not experimentally verifiable (i.e. is not supported). I think it is better to say that the act of measurement brings out a property by reducing the number of possible outcomes.

There are some similarities with photon polarization and polarizers.

Say we take two SG apparatuses and pass the particles trough them so that one output of first (A) SG apparatus (say up) is going through the second (B) SG apparatus with the same orientation. Now we will have situation where all particles appear in one output of B apparatus (up) and there are no particles at the other output (down).
Next we insert third (C) SG apparatus oriented orthogonally between the first two with one of it's outputs directed at B apparatus. We should expect that now particles are equally divided between two outputs of B apparatus.
And that can be viewed as argument that this C apparatus is actively changing spin of the particles.