# Stern-Gerlach experiment as a measurement

1. Feb 23, 2016

### ShayanJ

Its been a while that I'm thinking in what sense we can say the SG experiment is a measurement. What I concluded, is that there are two kinds of measurements. 1) Measurements that advocates of the ensemble interpretation (like our own @vanhees71) declare as the only one that QM has anything to say about, i.e. preparing an ensemble of similar systems in a given state and figure out the probability distribution of the values of different observables. 2) Measurements involving a single system where some people think should also be explainable by QM. So they invoke wave-function collapse and then point out that its a black box that should be explained by either an interpretation or using decoherence.
It seems to me that the SG experiment is a measurement of the first kind because it seems to me that in this experiment, we don't treat the beam of atoms as a single entity but as a bunch of atoms. By treating the beam of atoms as a single entity, I mean trying to measure an observable which belongs to the beam as a whole, like its total angular momentum or something like this.
But in the books and papers that I've seen, I could hardly find a clear and through discussion of the above issues that clearly distinguishes between the two kinds of measurements and analyzes the SG experiment in a way that makes it clear its just another measurement of the first kind I described above.
I'll appreciate any comments and discussions on this issues.
Thanks

2. Feb 23, 2016

### Staff: Mentor

Could yoiu give details as exactly what you consider in your Stern-Gerlach experiment? Do you measure all the atoms, or do you block those with a certain spin? Do you consider the possibility of working with a single atom at a time?

3. Feb 23, 2016

### ShayanJ

For now, what I'm considering is letting a whole lot of atoms come out of the oven, collimate them, letting them into a non-uniform magnetic field and then observing that the beam gets separated into two beams that form two distinguished spots on the screen(if done by silver atoms). People call this a measurement that shows us the angular momentum of the atoms has only two base states.

4. Feb 23, 2016

### naima

You have to add that if there is not a screen to register the spots the SG is not a measurement device in the usual way. the output beams could be merged and the which-path information erased.

5. Feb 23, 2016

### drvrm

The S-G experiment has certain important features which helps one to understand the formalism/representation/construct of QM
(i)one can learn how to prepare a
specific quantum state starting from an arbitrary state
(ii) issues related to the time evolution of the
wave function and quantum measurement.
(iii) can be used to demonstrate the distinction between the physical space where the experiment is performed and
the Hilbert space where the state of the system is described

(iv)how information about the state of the system in the Hilbert space can be exploited to interpret the possible outcomes of the experiment in physical space.

(v) one can learn the advantages of choosing an appropriate basis to make predictions about the
outcomes of experiments with different arrangements of Stern–Gerlach devices.

(vi) help students to understand that an ensemble of identically prepared systems is not the same as a
mixture.
<We discuss student difficulties with the Stern–Gerlach experiment based on written tests
We discuss preliminary data which suggest that the Quantum Interactive Learning Tutorial on
the Stern–Gerlach experiment is helpful in improving student understanding of these concepts.>
the above quote is from<http://www.if.ufrj.br/~carlos/fismod/seminarios/SternGerlach/SternGerlach_Zhu_AJP2011.pdf> [Broken]

Last edited by a moderator: May 7, 2017
6. Feb 23, 2016

### A. Neumaier

One doesn't observe the beams getting separated, one observes the two spots. The latter is the measurement: No screen where to look for spots = no measurement. One (only) infers that there are two entangled beams based on the preparation and the two spots.

The spin measurement device consists of the magnet plus the screen. Depending on the orientation of the magnet it measures a different property of the beam. Take a way the screen and you have a reversible situation, which is incapable of measuring anything. It just prepares the system such that a subsequent measurement on the spot gives the desired information about the system.

All this has nothing to do with the number of particles in the beam. The latter only determine the intensity of the spots.

7. Feb 23, 2016

### ShayanJ

I appreciate all the mentioned points. But They where not in the direction of what I asked!

8. Feb 23, 2016

### Jilang

Does the magnetic field change the direction of the spin?

9. Feb 23, 2016

### strangerep

Perhaps you need to be more specific?

10. Feb 23, 2016

### atyy

1) The ensemble interpretation when done correctly is not different from Copenhagen where probability is given a frequentist interpretation, hence there is no difference (except terminology, where one would use terms like "sub-ensemble" instead of assigning a state to an individual system).

2) In all forms of Copenhagen, where there is only a single measurement (instead of a sequence of measurements), wave function collapse is not needed.

11. Feb 23, 2016

### ShayanJ

1) Is my explanation correct?
2) Is there any reference that clearly and thoroughly discusses the two types of measurements I described and distinguishes between them?
3) Is there any reference that treats the SG experiment in a way that makes it clear its a measurement of the first kind?

12. Feb 23, 2016

### ShayanJ

But I think they are different. The difference is that the ensemble interpretation says that QM is only about ensembles but Copenhagen insists that QM is about individual systems too. But if we want to use QM on an individual system, we need collapse for consistency. And that's where we hit the measurement problem.

2) In all forms of Copenhagen, where there is only a single measurement (instead of a sequence of measurements), wave function collapse is not needed.[/QUOTE]
But we want to know how the system evolves in time and whether there is a collapse or not, affects that evolution. We want theories that are useful in general situations. Not theories that say "if there is a sequence of measurements, then there is collapse, and if there is only one measurement, then...who cares?" !

13. Feb 24, 2016

### atyy

The ensemble interpretation when pitched as if there is no measurement problem is misleading. Fundamentally, the space of density matrices in QM is a convex set that is not a simplex. That is a mathematical statement true in Copenhagen and Ensemble, and it is this difference from classical probability that makes it difficult to assign reality to quantum states. The set of states in classical probability is a convex set that is a simplex, which is why stochasticity in classical probability is always consistent with ignorance of an underlying definite reality. Quantum mechanics interfaces the quantum states with classical probability, and so it interfaces non-reality with reality.

In the language of the ensemble interpretation, to define a conditional probability, one has to condition on a sub-ensemble. However, the non-simplex nature of the state space means that there is no unique way to define sub-ensembles given an ensemble. Hence one needs an additional rule defining the sub-ensembles within an ensemble, in order to talk about conditional probability (especially for sequences of measurements with non-commuting observables). The rule defining sub-ensembles in the Ensemble interpretation is the collapse rule in Copenhagen. So as long as one takes a frequentist view of probability, Copenhagen is the correct form of the Ensemble interpretation.

http://arxiv.org/abs/1112.2347v2
Geometry of the set of mixed quantum states: An apophatic approach
Ingemar Bengtsson, Stephan Weis, Karol Życzkowski

Well, one can always say we don't care about time evolution. We do get a "series" of time readings, but it is only the single observations of multiple time stamps that is real, not the sequence of time stamps. It's the same sort of idea that in Copenhagen one is allowed to draw the classical-quantum boundary so that Alice is not real to Bob, and Bob never observes violation of the Bell inequalities at spacelike separation. So the freedom in drawing the classical-quantum boundary allows us to avoid measurement sequences.

Last edited: Feb 24, 2016
14. Feb 24, 2016

### naima

People discuss the difference between single systems and macroscopic ones. We have to remenber that a system can be in a superposition of 1 and $10^{10}$

15. Feb 24, 2016

### atyy

I would like to stress that this statement is true in Copenhagen with a frequentist interpretation of probability. So it is not the distinguishing factor between Ensemble and Copenhagen, rather Copenhagen and correct Ensemble are indistinguishable. However, there are incorrect forms of Ensemble, such as those in Ballentine and some of vanhess71's remarks concerning collapse which are wrong, so those are not the same as the correct Copenhagen interpretation.