Undergrad Does a measurement setup determine the reality of spin measurement outcomes?

[Demystifier]

Whatever terms we use, they are terms of philosophy (or perhaps "metaphysics"), not physics.

There is no physics without philosophy (meta-physics). For instance, when you systematically collect empirical data on nature and compare them with testable theoretical predictions, that's science. When you say that this is what science is, that's philosophy.

 

[kith]

I don't agree with this. The wave function is a separate thing from the Bohmian particle positions.

I don't see the disagreement with what I wrote. You compare the wave function with particle positions. So your statement seems to say that the wave function is conceptually on equal footing with a property of the system and not with the system itself. Or would you consider the particle position to be a physical system?

So it's perfectly possible to look at the wave function in dBB as a separate entity, not dependent on particle positions.

The Schrödinger equation indeed doesn't depend on the Bohmian particle positions. But this is not the important point for the analogy with the electric field. On the contrary, the Maxwell equations do depend on the position of the charged particles.

So this isn't an argument for considering the pilot wave a separate entity in a sense similar to the electric field (see my example in post #58). Without something to attribute a position to there is no wave function.

 

[martinbn]

I think the electric field itself can be confusing because the same term "electric field" is used for both the system and the mathematical description. May be a better analogy is a fluid and its velocity field. Is the wave function like the fluid or like the velocity field? To me it makes no sense to say that it is like the fluid.

 

[Demystifier]

I think the electric field itself can be confusing because the same term "electric field" is used for both the system and the mathematical description. May be a better analogy is a fluid and its velocity field. Is the wave function like the fluid or like the velocity field? To me it makes no sense to say that it is like the fluid.

That's an interesting analogy, but begs a question. If the wave function is analogous to the velocity field, then what is the thing that is analogous to the fluid?

 

[PeterDonis]

You compare the wave function with particle positions.

You can s/particle positions/particles/ in my post and it would still be correct. The point is that in Bohmian mechanics both the particles and the pilot wave (the wave function) are separate entities; the wave function is not assumed to only have meaning as a probability amplitude for various particle positions. It's an actual physical thing that pushes the particles around. Deriving the fact that the wave function also gives the probability amplitude for particle position measurements requires also assuming that the initial distribution of particle positions satisfies a particular constraint; it's not built into the wave function from the start.

Without something to attribute a position to there is no wave function.

I don't think this is correct in the Bohmian interpretation. See above.

 

[martinbn]

That's an interesting analogy, but begs a question. If the wave function is analogous to the velocity field, then what is the thing that is analogous to the fluid?

Whatever the quantum mechanical system is, say an electron.

 

[A. Neumaier]

Whatever the quantum mechanical system is, say an electron.

But the system may be $N=10^{23}$ electrons

 

[martinbn]

But the system may be $N=10^{23}$ electrons

Yes, whatever it is. The point was that it wasnt the wave function.

 

[kith]

[...] the wave function is not assumed to only have meaning as a probability amplitude for various particle positions. It's an actual physical thing that pushes the particles around. Deriving the fact that the wave function also gives the probability amplitude for particle position measurements requires also assuming that the initial distribution of particle positions satisfies a particular constraint; it's not built into the wave function from the start.

I haven't written anything about probabilities and agree that they are not what gives meaning to the wave function in dBB. The wave function is as real as position and isn't secondary to it. But the two are not separate entities in the sense that you can have one without the other (see below).

Without something to attribute a position to there is no wave function.

I don't think this is correct in the Bohmian interpretation.

Then please give an example of a physical situation where the dBB description uses a wave function but no particle position. In the case of the electromagnetic field, I gave such an example of a light pulse traveling in a vacuum.

 

[PeterDonis]

Then please give an example of a physical situation where the dBB description uses a wave function but no particle position.

Of course I can't; dBB uses both to make predictions. But the claim of yours I was responding to was not "dBB uses both positions and the wave function to make predictions". It was "without something to attribute a position to there is no wave function", which I think is simply false for dBB since it attributes separate reality to the pilot wave.

 

[kith]

I'm not interested in discussing further whether the statement "without something to attribute a position to there is no wave function" is justified or not when we both can't think of a physical situation where the wave function is used in the absence of something to attribute a position to.

I'm still interested in discussing the commonalities and differences between the pilot wave and the electromagnetic field / @martinbn's fluid and how significant the differences are.

 

[Demystifier]

Whatever the quantum mechanical system is, say an electron.

But I can describe the fluid itself mathematically, without referring to the velocity field. For instance I can talk about its density and pressure. What can I say mathematically about the electron itself, without referring to its wave function?

 

[A. Neumaier]

But I can describe the fluid itself mathematically, without referring to the velocity field. For instance I can talk about its density and pressure. What can I say mathematically about the electron itself, without referring to its wave function?

In Bohmian mechanics, its position.

 

[Demystifier]

In Bohmian mechanics, its position.

Of course, but I wanted to see what martinbn will say.

 

[vanhees71]

This is interpretation dependent.

In the Copenhagen interpretation, the spin is not real before the measurement.

In Bohmian mechanics, the spin is determined before the measurement (by the beam in which it is)

In the thermal interpretation, the spin is a real number and the measurement outcome discretizes it, hence is only approximate.

I'd not use the word "real" here. It's misleading. According to QT in the orthodox interpretation (minimal interpretation, almost Copenhagen but without collapse and without "Heisenberg cut") observables are always "real" in the sense that you always have the oppotunity to measure them, independent of the state the system is prepared in. The state, however, determines whether the meaured observable has a determined value or not. If it has a determined value, you'll always obtain this certain value when you measure it. Otherwise, you get a random result when measuring this observable, and the state preparation implies the probabilities (or probability distribution in the case of continuous observables) for finding one of the possible values of the observable when measuring it.

I don't understand, what you mean by "the measurement outcome discretizes" the spin. Any spin component takes discrete values $m \in \{-s,-s+1,\ldots,s-1,s \}$. That's the possible values you get when measuring this spin component accurately (enough). If your detector resolution is not sufficient, you get some continuous distribution around these values of course, but that's due to the detector resolution and has nothing to do with the observable "spin component" per se.

 

[vanhees71]

Related to what @A. Neumaier said above, in the Copenhagen interpretation Spin is a phenomena that occurs in a classical system as a result of interaction with a microscopic system. It has no meaning outside of that interaction.

Well, it's not that simple unfortunately, at least not in the relativistic case. The macroscopic manifestation of spin is, e.g., ferromagnetism through the magnetic moments of the particles due to spin.

 

[vanhees71]

So what I am wondering about is if the spin is defined as a certain outcome of a certain measurement, or that it is regarded as something ontological real, in which case the measurement doesn't necessarily has to represent the value of it.

I am aware that these measurements don't commute, but if one took the correlation between two measurements on the same spin to be real, but not de measurements themselves*, then we might have less of a problem for instance in considering that a two dimensional operator yields two real worlds in MWI, because the measurement outcomes are not real*.

Observables are generally defined as a quantified phenomenon that can be measured. This is true for all of physics, also in the realm, where classical physics is applicable as an approximation.

If you have two observables which are not compatible, i.e., if their representing self-adjoint operators do not commute, it's generally impossible to prepare states, where both observable take determined values. In your example: If you prepare a state, where the spin component $s_z$ of a particle is determined, spin components in other directions are necessarily indetermined.

It's also easy to understand, why this is the case in this example: To prepare a spin component you can use the Stern-Gerlach setup, i.e., you let the particle run through a magnetic field with a large homogeneous part in the $z$ direction and some gradient also in the $z$ direction (then, because of $\vec{\nabla} \cdot \vec{B}=0$ it necessarily has also a gradient in some other direction, but that you can almost neglect, as will become clear below). Then the spin rapidly precesses around the spin direction, and thus almost only the force in $z$ direction due to the field gradient is relevant for the motion of the particle. This leads to an almost perfect entanglement of the $z$-component of the particle's position with the spin component $s_z$, i.e., if you use an appropriate beam of particles this beam splits into $s$ partial beams, each of which contains particles with (almost) determined spin-$z$ components.

Now it's already clear even from these qualitative considerations only that in this way you can only determine the spin-$z$ component, while all others are necessarily pretty indetermined. So if you decide to determine the spin-$z$ component you cannot determine another spin component at the same time. To determine the other spin component you'd have to use a magnetic field in its direction rather than the $z$ direction. If you send a particle with determined $z$ direction, prepared using the corresponding Stern-Gerlach apparatus, through another Stern-Gerlach apparatus to determine, e.g., the spin-$x$ component this apparatus randomizes the spin-$z$ component again, i.e., you destroy the preparation of the spin-$z$ component necessarily if you want to determine the spin-$x$ component instead. For each individual particle with a determined spin-$z$ component you cannot say which value the spin-$x$ component you will get when running it through the Stern-Gerlach apparatus for the spin-$x$ prepration. All you know from the preparation in the state with determined spin-$z$ component are the probabilities to end up in any of the possible spin-$x$ states.

 

[vanhees71]

The common wave function that serves as a pilot wave for the particles.

That's another quibble I have with de Broglie Bohm. How do you define "spin" as a classical variable. In non-relativistic theory there may be a chance to define it from a classical model of a point particle with some intrinsic angular-momentum like direction (e.g., as a small rigid body) or simply only by the Bohmian trajectories of a particle with spin in an external magnetic field, leading in Stern-Gerlach like setups to an entanglement between spin component and position? In the latter case, it's however not clear to me, in which sense the spin is then defined as an observable in the Bohmian interpretation to begin with, and then of course it's even harder to decide whether, within the Bohm interpretation, the spin has some determined value or not.

 

[vanhees71]

The action has the dimension M·L²·T^-1. I don't think that the wave function has a dimension.

if the wave function is just a calculation tool for calculating measurement predictions, can it then be considered as an "ontic/beable entity"? A Platonist may answer yes, hence the ambiguity of these metaphysical notions of existence, ontology.

/Patrick

The wave function has a dimension. It's a probability density. In the position representation of a single particle the wave function has thus the dimension $L^{-3/2}$. I cannot say whether this has anything to do with philosophy or being ontic/beable or whatever, but that's a mathematical and physical fact ;-)) SCNR.

 

[vanhees71]

When Bohmians talk about ontology, they usually mean fundamental ontology. Temperature, in that sense, is not a fundamental ontology. Even kinetic energy of a classical nonrelativistic particle, given by $E=mv^2/2$, is not a fundamental ontology in classical mechanics. The only fundamental ontology in classical mechanics is the trajectory ${\bf x}(t)$, while everything else can be expressed in terms of that.

In the thermal interpretation of QM, on the other hand, there is no fundamental ontology from which everything else can be expressed. All observables are on the same footing. I find it very weird, especially if I look at the classical limit.

Well, all this gibberish about ontic or not is just empty erudition. It reminds me of the debate whether forces are "ontic" or not, and one philosopher hit the other, who claimed forces are fictitious asking, whether he still believes what he just said ;-)).

Then it's also a bit a quibble, why you consider only position as ontic. Maybe you can get through with this quite radical view within classical Newtonian mechanics, but is it sufficient in connection with fields and quantum theory? There spin is obviously an additional fundamental degree of freedom. It depends a bit on how you define observables, but following the symmetry-principle arguments usually used to decide about the proper description of observables in QT, spin is a phenomenon appearing in addition to the classical point-particle observables that indeed can be traced back to the notion of position (and trajectories in position space) as the fundamental observable.

 

[DarMM]

Well, it's not that simple unfortunately, at least not in the relativistic case. The macroscopic manifestation of spin is, e.g., ferromagnetism through the magnetic moments of the particles due to spin.

How is that different from what I said?

 

[vanhees71]

I understood you statement to say that spin is not a phenomenon related to the object but emergent in its interaction with a macroscopic system. The point is that spin is an additional generic degree of freedom, which is generically quantum.

 

[martinbn]

But I can describe the fluid itself mathematically, without referring to the velocity field. For instance I can talk about its density and pressure. What can I say mathematically about the electron itself, without referring to its wave function?

I am not sure how this is related! The point was not that the velocity field is all that is needed for the mathematical description, add to it density, pressure, temperature etc. The point was to distinguish the thing that exists and interacts with other things on one hand and the mathematical notions that are used to model it on the other. The examples were obviously not exhaustive, they were there to make @kith 's point even more clear. Although I thought that he had said everything perfectly clearly.

 

[ftr]

The point was to distinguish the thing that exists and interacts with other things on one hand and the mathematical notions that are used to model it on the other.

Very good. How do you do that? There is no way, you will always describe the "things" mathematically by what they do and how they affect other "things" mathematically, Once you reach the theory that is exact (even in equivalent forms), then the "things" ARE the mathematical objects. This is the conclusion of MUH.

 

[vanhees71]

Mathematics is the language to talk about physics. As any language it's a description of real-world objects but not the same as the objects themselves. I've never seen a Hilbert space or a self-adjoint operator, a tensor field, or a time derivative, in any lab on the world. There are accelerators (preparation devices) and detectors (measurement devices) around but no abstract mathematical objects!

 

[ftr]

Well, you also have an electron in the lab, but you don't actually see it, do you?

 

[Demystifier]

That's another quibble I have with de Broglie Bohm. How do you define "spin" as a classical variable.

I don't.

In the latter case, it's however not clear to me, in which sense the spin is then defined as an observable in the Bohmian interpretation to begin with, and then of course it's even harder to decide whether, within the Bohm interpretation, the spin has some determined value or not.

You are using a wrong language. An observable is a hermitian operator, so spin is an observable in BM in exactly the same way as it is in standard QM. The right question, with right terminology, is whether the spin is a beable? (The terminology is explained in my paper which you said you read.) The answer is that spin is not a beable in BM. Only positions are beables. That's perfectly OK to explain the measurement of spin because, as you more or less agreed, all measurements can be reduced to measurements of position. All this is explained in the paper you said you read.

 

[vanhees71]

There are no hermitian operators in the lab. There's real-world equipment to prepare objects (like an "electron") and to measure its properties (mass, charge, magnetic moment, $g-2$, etc.).

It's of course true that, e.g., the SG apparatus uses a position preparation to measure spin (or more precisely the magnetic moment associated with spin), but still it's not clear to me, how to define spin in BM. It doesn't help to use buzz words like "beable". You have to give operational definitions together with the mathematical description. Spin, e.g., is no problem in standard QT whatsoever, but I thought the aim of BM is a kind of reestablishment of classical notions though (according to what we know today unavoidable) including some additional non-local dynamics. Neglecting spin, that's not a problem since you have a classical notion of the classical observable, which are after all maybe derivable by position only.

 

[vanhees71]

Well, you also have an electron in the lab, but you don't actually see it, do you?

Sure, and electron is defined through what can be observed about it. It was found in gas discharge tubes and then its properties were carefully investigated. An electron is the collection of its unique properties, which are now all nicely formalized in a more or less simple mathematical scheme called the Standard Model of elementary particle physics, but the electron is not some quantized Dirac field living in a sloppily defined Fock space but it's an entitity measurable in the real world using all kinds of equipment in the lab.

 

[Demystifier]

There are no hermitian operators in the lab.

Of course. In the lab there are only perceptibles, which is also a term explained in the paper.

It's of course true that, e.g., the SG apparatus uses a position preparation to measure spin (or more precisely the magnetic moment associated with spin), but still it's not clear to me, how to define spin in BM. It doesn't help to use buzz words like "beable". You have to give operational definitions together with the mathematical description.

The operational definition of spin in BM is identical to the operational definition of spin in standard QM. You observe the position of the detector that clicked in the SG apparatus and from this you compute the spin from the standard formula.