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

[vanhees71]

Again this solidifies my view that there's no need for Bohmian mechanics to begin with. I don't need additional deterministic trajectories determined by a non-local pilot-wave concept to describe what's observed.

 

[Demystifier]

Again this solidifies my view that there's no need for Bohmian mechanics to begin with.

So effectively you reject Axiom 1 in my paper:
Axiom 1: All perceptibles are beables.

 

[A. Neumaier]

This is interpretation dependent.

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

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.

I had meant the ''value of the spin'' (usually just called ''the spin''), and before the measurement.
This value does not exist. For me, real and existent are synonyms.

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

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.

Yes, and this discrete response (a few well-separated blobs when $s$ is small) is what I refer to as discretizing. Note that in the thermal interpretation, the true value of a spin component is a real number, approximately found out by the measurement, with a discretization error of order $\hbar$, which is 1 in the units you are using.

The measurement by the Stern-Gerlach apparatus necessarily discretizes the outcome since the unitary dynamics of the magnet prepares the silver current in two discrete beams - already before measurement. The measurement therefore can do no more than find out which beam carries a particle, and hence gives an essentially binary response. Thus the continuous spin variable measured will produce only a single bit of information, and a large discretization error.

 

[A. Neumaier]

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

There was already an answer in this thread:

From the Bohmian perspective it's indeed silly to call it measurement of spin. But Bohmians use such a silly language because that language is borrowed from standard QM (which is silly too, because standard QM says that spin doesn't exist before you measure it, so what does it mean to measure something which doesn't exist before measurement?). In other words Bohmians speak to "ordinary" physicists by saying something like this: The procedure that you call measurement of spin is really a measurement of position and I will tell you what is really going on when you think you measure spin.

 

[A. Neumaier]

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!

This sounds like you'd agree to the quote from Asher Peres in another thread!

There are also no observables described by linear operators, but only positive operators describing the response of the detectors to the preparation devices.

 

[ftr]

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.

Suppose no humans ever existed would you say that the concept of a circle is non existent, I hope you wouldn't. Let's say humans came about and wrote an equation for a circle, would you make any real distinction between the two, i.e. the concept and the equation, I hope you wouldn't. Just think of the electron in the same way, after all you admit that only its properties which are mathematical describe it.

 

[A. Neumaier]

Suppose no humans ever existed would you say that the concept of a circle is non existent, I hope you wouldn't. Let's say humans came about and wrote an equation for a circle, would you make any real distinction between the two, i.e. the concept and the equation, I hope you wouldn't. Just think of the electron in the same way, after all you admit that only its properties which are mathematical describe it.

A circle and its equation is like your income and the corresponding bank account statement.

 

[ftr]

A corle and its equation is like your income and the corresponding bank account statement.

That is not true for the circle is it, both the equation( what does its jotting represent!) of the circle and the conceptual ethereal are the same, both mathematical in nature. The equations explain what matter properties and their interactions are which are mathematical. That makes sense because we only know of two things that exist, matter and mathematics(relations between numbers) and so science seem to strongly suggest that the former is really nothing but the later. And there is nothing else to explain what matter is, you can't explain matter with matter or matter with some unknown that will be ultra ultra metaphysics.

 

[vanhees71]

So effectively you reject Axiom 1 in my paper:
Axiom 1: All perceptibles are beables.

Can you translate this into understandable language?

 

[vanhees71]

I had meant the ''value of the spin'' (usually just called ''the spin''), and before the measurement.
This value does not exist. For me, real and existent are synonyms.Yes, and this discrete response (a few well-separated blobs when $s$ is small) is what I refer to as discretizing. Note that in the thermal interpretation, the true value of a spin component is a real number, approximately found out by the measurement, with a discretization error of order $\hbar$, which is 1 in the units you are using.

The measurement by the Stern-Gerlach apparatus necessarily discretizes the outcome since the unitary dynamics of the magnet prepares the silver current in two discrete beams - already before measurement. The measurement therefore can do no more than find out which beam carries a particle, and hence gives an essentially binary response. Thus the continuous spin variable measured will produce only a single bit of information, and a large discretization error.

In my understanding of the quantum formalism there are observables, i.e., measurable quantities. You can always measure these quantities, no matter in which state the system is prepared in. Whether or not a specific observable takes a determined value is completely described by the state. It takes a determined value if and only if with 100% probability you find one and only one value when measuring the observable. Otherwise it does not take a determined value, and the outcome of the measurement is irreducibly random. The only thing the state preparation tells you are the probabilities for the outcome of measurements of this observable.

A spin component is discrete. If measured accurately, you get one of the eigenvalues of the corresponding operator, i.e., it's in the discrete set $\{-s,-s+1,\ldots,s-1,s \}$. The SGA, if properly set up, entangles (almost perfectly) the position of the particle with the spin component in the direction given by the magnetic field. An unpolarized beam splits in $(2s+1)$ discrete partial beams because the measured spin component is discrete. That's why you can use the SGA as (almost perfect) von Neumann filter measurement of the corresponding spin component. It's not the expectation value of the spin component what's measured, as you seem to claim in your "thermal interpretation" but the resolution of the SGA is sufficient to accurately resolve the discrete values of the spin components. The measurement of the magnetic moment of the electron is among the most accurate fundamental quantities ever meausured (though of course not with a simple SGA of course).

 

[vanhees71]

This sounds like you'd agree to the quote from Asher Peres in another thread!

There are also no observables described by linear operators, but only positive operators describing the response of the detectors to the preparation devices.

Sure. Peres is only much more eloquent in expressing these ideas. There's always verbatim what I also always state: There are no Hilbert spaces and operators in the lab but real-world equipment like accelerators ("preparation devices") and detectors ("meausrement apparati") of various kinds, all of which function according to the generally valid physical laws, including QT (as far as we know today).

Of course, if you want to describe inaccurate measurements (i.e., 99.9% of measurements done in daily live) you must use the POVM formalism, but I don't see, where this would contradict any part of the standard minimal interpretation. The POVM formalism is just a generalization of the idealized treatment of von Neumann filter measurements discussed in introductory textbooks.

Peres's rightfully famous textbook as well starts with the usual formalism of self-adjoint operators in Hilbert spaces. How else should he be able to formulate the theory?

 

[Demystifier]

Can you translate this into understandable language?

It's explained in the paper, which you said you read. In ordinary language, the axiom says that macroscopic things that we can directly perceive (e.g. the Moon) exist even when we don't observe them. This is a rather innocent axiom, yet in the paper I explain how this axiom naturally leads to Bohmian mechanics.

 

[A. Neumaier]

both mathematical in nature.

but one refers to the other, hence the semantic relation is the same. Just with Platonic reality in place of physical reality.

 

[vanhees71]

It's explained in the paper, which you said you read. In ordinary language, the axiom says that macroscopic things that we can directly perceive (e.g. the Moon) exist even when we don't observe them. This is a rather innocent axiom, yet in the paper I explain how this axiom naturally leads to Bohmian mechanics.

I've to read the paper again, but that the moon is there when nobody looks is for sure not necessarily leading to Bohmian mechanics. The usual conservation laws are sufficient.

 

[A. Neumaier]

A spin component is discrete.

A spin component is an operator. In classical and semiclassical (large quantum number limit) physics, the value of a spin component is a real number. It is a matter of interpretation what a spin component means in terms of measurement; the quantum formalism doesn't say anything about it, except through Born's rule which is about measurement.

The thermal interpetation negates Born's rule as a fundamental principle and degrades it to an approximate law with limitations like most law of physics. Thus Born's rule cannot be invoked directly in the thermal interpretation. Instead, the thermal interpretation preserves the classical and semiclassical continuous nature of the spin, which is much more intuitive. The discrete response is therefore due to the experimental setup.

The measurement of the magnetic moment of the electron is among the most accurate fundamental quantities ever measured

But it is neither a measurement in the sense of Born's rule, nor is it discrete.

 

[A. Neumaier]

I've to read the paper again, but that the moon is there when nobody looks is for sure not necessarily leading to Bohmian mechanics. The usual conservation laws are sufficient.

Are the usual conservation laws valid in each single case or only statistically in the mean? From your minimal foundations you can conclude only the latter, hence cannot claim anything for the single instance of the moon that we have.

 

[vanhees71]

A spin component is an operator. In classical and semiclassical (large quantum number limit) physics, the value of a spin component is a real number. It is a matter of interpretation what a spin component means in terms of measurement; the quantum formalism doesn't say anything about it, except through Born's rule which is about measurement.

The thermal interpetation negates Born's rule as a fundamental principle and degrades it to an approximate law with limitations like most law of physics. Thus Born's rule cannot be invoked directly in the thermal interpretation. Instead, the thermal interpretation preserves the classical and semiclassical continuous nature of the spin, which is much more intuitive. The discrete response is therefore due to the experimental setup.But it is neither a measurement in the sense of Born's rule, nor is it discrete.

A spin component is an observable, formally described by an operator. Spin has no classical counterpart. It's generically quantum. Classical mechanics/field theory is an approximation of QT not the other way around. It's not the response that's discrete but the observable. It's true that through the SGA the measurement of the discrete spin observable is through entanglement with a continuous position observable, but with the properly set up SGA the determination of this continuous observable is sufficiently accurate to resolve the discrete spin values.

 

[Demystifier]

but that the moon is there when nobody looks is for sure not necessarily leading to Bohmian mechanics. The usual conservation laws are sufficient.

No, as I explained to you several times, the conservation laws are not sufficient. The conservation laws cannot prohibit the transformation of Moon into a completely different object (perhaps a giant pink elephant) carrying the same total energy, momentum and charge. With conservation laws you can be sure that something is there when you don't look, but you cannot be sure that it is the Moon and not something else. The Moon has some fine structure that makes it different from the giant pink elephant of the same mass. Bohmian mechanics has something to do with this fine structure. The claim that the Moon is there when you don't look means that its fine structure is there when you don't look, and this fine structure is positions of small parts of which the Moon is made. The simplest extrapolation of the notion of "positions of small parts" to smaller and smaller distances naturally leads to Bohmian mechanics. Different extrapolations are imaginable too, but Bohmian mechanics is the simplest.

 

[A. Neumaier]

A spin component is an observable, formally described by an operator. Spin has no classical counterpart. It's generically quantum.

Though you seem to be ignorant about it, spin has a classical counterpart. It is not specifically quantum.

Classical spin is given by the coadjoint representation of SO(3) on the Bloch sphere.
Its (geometric) quantization naturally produces the spin s representations for half-integral s.

See, e.g., Section 2 of the paper

• Müller, L., Stolze, J., Leschke, H., & Nagel, P., https://www.researchgate.net/profile/Hajo_Leschke/publication/13383184_Classical_and_quantum_phase-space_behavior_of_a_spin-boson_system/links/00b49536cef105ea27000000.pdf, Physical Review A, 44 (1991), 1022.

 

[vanhees71]

Sect. 2 is a nice mathematical game, but what's the physics of their $\vec{s}$?

 

[Demystifier]

Though you seem to be ignorant about it, spin has a classical counterpart. It is not specifically quantum.

Classical spin is given by the coadjoint representation of SO(3) on the Bloch sphere.

It's interesting to note that it is rarely mentioned in high-energy QFT textbooks, but often discussed in condensed-matter QFT textbooks.

 

[vanhees71]

This is no surprise since in non-relativistic physics you have rigid bodies that can intrinsically rotate, and you may call this a classical analogue of "spin" though it's of course not more than that. If it were the same as quantum-mechanical spin, any gyro-factor different from 1 would be a mystery!

 

[Demystifier]

and you may call this a classical analogue of "spin" though it's of course not more than that.

It is more than that. When you quantize it by path integrals, you get exactly nonrelativistic QM of spin.

 

[A. Neumaier]

Sect. 2 is a nice mathematical game, but what's the physics of their $\vec{s}$?

Its the classical spin vector. Its geometric quantization by the standard recipes produces standard quantum spin, of any spin 1/2, 1, ..., corresponding to the irreducible representations of SU(3).

 

[PeterDonis]

corresponding to the irreducible representations of SU(3)

Do you mean SU(2)?

 

[A. Neumaier]

Do you mean SU(2)?

I meant the irreducible projective representations of SO(3), which are the same as the irreducible linear representations of SU(2). The relevant group is the rotation group as a subgroup of the Poincare group ISO(1,3).

 

[DarMM]

Irredicible projective reps of $SO(3)$?

 

[A. Neumaier]

Irredicible projective reps of $SO(3)$?

Yes, typo corrected.

 

[A. Neumaier]

Sure. Peres is only much more eloquent in expressing these ideas. There's always verbatim what I also always state: There are no Hilbert spaces and operators in the lab but real-world equipment like accelerators ("preparation devices") and detectors ("meausrement apparati") of various kinds, all of which function according to the generally valid physical laws, including QT (as far as we know today).

Of course, if you want to describe inaccurate measurements (i.e., 99.9% of measurements done in daily live) you must use the POVM formalism, but I don't see, where this would contradict any part of the standard minimal interpretation.

Well, read his paper from which I took the quote. He says explicitly,

Traditional concepts such as “measuring Hermitian operators,” that were borrowed or adapted from classical physics, are not appropriate in the quantum world.

 

[vanhees71]

Interesting, I've to read the paper in more detail. In his book, he refers to the standard formulation of the theory to begin with. He also gives a detailed account on the more modern theory of measurement in terms of POVMs too, and I don't see, where this contradicts the foundations in any way. I rather understood the POVM formalism as derived from the foundational standard.

In which sense contradicts the POVM formalism the standard formalism? Is this a proper revision of QT and if so, what are differences in the physical predictions? If it's an alternative theory to QT, is now QT obsolete and has to be substituted by the POVM formalism and if so, how can it be formulated in a self-consistent way, i.e., without reference to the standard formalism?

I also never claimed that one "meaures Hermitian operators". As I said above, there are no Hermitian operators in the lab (which statement also Peres makes almost verbatim).