I Does the concept of an "object" belong in Quantum Mechanics?

[Robert Shaw]

Consider the following examples:

1) combine a spin 1/2 state (with 2D Hilbert space and three spin 0 states (each with 1D Hilbert space). The resultant state is in 3D Hilbert space.

2) combine the same spin 1/2 state (with 2D Hilbert space and one spin 0 state.

The states in (1) and (2) are identical except for phase factor.

There appears to be no way of determining the number of "objects".

3) combine three spin 1/2 states (2D Hilbert).==>.8D Hilbert state

4) combine one spin 1/2 state (2D Hilbert) and one spin 1.5 (4D Hilbert)===>8D Hilbert vector.

There seems to be nothing to tell how many "objects" are being combined.

Does the concept of an "object" not belong in Quantum Mechanics?

 

[AlexCaledin]

I was reading Many Worlds?: Everett, Quantum Theory, & Reality and got this answer: in the post-Everett QM, "objects" are emergent things; or, which is same, QM is "simulating" all the possible ever-branching (quasi)classical observable worlds with all their objects - but that of course is only if the Hilbert space is multidimensional enough.

( —to me, within physics, that is simply the final proof of the good old Shut-Up-And-CalculateInterpretation—because, whatever Niels Bohr says about the classical environment, it's just as well the necessary specification of the Everettian branches.)

 

[kith]

Similar situations to the ones you outlined above occur in classical mechanics. If you have a system of N particles, the state of the system is described by a point in 6N-dimensional phase space. If someone only hands you the phase space and doesn't tell you the physical situation, you cannot deduce whether there are N particles in 3 dimensions or one particle in 3N dimensions because the mathematical model fits both these physical situations.

 

[Robert Shaw]

Similar situations to the ones you outlined above occur in classical mechanics. If you have a system of N particles, the state of the system is described by a point in 6N-dimensional phase space. If someone only hands you the phase space and doesn't tell you the physical situation, you cannot deduce whether there are N particles in 3 dimensions or one particle in 3N dimensions because the mathematical model fits both these physical situations.

Good answer, thanks. Do you have any references to amplify your position?

In particular, your answer implies that any model in physics requires

1) equations
2) explanation of the symbols in the equations
3) an interpretive narrative in addition to (2)...e.g. this model applies to two particles.

That's very interesting. It means that we feed in interpretive narrative about the objects in our model.

QUESTIONS
A) Are there restrictions or rules about what can or cannot be included in such a narrative? For example the word "particle" is very poorly defined, so can it be used in a narrative? Likewise Schrödinger's cat is not very well defined.
B) What tests are there for consistency between (1), (2) and (3)

I'd be interested to see any textbooks or papers that take this approach. It seems promising.

 

[kith]

Do you have any references to amplify your position?

I don't know any texts which systematically generalize the observation I noted above. I mostly don't enjoy reading formal texts about the philosophy of science and I haven't come across physics texts which talk about this in detail.

For example the word "particle" is very poorly defined, so can it be used in a narrative?

I think that ultimately, we always have to rely on poorly defined human notions as starting points in science and maths. See e.g. the following definition from Cantor: "A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] or of our thought—which are called elements of the set."

 

[Robert Shaw]

I don't know any texts which systematically generalize the observation I noted above. I mostly don't enjoy reading formal texts about the philosophy of science and I haven't come across physics texts which talk about this in detail.I think that ultimately, we always have to rely on poorly defined human notions as starting points in science and maths. See e.g. the following definition from Cantor: "A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] or of our thought—which are called elements of the set."

Me too.

However I like to test the limits from time to time.

Quantum optics and information theory arose when Glauber and Deutsch tested the limits. Glauber was frustrated with steady states as the dominant approach. Deutsch poked and prodded at "probability" and both made useful advances.

I would agree that the ultimate test is whether anything useful comes out.

I do think probability will yield more. In particular the frequency interpretation is lousy but propensity as an alternative is problematic.

Have you seen the Grasshopper problem that Adrian Kent discovered recently...proof that probability can still yield new quantum insights!

 

[kith]

I think that testing the limits is fine and I like it that people still work on the foundations of quantum physics. But I also think that the main foundational point of quantum physics is to highlight that physics doesn't just uncover facts about the world. The whole endeavor of science is done by people and depends fundamentally on their notions and the questions they are able to ask.

I don't think that there's much progress to be made towards removing the observer from quantum physics but quite a bit towards a better understanding of his role (i.e. how he manifests in the different interpretations).

I share your feeling that probability itself is a key concept to look at.

 

[PeterDonis]

three spin 0 states (each with 1D Hilbert space).

What Hilbert space are you talking about? A spin-0 object has no spin Hilbert space at all; it has no spin degree of freedom.

 

[blue_leaf77]

There seems to be nothing to tell how many "objects" are being combined.

If you calculate the expectation value of number operator, does it not give you at least the idea about how many particles we have?