Quantum state of a macroscopic object?

[Sayestu]

TL;DR Summary

Is an object defined by the quantum state of all its particles?

(Mods, I posted a lot on the MWI yesterday, but this seemed different enough to warrant its own thread. If you disagree, I apologize.)
The Stanford Encyclopedia of Philosophy says the following in its article on the Many Worlds Interpretation:

The essence of an object is the (massively entangled) quantum state of its particles and not the particles themselves. One quantum state of a set of elementary particles might be a cat and another state of the same particles might be a small table. An object is a spatial pattern of such a quantum state (Section 3.1).

Is this backed by science? It reminds me of Aquinas's idea of forms vs. substance.

 

[PeterDonis]

Is this backed by science?

The part about the quantum state of a macroscopic object being a massively entangled state of its particles is; that's what QM, to the extent we can apply it to a macroscopic object, tells us. Whether this is "the essence of an object" is interpretation dependent.

 

[Sayestu]

Thanks!

 

[A. Neumaier]

TL;DR Summary: Is an object defined by the quantum state of all its particles?

No, not at all.

A pure state of an N-particle system is a function of 3N variables, while the corresponding mixed states of the N particles are N functions of 6 variables only. The mapping from the first to the second is onto, but very, very far from one-to-one. One gets a one-to-one correspondence only if the particles are assumed not to be entangled.

Thus one may say that the various possible ways of being entangled quantify how the state of a system differs from the family of states of its particles.

 

[Sayestu]

That was Greek to me. The person before you also seems to have given a "yes, it is." Would someone please explain in basic terms? >_<

 

[PeterDonis]

The person before you also seems to have geiven a "yes, it is."

Not quite. What I said was that the quantum state of a macroscopic is a massively entangled state of all its particles. I did not say that the object is "defined" by the quantum state of all its particles. So what I said is perfectly consistent with what @A. Neumaier said.

One thing that might help here is to realize that what we actually observe of a macroscopic object does not correspond to a single quantum state for all of its particles, but to a huge space of such states. In fact we do not and cannot know the exact quantum state of all the particles, or exactly how they are all entangled.

 

[A. Neumaier]

That was Greek to me. The person before you also seems to have given a "yes, it is." Would someone please explain in basic terms? >_<

The basic explanation is that there are far, far more allowed quantum states of an N-particle system than there are collections of N single particle quantum states. Thus the latter only contains a minute amount of information about the former.

Maybe you'd learn some ''Greek'' if your interest is to better understand quantum mechanics.

 

[PeterDonis]

there are far, far more allowed quantum states of an N-particle system than there are collections of N single particle quantum states.

I'm not sure that the article the OP referred to meant "a collection of N single particle quantum states" when it used the expression "quantum state of its particles". Note that the article qualified that expression with "(massively entangled)", which rules out product states of N particles.

 

[A. Neumaier]

I'm not sure that the article the OP referred to meant "a collection of N single particle quantum states" when it used the expression "quantum state of its particles". Note that the article qualified that expression with "(massively entangled)", which rules out product states of N particles.

But then the verbal expression ''quantum state of its particles'' in the article on the Many Worlds Interpretation is meaningless. (I am not surprised, since I find most of what those explaining MWI write to be meaningless. But here it is particularly obvious.)

Perhaps what was meant is ''The essence of an object is its quantum state and not the particles it is composed of.'' This is of course true in the sense that the quantum state of an object determines everything one can say about the object without reference to its environment, including its particle composition.

 

[PeterDonis]

But then the verbal expression ''quantum state of its particles'' in the article on the Many Worlds Interpretation is meaningless.

Without some math to back it up, yes. The article does give some math, but that is not to say the math it gives is sufficient to give a well-defined meaning to the ordinary language expressions it uses.

 

[A. Neumaier]

Without some math to back it up, yes. The article does give some math, but that is not to say the math it gives is sufficient to give a well-defined meaning to the ordinary language expressions it uses.

''its particles'' don't have a quantum state! Each particle has one, and the whole system has one, but not ''its particles''!

 

[PeterDonis]

''its particles'' don't have a quantum state!

Ordinary language is vague. The article seems to mean "the (massively entangled) quantum state that includes all of the degrees of freedom that we assign to the object, and no others". But of course we have no way of explicitly writing down such a state, or even knowing it; we can't do precise quantum tomography on a system with ##10^{25}## or so degrees of freedom.

 

[A. Neumaier]

Ordinary language is vague. The article seems to mean "the (massively entangled) quantum state that includes all of the degrees of freedom that we assign to the object, and no others".

What you describe is simply 'the quantum state of the system' (and my phrase is in very precise ordinary language); particles are not even mentioned in your interpretation of the phrase.

 

[PeterDonis]

particles are not even mentioned in you interpretation of the phrase.

"Particles" is just an alternate term for "degrees of freedom", which we are stuck with for historical reasons.

 

[A. Neumaier]

"Particles" is just an alternate term for "degrees of freedom", which we are stuck with for historical reasons.

No. A particle conventionally has 6 (3 position and 3 momentum) degrees of freedom. My phrase is very precise ordinary language in spite of your historical reasons.

 

[PeterDonis]

A particle conventionally has 6 (3 position and 3 momentum) degrees of freedom.

Not in QM, correct? In QM position and momentum are just different choices of basis on the same configuration space, which has 3 degrees of freedom per particle. (And in quantum field theory even what I just said is no longer true, since "particles" are just particular states of quantum fields, and quantum fields have an infinite number of degrees of freedom.)

In any case, I didn't mean to imply that the counts were identical, just that, at the level of vagueness of the article that was referenced, the two terms can be taken to refer to the same thing. If your argument is that you don't like that level of vagueness, I don't disagree. But the article is what it is.

 

[A. Neumaier]

If your argument is that you don't like that level of vagueness, I don't disagree. But the article is what it is.

I was asserting that there is no need for this level of vagueness. Vagueness only creates misunderstanding, as in the case of the OP.

 

[Sayestu]

I'm sure as heck confused. Ignorant, anyway. What's a good intro to this stuff for someone who only went as far as Calc I?

 

[PeterDonis]

What's a good intro to this stuff for someone who only went as far as Calc I?

If you don't have a good understanding of basic QM, i.e., the mathematical framework and how it is used to make predictions, independent of any particular interpretation, then wading into the swamp of interpretations, particularly one as counterintuitive as the MWI, is not going to be very helpful.

There are a lot of good QM textbooks out there. I personally like Ballentine, but different people have different preferences and there is no single source that works for everybody. I believe @A. Neumaier has his own introduction to QM available online.

 

[vanhees71]

No. A particle conventionally has 6 (3 position and 3 momentum) degrees of freedom. My phrase is very precise ordinary language in spite of your historical reasons.

In the usual definition of the theoretical HEP community, an elementary particle is described as an (asymptotic) free single-particle Fock state of an irreducible representation of the proper orthochronous Poincare group. As such it's characterized by its mass, ##m## and its spin, ##s##. A complete and convenient basis for ##m>0## are the momentum-spin-eigenstates ##|\vec{p},\sigma \rangle##, where ##\sigma \in \{-s,-s+1,\ldots,s-1,s \}##, where ##\sigma## is the value of ##\sigma_z## in the rest frame of the particle (using the most convenient choice of this kind of basis, the Wigner basis). For ##m=0## the analogous basis is the momentum-helicity basis ##|\vec{p},\lambda## with ##\lambda \in \{s,-s \}##, where ##\lambda## is the helicity (which is the same in any inertial frame).

How do you reconcile this with your statement about classical phase-space degrees of freedom?

 

[A. Neumaier]

I believe @A. Neumaier has his own introduction to QM available online.

Neumaier, A., & Westra, D. (2008,2011). Classical and quantum mechanics via Lie algebras. arXiv preprint arXiv:0810.1019.

 

[gentzen]

Neumaier, A., & Westra, D. (2008,2011). Classical and quantum mechanics via Lie algebras. arXiv preprint arXiv:0810.1019.

Do you still have plans to publish a polished version of this with De Gruyter, as part 1 of a treatise on Algebraic Quantum Physics?

 

[A. Neumaier]

In the usual definition of the theoretical HEP community, an elementary particle is described as an (asymptotic) free single-particle Fock state of an irreducible representation of the proper orthochronous Poincare group. As such it's characterized by its mass, ##m## and its spin, ##s##. A complete and convenient basis for ##m>0## are the momentum-spin-eigenstates ##|\vec{p},\sigma \rangle##, where ##\sigma \in \{-s,-s+1,\ldots,s-1,s \}##,

How do you reconcile this with your statement about classical phase-space degrees of freedom?

Counting number of parameters in the representation does not give a unique count of degrees of freedom. One can do quantum mechanics also over classical phase space. This is much more intuitive, has a much better classical limit, and gives an explicit description of a larger group of operators (namely a metaplectic group in place of a Heisenberg group). See

G.B. Folland, Harmonic Analysis in Phase Space, Princeton University Press (2016).

 

[A. Neumaier]

Do you still have plans to publish a polished version of this with De Gruyter, as part 1 of a treatise on Algebraic Quantum Physics?

Yes. The pandemic made my old schedule obsolete. But if I can proceed according to my present revised plans, Part 1 will appear in Fall 2024. Would you like to proofread a draft?

 

[gentzen]

TL;DR Summary: Is an object defined by the quantum state of all its particles?

No, not at all.

A pure state of an N-particle system is a function of 3N variables, while the corresponding mixed states of the N particles are N functions of 6 variables only. The mapping from the first to the second is onto, but very, very far from one-to-one. One gets a one-to-one correspondence only if the particles are assumed not to be entangled.

That was Greek to me. The person before you also seems to have given a "yes, it is." Would someone please explain in basic terms? >_<

Not quite. What I said was that the quantum state of a macroscopic is a massively entangled state of all its particles. I did not say that the object is "defined" by the quantum state of all its particles. So what I said is perfectly consistent with what @A. Neumaier said.

I'm sure as heck confused. Ignorant, anyway. What's a good intro to this stuff for someone who only went as far as Calc I?

I think A. Neumaier should have the same right as everybody else here to be told that he misinterpreted some quote from some challenging philosophical text. Independent of whether it was the fault of the unclear language of that text, or the fault of A. Neumaier himself, his answer was not "perfectly consistent" with Peter Donis' answer.

And Sayestu has every right to be confused by that discussion between Peter Donis and A. Neumaier.

What's a good intro to this stuff for someone who only went as far as Calc I?

If you want to get familiar with MWI, Lev Vaidman's SEP article from which you quoted is not that bad, in my opinion. At least he doesn't make any "stupid" mistakes. In my opinion, it is easy in MWI to make "stupic" mistakes such that what you write or say is simply wrong, independent of philosophical or interpretational issues.

 

[gentzen]

Yes. The pandemic made my old schedule obsolete. But if I can proceed according to my present revised plans, Part 1 will appear in Fall 2024. Would you like to proofread a draft?

Yes, I would like to proofread a draft. (I will sent you an email.)

 

[A. Neumaier]

One can do quantum mechanics also over classical phase space. This is much more intuitive, has a much better classical limit

The reason is that in the phase space approach the density matrix is the basic object. It has twice the number of arguments than the wave function, has a straightforward classical limit (Koopman's stochastic mechanics, with commuting operators acting diagonally), and has the advantage of being in one-to-one correspondence with the states, while the wave function has an additional unphysical phase and no classical analogue.

That's why I count 2 x 3 = 6 degrees of freedom.

 

[A. Neumaier]

Yes, I would like to proofread a draft. (I will sent you an email.)

Thanks. I am looking forward to the cooperation!