How does one make a macroscopic object?

[Paul Colby]

TL;DR Summary

All mater is comprised of indistinguishable bits, electrons nuclei molecules etc. At what point in adding these things together does one object become distinguishable from another?

The question bothering me is when does an object become classical? I believe the answer is actually never. The summary is perhaps a better way to frame my question.

 

[PeterDonis]

Summary:: All mater is comprised of indistinguishable bits, electrons nuclei molecules etc. At what point in adding these things together does one object become distinguishable from another?

Distinguishable objects are not distinguished by "which bits" they are made of. They are distinguished by having distinct values of appropriate observables. For example, you and I occupy different regions of space; that observable can be used to distinguish you and me even though the electrons in your body are not distinguishable from the electrons in mine.

The question bothering me is when does an object become classical?

This is actually not the same question as the above. Notice that when I described how to distinguish you and me I said nothing about whether either one of us was "classical".

 

[Paul Colby]

They are distinguished by having distinct values of appropriate observables. For example, you and I occupy different regions of space; that observable can be used to distinguish you and me even though the electrons in your body are not distinguishable from the electrons in mine.

Agreed, but doesn't this just push the question down the road? Two electrons may have different momenta but they are still considered indistinguishable. When does an object acquire enough bits to be considered distinguishable from a similar object made of the same sort of bits?

This is actually not the same question as the above

Also agreed. Are they related in your view?

 

[PeterDonis]

Two electrons may have different momenta but they are still considered indistinguishable.

The electrons are indistinguishable, but the momenta are not. You still have a state with two different momenta present. The momenta are distinguishable in the same sense as you and I are distinguishable: the different values of the momentum observable are what distinguishes them.

Describing this in ordinary language is actually a poor way of describing it. When we say the two electrons are "indistinguishable" we don't mean they are identical in all possible respects; all we mean is that the wave function of the two-electron system has a particular property (it changes sign on particle exchange). The wave function of the total quantum system that describes you and me combined has the same property--swap any pair of electrons and the total wave function changes sign. But that doesn't mean you and I are identical.

Are they related in your view?

Not really, no.

 

[Paul Colby]

The electrons are indistinguishable, but the momenta are not.

Thanks, this is helpful. I'm still left not quite understanding how one describes macroscopic objects quantum mechanically.

 

[PeterDonis]

I'm still left not quite understanding how one describes macroscopic objects quantum mechanically.

The short answer is, nobody really does. An object like you or me (or a rock or a baseball or a spacecraft ) is treated using the classical limit, which means any quantum mechanical properties that could lead to predictions different from those of classical physics are simply assumed to be negligible. Nobody uses wave functions and the Schrodinger Equation for macroscopic objects.

 

[Paul Colby]

The short answer is, nobody really does.

Well, measuring devices would appear to be macroscopic objects at least the ones that I've seen. So I view this as not entirely a moot point. Can you think of a purely quantum mechanical detector? If so it would have to have a readout that's macroscopic.

 

[PeterDonis]

measuring devices would appear to be macroscopic objects at least the ones that I've seen.

Yes, and nobody uses QM to model them. Even proponents of the MWI, who believe that everything is unitary evolution all the time and there is a wave function for the entire universe, never actually use a wave function even for a single macroscopic object or measuring device, let alone the entire universe, to make predictions. To actually make predictions with QM, you have to treat the measuring device as classical and only the system being measured as a quantum system with a wave function.

 

[vanhees71]

Thanks, this is helpful. I'm still left not quite understanding how one describes macroscopic objects quantum mechanically.

You decribe it using quantum-many-body theory to descibe the macroscopic object's macroscopic "relevant" degrees of freedom by summing/averaging out the very many microscopic details irrelevant to the description of the macroscopic body's behavior (coarse graining).

To observe quantum effects on a macroscopic body is very challenging. Usualy you have to cool it down to low temperature to avoid decoherence. That has been demonstrated, e.g., by double-slit experiments with buckyballs (C60 molecules) which are not really macroscopic: if they were too warm, the emission of a few thermal photons was sufficient to destroy the coherence and to destroy the interfrence fringes, which could be demonstrated with cool enough buckyballs:

https://arxiv.org/pdf/quant-ph/0402146

 

[PeterDonis]

You decribe it using quantum-many-body theory

Can you give a good general reference? I know this body of theory exists but I don't know of a good place to go to get a presentation of the essentials.

 

[Morbert]

Can you give a good general reference? I know this body of theory exists but I don't know of a good place to go to get a presentation of the essentials.

I found this paper helpful

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.47.3345
(preprint https://arxiv.org/abs/gr-qc/9210010 )

It discusses the coarse-graining that gives rise to hydrodynamic variables that are often used to characterise macroscopic objects.

 

[Nugatory]

The question bothering me is when does an object become classical? I believe the answer is actually never.

”Become classical” is a misleading way of framing the question. It is more helpful to consider whether the classical approximation is good enough for the problem at hand; if it is, then the object “is classical”.

Your question isn’t unique to quantum mechanics. For example, we all know that we can accurately describe the trajectory of a cannonball by treating it as a classical object of given mass - but to describe what’s really going we’d have to apply the methods of statistical mechanics to the ensemble of $10^{25}$ iron atoms that make up the cannonball, or (even worse) turn the calculation over to Laplace’s demon. That doesn’t stop us from considering the cannonball a classical object, and there’s no reason to feel differently about a quantum mechanical treatment of it.

Well, measuring devices would appear to be macroscopic objects at least the ones that I've seen.

QM does allow for some unnecessary additional confusion because some interpretations (notably orthodox Copenhagen) bring in the notion of a classical/quantum split, with the measuring apparatus on side and the system being measured on the other side. The answer here is that if your choice of interpretation isn’t helping understand a problem... choose a different interpretation. For example, you might find it more helpful to consider a measurement to be a thermodynamically irreversible change in the entire system including the measuring device - that makes it clear that the classical behavior is an emergent phenomenon in the same way that the idealized cannonball is.

 

[PeterDonis]

It discusses the coarse-graining that gives rise to hydrodynamic variables that are often used to characterise macroscopic objects.

Note that this paper uses the decoherent histories interpretation. On a quick skim, not much of what it says is critically dependent on that interpretation, but it's still something to be aware of.

 

[Paul Colby]

choose a different interpretation.

I'm trying not to use one. My question is more a how does one describe macroscopic objects in terms of quantum mechanics. Anyway there's much that's been written on this subject that I should try to look at. The fact that hot molecules become more classical as temperature increases is quite interesting.

 

[Vanadium 50]

This is just the paradox of the heap. How big is "big"?
QM applies at all scales. QM calculations are not practical at all scales.

 

[Paul Colby]

I think the "paradox of the heap" is definitely not the way to approach or look at the problem nor the way I should have ask about it. Macroscopic measuring devices seem cooked into the rules of QM. If QM applies at all scales (no question there) is it fair to ask if the QM rules dealing with measurement are deducible from the others? Anyway, I think my initial question has been addressed here, thank you.

 

[TeethWhitener]

Can you give a good general reference? I know this body of theory exists but I don't know of a good place to go to get a presentation of the essentials.

How about this?
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.90.025004

 

[Nugatory]

Macroscopic measuring devices seem cooked into the rules of QM.

They are not. They are cooked into some interpretations of QM - there are other interpretations in which the distinction between ”quantum” and “macroscopic” does not appear.

further discussion along these lines will likely move us into the Interpretations forum...

 

[Vanadium 50]

Macroscopic measuring devices seem cooked into the rules of QM.

No, they are not.

 

[PeterDonis]

They are not. They are cooked into some interpretations of QM

Measurements are right there in the 7 basic rules of QM that are the basis for discussion in this forum:

https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

The rules as stated don't explicitly require that "measurements" are made by macroscopic devices, but they are for all of the examples given in the article (or indeed anywhere I've seen measurements discussed or described).

further discussion along these lines will likely move us into the Interpretations forum...

Yes, agreed, but I think it's well to be aware of what the agreed basis for discussion is in this forum as well.

 

[PeterDonis]

is it fair to ask if the QM rules dealing with measurement are deducible from the others?

In terms of basic QM (as seen, for example, in the 7 basic rules Insights article I linked to just now in response to @Nugatory), they're not; they're postulates of the theory.

As has been said, discussion of how the various interpretations of QM deal with this issue belongs in the interpretations forum.

 

[PeterDonis]

How about this?

Arxiv preprint here since the previous link leads to a paywall:

https://arxiv.org/abs/1706.06173

 

[A. Neumaier]

When does an object acquire enough bits to be considered distinguishable from a similar object made of the same sort of bits?

3 DOF suffice. A particle localized in an ion trap is distinguished by its position, since there is only one particle in a given trap. So is a single particle adsorbed at a surface and made visible by an atomic resolution microscope. No classicality assumption enters.

how one describes macroscopic objects quantum mechanically.

By their density operator in local equilibrium. This can be found in treatments of quantum statistical mechanics, for example, the book by Linda Reichl on Statistical Physics. No classicality assumption enters, but in simple cases one may use classical statistical mechanics to get approximately the same results.

nobody uses QM to model them. [measuring devices]

This is not true. Devising high resolution equipment requires to model it quantum mechanically. Also foundational work such as

• A.E. Allahverdyan, R. Balian and T.M. Nieuwenhuizen, Understanding quantum measurement from the solution of dynamical models, Physics Reports 525 (2013), 1-166.

deals with quantum models of measurement processes.

 

[vanhees71]

Can you give a good general reference? I know this body of theory exists but I don't know of a good place to go to get a presentation of the essentials.

As a standard source, I'd recommend to start with Landau-Lifshitz vol. X.

Generally, you have a kind of "hierarchy of descriptions" going from the microscopic description via various steps of approximations "down" to more and more "coarse grained" effective theories describing macroscopic observables.

You start with the quantum many-body level. The most convenient way is to use quantum field theory, because this deals in the most convenient way with the (anti-)symmetrization for many-body boson (fermion) states. This can be done both in the non-relativistic realm (usually sufficient for most things concerning "condensed-matter physics") and the relativistic (needed mostly in my field of "relativistic heavy-ion collisions", where you deal with "fireballs" of rapidly expanding "blobs" of strongly interacting matter, which behaves astonishingly like a fluid close to local thermal equilibrium).

There are two main formalisms in the literature to get to classical equations. One of them is to use the socalled two-particle irreducible formalism in the Schwinger-Keldysh real-time method to get closed equations for the exact two-point Green's function, which in Wigner-transformed form, is close to a classical phase-space distribution function, though not positive definite. That's because these socalled Kadanoff-Baym equations still contain all quantum effects.

The next step is some "coarse-graining formalism", i.e., you "forget" some too-detailed information. The idea behind this is that there's a separation of space-time scales: On the one hand a relatively slow time scale of macroscopic properties and macroscopic distances along which the macroscopic quantities significantly change and on the other hand the rapid oscillations/fluctuations around the mean values of these quantities. That's why one formal mathematical way of coarse-graining is the gradient expansion, i.e., you expand in powers of the space-time gradients of the macroscopic quantities. From another point of view you can also understand this as an expansion in powers of $\hbar$.

This then leads to Boltzmann-like transport equations, usually with non-Markovian (memory) effects for a true positive definite one-particle phase-space distribution function with a hierarchy of $n$-body correlation functions in the collision term. The usual Boltzmann equation truncates this at the one-particle level employing what's known in the classical case the "molecular-chaos assumption", i.e., the two-body distribution function is approximated as the product of two one-body distribution functions. At this point you through away information and the H-theorem (increasing entropy) can be proven.

The next step then is to identify the local-thermal equilibrium states, leading to Maxwell-Boltzmann (or Fermi-Dirac/Bose-Einstein distributions if you take Pauli blocking or Bose enhancement in the collision term into account) distributions with time-dependent temperature and chemical potentials as well as a flow velocity. If you then assume that the evolution of the system is slow compared to the typical relaxation-time scales to equilbrium you are at the level of ideal hydro. Expanding the distribution function around the local-thermal-equilibrium solutions you get in a systematic way various versions of dissipative hydro dynamics, with the Navier-Stokes equations as the leading order correction. At this level the microscopic origin (cross sections in the collision term of the Boltzmann equation) is just lumped into the various transport coefficients like shear and bulk visicosity, heat conductivity, diffusion constants etc.

Of course there are similar approaches also not only for fluids but also solids, where however you can describe many things using a quasi-particle picture, where collective excitations like lattice vibrations of a crystal are described by annihilation and creation operators of the corresponding (quantized) modes, which leads to a formalism which looks like the description of particles. In the Green's-function formalism this is always possible, if you have sharp peaks in the spectral function (which are just the imaginary parts of the retarded one-body propagator/two-point function). Then you can describe these excitations as "quasi-particles"/long-lived resonances.

 

[dRic2]

Off-topic (question for @vanhees71 )

Spoiler

Here you said

The usual Boltzmann equation truncates this at the one-particle level employing what's known in the classical case the "molecular-chaos assumption", i.e., the two-body distribution function is approximated as the product of two one-body distribution functions. At this point you through away information and the H-theorem (increasing entropy) can be proven.

This is something I always wanted to understand but couldn't. Do you have any good sources ? I mean, the Stosszahlansatz is a mathematical assumption which is not true, yet it is necessary to explain macroscopic irreversibility. Does it mean that macroscopic irreversibility does not actually exist ? This is strange because of its inner connection with the arrow of time. I know it is a fairly discussed problem, but I couldn't find a nice and simple book that explains it.

 

[vanhees71]

The problem of the "arrow of time" is unfortunately not "nice and simple". Neglecting the weak interaction, all the physical laws are time-reversal invariant, and as long as "closed systems" are concerned the time evolution is time-reversal invariant, i.e., if you could exactly follow the full dynamics of a closed system (within classical point mechanics solve exactly Hamilton's equations of motion and knowing exactly all the interactions, i.e., the Hamilton function of the system) you could by just at one point in time choose to prepare all the particles in the time-reversed state precisely (i.e., keeping their positions and reflecting their momenta) then you'd just see a trajectory of the system in phase space as if you look at a movie of the original motion backwards. A similar argument can be made for the quantum case: As long as you have the full unitary time evolution of the system at hand and the dynamics is time-reversal invariant you could in principle undo a time evolution by just start again at the time-reversed momentary state as the initial state.

In all physics, however there's an arrow of time in the very foundations, which I'd call the "causal arrow of time", i.e., we assume a spacetime model such that at each event there's some orientation of the time splitting for any observer the past and future of this event (at least in a local sense, as in the case of GR).

All the H-theorem says is, that if you consider only a coarse-grained picture of the evolution of a closed system, i.e., look at a subset of "relevant" macroscopic observables as an average/sum over many microscopic observables (e.g., some body consisting of $10^{23}$ molecules is described by its center of mass and the total momentum only and averaging over all the tiny fluctuations of this quantity by taking appropriate average over microscopically large butt macroscopically small spacetime volumes) then you can define the entropy as a measure for the "missing information" and show that it is, on average, never decreasing with time in the sense of the "causal arrow of time", i.e., the thermodynamic arrow of time based on Boltzmann's H-theorem is identical with the causal arrow of time.

I don't know any specific book about this issue, but I'd recommend to check the library for books by I. Prigogine, who is famous for his work on irreversibility and also the arrow of time.

 

[Gangzhen JIAO]

Summary:: All mater is comprised of indistinguishable bits, electrons nuclei molecules etc. At what point in adding these things together does one object become distinguishable from another?

The question bothering me is when does an object become classical? I believe the answer is actually never. The summary is perhaps a better way to frame my question.

In my opinion, the space relationship of every too indistinguishable bits makes responsbility for the object classical. That means the classical object is generated gradually but not at one point suddenly.

 

[Paul Colby]

In my opinion, the space relationship of every too indistinguishable bits makes responsbility for the object classical. That means the classical object is generated gradually but not at one point suddenly.

Pretty convincing arguments have been made to the contrary in the thread. Indistinguishability in QM is a technical term regarding the symmetry of the wave function under exchange of individual particle labels. This is expected to hold independent of the number of particles making up an object.

 

[physika]

Summary:: All mater is comprised of indistinguishable bits, electrons nuclei molecules etc. At what point in adding these things together does one object become distinguishable from another?

The question bothering me is when does an object become classical? I believe the answer is actually never. The summary is perhaps a better way to frame my question.

https://www.physicsforums.com/threads/experiments-probing-the-macroscopic-limits-of-qm.903867/