Description of isolated macroscopic systems in quantum mechanics

  • #26
What parameter do you think has a "very sharp squared amplitude function" for a bound system? What if there isn't any such parameter for a bound system?
I assumed it's possible to take a "picture" of the molecule at a certain time by interacting with short wavelength photons, so that the positions of it's atoms (and then the angles between them) are determined with good accuracy
 
  • #27
I think you should consider the possibility that you have misunderstood or misinterpreted what you have learned about QM.

If you insist that you have understood the material fully (and that it is we who are wrong), then I don't believe the contradictions you are finding will disappear. In fact, I think you'll only find more examples where QM appears to contradict itself - as those contrardictions are a result of your misunderstanding of QM and not with QM itself.
Surely I have misunderstood something, I just don't know what :-). Anyway, thanks for all explanations!
 
  • #28
PeroK
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I assumed it's possible to take a "picture" of the molecule at a certain time by interacting with short wavelength photons, so that the positions of it's atoms (and then the angles between them) are determined with good accuracy
You can't have a picture of a molecule the way you can have a picture of a chessboard, with clearly defined images of every piece in its starting square. Measuring the position of particles in a molecule is about what you can infer from a few scattered photons.

For example, it would be very useful to know the ground state of ammonia. But, you can't just take a picture showing where everything is. Information about a molecule is inferred from theoretical models and things like emission and absorption spectra.

In any case, if you do pinpoint a particle in a molecule, then the system must be thrown into a superposition of all energy states - including unbound states. Effcetively you have a very significant external interaction that may have destroyed the molecule.

Instead, what QM is really telling us is that we can only infer a limited amount of information about a microscopic system - especially when it comes to the precise position of sub-atomic particles. The development of the model of the hydrogen atom was achieved not by taking accurate pictures of the atom and seeing where the electron is, but by studying the emission spectra under various conditions.

This is why it's important not to see microscopic systems as classical-type systems with a bit of uncertainty thrown in, but as fundamentally quantum, with essentially unknowable classical parameters, such as position of each particle. Instead, you have to describe them in terms of what can be measured - hence for hydrogen we have the four quantum numbers described above, rather than a classical set of coordinates for the electron.
 
  • #29
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I assumed it's possible to take a "picture" of the molecule at a certain time by interacting with short wavelength photons
Doing so will destroy the molecule; photons of short enough wavelength to pin down the position of individual atoms inside the molecule are energetic enough to split the molecule apart. And at the level of atoms, photons of short enough wavelength to pin down the position of individual electrons inside an atom are energetic enough to ionize the atom. In both of these cases, you won't get any useful information from the photons.
 
  • #30
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Summary:: Is the evolution of an isolated system always periodic in QM?

If we prepare a macroscopic system (something like Shrodinger's cat) in a known quantum-mechanical state and we let it evolve for a very long time completely isolated,
Your assumption is meaningless. A macroscopic system is never even approximately isolated. You'd need to switch off the whole surrounding (particles, fields, etc.).
 
  • #31
Your assumption is meaningless. A macroscopic system is never even approximately isolated. You'd need to switch off the whole surrounding (particles, fields, etc.).
I know that is not practically achievable, but I don't think it's meaningless. Sometimes idealized experiments are very useful to understand the essential points of a physical theory.

Shrodinger's cat experiment, after all, is not considered to be meaningless, right?

As I see it, there's something missing in QM related to the explanation of what happens in the measurement process.

I now the theory (collapse of the wave function when the system is measured and unitary evolution of isolated system), but I think there should be a way to describe the measurement process as a quantum interaction between the system and the observer.

I was trying to find such a description that makes sense, but all that I was able to find are explanations that this "doesn't make sense"...
 
  • #32
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It seems that a pure state may evolve into another pure state whose properties appear thermal (pure state quantum statistical mechanics.).

https://arxiv.org/abs/1503.07538
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
C. Gogolin, J. Eisert
 
  • #33
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But if the evolution of the system is unitary, shouldn't it end up returning to the initial state after a very long time?

In post #2, @Paul Colby gives a reference to a quantum Poincare recurrence theorem (which I wasn't aware of). In any case, if it is like the classical case, Poincare recurrence doesn't imply periodicity, since the time evolution into the state and out of the state may be different each time. Also, the Poincare recurrence time may be very long, greater than the lifetime of the universe, so that it is not relevant for physics.
 
  • #34
In post #2, @Paul Colby gives a reference to a quantum Poincare recurrence theorem (which I wasn't aware of). In any case, if it is like the classical case, Poincare recurrence doesn't imply periodicity, since the time evolution into the state and out of the state may be different each time. Also, the Poincare recurrence time may be very long, greater than the lifetime of the universe, so that it is not relevant for physics.
Yes, I see.
My intuition would be that any system will have some spectrum of eigenvalues of the Hamiltonian.
If the spectrum is discrete, it means that the time evolution has to be the superposition of a finite set of periodic transformations. That doesn't mean that the system is periodic anyway, of course, because the ratio between the periods may be not rational. But anyway, it's a superposition of repeating behaviours (in some sense nothing really happens that will not be undone).

If instead the spectrum of eigenvalues is continuous, the behaviour of the system can be always changing, and even irreversible processes could be possible if the quantum system is seen form a macroscopic level.

Is this correct?
 
  • #35
It seems that a pure state may evolve into another pure state whose properties appear thermal (pure state quantum statistical mechanics.).

https://arxiv.org/abs/1503.07538
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
C. Gogolin, J. Eisert
This seems very interesting. Only I am not sure if I'll be able to understand it :smile:
Thank you very much!
 
  • #36
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Also, the Poincare recurrence time may be very long, greater than the lifetime of the universe, so that it is not relevant for physics.
It is quite relevant lMO. The theorem is a theorem. The physics comes from understanding why it’s not applicable. Then there’s the issue of cat isolation. Just closing a box isn’t isolating the cat in the manner assumed by the theorem.
 
  • #37
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One thing I don't believe has been mentioned in this thread is that it is not necessary for the "whole system" (whatever that means) to be described as a one single "quantum system". That is, we often have a situations where some macroscopic object has one (or a few) parameter which can exist in a coherent superposition despite the fact that the rest of the object is purely "classical".

There are some real-life experiments which illustrate this.
One would be superconducting qubits which are large (~mm in size) electronic circuits; when cooled down to low enough temperatures they behave as very good quantum two-state systems and can exhibit all the usual quantum effects (superposition etc) .
Nothing "special" has happened to the circuit on the chip; it is still there if you look ("looking" won't change anything if you are careful) but one or more of the circuit parameters (usually charge of phase) have become quantized. This corresponds to currents flowing in "two different directions at once" or charges being "on" and "off" an island "at the same time".
Note that this is NOT -in general- an effect where only a single electron is involved; it involves a "macroscopic" number of electrons/Cooper pairs flowing in the circuit and generally speaking it is quite difficult to "identify" what is quantized.

Another, perhaps more obvious example, would be vibrating nanomechanical resonators. These are still macroscopic (can be seen in an optical microscope) but it is possible to put then in superposition of two vibration modes (corresponding to two different quantum states). Again, the beam is still there and is "classical" but one parameter of the system has been quantized.
 
  • #38
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I know that is not practically achievable, but I don't think it's meaningless. Sometimes idealized experiments are very useful to understand the essential points of a physical theory.

Shrodinger's cat experiment, after all, is not considered to be meaningless, right?
Not if the cat is a tiny quantum system. But a real cat cannot be used for the experiment.
I think there should be a way to describe the measurement process as a quantum interaction between the system and the observer.
Try this thread!
 
  • #39
A. Neumaier
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It is quite relevant lMO. The theorem is a theorem. The physics comes from understanding why it’s not applicable.
it is not applicable since it applies only to Hamiltonian (i.e., isolated) systems in a compact region. Because of radiation, no such system exists.
 
  • #40
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we often have a situations where some macroscopic object has one (or a few) parameter which can exist in a coherent superposition despite the fact that the rest of the object is purely "classical".
In this case, the joint dynamics is not governed by a Schrödinger equation but by a mixed quantum-classical dynamics. This is a very different basis, which when assumed renders most pure discussions of the quantum measurement problem irrelevant.
 
  • #41
f95toli
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In this case, the joint dynamics is not governed by a Schrödinger equation but by a mixed quantum-classical dynamics. This is a very different basis, which when assumed renders most pure discussions of the quantum measurement problem irrelevant.

Sure, but I don't think this is necessarily obvious to everyone which is why I thought it would be worth pointing out; especially since the question was in the main QM forum and the OP wasn't necessarily asking about interpretations.
Sometimes you get the impression when reading pop-sci about e.g. Schroedinger's cat that coherence and superposition requires that the whole physical object (be it an atom or a solid state qubit) is in some weird "ghost-like" state. Even when doing "old-timey" QM experiments with say electrons or atoms we are usually only dealing with one or a few variables; the rest of the object can behave completely "classically" and there is no contradictions in that.
 
  • #42
In this case, the joint dynamics is not governed by a Schrödinger equation but by a mixed quantum-classical dynamics. This is a very different basis, which when assumed renders most pure discussions of the quantum measurement problem irrelevant.
I don't see much difference between the Schrödinger equation for an electron in the field of atomic nucleus (a potential with spherical symmetry) and the Schrödinger equation for an electron in a crystal (a periodic potential). For what I understand, the fact that the crystal is a macroscopic object is completely irrelevant for the electron, as long as it has not enough energy to interact with the other electrons and nuclei inside the crystal. The only thing that matters is the energy required to interact with the other parts of the system, and not their size.
So, basically, the cat is not a quantum object because is capable of interacting with electromagnetic radiation and gravitational fields at extremely low energies, so the box is not enough to limit the interaction.
 
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  • #43
it is not applicable since it applies only to Hamiltonian (i.e., isolated) systems in a compact region. Because of radiation, no such system exists.
But the same is true even for an electron orbiting around an hydrogen nucleus. The presence of radiation in space does not affect the electron because the atom's energy levels that are separated by large gaps, not because of the size of the atom.
 
  • #44
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But the same is true even for an electron orbiting around an hydrogen nucleus. The presence of radiation in space does not affect the electron because the atom's energy levels that are separated by large gaps, not because of the size of the atom.
The interaction of the EM radiation field effects the energy levels (Lamb Shift, spectral widths etc) and causes atoms to decay etc. The number of states of the radiation field are infinite.
 
  • #45
The interaction of the EM radiation field effects the energy levels (Lamb Shift, spectral widths etc) and causes atoms to decay etc. The number of states of the radiation field are infinite.
OK, but these effects are not due to interactions with external systems (well, maybe is not quite clear what can be considered "external"). For what I understand, the kind of interactions that can change the quantum status of a system (and make it behave as a classical system) are the ones that can be used to "observe" it, or acquire information about its status. Virtual particles do have an effect on the system, but cannot be used to acquire information about its status.
 
  • #47
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OK, but these effects are not due to interactions with external systems (well, maybe is not quite clear what can be considered "external"). For what I understand, the kind of interactions that can change the quantum status of a system (and make it behave as a classical system) are the ones that can be used to "observe" it, or acquire information about its status. Virtual particles do have an effect on the system, but cannot be used to acquire information about its status.
Your posts are now largely promoting your own misunderstanding of QM. Nothing you have written here is an accurate statement about QM.
 
  • #48
Your posts are now largely promoting your own misunderstanding of QM. Nothing you have written here is an accurate statement about QM.
Sorry for that. I'll try not to write things that are only my opinions.
 
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  • #49
A. Neumaier
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I don't see much difference between the Schrödinger equation for an electron in the field of atomic nucleus (a potential with spherical symmetry) and the Schrödinger equation for an electron in a crystal (a periodic potential). For what I understand, the fact that the crystal is a macroscopic object is completely irrelevant for the electron,
But an electron in a crystal is, unlike a cat, a microscopic quantum system - the crystal is not modeled at all, only the electron.
But the same is true even for an electron orbiting around an hydrogen nucleus. The presence of radiation in space does not affect the electron because the atom's energy levels that are separated by large gaps, not because of the size of the atom.
The presence of radiation matters for larger objects since then the energy levels are separated by submicroscopic gaps only.
these effects are not due to interactions with external systems
The effective potential of an electron (whether in a hydrogen atom or in a crystal) is only due to interactions with external systems (the nucleus or the crystal).
 

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