Description of isolated macroscopic systems in quantum mechanics

[Paul Colby]

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.

 

[f95toli]

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.

 

[A. Neumaier]

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!

 

[A. Neumaier]

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.

 

[A. Neumaier]

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.

 

[f95toli]

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.

 

[mephistomunchen]

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.

 

[mephistomunchen]

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.

 

[Paul Colby]

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.

 

[mephistomunchen]

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.

 

[Paul Colby]

OK, but

I’m not certain what your question has evolved into at this point.

 

[PeroK]

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.

 

[mephistomunchen]

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.

 

[A. Neumaier]

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).