What has changed since the Copenhagen interpretation?

[Auto-Didact]

Well, in an experiment such as measuring the spin in the x-direction of an electron that has been prepared to be spin-up in the z-direction, there is, a priori, more than one possible outcome, spin-up or spin-down. In BM, which is deterministic, only one of them is actually possible, and we only consider them both possible because we have incomplete knowledge of the current state.

Of course there is more than one outcome possible, no one is arguing that. The point is that there is only one outcome out of all possibilities selected in a measurement.

 

[atyy]

That's the practical approach to resolving paradoxes in QM: Assume that there is no such thing as a pure state consisting of a superposition of macroscopically different states. There can only be mixed states.

However, I find that assumption to be a "soft contradiction". QM does not in any way limit the size or complexity of the systems that can be described by it.

I was thinking a bit differently. If Wigner accepts that a measurement has been performed, then the wave function collapses. If Wigner knows the measurement outcome, then his state is the pure state obtained after collapse. However, if he does not know the outcome, then he uses a state that he considers a proper mixture (the collapsed states for the different outcomes weighted by the Born rule probabilities).

 

[stevendaryl]

I was thinking a bit differently. If Wigner accepts that a measurement has been performed, then the wave function collapses. If Wigner knows the measurement outcome, then his state is the pure state obtained after collapse. However, if he does not know the outcome, then he uses a state that he considers a proper mixture (the collapsed states for the different outcomes weighted by the Born rule probabilities).

That's what I would call a "soft contradiction". Wigner thinking of his friend as a collection of atoms that obey Schrodinger's equation tells him one thing. Thinking of his friend as an observer capable of performing measurements tells him something else.

 

[atyy]

That's what I would call a "soft contradiction". Wigner thinking of his friend as a collection of atoms that obey Schrodinger's equation tells him one thing. Thinking of his friend as an observer capable of performing measurements tells him something else.

Isn't that's just the measurement problem?

 

[stevendaryl]

Isn't that's just the measurement problem?

I suppose so.

 

[DarMM]

Maybe QBists try to do that, since I think FR say QBism is inconsistent?

FR more says that if you want to have subjective collapse, you have to move to a position like yours or QBism, i.e. Wigner must not even consider his friend's events.

QBism is like your view and is explicitly compatible with FR.

As Matthew Pusey says in his summary it strengthens positions like yours and QBism.

Are there really Copenhagen versions in which an agent can be on both sides of the quantum-classical cut? I mean, it would be like saying that the cat is both "dead and alive" and "dead or alive", which seems ridiculous.

This is essentially what I was saying to @Demystifier , yes it seems ridiculous, but is has never been proven to actually be contradictory until now. That's really all FR is in a way.

As @Demystifier said the only surprising thing is that you need such an extreme scenario to demonstrate the contradiction.

I don't have the freedom for a long post right now but when I do I'll go into why some people thought it might be possible to consider an agent on both sides of the cut.

 

[ftr]

Why does the particle have to be in superposition in the first place.

 

[PeterDonis]

In BM, which is deterministic, only one of them is actually possible, and we only consider them both possible because we have incomplete knowledge of the current state.

But after the measurement, our knowledge of the current state has changed, because we know which outcome occurred. And we reflect that changed state of knowledge in the new wave function we use to predict further measurement results. So it seems like BM is perfectly consistent with an epistemic view of wave function collapse.

 

[DarMM]

Why does the particle have to be in superposition in the first place.

Which particle?

 

[ftr]

Say particle in a box for example, or electron in hydrogen atom ... etc

 

[atyy]

This is essentially what I was saying to @Demystifier , yes it seems ridiculous, but is has never been proven to actually be contradictory until now. That's really all FR is in a way.

As @Demystifier said the only surprising thing is that you need such an extreme scenario to demonstrate the contradiction.

If FR is a technical result about the extent to which the classical-quantum cut can be shifted, could it be understood as an extreme variant of Hay and Peres's "Quantum and classical descriptions of a measuring apparatus" https://arxiv.org/abs/quant-ph/9712044 ?

 

[stevendaryl]

But after the measurement, our knowledge of the current state has changed, because we know which outcome occurred. And we reflect that changed state of knowledge in the new wave function we use to predict further measurement results. So it seems like BM is perfectly consistent with an epistemic view of wave function collapse.

My comment was in reference to @atyy saying:

Anyway, would you agree with Demystifier that collapse in BM is objective (post #17)?

I would think that objective means that it's not epistemic.

 

[Demystifier]

I'm not exactly sure what @Demystifier would say about it, but it seems to me that BM is not consistent with the usual idea of wave function collapse.

Let me put it in a slightly metaphorical form. In BM, there is no collapse from the bird's view, but there is from the frog's view.

 

[Demystifier]

If FR is a technical result about the extent to which the classical-quantum cut can be shifted, could it be understood as an extreme variant of Hay and Peres's "Quantum and classical descriptions of a measuring apparatus" https://arxiv.org/abs/quant-ph/9712044 ?

Yes, it seems related.

 

[Demystifier]

So it seems like BM is perfectly consistent with an epistemic view of wave function collapse.

In BM there are two different notions of the wave function: (i) the wave function of the full system and (ii) the wave function of the subsystem. The collapse of (i) is epistemic, but the collapse of (ii) is ontic.

Let me explain a bit. Suppose that the full system consists of two particles, with positions $x_1$ and $x_2$. The full wave function is $\Psi(x_1,x_2,t)$. In BM there are also particle trajectories $X_1(t)$ and $X_2(t)$. Then the wave function of the subsystem 1 is
$$\psi_1(x_1,t)=\Psi(x_1,X_2(t),t)$$
The wave function $\psi_1(x_1,t)$ is ontic, it does not always satisfy the Schrodinger equation, and in a measurement setup it may collapse. This collapse of $\psi_1(x_1,t)$ is ontic.

Not also that standard QM does not have an analog of $\psi_1(x_1,t)$. To describe a subsystem, the standard QM must use a density matrix (a partial trace of the full density matrix), rather than a wave function.

 

[A. Neumaier]

In BM there are two different notions of the wave function: (i) the wave function of the full system and (ii) the wave function of the subsystem. The collapse of (i) is epistemic, but the collapse of (ii) is ontic.

What if there are three nested systems? Doesn't the full system have to be the whole universe? Otherwise the nature of the wave function changes depending on what one regards as the full system.

 

[Demystifier]

What if there are three nested systems?

Than only the biggest one is counted as the full system, while the other two are subsystems. One of those two is in fact a sub-subsystem, but it doesn't change much.

Doesn't the full system have to be the whole universe?

Strictly speaking, yes. But if a smaller system is not much entangled with the rest of the Universe, then one can use an approximation by treating this system as a "full" system.

Otherwise the nature of the wave function changes depending on what one regards as the full system.

Fortunately this is no the case, because there is a well defined criterion for a definition of full system - a system with zero (or small, for practical purposes) entanglement entropy.

 

[A. Neumaier]

if a smaller system is not much entangled with the rest of the Universe

But any observable system is significantly entangled with the rest of the universe. Otherwise we (being part of the rest of the universe) cannot observe it.

 

[Demystifier]

But any observable system is significantly entangled with the rest of the universe. Otherwise we (being part of the rest of the universe) cannot observe it.

If that was true, then we could never use pure states in quantum theory, except when we describe the whole Universe. Obviously, it is not true. Sure, when Prof. Zeilinger performs measurement of an electron, then the electron is entangled with the measuring apparatus and with Prof. Zeilinger. In this case, the full system consists of electron, measuring apparatus and Prof. Zeilinger. But it still does not need to include the whole Universe. The entanglement between Prof. Zeilinger and his dog, for instance, can be neglected for the purpose of studying the electron in the Zeilinger's laboratory.

 

[martinbn]

Can BM treat the whole universe at least in principle, or any infinite number of particles?

 

[A. Neumaier]

If that was true, then we could never use pure states in quantum theory, except when we describe the whole Universe.

Indeed, pure states are almost never used, except for very tiny systems where we know the state because we either just measured a complete set of commuting observables, or projected away all alternatives.

Essentially all quantum optical studies (except for textbook ones) are described using Lindblad equations (for density matrices!) to account for the unavoidable dissipation. All analyses that use pure states only need to be corrected by accounting (often in some hand-waving way) for losses.

 

[A. Neumaier]

The entanglement between Prof. Zeilinger and his dog, for instance, can be neglected for the purpose of studying the electron in the Zeilinger's laboratory.

But the entanglement entropy, your measure that decides what can be neglected, will be large! It can perhaps be neglected for studying an electron spin only (except if the dog jumps at the equipment) but not for studying the full system consisting of electron, equipment, and Zeilinger.

 

[DarMM]

Say particle in a box for example, or electron in hydrogen atom ... etc

Oh, we don't know. What is actually going on in superposition is unknown. Knowing that might entail an answer to the measurement problem.

 

[Demystifier]

Essentially all quantum optical studies (except for textbook ones) are described using Lindblad equations (for density matrices!)

It looks a bit like an overstatement to me.

 

[Demystifier]

Can BM treat the whole universe at least in principle, or any infinite number of particles?

Yes.

 

[A. Neumaier]

It looks a bit like an overstatement to me.

To convince yourself, look at the details of an analysis of the conditions for making experiments checking the Bell inequalities fully trustworthy.
Whenever quantitative details matter you need more accurate models than what you get just from pure states.In diffraction experiments for buckyballs, the pure state prepared is just one qubit, not the multiparticle state. Most pure states are approximate, and comprise very few qubits since one cannot prepare the pure states for bigger systems. An exception are ground states and low lying excited states of molecules with well separated energy levels, these can be prepared reasonably well - but not their superpositions!

 

[martinbn]

Yes.

How?

 

[Demystifier]

How?

You would help me to explain it to you if you would first tell me why do you think that it can't.

 

[A. Neumaier]

why do you think that it can't.

How does Bohmian mechanics model the destruction of particle pairs? It would presumably require that the particles meet at the same position, which is exceedingly improbable.

 

[DrDu]

Can BM treat the whole universe at least in principle, or any infinite number of particles?

I don't think it is possible, for any theory, to describe the whole universe. This is especially ridiculous in thermodynamics. People derive entropy considering some simple thermal machines from the 18th century and in the next sentence they speak of the entropy of the universe.

 

[Demystifier]

How does Bohmian mechanics model the destruction of particle pairs? It would presumably require that the particles meet at the same position, which is exceedingly improbable.

It is a part of the question how to generalize BM to relativistic QFT. As you know, there is no one generally accepted approach to that question. I myself have presented several different approaches. Currently I prefer the approach outlined in Sec. 4.3 of my https://lanl.arxiv.org/abs/1703.08341 Soon I will upload a more detailed paper on arXiv.

 

[DrDu]

Strictly speaking, yes. But if a smaller system is not much entangled with the rest of the Universe, then one can use an approximation by treating this system as a "full" system.

The problem with this view are infrared divergencies. We know that even to describe a simple system like an electron, we have to take the coupling to soft photons into account. The problem is that soft photons have arbitrary large wavelength and cannot be screened off. So even small systems are strongly coupled to the rest of the universe. The best you can hope is that these coupling doesn't change much when two systems are interacting.

 

[Demystifier]

The problem with this view are infrared divergencies. We know that even to describe a simple system like an electron, we have to take the coupling to soft photons into account. The problem is that soft photons have arbitrary large wavelength and cannot be screened off. So even small systems are strongly coupled to the rest of the universe. The best you can hope is that these coupling doesn't change much when two systems are interacting.

Well, the experience teaches us that approximations that ignore this effect are often in agreement with experiments. Take, for example, quantum mechanical treatment of the hydrogen atom.

 

[martinbn]

You would help me to explain it to you if you would first tell me why do you think that it can't.

I don't have an opinion yet. But it isn't obvious to me, so I suspect that it isn't straightforward. For example what would be the function space that the wave function belongs to? Just to clarify, because you may say "why do you ask that?", if you have infinitely many particles the wave function will be a function of infinitely many variables, that would make any integration tricky.

 

[A. Neumaier]

approximations that ignore this effect are often in agreement with experiments. Take, for example, quantum mechanical treatment of the hydrogen atom.

Already for hydrogen, the agreement is only reasonable but not perfect. One needs the radiation corrections to get a nonzero Lamb shift. This is experimentally measurable.

The bigger the system, the more difficult it is to shield the system from the environment in order to keep the dynamics approximately unitary. Already for helium clusters of around 100 atoms, the concept of temperature becomes relevant - signalling dissipative (non-unitary) behavior. The dissipation is always to the environment.