What has changed since the Copenhagen interpretation?

[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.

 

[Demystifier]

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.

Ah, you ask from a rigorous mathematical point of view. My view is that in physics one does not need to worry too much about that, because infinities in physics are only potential infinities. For instance, if the visible universe has about $10^{80}$ particles, then one can study only those $10^{80}$ particles and approximate it by infinity only when it makes the analysis simpler.

 

[Demystifier]

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.

That's all true, but note that the measurable Lamb shift is not an effect of dissipation.

 

[A. Neumaier]

That's all true, but note that the measurable Lamb shift is not an effect of dissipation.

This is not quite true. Though generally only the real part is considered, the Lamb shift is actually complex, leading to observable broadened lines in the spectrum. Complex energies are the hallmark of dissipative effects. Note that real spectra always exhibit line broadening.

 

[stevendaryl]

Ah, you ask from a rigorous mathematical point of view. My view is that in physics one does not need to worry too much about that, because infinities in physics are only potential infinities. For instance, if the visible universe has about $10^{80}$ particles, then one can study only those $10^{80}$ particles and approximate it by infinity only when it makes the analysis simpler.

Here's something that I've never heard discussed before: If the universe is infinite (and the mass/energy is roughly uniformly distributed), then the wave function of the universe would involve an actual infinite number of particles. The perturbative calculations in QFT assume that the state is a perturbation of the vacuum, but no state with an infinite number of particles can be obtained from the vacuum by any finite number of applications of creation/destruction operators. So is there a mathematical treatment for a truly infinite universe?

 

[Demystifier]

So is there a mathematical treatment for a truly infinite universe?

I'm sure there is, but I'm not sure how rigorous it is.

 

[A. Neumaier]

. The perturbative calculations in QFT assume that the state is a perturbation of the vacuum, but no state with an infinite number of particles can be obtained from the vacuum by any finite number of applications of creation/destruction operators. So is there a mathematical treatment for a truly infinite universe?

Yes. The vacuum sector (zero density and temperature) is relevant for few particle problems, where the asymptotic in-out behavior reflected in the S-matrix is the relevant object for making predictions. This is the textbook material. For finite density and temperature other sectors of the same quantum field theories matter.
These are treated in terms of CTP (closed time path) techniques, and only need finite densities, never total energies or total particle numbers. Thus they can cope with an infinite universe with a finite density.

Of course the mathematics is as nonrigorous as for perturbative QFT, but this is a different matter.

 

[A. Neumaier]

These are treated in terms of CTP (closed time path) techniques, and only need finite densities, never total energies or total particle numbers. Thus they can cope with an infinite universe with a finite density.

On the other hand, Bohmian mechanics needs an explicit multiparticle Hamiltonian, hence cannot cope with an everywhere positive density. The approximate recipe by Demystifier does not work there.

 

[DrDu]

Here's something that I've never heard discussed before: If the universe is infinite (and the mass/energy is roughly uniformly distributed), then the wave function of the universe would involve an actual infinite number of particles. The perturbative calculations in QFT assume that the state is a perturbation of the vacuum, but no state with an infinite number of particles can be obtained from the vacuum by any finite number of applications of creation/destruction operators. So is there a mathematical treatment for a truly infinite universe?

The problem is that even electrons moving at different speed are states which differ by an infinite amount of soft photons. So you can't treat both in the same hilbert space. Also free and interacting QFT differ by an infinite amount of particles, which is paraphrased as Haags theorem.

 

[Demystifier]

On the other hand, Bohmian mechanics needs an explicit multiparticle Hamiltonian, hence cannot cope with an everywhere positive density. The approximate recipe by Demystifier does not work there.

Yes, but Bohmian mechanics is not a technique. It is an explanation. It is similar to the Boltzmann's interpretation of thermodynamics as a motion of $10^{23}$ point-like atoms obeying the laws of classical mechanics. It is an explanation of thermodynamics, not a technique that should replace the standard techniques of the 19th century thermodynamics.

 

[Demystifier]

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.

It's uploaded now: http://de.arxiv.org/abs/1811.11643

 

[edmund cavendish]

What about Penroses speculations about gravity induced wave function collapse? Challenged I know but potentially a significant development since/ challenge to Copenhagen? Fascinating thread.

 

[stevendaryl]

What about Penroses speculations about gravity induced wave function collapse? Challenged I know but potentially a significant development since/ challenge to Copenhagen? Fascinating thread.

When I first heard it, it sounded like a completely goofy idea. But on the other hand, who knows what might come out of the effort to reconcile quantum mechanics and gravity? And maybe it relates to the EPR=ER conjecture.

 

[Auto-Didact]

What about Penroses speculations about gravity induced wave function collapse? Challenged I know but potentially a significant development since/ challenge to Copenhagen? Fascinating thread.

To be clear for others reading, the Diosi-Penrose objective reduction scheme (OR) i.e. non-unitary wave function collapse as an objectively occurring physical phenomenon is actually more than an interpretation; this is because it postulates that standard QM literally breaks down for masses greater than $m_{\mathrm {Planck}}$. This happens because above this limit, gravitational fields per GR will also be in superposition leading to vacuum state issues which are explicitly not allowed in QFT.

Penrose therefore, using a bifurcation theory argument, says that gravitational field superpositions are intrinsically unstable with superposed mass functioning as the bifurcation parameter. In other words, OR explicitly predicts that all mass superpositions have a natural decay rate proportional to the superposed mass per $\Delta t \geq \frac {\hbar} {\Delta E}$. This prediction is in direct contradiction to standard QM.

This means that OR predicts very specific different experimental results compared to standard QM, namely spontaneous collapse of any object in superposition within a time $\tau$ into a single random one of the orthogonal states. The problem is however that to date no QM experiment has ever been carried out with large enough masses for this effect to be noticeable. This OR effect will only become experimentally distinguishable from standard QM when $\sim10^{-8} \mathrm{kg}$ objects can be put into superposition. There are multiple experiments being carried out to test this.

When I first heard it, it sounded like a completely goofy idea. But on the other hand, who knows what might come out of the effort to reconcile quantum mechanics and gravity?

The fact that the OR scheme is so simple is what I find makes it so interesting; the same is true of Bohmian mechanics (BM). The difference however is that BM is mathematically equivalent to QM and explains QM while OR goes beyond QM i.e. QM is a limiting case of (a theory with) OR and OR therefore directly points the way to quantum gravity, or more accurately 'gravitized QM' as Penrose puts it.

 

[A. Neumaier]

BM is mathematically equivalent to QM

No, Bohmian mechanics predicts additional observables (exact position values at all times), in contradiction to ordinary quantum mechanics.

 

[Demystifier]

No, Bohmian mechanics predicts additional observables (exact position values at all times), in contradiction to ordinary quantum mechanics.

The version of BM I recently proposed in http://de.arxiv.org/abs/1811.11643 even makes a new generic measurable prediction. (But not measurable with current technology.)