Epistemic view of the wave function leads to superluminal signal

[Fra]

Btw, how is understanding of QFT may be more important/critical than of QM? I thought that they both have basically the same foundational problems i.e. that QFT does not resolve any foundational problem QM has, just inherits all of them.

One note that i personally think is important if you have unification of interactions in mind is that the QM vs QFT foundation issue fades as you try to reconstruct state spaces from an abstract starting points and general informationspaces without assuming a classical spacetime index that is a priori separated from internal spaces.

In this sense, QFT just has more baggage which isn't necessarily helpful. Thats not to say Newtonian spacetime is better than relativity but just a note that spacetime itself as we know it may not come out in one piece in this quest at extreme energies and QFT cements more classical spacetime stuff into the picture and i am not sure that is the best approach.

/Fredrik

 

[A. Neumaier]

Formally there are no difficulties with QM - its what it means that's at issue and what the various interpretations grapple with. They all have problems - every single one of them.

I think Dr Neumaier has a good point - QFT may indeed be a better place for interpretations. I do not know enough of his thermal interpretation to comment on its specifics.

Dr Neumaier is correct in emphasizing understanding QM is not really the critical thing - QFT is. But in that he has left me far behind as my knowledge of QFT is not on a par with his. But first try to understand normal QM as much as you can - going to QFT without a good foundation in ordinary QM is not advisable.

how is understanding of QFT may be more important/critical than of QM? I thought that they both have basically the same foundational problems i.e. that QFT does not resolve any foundational problem QM has, just inherits all of them.

There is a basic difference between QM and QFT.

In QM, one prepares tiny systems with very few degrees of freedom, and one can prepare large ensembles of essentially independent systems in the same state. Thus the statistical interpretation makes sense. On the other hand, the question whether a state can be assigned to individual systems, or, if not, how measurements select individual results for each system, pose the well-known interpretational problems.

In (nonrelativistic or relativistic) QFT the fields are functions of space and time, and hence the associated observables can be measured at most once once. Thus the statistical interpretation of their ensemble mean (expectation) makes no experimental sense. However, this is not a problem since no use is made of it anywhere. Indeed, only two kinds of predictions are compared with experiments: Either S-matrix elements, which have an interpretation as transition amplitudes of asymptotic collision events of few particles (a case where Born's rule applies without the slightest philosophical problems), or field expectation values and field correlation functions, which are treated as macroscopic observables, without any statistics involved on the experimental side. Therefore as far as the relation to experiment is concerned, the interpretation of QFT poses no fundamental problems.

What requires interpretation is how the dynamics in the particle view of QM arises from interacting relativistic QFT, which has no number operator and hence no concept of particles at finite time. Related to this question are the issues involved in the measurement problem, since these are about mixing the particle view (for tiny systems) with the field theoretic view (for detectors).

 

[ftr]

one just has beams of light in an entangled state

Are you saying that there is no single particle double slit experiment. Or only in high energy experiments.

 

[A. Neumaier]

Are you saying that there is no single particle double slit experiment. Or only in high energy experiments.

In a double slit experiment, a monochromatic beam of light (i.e., an electromagnetic field in a special state deserving to be called a ''monochromatic beam of light'') passes through a screen with two slits and causes a response on a screen. That's all.

In the single particle case: If the beam of light before the screen can be approximated by a single wave packet (in a Fock state) whose total energy is $\hbar\omega$ where $\omega$ is the frequency (this is a ''single photon on demand''), then it can be approximated after the screen by a superposition of two wave packets (this is still a ''single photon''). The energy is enough to cause only a single detection event on the screen, with a probability proportional to the incident field energy. This implies that the event generated is consistent with the diffraction pattern generated by the slits. It this happens a number of times, the events will display the full diffraction pattern. This explanation works whether the field is treated classically or by QED.

In the multiparticle case: There is no consistent interacting relativistic multiparticle theory, neither in a classical nor in a quantum version. (This excludes for simplicity a trickle of papers not accounted for by the main stream.) Thus any consistent model featuring a natural speed limit will have to be a relativistic quantum field theory.

In the thermal interpretation, the only thing left of the particle picture is the detection event. One doesn't need more.

 

[MichPod]

The energy is enough to cause only a single detection event on the screen, with a probability proportional to the incident field energy.

But how does this "detection event" happen to appear only at one particular coordinate, while the quantum field is spread over the whole screen? I.e. what causes the "wave collapse" on measurement in your way of interpretation?

QM just postulates "measurement" and "wave collapse", at least in the Copenhagen interpretation. Is it not the case that you also postulate the existence of local detection events?

 

[A. Neumaier]

But how does this "detection event" happen to appear only at one particular coordinate, while the quantum field is spread over the whole screen? I.e. what causes the "wave collapse" on measurement in your way of interpretation?

Presumably the chaoticity of the macroscopic nonlocal observables (field correlations) of the screen, together with conservation of energy. The latter implies that there can be at most one detection event, the former means that it happens at an unpredictable position.

That field intensity is responsible for the firing rate of the Poisson process at one spot of the screen (i.e., the occurrence of detection events) is a local feature described in any textbook of quantum optics, e.g., in Mandel and Wolf.

 

[ftr]

the only thing left of the particle picture is the detection event.

But isn't it that in cathode tube and cloud chamber the charged particles are deflected by the mass/charge ratio,this sounds even weirder to me than EPR if the electrons were all jumbled up yet displayed individuality.

 

[A. Neumaier]

the charged particles are deflected by the mass/charge ratio

The electron field of a cathode ray also has a definite mass/charge ratio. One doesn't need individual electrons for that.

 

[ftr]

There is no consistent relativistic multiparticle theory,

do you mean that there is no consistent QFT bound state, or Dirac multiparticle(>2).

 

[A. Neumaier]

do you mean that there is no consistent QFT bound state, or Dirac multiparticle(>2).

In an interacting relativistic QFT there may be bound states, but one cannot say that these are composed of 2 or 3 particles, say. There are no multiparticle states, since the Hilbert space of a QFT is not a Fock space. See https://physics.stackexchange.com/questions/398200/

This means that interacting relativistic QFTs are field theories, not multiparticle theories. Particles exist only as asymptotic (i.e., approximate, essentially free) states.

 

[MichPod]

Presumably the chaoticity of the macroscopic nonlocal observables (field correlations) of the screen, together with conservation of energy. The latter implies that there can be at most one detection event, the former means that it happens at an unpredictable position.

That field intensity is responsible for the firing rate of the Poisson process at one spot of the screen (i.e., the occurrence of detection events) is a local feature described in any textbook of quantum optics, e.g., in Mandel and Wolf.

But what then prevents a creation of a superimposed state of a screen+electron field where each possible detection event of the electron "happened" with some probability amplitude? We know that a linearity of Shredinger equation in QM does not prevent that to happen yet the measurement postulate demands a collapse to "happen". Then what is different in principle when you consider QFT or your interpretation of QFT? (disclaimer: I do not know qft nor quantum optics and I cannot learn enough just in one morning, so I cannot make any argument, just want to understand briefly how you resolve this problem, if possible).

 

[A. Neumaier]

But what then prevents a creation of a superimposed state of a screen+electron field where each possible detection event of the electron "happened" with some probability amplitude?

In the thermal interpretation, states are described by density operators of the form $\rho=e^{-S/k}$, where $S$ is an entropy operator and $k$ the Boltzmann constant. The notion of superposition becomes irrelevant on this level; one cannot superimpose two density operators. Pure states, where superpositions are relevant, appear only in a limit where the entropy operator has one dominant eigenvalue and then a large gap. For example, this is the case near equilibrium if the Hamiltonian has a nondegenerate ground state and the temperature is low enough. For this one needs a sufficiently tiny system. A system containing a screen is already far too large.

We know that a linearity of Schroedinger equation in QM does not prevent that to happen yet the measurement postulate demands a collapse to "happen". Then what is different in principle when you consider QFT or your interpretation of QFT?

We observe only a small number of field and correlation degrees of freedom. The quantum dynamics coarse-grained to a dynamics of these degrees of freedom is the one we actually observe. This coarse-grained system (at increasing level of coarse-graining described by the Kadanoff-Baym equations, Boltzmann-type equations, and hydrodynamic equations) behaves like a classical, highly chaotic dynamical system. Compare with the Navier-Stokes equations, which are one example of such a coarse-grained system.