Is quantum theory a microscopic theory?

[vanhees71]

I was referring to your claim that there are "effects of local preparations at positions light years away". This is a claim on the dynamics. The paper of Hegerfeldt is no surprise. It's known since the first attempts to generalize Schrödinger's successful formulation of wave mechanics to the relativistic realm. It's well known that this fails for exactly the reason we discuss here. That's why in the 21st century relativistic QT is introduced right away as relativistic (microcausal) QFT (see e.g., Peskin/Schroeder).

 

[A. Neumaier]

I was referring to your claim that there are "effects of local preparations at positions light years away". This is a claim on the dynamics.

Yes. But it is a claim for probabilities for measurement results, governed by Born's rule for the dynamically propagated wave function, and Hegerfeldt's paper is about that.

On the other hand, the theoretical apparatus of relativistic QFT is about q-expectation values of products of field operators (n-point functions), and causal results are valid only for these. Since expectation values say nothing at all about low probability events, the causal commutation relations have no implications for very low probability "effects of local preparations at positions light years away".

 

[A. Neumaier]

From

• G.C. Hegerfeldt, Instantaneous spreading and Einstein causality in quantum theory, Annalen der Physik 7 (1998), 716--725.

a few sentences (see p.7):

The Hamiltonian can be quite general, only boundedness from below is required, and this ensures either instantaneous spreading or confinement in a fixed bounded region for all times. [...]
This example [of the Dirac equation] is instructive since it shows the importance of the positive energy condition. The Dirac equation contains positive and negative energy states, and therefore we conclude from our results that positive-energy solutions of the Dirac equation always have infinite support to begin with! This is phrased as a mathematical result for instance in the book of Thaller [17].

Thus a single QED electron prepared in an arbitrary state has - according to the Born rule, taken at face value - a nonzero probability of being immediately detected arbitrarily far away.

 

[Auto-Didact]

You're correct here of course, but I think @Auto-Didact is getting at the fact that some no-go theorems or thought experiments are based on literally every self-adjoint operator being an observable. As Jürg Fröhlich mentioned in his recent paper the idealizations in the thought experiments of some quantum foundations papers might be more a hindrance than a help.

See, this is why I love physicsforums; this is literally a discussion we have had here quite recently purely through honest discussion with multiple participants, who only have partially overlapping viewpoints constantly engaging each other from multiple sides, which is now also reflected in the literature. Some of the things I have learned here from by reading and engaging in discussions open to criticism from all, are in some cases so novel I cannot even find it in the literature, let alone in books.

Moreover, both the respect and criticism I experience w.r.t some recurring 'allies' and 'opponents' here is to me of quite a similar nature as the deferential and deontic attitudes I have gained professionally, by attending weekly meetings for critical scientific appraisal of specific issues and medical-ethical analysis; these are both proven philosophical methods which can be utilized in order to come to a consensus for what the appropriate course of action is in wickedly vague and complicated situations together with fellow clinicians, who all moreover tend to have conflicting opinions on how to proceed yet still are willing to try working together in good faith.

I dare say that physicsforums by exhaustively discussing the foundations of QM issues, has in the last years actually become a beacon for direct access to reliable knowledge on this domain, given that one goes through a representative portion of these threads and that the descriptions and terminology continue to be used reliably within these subforums; this seems to be quite a unique feat among scientific communities on the internet or elsewhere as far as I am aware. Who said that these philosophical discussions do not contribute to the foundations of physics?

 

[vanhees71]

Yes. But it is a claim for probabilities for measurement results, governed by Born's rule for the dynamically propagated wave function, and Hegerfeldt's paper is about that.

On the other hand, the theoretical apparatus of relativistic QFT is about q-expectation values of products of field operators (n-point functions), and causal results are valid only for these. Since expectation values say nothing at all about low probability events, the causal commutation relations have no implications for very low probability "effects of local preparations at positions light years away".

But you cannot describe this in terms of a non-local single-particle Hamiltonian, $\hat{H}=\sqrt{\hat{p}^2+m^2}$. This has been abandoned for a long time by now for exactly the reason, it leads to the acausal behavior, we discuss here. Relativistic QM isn't even consistent with relativistic causality constraints for free particles, if treated in this way!

Maybe I don't understand what you mean by "local preparations light years away", because if they are assumed to be "local", how then can they be causally connected at the same time? It's a contradiction in adjecto!

 

[A. Neumaier]

But you cannot describe this in terms of a non-local single-particle Hamiltonian, $\hat{H}=\sqrt{\hat{p}^2+m^2}$. This has been abandoned for a long time by now for exactly the reason, it leads to the acausal behavior, we discuss here. Relativistic QM isn't even consistent with relativistic causality constraints for free particles, if treated in this way!

But the free QED electron can be described in terms of a more complicated non-local single-particle Hamiltonian!

The single electron sector of renormalized QED including infrared dressing is invariant under Poincare transformations, since there is no scattering. Its Hilbert space is the Hilbert space of a Poincare invariant infraparticle, and the time shift generator defines the Hamiltonian. The infraparticle structure is discussed in posts #30 and #31 of another thread. The Hamiltonian is that of a quasifree particle with a reducible representation of the Poincare group given by a mass spectrum with a branch point at the physical electron mass, where the continuous mass spectrum has a sharp peak. The details of the mass density are not completely known but the basic structure is in the reference of #31 of the other thread. The resolvent $(E-H)^{-1}$ is the renormalized electron propagator, as given by the Kallen-Lehmann formula associated with this mass density.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

The thread has run its course and will remain closed.