Question about the Feynmann-Stuckelberg interpretation

[madScientist404]

the Feynmann-Stuckelberg interpretation: a negative energy solution of the Dirac equation is interpreted (1) as a negative energy particle traveling backwards in time or (2) as a positive energy anti-particle going forwards in time.
However, if a positron and an electron annihilate each other a photon is sent out.
A photon does not experience time. Therefore doesn't interpretation (1) makes a lot more sense as time is also "cancelled out" ?

 

[vanhees71]

It's of course (2). That's the "trick"! Instead of a weird esoteric interpretation of something "traveling backward in time", contradicting the causality postulate underlying all of physics you have a causal interpretation of the negative-frequency modes of free relativistic fields. The important point is that the trick works for quantum fields, and here it's mathematically extremely elegant:

(a) you look for the irreducible ray representations of the proper orthochronous Poincare group (in fact boiling down to the proper unitary representations of that group, because it has no non-trivial central charges)

(b) you assume locality/microcausality as well as stability (i.e., that the Hamiltonian is bounded from below and there is thus a ground state)

(c) this inevitably leads to the necessity to superimpose both positive- and negative-frequency modes in a specific way to get local quantum fields, realizing microcausality of local observables and local realizations of the Poincare group.

(d) Quantization implies that the operator-valued coefficients in the mode decomposition in front of positive (negative) frequency modes must interpreted as annihilation (creation) operators to have a causal interpretation.

(e) Taking all this together you end up with the profound very general properties of local relativistic QFT: physically interpretable are the representations with $m^2>0$ and $m^2=0$ (massive and massless particles; tachyons make trouble, at least whenever you try to make them interacting); the connection between spin and statistics: half-integer-spin fields have to quantized as fermions and integer-spin fields as bosons; the discrete operation CPT (charge conjugation, space reflection, time reversal) is necessarily a symmetry. All of these conclusions are experimentally confirmed at high accuracy (including the violation of P, T, CP, etc. symmetries by the weak interaction).

You find all this described in a very concise way in Weinberg, Quantum Theory of Fields, Vol. 1.

 

[madScientist404]

Thank you very much for this answer. I was wondering how esoteric interpretation (1) actually is. But apparently (1) has already been falsified. I will take a look at Weinberg.