Question about the Feynmann-Stuckelberg interpretation

In summary, the Feynmann-Stuckelberg interpretation states that a negative energy solution of the Dirac equation can be interpreted as either a negative energy particle traveling backwards in time or a positive energy anti-particle going forwards in time. However, the annihilation of a positron and an electron results in the emission of a photon, which does not experience time. This suggests that interpretation (1) is more reasonable as it cancels out the effects of time. This interpretation is also supported by the fact that it is mathematically elegant and aligns with the principles of locality and stability. Furthermore, it leads to the important properties of local relativistic quantum field theory, such as the connection between spin and statistics and the necessity of C
  • #1
madScientist404
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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" ?
 
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  • #2
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.
 
  • #3
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.
 
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Related to Question about the Feynmann-Stuckelberg interpretation

1. What is the Feynmann-Stuckelberg interpretation?

The Feynmann-Stuckelberg interpretation is a theoretical framework in quantum mechanics that seeks to explain the behavior of particles and their interactions. It was developed by Richard Feynmann and Ernst Stuckelberg in the 1940s and is based on the idea that particles can travel backward in time.

2. How does the Feynmann-Stuckelberg interpretation differ from other interpretations of quantum mechanics?

The Feynmann-Stuckelberg interpretation differs from other interpretations in that it allows for the possibility of particles traveling backward in time. This is in contrast to the Copenhagen interpretation, which states that particles only exist as probabilities until they are observed.

3. What evidence supports the Feynmann-Stuckelberg interpretation?

There is currently no direct evidence that supports the Feynmann-Stuckelberg interpretation. However, some physicists argue that it provides a more intuitive explanation for certain quantum phenomena, such as the double-slit experiment, than other interpretations.

4. Are there any potential implications or applications of the Feynmann-Stuckelberg interpretation?

The Feynmann-Stuckelberg interpretation has not yet led to any practical applications or implications. However, some scientists believe that further research into this interpretation could potentially lead to a better understanding of quantum mechanics and potentially even new technologies.

5. Is the Feynmann-Stuckelberg interpretation widely accepted by the scientific community?

The Feynmann-Stuckelberg interpretation is not widely accepted by the scientific community. While some physicists find it to be a compelling and intuitive explanation for quantum phenomena, others argue that it is not supported by enough evidence and is too speculative to be considered a valid interpretation.

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