Virtual particles and Einstein energy relation

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Discussion Overview

The discussion revolves around the concept of virtual particles and their relationship to the energy-momentum relation, specifically whether virtual particles satisfy the equation E² = p² + m². Participants explore mathematical implications and examples, including interactions involving electrons and virtual photons.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether virtual particles truly do not satisfy the energy relation, suggesting a need for mathematical demonstration of this violation.
  • Another participant suggests that the question has been frequently asked and implies that existing literature could provide the necessary derivations.
  • A later reply introduces the concept of higher order perturbation theory, noting that virtual particles can have contributions from a range of momentum 4-vector values, with varying significance.
  • One participant expresses interest in the topic due to its implications regarding superluminal phenomena, mentioning that the mass in the propagator is the real mass.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of virtual particles and their adherence to the energy-momentum relation. Multiple competing views and interpretations remain present in the discussion.

Contextual Notes

Some assumptions about the definitions of virtual particles and the context of their interactions may not be fully articulated, leading to potential misunderstandings. The discussion also touches on advanced concepts like perturbation theory, which may require additional context for clarity.

superphillain
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So, all I ever keep reading is that virtual particles don't HAVE to satisfy E2 = p2 + m2. Should it instead be that they don't satisfy the energy relation. Also, can someone show the general case mathematically how the energy relation is violated. If it's easier maybe a simple example of an electron emitting and absorbing a virtual photon or some simple electron-positron interaction. Thanks
 
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this question is asked everywhere here, why don't you just pick up any book or lecture notes set found on the internet and derive that yourself? :)

I can give you links if you want to see it...
 
I might add to the above answers that in higher order perturbation theory, with diagrams containing loops, there are virtual particles for which all values of the momentum 4-vector contributes to the amplitude. The amount of contribution, however, varies a lot between different values of this 4-vector.

Torquil
 
I think that people is interested in the topic because of space-like thing. Superluminal mystic. Fortunately the mass in the propagator is the real mass.
 

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