Energy conservation for virtual photon

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Discussion Overview

The discussion revolves around the concept of virtual photons and the conservation of energy and momentum in quantum mechanics. Participants explore the implications of virtual particles in relation to Feynman diagrams and the differences between real and virtual particles, focusing on the conditions under which energy and momentum conservation can be applied.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why energy and momentum cannot be conserved simultaneously for virtual photons, suggesting a preference for momentum conservation over energy conservation.
  • Another participant proposes a specific frame of reference to simplify calculations, indicating that the change in the energy-momentum 4-vector for virtual photons leads to results that are not permissible for real particles.
  • A different viewpoint asserts that energy conservation is maintained in the context of virtual particles, emphasizing that 4-momentum is conserved as required by Lorentz covariance, and highlighting the distinction between real and virtual particles based on their adherence to Einstein's energy-momentum relationship.
  • Further clarification is provided that the difference between real and virtual particles lies in the on-shell versus off-shell conditions, with real particles following classical paths and virtual particles arising from quantum fluctuations.
  • Participants engage in a light-hearted debate about the definitions of real versus virtual particles, with one emphasizing the fundamental nature of the distinction based on their "realness."

Areas of Agreement / Disagreement

Participants express differing views on the conservation of energy in relation to virtual particles, with some asserting that energy is conserved while others suggest it is not applicable in the same way as for real particles. The discussion remains unresolved with multiple competing perspectives on the topic.

Contextual Notes

There are limitations in the assumptions made regarding the definitions of energy and momentum conservation in the context of virtual particles, and the discussion does not resolve the mathematical implications of these concepts.

neelakash
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In introducing the concept of 'virtual photon',Halzen Martin writes (ch#1,P#7) "An ekectron emits a photon (the quantum of electromagnetic field) and as a result,recoils in order to conserve momentum.it is clearly impossible to conserve energy as well,so the emitted photon is definitely not a real photon"...

Why energy and momentum cannot be simoultaneously satisfied?Is momentum conservation is a bit prefferred over energy conservation?
 
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Hi neelakash! :smile:

To simplify the calculations, let's do it in the frame in which the initial and final velocities of the electron are equal and opposite …

change in energy-momentum 4-vector = (E,p) - (E,-p) = (0,2p), which is faster than light (infinitely fast, in this case), and so it can't be the energy-momentum 4-vector of a real photon (or a real anything)! :wink:

(same in any other frame … the change cemes out as (∆E,∆p) with ∆E2 < ∆p2, which isn't allowed)
 
I think the statement that "energy is not conserved for a virtual particle" is not right. The 4-momentum including energy is always conserved as the requirement of Lorentz covariance. This is manifest in Feynman diagrams: when we go from the space-time representation to momentum representation, each vertex contributes a delta function which exactly results in 4-momentum conservation.

The true difference between a real and a virtual particle is, a real particle is on-shell, ie., satisfying Einstein's energy momentum relationship: E^2=m^2+p^2 (with c=1); while a virtual particle does not satisfy this relationship. This difference manifests the difference between classical mechanics and quantum mechanics. A real particle satisfies the classical equation of motion(equivalent to the on-shell condition), so it follows a classical path of motion. A virtual particle is caused by quantum fluctuation, and follows "other paths" in the path integral, so it's off-shell.
 
Hi Phiphy! :smile:

(try using the X2 tag just above the Reply box :wink:)
Phiphy said:
I think the statement that "energy is not conserved for a virtual particle" is not right.

ah, but nobody said that "energy is not conserved for a virtual particle" …

Halzen Martin (ch#1,P#7) says …
it is clearly impossible to conserve energy as well,so the emitted photon is definitely not a real photon

and I said …
tiny-tim said:
… so it can't be the energy-momentum 4-vector of a real photon (or a real anything)!

We're all saying that energy-momentum is not conserved for a real particle. :smile:
Phiphy said:
The true difference between a real and a virtual particle is, a real particle is on-shell, ie., satisfying Einstein's energy momentum relationship: E^2=m^2+p^2 (with c=1); while a virtual particle does not satisfy this relationship.


Nah … the true difference between a real and a virtual particle is, a real particle is real and a virtual particle isn't. :wink:

(the clue's in the name! :biggrin:)
 

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