FrediFizzx wrote:gill1109 wrote:Please pardon my extraordinary ignorance, but what does "off mass shell" mean? Does it just mean: far away? Far away from where the mathematical model says that *most* of the mass is? (Which is not the same as *all* of the mass). Does sound to me like a hand-waving trick to resolve the problems of using a model with infinite space when actually space is presumably better thought of as being limited.

"A virtual particle does not precisely obey the energy–momentum relation . Its kinetic energy may not have the usual relationship to velocity. It can be negative. This is expressed by the phrase off mass shell."

https://en.wikipedia.org/wiki/Virtual_particle

The W boson involved in charged muon decay is way off mass shell. Basically all photons are virtual. They are never exactly on mass shell. Welcome to particle physics.

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OMG. I think I want to keep away from particle physics. I will go back to modelling epidemics for the time being. Though I recall mathematicians who did differential equations calculations for epidemics which involved periods when the number of individuals on a smallish island went down to 10 to the minus 50 per square kilometer and these guys confidently predicted *exactly when* the population would recover and get back to something big. And another mathematician who did something similar for a cosmologist and never twigged on he was only interested in positive solutions to some function called "p(x, t)". He never asked why the cosmologists actually did use the letter "p" to denote this function. The cosmologist simply could not imagine that one of the best pure mathematicians in the Netherlands could have no idea at all what their problem was actually about and moreover have no interest at all in finding out.