I have heard many people mention that heisenberg uncertainity prinicple doesn't really allow 'violation of energy conservaiton for a short time'. i.e, virtual particles, are just a mathematical tool. If so, how are the ranges of fundamental forces explained?. Electro-magnetic field is long range, as its force carrier is a ,mass less photon. Weak force is short range because its force carrier has mass, and can exist only for a little duration in accordance with HUP. So if "borrowing energy for a short while", interpretation is wrong. then how are the ranges of fundemental forces explained
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$\begingroup$ Short range interactions are not particularly quantum: en.wikipedia.org/wiki/Evanescent_field $\endgroup$– John DotyCommented Mar 5 at 19:02
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I think the reason for resistance to the notion of "borrowing energy" is that in the Feynman method the energy and momentum is strictly conserved at every stage: in every vertex and in every free propagation. What happens is that the virtual particles are like particles in some respects, but they typically have $E^2 - p^2 c^2$ different from $m^2 c^4$ for the corresponding particle. They are said to be "off the mass shell" or "off-shell". Contributions of this kind decay as they propagate, and the decay rate is faster if they are further off the mass shell. A quick dimensional analysis is then able to give a good indication of the decay distance (as in the "borrowing energy" idea) and this does estimate correctly the range of the force.
answered Mar 5 at 18:38
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$\begingroup$ Thanks a lot for taking your time to answer the question. However, i have a follow up question. If not for heisenberg's energy time uncertainty, how is the range of fundemental forces explained. $\endgroup$ Commented Mar 5 at 19:03