Chapter5_10 - ∆ E where the ∆ E is the amount that...

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PHY3063 R. D. Field Department of Physics Chapter5_10.doc University of Florida Virtual Particles Center-of-Mass Frame (before decay) m e v = 0 Center-of-Mass Frame (after decay) p e p γ photon γ electron Energy and momentum conservation forbid an electron from decaying into another electron plus a massless photon. This is easiest to see in the center-of-mass frame. Energy conservation gives cp c m cp E E c m e e e + + = + = 2 2 2 2 ) ( ) ( γ , where I have used momentum conservation to set |p e | = |p γ | = p and E γ = cp . We see that 2 2 2 2 ) ( ) ( c m cp cp c m e e + = and 2 2 2 2 2 ) ( ) ( ) ( c m cp cp c m e e + = Thus, 2 2 2 2 2 2 2 ) ( ) ( ) )( ( 2 ) ( ) ( c m cp cp c m cp c m e e e + = + and 0 ) )( ( 2 2 = cp c m e , which implies that either cp = E γ = 0 or m e = 0 . Hence, the process cannot occur. Similarly, an electron with mass m e cannot absorb a photon and remain an electron with mass m e . However due to the uncertainty principle an electron can emit a photon and remain an electron for a short time t h/
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Unformatted text preview: ∆ E , where the ∆ E is the amount that energy conservation has been violated. These “virtual” photons form a “cloud” around the electron. Electrons are constantly emitting and absorbing virtual photons. This “cloud” is the classical electric field. The “virtual” photon can be absorbed by another electron ( within the time allowed by the uncertainty principle ) in such a way that the overall energy and momentum is then conserved. These “virtual” photons carry the information about the force between the two electrons. “Virtual” particles are the basic quantum ( i.e. carriers) of the forces between the “real” particles . Q em γ e-e-e-e-Q em Time Space ∆ t ~ h/ ∆ E γ e-e-e-Time Space ∆ t ~ h/ ∆ E “virtual” particle...
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