8 27.1 The Heisenberg uncertainty principles The mass of the neutron can be determined quite precisely because it is a relatively long lived particle The values of the masses of very short-lived particles will have intrinsic spread because of the Heisenberg uncertainty principle. b. The nature of a vacuum vacuum is not empty The idea of a vacuum in quantum physics is quite different from classical idea of a vacuum as simply a volume with nothing in it. s 27.1 The Heisenberg uncertainty principles Classical mechanics KE=E-PE=P>0 2n Relativity quantum mechanics E=Pc+mc, E=tpc+mc Dirac sea: positive energy states are empty, negative energy states are filled fully. E E=mc2 E=0 E=0 E=-mc2 E=-mc2 AE=E-E pc +m c P 88 The mass of the neutron can be determined quite precisely because it is a relatively long￾lived particle. The values of the masses of very short-lived particles will have intrinsic spread because of the Heisenberg uncertainty principle. b. The nature of a vacuum —vacuum is not empty The idea of a vacuum in quantum physics is quite different from classical idea of a vacuum as simply a volume with nothing in it. §27.1 The Heisenberg uncertainty principles 0 2 2 = − = ≥ m p Classical mechanics KE E PE 2 2 2 2 4 2 2 2 4 E = p c + m c , E = ± p c + m c Relativity quantum mechanics E+=mc2 E- =-mc2 E=0 E+=mc2 E- =-mc2 E=0 Dirac sea: positive energy states are empty, negative energy states are filled fully. 2 2 2 4 2 2 2 4 E = E − E = p c + m c + p c + m c ∆ + − §27.1 The Heisenberg uncertainty principles