Quantum Interference: From Kaons to Neutrinos (with Quantum Beats in between)

Using the vehicle of resolving an apparent paradox, a discussion of quantum interference is presented. The understanding of a number of di erent physical phenomena can be uni ed, in this context. These range from the neutral kaon system to massive neutrinos, not to mention quantum beats, Rydberg wave packets, and neutron gravity. Email: [email protected] This work is dedicated to the memory of Bernie Deutch, our friend and colleague, whose love of physics was exempli ed by his words and by his actions. 1 The Neutral Kaon System One of the most important \modern, quantum-interference" phenomenon was discovered in particle physics. The background was that, in the 1950's, it was observed that the strongly-interacting, neutral, K meson, sometimes appeared to decay via the weak interaction into + . Mind you, the full quantum eld theory of the CPT theorem was not formulated until 1957 [1]. Even so, in 1955 Gell-Mann and Pais [2] predicted an astounding new e ect on the bsis of these experimental results. They predicted (in terms of our present terminology) that there must be an antiparticle to the K, called the K0, with opposite quantum number \strangeness" or \hypercharge." Further, the origin of the decay to the 2 state is not the pure strangeness eigenstate, but rather the coherent mixture jK1i = 1 p 2 jKi+ j K0i : (1) This state is an eigenstate of CP with eigenvalue +1. Another prediction was that there should be an eigenstate of CP with eigenvalue 1. This state would be jK2i = 1 p 2 jKi j K0i : (2) The K2 would have a slightly di erent mass than the K1, and have a much longer lifetime. Finally, because of this superposition, a beam of particles that was originally composed of K's (or K0's) would evolve in time in an interference mode, oscillating between the two decaying species. In particular, inverting Eqs. (1) and (2), inserting the time-dependence, and using the proper time, jK( )i = 1 p 2 exp[ (imS + S=2) ]jK1i + exp[ (imL + L=2) ]jK2i ; (3) where the m's are the masses and the 's are the decay widths of the shorterand longer-lived particles. Similarly for the K's. Eventually, all of these predictions were found to be true. The rst veri cation was the discovery of the long-lived K2, which decays into a 3 state [3]. But there was a problem in verifying the interference. The K1's and the K2's did not decay into the same nal states. Therefore, one could not measure jhF jK( )ij, for some nal state F . Pais and Piccioni overcame this problem [4] when they realized one could go back and use the strong interactions to remix the particles. Since the K1's and K2's are time-dependent linear combinations of the K 's and K's, the reverse is also true. Thus, at any given time, jK( )i is not only a linear combination of jK1i and jK2i, it is also a linear combination of jKi and j K0i. If this