15.4: When can things interfere? What counts as a measurement?
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Interference from two slits of a single particle with itself remains a difficult concept to understand.
Feynman introduced an nice argument based on the uncertainty principle. He argued that the wavelength of light required to detect which way a particle went must be smaller than the slit separation. From the uncertainty principle, it follows that the momentum transfer must be so large that it would destroy the interference pattern. Thus the measurement device destroyed the interference. Unfortunately, more recent experiments show things are more complicated than that.
Eichmann et al (Phys.Rev.Lett, 1993) set up a ‘two slit’ experiment using photon with lead atoms as the scatterers. With careful choice of energy, he was able to arrange that the scattering event changed the internal electronic state of the atom: a process which requires negligible momentum transfer but would allow subsequent measurement of the atomic state and determination which way the particle went. As a consequence, the interference fringes vanish.
Durr et al (Nature, 1998) used a standing light wave to scatter rubidium atoms. Added to this was a microwave source which changed the hyperfine state of the atoms at one of the “slits”, which could in principle be measured but supplies negligible momentum. The interference pattern disappeared.
Again, quantum mechanics has been shown to give a correct description: non-identical wavefunctions do not interfere even if they describe the same particle! It does not matter whether the measurement of the internal states is actually performed: the mere fact that it could be is enough to destroy the interference.