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It is a key principle of quantum mechanics that plane matter waves are proportional to exp(-ipμxμ/ℏ)=exp(-iω0τ), where pμ and xμ are respectively 4-momentum and position, and τ is the proper time measured along the particle's tra-jectory. Thus, the quantum state of a free particle of mass m accumulates the same phase as a clock ticking at the particle's Compton frequency of ω0=mc2/ℏ travelling along...
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