Abstract

It is a key principle of quantum mechanics that plane matter waves are proportional to exp(-ip_μx_μ/ℏ)=exp(-iω₀τ), where p_μ and x^μ are respectively 4-momentum and position, and τ is the proper time measured along the particle’s trajectory. 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 the particle’s trajectory. This equality, if it is not just an artifact of the theory, implies that a single particle can be a reference for a clock. In principle, such a clock could be built by annihilating particle-antiparticle pairs and counting the frequencies of the generated photons. This would provide a frequency reference with virtually infinite quality factor Q and unsurpassed stability against systematic influences. The frequency (ω₀/2π=3×10²⁵ Hz for a Cesium atom), however, is far beyond modern counting techniques. A method to divide it into a technically accessible range is thus required.

© 2013 IEEE