Measuring the speed of quantum particles without a round-trip under non-synchronized quantum clocks

TL;DR

This paper proposes a quantum measurement method to determine the one-way speed of particles traveling at light speed without synchronized clocks, overcoming traditional relativistic synchronization issues.

Contribution

It introduces a quantum framework using weak values and the two-state-vector formalism to measure particle velocities without synchronized clocks, a novel approach in quantum physics.

Findings

Weak velocity corresponds to the two-way speed of light when clocks are not synchronized.

The method allows measurement of particle velocity without assuming clock synchronization.

Implications for fundamental physics and relativistic measurements are discussed.

Abstract

One of the main issues in measuring the speed of light when it only travels from one spatial position into another position, known as the one-way speed of light, is that the clocks belonging to each separated spatial position are not and, in principle, cannot be synchronized with sufficient precision. This issue is the main reason why all of the measurements of the speed of light until now have measured the two-way speed of light, i.e., measuring the speed of light that travels from a source to another location and back to the source, and so there is a need for only one clock to measure the speed. Here, we show that it is possible, in principle, to measure the velocity of particles that travel at the speed of light without assuming a round-trip once we adopt a quantum mechanical description under two boundary conditions to the state of the quantum system followed by the two-state-vector formalism while assuming non-synchronized quantum clocks with unknown time dilation. We show that the weak value of velocity can be measured for a test particle that has a clock that is not synchronized with the clock of the quantum particle. Following the proposed setup, when the weak value of the velocity is known even without knowing the time states of the system, such a weak velocity is the two-way speed of light. Otherwise, one has to impose assumptions regarding the time states of the quantum clocks, which then give weak velocities that can be slower or even faster than the two-way speed of light. We further explore some fundamental implications of the setup. The proposed approach opens a new avenue toward measuring the velocities of quantum particles while overcoming relativistic issues regarding the synchronization of clocks.