Oscillatory systems with relative velocity or gravitational potential difference experience phase shifts, causing wave energy loss and errors in clock time readings.

[Author ORCID: 0000-0003-1871-7803]

When a clock or any other oscillatory system is subjected to either relative velocity or a gravitational potential difference, it can experience a phase shift in its oscillations. This phase shift is associated with an infinitesimal loss of wave energy, which can result in errors in the reading of clock time.

The phase shift arises due to the interaction between the clock's oscillations and the influence of relative velocity or gravitational potential difference. This interaction alters the frequency and period of the oscillations, causing a deviation from the expected or proper time.

In the case of relative velocity, the moving clock experiences a change in its oscillation rate and exhibits a phase shift, leading to a discrepancy between the measured time on the moving clock and the time measured by a stationary observer.

Similarly, in the presence of a gravitational potential difference, clocks at different heights in a gravitational field experience variations in gravitational potential, causing differences in their oscillation rates and introducing phase shifts in their oscillations.

These phase shifts and infinitesimal energy losses can accumulate over time, resulting in errors in the reading of clock time. However, it's important to note that these errors are typically infinitesimal and are only significant in extreme conditions involving high velocities or strong gravitational fields. For everyday situations and conventional clock systems, these relativistic and gravitational effects are taken into account to provide accurate timekeeping.

Reference: Relativistic effects on phaseshift in frequencies invalidate time dilation II