Time shift in GPS Sattelites:

The GPS satellites orbit at an altitude of about d = 20,000 km.

Experiments carried out in electronic laboratories on piezoelectric crystal oscillator show that the variations in wavelength, due to relativistic effects, correspond to time shift.

We also know that  wavelength (λ) of a wave is directly proportional to the period (T) of the wave, i.e. λ ∝ T, derived from f = E/h

= 1/T = v/λ

The time interval T(deg) for 1° phase is inversely proportional to the frequency (f). We get a wave associated with time change.

For example, a 1° phase shift in a 5 MHz wave corresponds to a time change of 555 picoseconds:

As we know, 1° phase shift = T/360.

As T=1/f, 1° phase shift = T/360

= (1/f)/360.

For a wave of frequency f = 5 MHz, we get the phase shift (degrees°).

= (1/5000000)/360

= (5.55x10^-10)

= 555 ps.

Thus, for a 1° phase shift for a wave frequency f = 5 MHz, the time shift (time delay) Δt = 555 ps (approx).

Accordingly, for a 360° phase shift (one complete cycle: 1Hz.) of 9192631770 Hz wave of Cesium-133 atomic clock, the time shift (time delay) Δt = 0.0000001087827757077666 ms.

Therefore, for a 1455.5° phase shift (or, 4.0430556 cycles) of the 9192631770 Hz wave of the Cesium-133 atomic clock, time variation (time delay) Δt = 0.0000004398148148148148 ms

or, 38 microseconds are taken per day.

Conclusion: Relative time emerge from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential, results error in the reading of clock time, which is wrongly presented as time dilation.

#GPS #GPSSatellites