RG DOI https://www.qeios.com/read/7OXYH5
The concept of time distortion due to phase shift in oscillating waves is discussed, focusing on its effect on clocks with mass under relativistic conditions. This phenomenon is not observed in electromagnetic waves, but in oscillators or clocks with specific conditions of mass and velocity or gravitational potential. The relationship between phase shift and time delay is established, calculations involving frequency and wavelength are demonstrated, and real-world examples, such as the atomic clocks of GPS satellites, are provided to illustrate practical applications. The distinction between time distortion and time delay in electromagnetic waves is emphasized, with a particular focus on Planck time and its role in defining a fundamental limit. The concept of the ratio of the Planck period to the Planck length has been introduced as a representation of the speed limit of electromagnetic waves, leading to a derived value of time delay per kilometer. This value is used to underline that electromagnetic waves experience a time delay, not the same kind of time distortion as massive objects, emphasizing their speed of propagation and the absence of relativistic effects.
1. Time distortion due to phase shift in oscillating waves:
Any oscillatory wave, including electromagnetic waves, carry energy. Due to the infinitesimal loss of wave energy, the phase shift in relative frequencies cause time distortion which is only possible with clocks or oscillators with mass and whose speed is less than the speed of light relative to its origin, or in the gravitational potential difference, located at an altitude greater than zero relative to ground state. Accordingly, Time distortion of clock or oscillator with rest-mass (m), when speed v < c or, gravitational potential difference h > 0 is applied. Where, v denotes for velocity (m/s) and h denotes height above ground in meters, respectively.
The time is called T, the period of oscillation, so that T = 2π/ω, where the angular frequency is ω. The period (T) or frequency (f) of oscillation per second is given by the reciprocal expression; f = 1/T. Hence, we get, f = 1/T = ω/2π. where the time interval T(deg) is inversely proportional to the frequency (f) for 1° phase. We get a wave associated with time variation, which represents the distortion of time under relativistic effects, such as speed or gravitational potential differences.
"1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps). 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 (in degree°) = (1/5000000)/360 = 5.55 𝑥 10ˉ¹º = 555 𝑝𝑠.
Therefore, for 1° phase shift for a wave having a frequency 𝑓 = 5 𝑀𝐻𝑧, and so wavelength 𝜆 = 59.95 𝑚, the time shift (time delay) 𝛥𝑡 = 555 𝑝𝑠 (approx)."
A 1° phase shift in a 5 MHz wave corresponds to a time shift of 555 picoseconds, which is a time distortion of 555 picoseconds. The GPS satellite's cesium-133 atomic clock orbits at an altitude of about 20,000 km. Such an atomic clock, if not automatically adjusted, would exhibit a time shift. A 1455.5° phase shift in a 9192.63177 MHz cesium-133 atomic clock oscillator corresponds to a time shift of 0.0000004398148 ms, or or, 38 microsecond (µs) time distortion per day. [1]
2. Why is light not subject to time distortion?
Electromagnetic waves do not experience time distortion, but such waves maintain a time delay of ≈ 3.33246 µs/km; propagating at speed (ℓP/tP), where, ℓP/tP represents the ratio of the Planck period to the Planck length in vacuum. As such, the Doppler redshift corresponds to a time delay.
The Planck time tp is the time required for light to travel a distance of 1 Planck length in a vacuum, a time interval of about 5.39e−44 s, no current physical theory can describe a timescale smaller than the Planck time (tP). .
Thus, the ratio of the Planck length to the Planck period (ℓP/tP) gives a value to represent the speed limit of electromagnetic waves. Where, ℓP/tP = 1.61626e-35 m/5.39e-44 s. Hence, the ratio of Planck period to Planck length (ℓP/tP) gives a value per kilometer as given below –
• 1 kilometer = 1000 meters,
• ℓP/tP = 1.61626e-35 m/5.39e-44 s ≈ 3.00095e8 m/s;
• Time interval per kilometer = 1000 meters / (ℓP/tP) seconds = 1000 / (3.00095e8) s ≈ 3.33246e-6 s;
• Converting this time interval to microseconds (µs) = 3.33246e-6 s * 1e6 µs/s ≈ 3.33246 µs/km
• Thus, the approximate time delay of electromagnetic waves ≈ 3.33246 µs/km.
Therefore, light, especially electromagnetic waves, is not subject to time distortion, but time delay of 3.33246 µs/km (aprox).
In summary, Time Distortion due to Phase Shift in Oscillating Waves shows how phase shift can cause time delay or distortion, calculation and explanation using frequency and wavelength is given, which makes the concept more clear. An example involving the GPS satellite's atomic clock and its orbital altitude illustrates the practical application of these concepts in real-world situations. Time distortion and time delay associated with electromagnetic waves emphasized that electromagnetic waves do not experience the same type of time distortion as massive objects under relativistic effects.
References
[1]
^Soumendra Nath Thakur, Priyanka Samal, Deep Bhattacharjee. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. doi:10.36227/techrxiv.22492066.v2.
