Phase shift - this is how ChatGPT described phase shift:

Phase shift refers to a change in the relative timing or alignment of a wave or signal compared to a reference point. It is commonly used to describe the displacement or delay of one wave with respect to another.

In the context of waves, such as sound waves or electromagnetic waves, phase represents the position of a wave at a given point in time. It is usually measured in degrees or radians. A phase shift occurs when the wave is shifted or displaced from its original position.

When two or more waves are combined, their individual phases can interact, resulting in a phase shift. The phase shift can be positive, negative, or zero. A positive phase shift means that the wave is shifted forward in time compared to the reference wave, while a negative phase shift means it is shifted backward. A phase shift of zero means that the waves are in perfect alignment.

Phase shifts have significant implications in various fields, including physics, engineering, and signal processing. For example, in electronics, phase shift is used to describe the time delay between input and output signals in circuits, which can affect the behavior and performance of the system.

In summary, phase shift refers to the change in timing or alignment of a wave compared to a reference point, and it is an important concept in understanding wave behavior and signal processing.

Doppler effect and phase shift under relativistic effects:

Quote from Ref.1. (FEBRUARY 01 1956) https://doi.org/10.1119/1.1934140

''If the path between a source S and an observer O is changed by an amount Δx⁠, the phase of the wave received by O is shifted by Δn = −Δx/λ = −fΔx/c, where λ and f are, respectively, the wavelength and frequency of the disturbance and c is the speed of propagation, all measured by an observer fixed in the medium. The resulting change in observed frequency is Δf  = Δn/Δt⁠, where Δt is the time taken for the observation of the phase change. It is shown that these two statements are sufficient for the derivation of the acoustic Doppler effect equations in all cases. The extension to the relativistic optical Doppler effect also follows if the Einstein time dilatation is taken into account.'' 

Quote from Ref.2. (MAY 27 2023) http://dx.doi.org/10.36227/techrxiv.22492066.v2

''Experiments made in electronic laboratories on piezoelectric crystal oscillators show that the wave corresponds to time shift due to relativistic effects. We get the wavelength 𝜆 of a wave is directly proportional to the time period T of the wave, that is 𝜆 ∝ 𝑇, derived from the wave equation 𝑓 = 𝑣/𝜆 = 1/𝑇 = 𝐸/ℎ, where h is Planck constant and 𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 represent frequency, velocity, wavelength, time period and Energy of the wave respectively.

ϕ represents an angular shift between two relative sine waves and is measured in degrees. After a time Δt, the two relative sine waves are initially synchronized in phase but differ in frequency by Δω degrees per second, developing a differential total phase shift ΔΦ = Δω × Δt. Whereas the time interval 𝑇(𝑑𝑒𝑔) for 1° of phase is inversely proportional to the frequency (𝑓). We get a wave corresponding to the time shift. Time shift of the caesium-133 atomic clock in the GPS satellite: The GPS satellites orbit at an altitude of about 20,000 km. with a time delay of about 38 microseconds per day. For 1455.50° phase shift (or, 4.04 cycles/s) of a 9192631770 Hz wave; time shifts (time delays) 𝛥𝑡 = 0.0000004398148148148148 ms. or, 38 microsecond time is taken per day. ''

Therefore, the phase shifts of frequency due to gravitational potential differences or relativistic effects correspond to dilation of wavelengths of the clock oscillation, which show errors in the clock reading and are misrepresented as time dilation. It is the phase shift (ΔΦ) in relative frequencies due to infinitesimal loss in wave energy (ΔE) and corresponding enlargement in the wavelengths (Δλ) of oscillations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time.

Citations:

Ref.1. Walter, W. C. (1956, February 1). Phase Shifts and the Doppler Effect. American Journal of Physics. Retrieved June 21, 2023, from https://doi.org/10.1119/1.1934140

Ref.2. Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. Techrxiv.org, Version: 2.2(About Time and Wavelength Dilation), 1-6. https://doi.org/http://dx.doi.org/10.36227/techrxiv.22492066.v2

#dopplareffect #phaseshift #relativisticeffects