ChatGPT describes Relativistic effects on phase shift in frequencies and corresponding energy of wave:

Relativistic effects can have an impact on the phase shift, frequency, and energy of a wave. These effects arise from Einstein's theory of relativity, which describes how the properties of space and time are affected by the motion of objects with respect to each other {validation needed].

According to relativity, when an observer is moving relative to a wave source, they will perceive a change in the frequency of the wave. This is known as the Doppler effect. If the observer is moving toward the source, they will perceive the frequency to be higher than the source's rest frequency. Conversely, if the observer is moving away from the source, they will perceive the frequency to be lower.

The phase shift of a wave is related to its frequency. As the frequency of a wave changes due to the relativistic Doppler effect, the phase shift will also be affected. The phase shift represents the relative position of the wave at a given point in time. A change in frequency will result in a corresponding change in the rate at which the phase of the wave advances.

In terms of energy, the energy of a wave is directly proportional to its frequency. Therefore, as the frequency changes due to relativistic effects, the energy of the wave will also be affected. An increase in frequency leads to an increase in energy, while a decrease in frequency corresponds to a decrease in energy.

It's worth noting that relativistic effects become more significant as the speeds involved approach the speed of light. At everyday speeds, these effects are negligible and can be approximated using classical physics. However, when dealing with particles or objects moving at high velocities, such as in particle accelerators or astrophysics, the relativistic effects on phase shift, frequency, and energy must be taken into account for accurate calculations and predictions.

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

Time is invariant irrespective of frame of references.

Time is invariant means, it's succession remains unchanged irrespective of transformation applied on it. And it is universally acceptable.

A clock is not invariant means since it's mechanism subjects to various distortions, it cannot maintain invariant succession of time unless periodic adjustments applied in it to make it run as per the invariant succession of time.

When any made up reference frames are introduced within the universal frame of reference, then those introduced reference frames too ought to abide by the universal frame of reference, as no eventual frame of reference can be introduced beyond the universal frame of reference.

And time is invariant within universal frame of reference also mean time within all introduced frame of references would abide by the time in universal frame of reference, irrespective of those introduced frames of references are in relative motion or not.

The concept of universal time is always invariant so is any form of times in all reference frames.

Why time is invariant against events:

Time is mathematical parameter and not existential event, and time is invariant. Events invoke time.

For better understanding, when someone plots some variable event against y-axis in a co-ordinate system  against time scale in x-axis, since the changes in that event varies and so it makes a curved line along y-axis and since time is invariable, the x-axis remains a straight line against corresponding values of time.

This is possible, since events are variable hence changes, and represent a curved line, but since time is invariable in its scale, it is presented in a straight line in x-axis, against corresponding values of time.

If somehow, the clock for representing time gets distorted by external influences, the reading of time would be erroneous and this is exactly shown in my paper.

It is not that the scale of time is varying but it is the external distortions in the clock's oscillation frequency which is actually distorted and so the clock is presenting erroneous time ,

Therefore, the clock failed to present proper time not because of a change in time's scale but because of distortion in frequency or wavelength of the clock oscillation.

Time is invariant unless time keeping clock gets distorted.

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

#invarianttime #invariant