A good clock cannot show dilated time:

The clocks are required to tell time, and that clocks oscillate so such oscillations follow the wave equation.

In addition, the flow of time requires a 360 degree dial or scale so that the oscillating part of the clock can represent the correct time at a specific frequency, so that the oscillating state of a certain fixed frequency is maintained.

But if time dilates due to motion or gravitational effect then the dilated time within the dial of a 360 degree watch will not be able to accurately display the time dilated, so the watch cannot display the dilated time on its specific 360 degree dial. Can't be seen at all. So how can you measure time dilation on the clock? No one can do that.

Relativistic events and frames of reference are universal, follow universal applicability:

The Special Theory of Relativity introduces the relativistic frames of reference by introducing an additional frame of reference, mathematically, for presenting relativistic events within the universal frame of reference. 

A co-ordinate geometrical digram of relativistic frames of reference can be presented within the universal frame of reference under the influence of gravity.

As for example, when we present the digit 1, it's magnitude is considered as the difference between 1 and 0 so that  (1-0) = 1, necessarily we do not mention 0 or the difference between them to present the magnitude of 1. 

Similarly, when introducing an additional frame of reference, that would physically mean a mathematical or geometrical introduction of another frame of reference, within the universal frame of reference even when not defined. 

Therefore, relativistic events are relative universal events, and they occur within universal frame of reference, and therefore follow universal applicability. 

The Lorentz transformation is no exception in terms of universal applicability.

Author: Soumendra Nath Thakur, ORCID: 0000-0003-1871-7803

A photon passes near a massive object simultaniously gains and loses momentum:

The momentum of a photon is given by the equation p = E/c, where p represents momentum, E represents energy, and c represents the speed of light. Since the energy of a photon is directly related to its frequency or inversely related to its wavelength, any change in the photon's energy will result in a corresponding change in its momentum.

When a photon passes near a massive object, it simultaniously gains and loses energy (and thus momentum) due to gravitational interactions. This exchange of momentum causes the photon's path to be curved or deflected in the presence of a gravitational field.

Despite the exchange of momentum, a photon continues to travel at the speed of light (c) and covers the same distance (d) relative to its constant speed. The curvature of the photon's path is a result of the gravitational interaction and exchange of momentum.

Redshift due to motion, when phase shift T(deg) of the observed frequency and the source frequency f(rest) are know.:

Redshift due to motion - an alternative formula. 

A 1° phase shift in the wave oscillation is due to motion, we can calculate the redshift using the formula.

z = {1 - 360 * f(rest)} / {360 * f(rest)}.

Where, T(deg) represents the phase shift in degrees and f(rest) represents the source frequency

Frequency and phase in sin:

The equation y(x) = sin(f * x + p). What does f represent and what does p represent?

In the equation y(x) = sin(f * x + p), the variables f and p represent parameters that affect the behavior of the sine function.

f: The variable f represents the frequency of the sine wave. It determines how many oscillations occur over a given interval of x values. The frequency f controls the rate at which the sine function completes a full period, which is 2π radians or 360 degrees. Higher values of f result in more oscillations within the same interval, while lower values lead to fewer oscillations.

p: The variable p represents the phase shift of the sine wave. It indicates the horizontal displacement or translation of the wave along the x-axis. Specifically, it determines the initial position of the wave at x = 0. The phase shift p is measured in radians or degrees and can move the wave to the left or right. Positive values of p shift the wave to the left, while negative values shift it to the right.

By adjusting the values of f and p, you can modify the frequency and position of the sine wave, respectively, in the y(x) equation.