Question: Why is there no time dilation for the frequency of a wave?:

The answer to this question is based on the following conditions:-

(i) Experiencing time distortion involves motions that are less than the speed of electromagnetic waves.

(ii) Both the relevant event and the clock measuring such event will have mass.

The above mentioned two conditions are not fulfilled in the time measurement of the frequency of a wave in propagation.

Furthermore, (iii) at the frequency of the propagating wave, mass is not significantly involved and a clock with mass is not carried along with such propagation phenomena to measure time.

(iv) When the wave has propagation delay at such frequency. and, (v) there are other influential delays such as Doppler, gravitational or cosmic redshift, and other effects such as thermal or electromagnetic fluxes.

However, with respect to the frequency of the propagating wave, there are indeed time delays corresponding to propagation delay and redshift, etc., but they are not specifically measured as time distortions. Because the measurement of time distortion is relevant to some phenomena and clocks, on the other hand, to the phenomenon of wave frequency in propagation; Specifically, time is not measured.

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Analysis of the above statements:

Propagation Delay and Redshift:

Propagation delay and redshift are specific to electromagnetic waves, which travel at the speed of light ('c') as massless photons.

The conditions for time dilation involve motions less than the speed of electromagnetic waves, and clocks measuring events should have mass.

Massless clocks are not practical, and time dilation, therefore, is not specifically measured for wave propagation due to the inherent characteristics of electromagnetic waves.

Role of Mass in Time Dilation:

All clocks that measure time for humans will have mass.

Time dilation involves speeds less than the speed of light ('c'), and at 'c', only energy exists, not cold mass.

Time distortion (commonly referred to as time dilation) needs to be measured by a clock with mass, emphasizing the crucial role of mass in the context of time dilation.

Propagation Speed and Time Dilation:

Time dilation is not possible for propagating waves at the speed of light ('c') because the conditions for time dilation involve motions at speeds less than 'c', and wave frequency in propagation is equal to 'c'.