The special theory of relativity wherein, Time dilation dependent on the relative speeds of the observers' reference frames and concerns a twin who flies off in a spaceship travelling near the speed of light and returns to discover that the travelling twin sibling has aged much less. There are several direct proofs of time dilation. Extremely accurate clocks have been flown on jet aircraft. The clock in motion shows a slightly slower passage of time than the one at rest.
However, the Planck's law helps us to calculate the energy when their frequency is known, as such wavelength is known, so one can calculate the energy by using the wave equation to calculate the frequency and then apply Planck's equation to find the energy.
Moreover, in general relativity, gravitational redshift, known as Einstein shift, is the phenomenon in which electromagnetic waves or photons travelling out of a gravitational well seem to lose energy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known as a redshift. The theory therefore predicts that the wavelength of electromagnetic radiation will lengthen as it climbs out of a gravitational well, this corresponds to an increase in the wavelength, or a shift to the red end of the electromagnetic spectrum – hence the name: gravitational redshift.
Frequency is related to energy (E) as in the Planck's equation E=hv, where v=frequency (Hz) and h=6.626 070 15 x 10^-34 J Hz^-1 represents relationship between energy and frequency. And, energy 'E' is equivalent to mass 'm' as in the Einstein's theory of special relativity E=mc².
Therefore, combining these above two equations we get energy-mass (m) is related to frequency of the wave the energy-mass ('f' in Hz or ‘v’ s^–1 in Hz).
Frequency 'f' or 'v' of the wave is inversely proportional to the wavelength λ (Lambda) 'f'∝1/λ or, 'v'∝1/λ {Equation No.... (1)}
'f' or 'v' of the wave too is inversely proportional to time period 'T' s (second). 'f'∝1/T or, 'v'∝1/T {Equation No.... (2)}
The derived equation from the combination of the above said equations, the frequency (v; f) of mass-energy if somehow gets changed due to the effect of relative gravity or relative speed then the wavelength (λ) of that mass-energy would also change.
The wavelength (λ) of that mass-energy is directly proportional to the time period (T) of the wave. λ∝T {Equation No.... (3)}
In the experiments, it is observed that the time interval for 1° of phase is inversely proportional to the frequency. If the frequency of a wave is given by ‘f’, then the time tdeg (in seconds) corresponding to 1° of phase
tdeg = 1 / (360f) = T / 360. {Equation No.... (4)}
Therefore, a 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds.
The mathematics and result of practical experiments behind energy body/particle/electromagnetic wave is affected by gravitational stress exerted on them, accordingly wavelength of the energy body change.
So in determining the crystal oscillator’s frequencies between two identical clocks under relative speed or gravitational potential, the crystal oscillator’s frequency of the fast moving clock will decrease causing longer wavelength, than the clock on the ground, this happens since gravity exerts mechanical stress on both of the clock’s crystal oscillators, exerts more stress on the clock on ground and less stress on the clock in fast moving airplane,
The above said effect will decrease frequency of the clock on fast moving airplane resulting a longer wavelength of the crystal oscillator, so the fast moving clock will be slightly behind than the clock on the ground, as the mechanical stress on the ground is higher than the fast moving airplane.
This delay in time actually causes due to the wavelength dilation of the clock frequency of the clock in the fast moving airplane, of course due to gravitational difference or due to relative speed in consideration of the above Equation Nos. (2), (3) & (4).
Note: What actually happened in the experiment as can be seen in the relationship λ∝T. The experiment actually considered dilated wavelength and not dilated time. If the experiment is considered that it observed dilation of time then it will violate fundamental properties of time. It rather miscalculated T instead of λ, because by appropriately changing either of the value of λ or even the value of T, one will get same result. But the illegality would be considering T as gravity affected factor instead of appropriately considering λ as the gravity affecting factor. A λ can be influence by gravity and change its wavelength but none can change T with the effect of gravity as time is not something changeable by any external influence or interaction unless such changes is in the structure of the events itself, then only time comes into a relative consideration with the changeable events. Time does not participate in any eventual act rather time tracks changes in the events. So a question of changing time is not only absurd but is illegal too as per valid definition and properties of time. Time dilation necessarily needs to be wavelength dilation, when λ∝T comes in to the consideration.
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