That considering an experiment that uses two identical crystal oscillator electronic clocks, set exactly to the same time, one clock stayed on Earth, while the other flew in an airplane. The crystal oscillators has been used in the clocks so that crystal oscillators have much better frequency stability than mechanical clocks and any effect in its signal characteristics can easily be determined.
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, where 'h' is plank’s constant. 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), whereas, 'c' and 'h' both are constant in respective equations relevant. --> '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.
So this would be the main consideration in the following steps.
- 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 is
- 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 maximum frequency of visible light (f) =7.5 x 1014 Hz, its wavelength (λ) = 400 manometer, and its velocity v=c=3 x 1010 cm/s. Einstein's theory of special relativity sets the absolute speed limit at which a wave can travel, which is the speed of light (c) is equal to 3 x 1010 cm/s.
- The maximum frequency of Gamma-rays (f) = 1024 Hz, its wavelength (λ) = <10-12 (i.e., <0.01 nanometres), and its velocity too (v) = 3 x 1010 cm/s.
However, Planck's equation
E=hv, represents relationship between energy and frequency, where 'h' is Plank's
constant, as such even in absence of speed (speed as
shown in the theory of
special relativity E = mc²) unknown for such frequencies of said clock under
consideration, we can easily go ahead with such frequencies of the energy and
determine respective frequencies between the clock on
Earth and the other clock that flew in an airplane in their relative locations so that the
frequency differences would enable us to determine their relative time, of
course due to the varied effect of gravity or considerable relative speed. Consider above Equation No.... (2), (3) & (4).
Moreover, in general relativity gravitational red-shift (also known as
Einstein shift), is the phenomenon in which electromagnetic waves or photons
travelling out of a gravitational well will lose energy resulting the photon's
longer wavelength affecting by the gravity. This gravitational red-shift supports wavelength dilation of the wave of the mass-frequency of a body under consideration.
Therefore, the gravity will apply a mechanical stress to the fast moving crystal by affecting its frequency causing longer wavelength, so the clock on the fast moving airplane will be slightly behind the clock on the ground as the mechanical stress on the ground is higher on the bodies than the bodies farther above.
This delay in time (known as time dilation) actually caused due to the wavelength dilation of the clock frequency in the clock on the fast moving airplane.
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.
