The equivalence:
1. Mass-energy equivalent frequency, are covariant, where space and time are mathematical parameters, they are invariants†¹.
2. The force of gravity is called gravitational force. It is a mechanical and universal force, one of the four fundamental interactions, also interacts with electromagnetism. †²
• Strain ∝ Stress
• The ratio between distortion and original dimension ∝ mechanical force exerted on a material object
• Phase shift in frequencies ∝ Infinitesimal loss in wave energy.†³
• Frequency distortion ∝ Mass-energy stress
The wave equations:
The frequency and wavelength are indirectly proportional to each other, π = 1/π.
The frequency of a wave multiplied by its wavelength gives the speed of the wave, ππ = π£ or, π = π£/π.
The frequency is inversely proportional to the time period of the wave, π = 1/π.
The frequency of a wave is directly proportional to the energy of the wave, π = πΈ/β, where h is Planck constant.
• Combined Equation given by π = π£/π = 1/π = πΈ/β.
Where π, π£, π, π and πΈ represent frequency, velocity, wavelength, time period and Energy of the wave respectively,
• The wavelength of a wave is directly proportional to the period of the wave, π ∝ T.
The instantaneous phase (Ο) represents an angular shift between two relative sine waves and is measured in degrees. After a time Ξt, the two relative sine waves are initially synchronized in phase but differ in frequency by ΞΟ degrees per second, developing a differential total phase shift (ΞΞ¦).
• Equation given by: ΞΞ¦ = ΞΟ × Ξt.
The time interval π(πππ) for 1° of phase is inversely proportional to the frequency (π). We get a wave corresponding to the time shift.
• 1° phase shift = π/360; π = 1/π.
• 1° phase shift = π/360 = (1/π)/360.
• A wave frequency = 5 ππ»π§, we get the phase shift (in degree°) corresponding time shift.
• 1° phase shift on a 5 MHz wave = (1/5000000)/360 = 5.55 π₯ 10Λ¹ΒΊ = 555 ππ . Corresponds to a time shift of 555 picoseconds
Therefore, for 1° phase shift for a wave having a frequency 5 ππ»π§, and so wavelength 59.95 π, the time shift π₯π‘ is 555 ππ .†⁴
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 of a 9192631770 Hz wave; time shifts π₯π‘ = 0.0000004398148148148148 ππ . or, 38 microsecond time is taken per day.
The Conclusion:
Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time; which is wrongly presented as time dilation.†⁵
The foundations:
†¹ In classical mechanics, where space and time are invariant and gravity causes attraction between bodies, but not distortions of spacetime at all. Lorentz invariant is the same interval of proper time. It also follows from the relation between Ξs and that c²ΞΟ that because Ξs is Lorentz invariant, the proper time t is also Lorentz invariant.
†²Gravity exerts a mechanical force on any object that deforms the object and pushes on the surrounding atoms. G-forces cause internal particles of matter to interact, resulting in stresses and deformation (strain). When mechanical stress is applied to a piezoelectric crystal, the structure of the crystal is deformed, the atoms push around and the crystal conducts an electric current. The mechanical stress of a piezoelectric crystal is greatest in the ground state. In the case of a gravitational potential difference, there is less gravitational stress on a piezoelectric crystal, which correspondingly reverses the deformation of the structure, thereby pushing the atoms around, causing the crystal to conduct less electric current than in the ground state.
†³ Time distortion always arises from frequency phase shift and corresponding wavelength distortion but relativistic time dilation cannot be understood from frequency phase shift and corresponding wavelength distortion and therefore they do not follow the general rule. Relativistic time dilation failed to identify any cause of time distortion. Whereas, a combination of general wave equation and Planck's equation, has been able to successfully identify that there is an influence factor of distorted frequency due to relativistic effects. The distorted frequencies in the equation provide a relative value of time for the corresponding wavelength distortions. The phase is shifted in frequency and the corresponding wavelength distortion exactly matches the time distortion as in the expression Ξ» ∝T.
†⁴,†⁵ Due to relativistic effects, phase shift in frequencies distort wavelength. So wavelength is not invariant but we know time is invariant and as per Lorentz transformation too. The equation of time dilation due to relativistic speed, attempts to modify time t through the influence of velocity v. This is illegal operation in mathematics, as none can modify invariant t with the effect of velocity v or speed. So called time dilation is relativistic error and not change in T, in order to get time dilation t'.
