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,
𝑓 = 1/𝜆.
The
frequency of a wave multiplied by its wavelength gives the speed of
the wave, 𝑓𝜆 = 𝑣 or, 𝑓 = 𝑣/𝜆.
The
frequency is inversely proportional to the time period of the wave,
𝑓 = 1/𝑇.
The
frequency of a wave is directly proportional to the energy of the
wave, 𝑓 = 𝐸/ℎ, where h is Planck constant.
• Combined
Equation given by 𝑓 = 𝑣/𝜆 = 1/𝑇 =
𝐸/ℎ.
Where
𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 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, 𝜆 ∝ T.
The
instantaneous phase (ϕ) represents an angular shift between two
relative sine waves and is measured in degrees. After a time Δt, the
two relative sine waves are initially synchronized in phase but
differ in frequency by Δω degrees per second, developing a
differential total phase shift (ΔΦ).
• Equation
given by: ΔΦ = Δω × Δt.
The
time interval 𝑇(𝑑𝑒𝑔) for 1° of phase
is inversely proportional to the frequency (𝑓). We get a wave
corresponding to the time shift.
• 1°
phase shift = 𝑇/360; 𝑇 = 1/𝑓.
• 1°
phase shift = 𝑇/360 = (1/𝑓)/360.
• A
wave frequency = 5 𝑀𝐻𝑧, we get the phase
shift (in degree°) corresponding time shift.
• 1°
phase shift on a 5 MHz wave = (1/5000000)/360 = 5.55 𝑥 10ˉ¹º
= 555 𝑝𝑠. Corresponds to a time shift of 555
picoseconds
Therefore,
for 1° phase shift for a wave having a frequency 5 𝑀𝐻𝑧,
and so wavelength 59.95 𝑚, the time shift 𝛥𝑡
is 555 𝑝𝑠.†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 𝛥𝑡 = 0.0000004398148148148148 𝑚𝑠.
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 Δs and that c²Δτ that because Δs 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
λ ∝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'.
