Proof of Invariant time even in relativity:

Abstract:

Due to the relative effects on the phase shift of the frequencies, it is concluded that the error in the clock mechanism distorts the wavelength of the clock oscillation. This made wavelength covariant in events, but time was invariant because time is invoked by events.

Introduction:

In mathematics time and space are mathematical parameters. Relativity represents space and time as relativistic covariants, but the relativistic effects on phase shift of frequencies invalidates time dilation; and, presents relativistic time (a component of relativistic spacetime) as invariant.

The event of existence invokes time. According to the definition of the SI unit of time, the frequency of the cesium 133 atom must be 9192631770 Hz. equals to s¯¹, subject to undisturbed ground condition. This means, continuous frequency represents time

The research paper titled, 'Relativistic effects on phaseshift in frequencies invalidate time dilation II.' It states, the relativistic time emerge from relativistic frequencies. It is the phase shift in relative frequencies due to the infinitisimal loss of wave energy and the corresponding increase in the wavelength of oscillation; which occurs at any clock between relative locations due to the relativistic effects or difference in gravitational potential; resulting error in clock time reading; which is improperly represented as time dilation. 

Relationship between time and wave oscillation:

Time is called 𝑇, the period of oscillation. The reciprocal of the period, or the frequency 𝑓, in oscillations per second, is given by the expression 𝑓 = 1/𝑇 = 𝜔/2𝜋 = 𝐸/ℎ = 𝑣/𝜆. Where h is Planck constant, 𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 respectively represent frequency, velocity, wavelength, time period and Energy of the wave.

Whereas 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. For example, 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps). 

Experimental Result:

We know, 1° phase shift = 𝑇/360. As 𝑇 = 1/𝑓, 1° phase shift = 𝑇/360 = (1/𝑓)/360. For a wave of frequency 𝑓 = 5 𝑀𝐻𝑧, we get the phase shift (in degree°) = (1/5000000)/360 = 5.55 𝑥 10ˉ¹º = 555 𝑝𝑠

Therefore, for 1° phase shift for a wave having a frequency 𝑓 = 5 𝑀𝐻𝑧, and so wavelength 𝜆 = 59.95 𝑚, the time shift (time delay) 𝛥𝑡 = 555 𝑝𝑠 (approx.)

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 1455.5° phase shift (or, 4.04 cycles) of a 9192631770 Hz wave; time shifts (time delays) 𝛥𝑡 = 0.0000004398148148148148 𝑚s approx) or, 38 microsecond time is taken per day.

Decision:

Time is the indefinite continued progress of existence and events in the past, present, and future regarded as a whole, succeeding in irreversible and uniformed succession, referred to in the fourth dimension above three spatial dimensions.

The undisturbed ground condition of continuous frequency represents time. However, wavelength distortions, due to the phase shift in relative frequencies correspond to time error; through the relationship 𝜆 ∝ 𝑇. 

Conclusion:

Therefore, it is concluded that the error in clock mechanism distorts the wavelength of the clock oscillation due to the relative effects on the phase shift of the frequencies; This made wavelength (𝜆) covariant in events, but time (𝑇) was invariant, because events invoke time and time as stated above is the indefinite continuous progression of existence and events.

Reference: Relativistic effects on phaseshift in frequencies invalidate time dilation II.

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