Authors:
Thakur, Soumendra Nath (Corresponding); Samal, Priyanka; Bhattacharjee, Deep (Co-authors) (Year 2023):
Preprint Repository:
TechRxiv. Preprint https://doi.org/10.36227/techrxiv.22492066.v2
Abstract:
Relative time is caused by a phase shift in relative frequencies due to infinitesimal loss in wave energy and enlargement in wavelengths of oscillations, resulting in error in the reading of clock time.
1. Introduction:
The Theory of Relativity adopts Minkowski spacetime, which combines three-dimensional Euclidean space and fourth dimensional time into a four-dimensional manifold. The proper time is dependent on relativistic effects and expressed as 𝑡 < 𝑡′. The equation of time dilation is 𝑡՚ = 𝑡/√(1− 𝑣²/𝑐²).
Proper time is an emerging concept, space is a three-dimensional extent, and spacetime is a four-dimensional extent as a mathematical concept. It is not natural, inevitable, or dependent on relativistic effects. Time is not distorted due to relativistic effects, it does not have time, rather error in the clock oscillation.
Counterexamples show that wave distortions are caused by relativistic effects, invalidating the conjectural equation of time dilation.
The conjectural equation of time dilation was based on Doppler's formula, which failed to identify any cause. The wave equation and Planck equation have been able to identify distorted frequencies due to the relativistic effect, yielding a relative value of time for wavelength dilation.
Time is defined as the indefinite progression of events in the past, present and future existences. Stephen Hawking upheld the concept of imaginary time in his book "The Universe in a Nutshell".
2. A scientific misconception in time dilation:
The equation 𝑡՚ = 𝑡/√(1− 𝑣²/𝑐²) is flawed because relativistic effects cannot interact with the proper time (t) in the fourth dimension. Piezoelectric crystal oscillators show that the error in the wave corresponds to time shift due to relativistic effects.
Dark energy does not affect time in any way, except enlarging the wavelength due to expansion of space, so enlargement in scale of time is unauthorized and disprovable.
G-forces cause internal particles of matter to interact, resulting in stresses and deformation (strain).
Wavelength distortions due to phase shifts in relative frequencies correspond to time distortion; through the relationship 𝜆 ∝ 𝑇, due to relativistic effects such as speed or gravitational potential differences. This result in errors in reading of the clock time, but incorrectly perceived as time dilation.
Real events in space cannot reach the fourth direction of time due to interactions or relativistic effects such as motion or gravity. As a result, any effects on proper time beyond its ideal succession will not cause time dilation. The dimension of time is considered abstract, rather conceptual.
Proper time should never be stripped of its independence and retained as 'natural' even in the four-dimensional continuum of spacetime. There is no time dilation anywhere, but the dilation of the wavelength of the clock oscillation causes errors in the clock time. Wavelength distortions mathematically correspond to time distortions, as in 𝜆 ∝ 𝑇.
3. General Foundations:
• Time is called T, and the reciprocal of the period, or frequency, is given by the expression 𝑓 = 1/𝑇 = 𝜔/2𝜋 = 𝐸/ℎ = 𝑣/𝜆, where h is the Planck constant.
• Doppler shift is the change in frequency of a wave relative to an observer moving.
• Time distortion arises from wavelength distortion, but special relativity's time dilation is not influenced by it.
• Special relativity cannot escape the fundamental equivalence between wavelengths and time, which is much more general than special relativity.
• Distortions of wavelengths exactly correspond to time distortions λ∝T.
• Time is the indefinite progress of existence and events in the past, present, and future, referred to as the fourth dimension above three spatial dimensions. It is not time dilation, but error in the in wave.
• Time is an imperceptible fourth dimensional concept, not subject to real interference or influence from cosmic events.
• Cosmic time is the relationship between time since the Big Bang and events in the Universe. Proper time is subject to synchronization with ideal time, as done with atomic clocks, due to wavelength distortion.
4. Experimental results:
Waves of piezoelectric crystal oscillators show a time shift due to relativistic effects.
Wavelength is directly proportional to time period, that is 𝜆 ∝ 𝑇, derived from the wave equation 𝑓 = 𝑣/𝜆 = 1/𝑇 = 𝐸/ℎ, where h is Planck constant and 𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 represent frequency, velocity, wavelength, time period and energy.
Time interval T(deg) for 1° of phase is inversely proportional to frequency. We get a wave corresponding to the time shift. For 1° phase shift on a 5 MHz wave equivalent time shift to 555 ps.
1° phase shift = 𝑇/360. 𝑇 = 1/𝑓.
1° phase shift = 𝑇/360 = (1/𝑓)/360.
Wave frequency 𝑓 = 5 𝑀𝐻𝑧,
we get the phase shift "in degree (°)"
= (1/5000000)/360 = 5.55 𝑥 10ˉ¹º = 555 𝑝𝑠.
The time delay for a 1° phase shift with a frequency of 5 MHz and a wavelength of 59.95 m, 𝛥𝑡 = 555 𝑝𝑠.
The time delay for a 360° phase shift with a frequency of 9192631770 Hz,
𝛥𝑡 = 0.0000001087827757077666 m𝑠.
The caesium-133 atomic clock of GPS satellites orbit at an altitude of 20,000 km with a time delay of 38 microseconds per day.
The time delay for a 1455.5° phase shift or 4.04 cycles (4.04 Hz.) with a frequency of 9192631770 Hz,
𝛥𝑡 = 0.00000010878 m𝑠. Hence 38 microsecond per day.
5. Conclusion:
Time dilation is actually wavelength dilation, caused by gravitational potential differences or relativistic effects, which causes errors in the clock reading. Time dilation is actually wavelength dilation.
