Invalidation of Time Dilation through Classical Mechanics and Wave Equations:

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. †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.

2. †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. †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. †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'.

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

Quantum physics or string theories have to develop their own mechanics of fundamental interactions or else share existing physics:

Classical mechanics, where space and time are invariant and gravity causes attraction between bodies, but not distortions of spacetime at all.

Relativity, where space-time is covariant, gravity distorts spacetime, but not attraction between bodies at all.

Time is probabilistic and invariant in quantum mechanics.

The four known fundamental interactions – gravitational, electromagnetic, strong and weak interactions, especially gravity – have different explanations, in different forms of science.

Gravitation is explained differently in classical mechanics, relativity and quantum mechanics.

Such fundamental interactions are interpreted differently based on different laws depending on the different types of science.

Gravity is shown differently in classical mechanics and relativity.

So quantum mechanics must also develop its own mechanics and its own laws, unless quantum mechanics follows classical mechanics or the laws of relativity etc.

Correlation of relative phase shift of frequency, wavelength and period of oscillation in erroneous time dilation:

1. Time dilation represents the difference in elapsed time measured by two clocks under relativistic effects. Time dilation due to relative velocity is based on the Doppler shift, which is the change in frequency of a wave relative to the motion of an observer relative to the wave source, the equation is t' = t/√(1 - v²/c²). And the gravitational time dilation between two events measured by observers located at different distances from the gravitational mass, the equation is T' = T/√1−2GM/rc².

2. Experiments made in electronic laboratories on piezoelectric crystal oscillators show that the wave corresponds to time shift due to relativistic effects.

Gravity 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). Using gravity, energy is obtained by the so-called piezo-method, which converts mechanical stress into electrical energy. Piezoelectric gravity devices can generate energy anywhere. 

We get the wavelength 𝜆 of a wave is directly proportional to the time period T of the wave, that is 𝜆 ∝ 𝑇, 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).

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.

From the above, we concluded that the phase shifts of frequency due to gravitational potential differences or relativistic effects correspond to dilation of wavelengths of the clock oscillation, which show errors in the clock reading and are misrepresented as time dilation. Time dilation is actually wavelength dilation.

Foundations: 

1. 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.

2. Effect of phase shift on relative frequencies versus time: The instantaneous phase (ϕ) represents an angular shift between two relative sine waves and is measured in degrees. A sine wave and a cosine wave are 90° out of phase with each other. 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). Eq. Given by: ΔΦ = Δω × Δt.

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. 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'.

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

Time is invariant but no clock is invariant under gravitational influence:

Is time Lorentz invariant? It 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 is also Lorentz invariant. 

Proper time Δτ, by definition, is the time measured by an observer in their own rest frame, we can say Δτ = Δt and therefore Δs² = c²Δt² = c²Δτ².

All observers in all inertial frames agree on the proper time intervals between the same two events.

So, how come time dilation t' possible when proper time t is Lorentz invariant? It cannot.

1. Considering t<t', where t' is not in the same scale of t, because of enlagement in t.  

Note: t' is not t+x or t-x, but it is t<t', where x is Δt. The Δt is infinitisimally small t.

2. The general rule is frequency represents time in inversed relationship f = 1/T = 1/λ, and wavelength equivalents period of time λ∝T.

So wavelength λ cannot be invariant but only T. 

Due to Relativistic effects, phase shift in frequencies distort wavelength. So wavelength is not invariant but we know time is invariant because Δs is Lorentz invariant too.

3. Time dilation equation t' = t/√(1 - v²/c²) 

The equation attempts to modify 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..

4. Experiment made on piezoelectric oscillator show that speed or gravity influence wavelength λ, and wavelength corresponds to period of time, so error occurs in T, as in the relationship λ∝T.

Conclusion so called time dilation is relativistic error and not change in T, in order to get time dilation t'.

There is no dilation in time but in wavelength.

Time dilation is wrong and it's equation too.

Reference: https://doi.org/10.36227/techrxiv.22492066.v2

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.

#invarianttime #CovariantWavelength