Doppler effect and phase shift under relativistic effects:

Quote from Ref.1. (FEBRUARY 01 1956) https://doi.org/10.1119/1.1934140

''If the path between a source S and an observer O is changed by an amount Δx⁠, the phase of the wave received by O is shifted by Δn = −Δx/λ = −fΔx/c, where λ and f are, respectively, the wavelength and frequency of the disturbance and c is the speed of propagation, all measured by an observer fixed in the medium. The resulting change in observed frequency is Δf  = Δn/Δt⁠, where Δt is the time taken for the observation of the phase change. It is shown that these two statements are sufficient for the derivation of the acoustic Doppler effect equations in all cases. The extension to the relativistic optical Doppler effect also follows if the Einstein time dilatation is taken into account.'' 

Quote from Ref.2. (MAY 27 2023) http://dx.doi.org/10.36227/techrxiv.22492066.v2

''Experiments made in electronic laboratories on piezoelectric crystal oscillators show that the wave corresponds to time shift due to relativistic effects. We get the wavelength 𝜆 of a wave is directly proportional to the time period T of the wave, 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 of the wave respectively.

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 = Δω × Δt. 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. 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/s) of a 9192631770 Hz wave; time shifts (time delays) 𝛥𝑡 = 0.0000004398148148148148 ms. or, 38 microsecond time is taken per day. ''

Therefore, 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. It is the phase shift (ΔΦ) in relative frequencies due to infinitesimal loss in wave energy (ΔE) and corresponding enlargement in the wavelengths (Δλ) of oscillations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time.

Citations:

Ref.1. Walter, W. C. (1956, February 1). Phase Shifts and the Doppler Effect. American Journal of Physics. Retrieved June 21, 2023, from https://doi.org/10.1119/1.1934140

Ref.2. Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. Techrxiv.org, Version: 2.2(About Time and Wavelength Dilation), 1-6. https://doi.org/http://dx.doi.org/10.36227/techrxiv.22492066.v2

#dopplareffect #phaseshift #relativisticeffects

Time is invariant irrespective of frame of references.

Time is invariant means, it's succession remains unchanged irrespective of transformation applied on it. And it is universally acceptable.

A clock is not invariant means since it's mechanism subjects to various distortions, it cannot maintain invariant succession of time unless periodic adjustments applied in it to make it run as per the invariant succession of time.

When any made up reference frames are introduced within the universal frame of reference, then those introduced reference frames too ought to abide by the universal frame of reference, as no eventual frame of reference can be introduced beyond the universal frame of reference.

And time is invariant within universal frame of reference also mean time within all introduced frame of references would abide by the time in universal frame of reference, irrespective of those introduced frames of references are in relative motion or not.

The concept of universal time is always invariant so is any form of times in all reference frames.

Why time is invariant against events:

Time is mathematical parameter and not existential event, and time is invariant. Events invoke time.

For better understanding, when someone plots some variable event against y-axis in a co-ordinate system  against time scale in x-axis, since the changes in that event varies and so it makes a curved line along y-axis and since time is invariable, the x-axis remains a straight line against corresponding values of time.

This is possible, since events are variable hence changes, and represent a curved line, but since time is invariable in its scale, it is presented in a straight line in x-axis, against corresponding values of time.

If somehow, the clock for representing time gets distorted by external influences, the reading of time would be erroneous and this is exactly shown in my paper.

It is not that the scale of time is varying but it is the external distortions in the clock's oscillation frequency which is actually distorted and so the clock is presenting erroneous time ,

Therefore, the clock failed to present proper time not because of a change in time's scale but because of distortion in frequency or wavelength of the clock oscillation.

Time is invariant unless time keeping clock gets distorted.

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

#invarianttime #invariant

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.