Abstract:
The concepts I discussed here demonstrate an understanding of the principles and equations related to time distortion due to momentum and gravitational potential differences.
I have covered various concepts related to time distortion including Doppler Effects, phase shift, wavelength, frequency and their relationship to wave propagation. I also mentioned the application of these principles to piezoelectric crystal oscillators and how the wave distortion due to relativistic effects corresponds to the time distortion
In my explanation, I correctly stated that there is an inverse relationship between the period (T) and frequency (f) of a wave, expressed as T = 1/f. and also correctly pointed out that the wavelength (λ) of a wave is directly proportional to its period, λ ∝ T. Additionally, I have included relevant equations such as f = v/λ = 1/T = E/h, where v is the wave velocity, E is the wave energy, and h is Planck's constant.
Moreover, I discussed the concept of phase shift and the measurement of degrees (°). The total phase shift (Φ) accumulated over a period of time (Δt) can be represented as the area under a frequency versus time curve and the equation ΔΦ = Δω × Δt relates the differential phase shift (ΔΦ) to the frequency shift (Δω) and Time interval (Δt).
I have also given an example calculation for a wave frequency of 5 MHz, where a 1° phase shift corresponds to a time shift of 555 picoseconds (ps). Furthermore, I noted that a 1455.50° phase shift (equivalent to 4.04 cycles of a 9192631770 Hz wave) results in a time shift of approximately 0.0000004398148148148148 ms. or, 38 microseconds per day
Overall, my explanation incorporates various scientific principles and equations related to time distortion due to speed and gravitational potential differences. It demonstrates an understanding of wave propagation and time measurement concepts and their applications
Keywords: Doppler Effects, phase shift, gravity, piezoelectric crystal oscillators, atomic clock.
Description:
The SI time unit of the International System of Units is defined as the time interval equal to 9192631770 vibrations of the ground state cesium-133 atom, represented as s or seconds. This means time is defined as vibrations or frequency (specifically) cesium-133 atom. Therefore, frequency represents time.
Time distortion due to speed follows the Doppler Effect, it is the change in frequency of a wave as the source moves relative to an observer. So when frequency changes, energy of frequency too changes.
Doppler shift considers the frequency change of a wave in propagation but gravitational potential difference considers the frequency change of the oscillating body.
It may be referred that 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 this.
This is the acoustic distortion in frequency due to speed. The wave equation shows that the energy of a wave is proportional to the square of its amplitude and its frequency. A change in the frequency of the sound wave can cause a corresponding change in the energy carried by the wave.
The Planck's equation helps us to calculate the energy when their frequency is known, as such wavelength is known, so one can calculate the energy by using the wave equation to calculate the frequency and then apply Planck's equation to find the energy. Incase of electromagnetic waves, Planck's equation shows us how frequency of the wave is proportional to energy of the wave.
However, in case of gravitational effects, gravity exerts a mechanical force on any object that deforms the object and pushes on the surrounding atoms. Using gravity, energy is obtained by the so-called piezo method, which converts mechanical stress into electrical energy.
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. It occurs when motion or mechanical energy is converted into electrical energy due to crystal deformation. Piezoelectric materials are materials that can generate electricity due to mechanical stress. 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.
Oscillatory systems with relative velocity or gravitational potential difference experience phase shifts, causing wave energy loss and errors in clock time readings.
Therefore, both acoustic distortion and electromagnetic distortion at their respective frequencies due to motion correspond to distortions of the corresponding wave energy.
However, Doppler shift considers the frequency change of a wave in propagation but gravitational potential difference considers the frequency change of the oscillating body.
Experiments made on piezoelectric crystal oscillators show that wave distortions correspond to time distortions due to relativistic effects such as speed or gravitational potential difference, besides, relative time between clock frequencies relativistic effects causes clock error, so time distortion is misrepresented as time dilation.
Relative time emerge from relative frequencies. A phase shift in relative frequency results in an infinitesimal loss of wave energy, and a corresponding enlargement in the wavelength of oscillation can lead to errors in clock time readings between relative locations due to differences in velocity or gravitational potential.
The phase shift in relative frequencies refers to a change in the timing or synchronization of oscillations between two clocks in different relative locations. This can occur due to factors such as differences in velocity or gravitational potential. As a result, there can be a discrepancy or error in the measurement of time between the clocks.
The wavelength, as a spatial property, can be affected by these factors and undergo distortion or enlargement. However, it's important to note that the wavelength itself does not directly represent clock time. Rather, it is the timing or synchronization of the oscillations that is relevant for measuring time.
The time-related distortion, which represents the temporal aspects of the phenomenon, can be influenced by the phase shift and changes in wavelength. This can lead to errors in the reading of clock time between relative locations.
A phase shift refers to the displacement of a wave form in time. A complete wave cycle, also known as a period (T), corresponds to a phase shift of 360 degrees or 2π radians.
When representing a complete wave cycle in degrees (°), it can be denoted as T(deg). In this notation, T(deg) represents the angular measure of one complete cycle of the waveform in degrees.
In terms of frequency (f), which represents the number of wave cycles per unit of time, there is an inverse relationship between the period and the frequency. The period (T) is the reciprocal of the frequency (f), and the relationship can be expressed as:
• T = 1 / f
If we express the period in degrees, T(deg), the relationship still holds:
• T(deg) = 360° / f
In this case, T(deg) represents the angular measure of one complete cycle of the waveform in degrees, and it is inversely proportional to the frequency (f).
Phase shifts can occur under the effects of relative velocities of observers and gravitational potential differences. These effects can introduce changes in the perception of time and the behavior of clocks, which may manifest as phase shifts in oscillatory systems and cause errors in time between relative clock oscillations under the effects of both relative velocities and gravitational potential differences.
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.
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). Where Φ is the total phase shift accumulated over a period of time (Δt) and ω(t) is the frequency shift that may vary as a function of time. The total accumulated phase shift (Φ) can be thought of as the area under a frequency vs time curve.
• 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.
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.
Concluding that the equation for time dilation, t' = t / √ (1 - v²/c²) is incorrect and fails to explain the cause of time distortion, whereas, the phase shifts can occur and cause errors in time between relative clock oscillations under the effects of both relative velocities and gravitational potential differences; it is actually error in clock time due to relativistic effects, misrepresented as time dilation.
Reference Paper : Relativistic effects on phaseshift in frequencies invalidate time dilation II
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