Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
05-08-2024
Abstract:
This paper explores the role of piezoelectric crystal oscillators in understanding various effects on material deformation. Piezoelectric crystals, such as quartz, are pivotal in electronic oscillator circuits due to their ability to generate an electric charge in response to mechanical stress, a property known as inverse piezoelectricity. The study examines how these oscillators operate with a high Q factor, providing stable frequency oscillations influenced by factors like mechanical deformation, temperature, and gravitational potential differences. The paper also discusses the relationship between wave distortions and time distortions due to relativistic effects, highlighting that wavelength distortions, caused by phase shifts in frequency, are directly linked to time distortions through the relationship λ ∝ T. Additionally, the analysis includes a comparison of theoretical concepts with practical observations from atomic clocks and the effects of phase shifts on time distortions in different frequency ranges.
Keywords:
Piezoelectric Effect, Crystal Oscillators, Inverse Piezoelectricity, Frequency Stability, Relativistic Effects, Time Distortion, Wave Distortions, Material Deformation, Mechanical Stress, Gravitational Potential, Temperature Effects, Atomic Clocks, Phase Shifts, Q Factor,
The Piezoelectric Effect is the ability of certain materials to generate an electric charge in response to applied mechanical stress. A crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. It relies on the slight change in shape of a quartz crystal under an electric field, a property known as inverse piezoelectricity. A voltage applied to the electrodes on the crystal causes it to change shape; when the voltage is removed, the crystal generates a small voltage as it elastically returns to its original shape. The quartz oscillates at a stable resonant frequency, behaving like an RLC circuit but with a much higher Q factor (less energy loss on each cycle of oscillation). Once a quartz crystal is adjusted to a particular frequency (which is affected by the mass of electrodes attached to the crystal, the orientation of the crystal, temperature, and other factors), it maintains that frequency with high stability.
Relativistic effects, such as speed or gravity of real events, cannot interact with the proper time (t) referred to in the fourth dimension. Relativistic effects, such as the speed or gravity of real events, cannot interact with the proper time (t) referred to in the fourth dimension. The term 1/√1-v²/c² in the equation of time dilation does not influence or interact with the proper time (t) to cause time dilation (t′). Wave distortions correspond to time distortions due to relativistic effects. Wavelength distortions, caused by phase shifts in relative frequencies, correspond exactly to time distortion through the relationship λ∝T.
Piezoelectric crystal oscillators demonstrate that errors in waves correspond to time shifts due to relativistic effects, mechanical deformation, motion, gravitational potential differences, and temperature. These oscillators show that wave changes correspond to time shifts under these conditions.
Piezoelectric crystals follow the equations F = ma and F = kΔL. Specifically, piezoelectric crystals also adhere to F𝑔 = G (m₁m₂)r², where m₂ is the mass of the piezoelectric material. Even very small changes in mechanical force or gravitational forces (G-force) cause internal particles of matter to interact, leading to stresses and associated deformations in the internal matter.
Material deformation can occur due to various causes, including:
• Wavelength distortions due to phase shifts in frequency.
• Mechanical forces causing stresses.
• Gravitational potential differences and forces.
• Relativistic effects.
• Temperature changes, causing thermal expansion, contraction, and stress.
• Electromagnetic forces, such as electric and magnetic fields.
• Chemical reactions, including corrosion and oxidation.
• Pressure, including hydrostatic and atmospheric pressure.
• Radiation, such as ionizing radiation and radiation pressure.
• Environmental factors, such as moisture and freeze-thaw cycles.
• Manufacturing processes, such as welding, casting, or machining, which can introduce residual stresses over time.
These causes correspond to time distortion in oscillation through the relationship λ∝T.
Applicable equations include:
F = ma,F = kΔL,F𝑔 = G (m₁m₂)/r².
The wave equation, in combination with the Planck equation, has successfully identified distorted frequencies due to the relativistic effect that has the influence factor. Therefore, events invoke time but not vice versa. What special relativity represents in time dilation is not time, and time dilation does not involve actual time. It is rather an error in the clock oscillation.
An atomic clock, which measures time by monitoring the resonant frequency of atoms, is based on the principle that electron states in an atom are associated with different energy levels. In transitions between such states, they interact with a very specific frequency of electromagnetic radiation. This phenomenon serves as the basis for the International System of Units' (SI) definition of a second: The second, symbol s, is defined by taking the fixed numerical value of the caesium frequency, Δvcꜱ, the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to to s⁻¹.
Phase Shift and Time Distortion:
The time interval T𝑑𝑒𝑔 for 1° of phase is inversely proportional to the frequency (f). For example, a 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps).
For a wave of frequency f = 5 MHz
1° of phase shift = 1/360f
T𝑑𝑒𝑔 = 1/(360 × 5 × 10⁶),T𝑑𝑒𝑔 = 555 ps.
Therefore, for 1° phase shift for a wave with frequency f = 5 MHz the time shift (Δt) is 555 ps.
Moreover, for a 360° phase shift or 1 complete cycle for a wave having frequency 1Hz of a 9192631770 Hz wave, the time shift (Δt) is approximately 0.0000001087827757077666 ms.
For a 1455.50° phase shift or 4.04 cycles of a 9192631770 Hz wave, the time shift (Δt) is approximately 0.0000004398148148148148 ms or 38 microseconds per day.
Applicable Equations:
1° phase shift
T𝑑𝑒𝑔 = 1/360f.
For a 1° time shift/distortion:
Δt = 1/360f.
Where:
• Δt is the time shift/distortion for 1 degree phase shift.
For an x° time shift/distortion:
Δtₓ = x(1/360f).
Where:
• Δtₓ is the time shift/distortion for x degrees,
• x is the number of degrees of phase shift.
#PiezoelectricEffect, #CrystalOscillators, #InversePiezoelectricity, #FrequencyStability, #RelativisticEffects, #TimeDistortion, #WaveDistortions,#MaterialDeformation, #MechanicalStress, #GravitationalPotential, #TemperatureEffects, #AtomicClocks, #PhaseShifts, #QFactor,
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