Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Tagore's Electronic Lab, WB, India
May 06, 2025
DOI: http://dx.doi.org/10.13140/RG.2.2.24780.32640
Description:
Experimental Findings A piezoelectric crystal device, when rotated at a high speed of 3000 RPM (equivalent to 50 Hz) at a radial distance of approximately 1.5915 meters from a central axis, spontaneously generates an alternating voltage signal with a frequency of 50 Hz. Notably, this signal arises without any external electrical bias applied to the system, indicating that the mechanical motion alone is sufficient to activate the piezoelectric effect. Over a one-second interval, the generated waveform exhibits a cumulative phase shift of 18,000 degrees, corresponding to a full 360° shift per rotational cycle. This direct synchronization between rotational motion and phase progression suggests that the physical acceleration imposed on the crystal structure induces a continuous and periodic internal stress. The resulting mechanical deformation gives rise to an alternating electrical output consistent with the inherent frequency of rotation. The phase shift observed acts as a precise indicator of temporal evolution within the system, effectively converting the rotational motion into a measurable time-dependent signal. Within the framework of Extended Classical Mechanics (ECM), this phenomenon supports the interpretation that sustained acceleration and inertial dynamics can induce measurable distortions in local time flow—expressed here as continuous phase displacement in the output signal. Material selection plays a key role: stable piezoelectric crystals such as quartz exhibit consistent phase-time correlation under sustained rotation, while synthetic materials with higher sensitivity may enhance the amplitude of generated signals in dynamic conditions. In either case, the mechanical-to-electrical energy transformation directly links the material's internal structure with externally imposed motion, producing a phase-encoded temporal signature. These findings validate a cohesive model wherein the rotational acceleration of a piezoelectric device results in not only stress-induced voltage generation but also in the modulation of time as expressed through waveform phase evolution. The result provides experimental support for ECM’s interpretation of motion-induced time distortion, where time is dynamically linked to motion and phase, rather than being an invariant external parameter.
In an electronics laboratory, when a piezoelectric crystal device is rapidly rotated at 3000 RPM (equivalent to a rotational frequency of 50 Hz) at a radius of 1.5915 meters from a central source point, an alternating current (AC) signal with a frequency of 50 cycles per second is observed. Over a time interval of 1 second, this rotation corresponds to a phase shift of 18000° per second, beginning from a null bias—that is, no external voltage is applied to the device prior to rotation. The spontaneous generation of voltage during rotation indicates a direct link between angular motion and time-dependent phase change. The consistent appearance of a 50 Hz signal, synchronized with rotational motion and phase progression, supports the interpretation that motion induces time distortion effects through continuous phase shift in the generated frequency. This reinforces the physical correlation between rotation-induced acceleration, phase evolution, and the apparent modulation of time, in agreement with extended classical mechanics (ECM) principles.
Theoretical Justification: Rotational Phase Shift and Time Distortion in a Piezoelectric System
The experimental observation of voltage generation in a piezoelectric crystal rotating at high speed without any external electrical bias can be theoretically justified by combining classical mechanics, wave dynamics, and the principles of Extended Classical Mechanics (ECM). Here's a breakdown of the justification:
1. Mechanical Basis: Rotational Acceleration and Inertial Force
When the piezoelectric device is rotated at 3000 RPM (50 Hz) at a radius of 1.5915 m, it experiences a centripetal acceleration given by:
a = ω²r = (2πf)²r = (2π × 50)² × 1.5915 ≈ 98696.04 m/s²
This high acceleration acts on the mass lattice within the piezoelectric crystal, generating internal mechanical stress due to the inertial resistance of the crystal’s structure.
2. Piezoelectric Effect: Stress-Induced Voltage Generation
In a piezoelectric material, mechanical stress directly results in electrical polarization due to the asymmetry of the crystal lattice. The stress induced by rotational acceleration thus causes a redistribution of charge, producing an alternating voltage output—even in the absence of a bias voltage.
Since the mechanical stress is periodic (from rotation), the resulting voltage is also periodic, with a frequency matching the rotational frequency: 50 Hz.
3. Phase Shift as a Manifestation of Time Evolution
The observation of a phase shift of 18000°/s corresponds to:
Phase shift per cycle = 18000°/50 cycles/sec = 360° per cycle
This is precisely the angular phase evolution expected for a sinusoidal waveform completing one full cycle per rotation.
Thus, the phase shift accumulates over time and directly tracks the temporal evolution of the oscillatory motion. This validates the relation:
x°/360f = Δtₓ
This shows that phase displacement can be interpreted as a temporal measure in systems undergoing periodic motion, consistent with ECM's concept of phase-driven time modulation.
4. ECM Interpretation: Motion-Induced Time Distortion
Within Extended Classical Mechanics, rotational systems exhibit effective acceleration, and the apparent mass-energy conversion associated with kinetic energy can influence local time evolution. Specifically:
• The effective force in ECM is determined by differences between matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ < 0).
• The periodic acceleration in rotation induces continuous energy exchange, leading to a measurable phase shift.
• This phase shift is equivalent to a temporal displacement, implying that motion modifies the effective flow of time—an interpretation consistent with relativistic and ECM-based principles.
Hence, the system exhibits time distortion not by altering physical clocks, but by altering phase-based event timing, measurable as a voltage phase shift in the output.
5. Material Basis of Time-Dependent Phase Shift in Rotating Piezoelectric Systems
The behaviour of the piezoelectric device under rotational motion is inherently tied to the electromechanical properties of the materials involved. A piezoelectric transducer, operating at 50 Hz, generates an electrostatic charge or measurable voltage in response to mechanical stress—an effect directly exploited in the observed experiment.
The most commonly used materials for this purpose include quartz, Rochelle salt, and synthetic compounds such as barium titanate and lead zirconate titanate. Of these, quartz exhibits exceptional thermal and mechanical stability, making it the preferred material in single-cut crystal oscillators for high-precision applications. Its stability under rotation contributes to the consistent frequency output and clear phase correlation seen in this experiment.
In contrast, synthetic piezoelectric materials—though less stable than quartz—offer higher sensitivity and lower manufacturing costs, which make them ideal for dynamic sensing applications involving rapidly varying mechanical inputs such as shock, vibration, or acceleration changes. These materials are often used in stacked configurations to amplify signal generation in real-time monitoring of mechanical disturbances.
In the context of high-speed rotation at 3000 RPM, the periodic mechanical stress imposed on the crystal lattice generates an alternating voltage signal synchronized with the rotational frequency. The generation of this 50 Hz output without any external bias directly links the material's internal stress response to the dynamic inertial forces experienced during rotation.
Most significantly, the voltage waveform’s phase evolution at a rate of 18000°/s arises from this material-specific piezoelectric interaction with rotational acceleration. This serves not merely as a passive signal but as an active phase-time marker, encoding the continuous temporal evolution of motion—thereby reinforcing the interpretation of motion-induced time distortion in line with Extended Classical Mechanics (ECM) principles.
Thus, the physical realization of time-modulating behaviour in rotating piezoelectric systems is inseparable from the material science foundations of piezoelectricity. The choice and configuration of the piezoelectric element determine not only the sensitivity and fidelity of the generated voltage signal but also the precision with which phase-time displacement can be measured and interpreted in rotating reference frames.
Note:
In the observed experiment, the rotation corresponds to a phase shift of 18,000° per second, beginning from a null bias—that is, no external voltage is applied to the piezoelectric device prior to rotation. This represents a non-ideal operational condition for the crystal.
Under ideal conditions, the device remains stationary, and a specified voltage is applied. In this configuration, the crystal oscillates at its nominal frequency of 50 Hz, generating a stable signal with no additional phase shift—only the ideal oscillation of 50 cycles per second.
However, if the voltage-applied piezoelectric device is rotated at 3000 RPM, which corresponds to a rotational frequency of 50 Hz, an additional phase shift of 18,000° per second is introduced. This phase shift begins from a biased condition (i.e., voltage already applied) and results in a time distortion relative to the ideal oscillation.
Therefore, initiating the experiment from a null bias—without applying voltage before rotation—serves as a deductive method to isolate and determine the exact time distortion caused by rotational phase shift under unbiased conditions.
Summary
The spontaneous generation of a 50 Hz signal and the associated 18000°/s phase shift in a bias-free rotating piezoelectric device are consistent with:
• Classical centripetal acceleration and mechanical stress,
• The direct stress-to-voltage conversion of the piezoelectric effect,
• Phase-time equivalence in periodic systems,
• And ECM’s interpretation of motion-driven time distortion.
This provides a cohesive physical and theoretical framework supporting the experimental observation and broadens the understanding of time modulation in dynamically accelerated systems.
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Figure-1: Graphical representation of the voltage signal generated by the rotating piezoelectric device. It shows a sinusoidal waveform with a frequency of 50 Hz and a continuously increasing phase, corresponding to a total shift of 18000° over 1 second. This supports your experimental claim of phase-time displacement due to rotational acceleration.
