Abstract
This document summarizes the key misunderstandings and their corrections regarding the derivation of pre-Planck frequency and phase transitions within the Extended Classical Mechanics (ECM) framework. It emphasizes both energetic and frequency-time perspectives, clarifies dimensional inconsistencies encountered in earlier works, and presents the corrected ECM-consistent methodology for obtaining the initial vibration frequency of the 0-D origin and its transition to the Planck frequency through one full 360° phase rotation.
Figure
Figure 1: ECM representation of the pre-Planck 0-D origin vibration transitioning to the first Planck frequency through a 360° phase rotation, showing both energetic and frequency-time perspectives.
1. Misuse of Planck Frequency in Earlier Papers
Paper Reference: March 24, 2025 ECM paper: “Mathematical Derivation of Frequency Shift and Phase Transition in Extended Classical Mechanics”
What happened:
- Planck frequency was incorrectly taken as: fp = 2.952 × 1042 Hz
- Using this in the correct derivation method, initial frequency f0 came out as f0 ≈ 2.15 × 1043 Hz
- The method was mathematically correct: phase–time relation, Δf calculation, Planck energy → frequency transition
- Error: incorrect numerical value of fp → f0 numerically incorrect
Correction:
- Use correct Planck frequency: fp = 1.8549 × 1043 Hz
- Then, using the same method, corrected initial frequency f0 comes out as: f0 = fp + Δf0
- With Δf0 = 1 Hz (minimal discrete step) → exactly consistent with one 360° phase rotation in Δt = tp
2. Misunderstanding of f0 vs fp and Dimensional Issues
Initial claim:
- Some reasoning attempted: f0 = 1 / tp = fp
- Then claimed Δf0 = 360° = 1 Hz, rejected Δt = tp → f0 = 1 / tp, citing dimensional inconsistency
Why this was incorrect:
- f0 (pre-Planck vibration) is sub-dimensional or non-dimensional (0-D origin’s phase domain)
- fp is fully dimensional (Planck threshold)
- Δf0,360° is sub-dimensional, so dimensional arguments against it are invalid
- This domain corresponds to superluminal phase motion, not superluminal frequency propagation
Correct conceptual understanding:
- f0: pre-manifestation, 0-D origin vibration
- Δf0: minimal discrete phase step per first 360° cycle
- fp: Planck threshold, fully dimensional, first kinetic manifestation
3. Correct Calculation Applied Later
- Phase–time relation (exact ECM form): Δt = x° / (360° f0), with x° = 360° → Δt = 1 / f0
- Minimal discrete frequency step per 360° phase rotation: Δf0 = 1 Hz (sub-dimensional phase change)
- Initial frequency f0 in ECM: f0 = fp + Δf0; after one 360° phase cycle (Δt = tp): f0 - Δf0 = fp
- Dimensional consistency: f0 (pre-manifestation) ≠ fp (manifested Planck frequency); Δf0 is sub-dimensional
- Energetic vs frequency-time views: pre-Planck potential energy → first kinetic events; 360° phase rotation → Δf0 → fp
4. Summary Table
| # | Misunderstanding | Corrected ECM Solution |
|---|---|---|
| 1 | Used wrong fp = 2.952 × 1042 Hz → f0 ≈ 2.15 × 1043 Hz | Correct fp = 1.8549 × 1043 Hz → f0 = fp + Δf0 = fp + 1 Hz |
| 2 | Claimed Δf0 = 360° = 1 Hz inconsistent dimensionally | Δf0 = 1 Hz is sub-dimensional phase step, valid in 0-D origin domain |
| 3 | Treated f0 = fp numerically = 1 / tp → ignored pre-Planck domain distinction | f0 is pre-manifestation 0-D vibration, fp is first manifested Planck frequency; Δf0 = 1 Hz → f0 - Δf0 = fp |
| 4 | Ignored superluminal phase motion vs frequency propagation | Phase rotates superluminally; actual frequency propagation irrelevant; Δf0 is phase-domain step |
| 5 | Earlier energetic and frequency-time views not linked | Energetic and frequency-time views converge: 0-D potential → Planck-scale kinetic → 360° phase → Δf0 → fp |
Conclusion
The analysis demonstrates that early misunderstandings regarding Planck frequency, initial pre-Planck vibration, and phase transitions in ECM were largely due to incorrect data usage and misinterpretation of dimensionality. By distinguishing between the sub-dimensional pre-manifestation frequency f0 and the fully dimensional Planck frequency fp, and by correctly applying the 360° phase rotation in Δt = tp, ECM provides a consistent framework linking energetic and frequency-time perspectives. This approach validates that the transformation from the 0-D origin to the first Planck-scale kinetic event is structured, deterministic, and coherent, preserving the ECM principles of smooth and continuous cosmic evolution.
References of the Papers with Incorrect Data
- Thakur, S. N. (2025, March 24). Mathematical Derivation of Frequency Shift and Phase Transition in Extended Classical Mechanics (ECM). DOI: 10.13140/RG.2.2.36663.02721
- Thakur, S. N., & Bhattacharjee, D. (2023). Phase Shift and Infinitesimal Wave Energy Loss Equations. preprints.org (MDPI). DOI: 10.20944/preprints202309.1831.v1
- Thakur, S. N., & Bhattacharjee, D. (2023, October 30). Phase Shift and Infinitesimal Wave Energy Loss Equations. Longdom Publishing SL. Link