Derivation of the Planck units based in a membranes model
Bibliographic record
Abstract
In this study, the Planck units (mass, time, and length) have only been derived, explained, and attributed a physical meaning when they were deduced based on the concept of interacting membranes (membranes instead of strings of string theory). For this purpose, a set of five assumptions were proposed: (a) the existence of the interacting membranes; (b) the curvatures of the membranes oscillate according to the classical wave equation; (c) the spatial period of the wave that arise when the membranes oscillate is given by <mml:math display="inline"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>ξ</mml:mi> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:math> ; (d) the membranes oscillate with wavelength given by de Broglie relation; and (e) <mml:math display="inline"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> holds. The parameter <mml:math display="inline"> <mml:mi>ξ</mml:mi> </mml:math> determines the period of oscillation of the given membranes. In deriving the Planck units in this work, <mml:math display="inline"> <mml:mi>ξ</mml:mi> </mml:math> must take the value 2 and determines a period <mml:math display="inline"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> , close to minimum value 1 or to fundamental period <mml:math display="inline"> <mml:mi>π</mml:mi> </mml:math> , respectively. In this context, Planck units must be fundamental. Moreover, the parameter <mml:math display="inline"> <mml:mi>ξ</mml:mi> </mml:math> was reported as a unification parameter between the formulas for the Coulomb's law and Newton's law of universal gravitation linking the forces of microworld and macroworld. Depending on the value <mml:math display="inline"> <mml:mi>ξ</mml:mi> </mml:math> takes, one force or another will be had. It is also shown that the potential <mml:math display="inline"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo>=</mml:mo> <mml:mi>h</mml:mi> <mml:mi>c</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ξ</mml:mi> <mml:mi>π</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:math> deduced from the above assumptions, and which contributes to deduce the Planck units, can be derived from Yukawa's equation. Hence, the present work would be contributing to theoretical physics, since at the Planck scale predictions of some theories like Standard Model, quantum field theory, and general relativity are not expected to be valid.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".