A simple way of unifying the formulas for the Coulomb’s law and Newton’s law of the universal gravitation: An approach based on membranes
Why this work is in the frame
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Bibliographic record
Abstract
In this work, a new approach is presented with the aim of showing a simple way of unifying the classical formulas for the forces of the Coulomb’s law of electrostatic interaction <mml:math display="inline"> <mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and the Newton’s law of universal gravitation <mml:math display="inline"> <mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . In this approach, these two forces are of the same nature and are ascribed to the interaction between two membranes that oscillate according to different curvature functions with spatial period <mml:math display="inline"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mi>π</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> , where <mml:math display="inline"> <mml:mi>ξ</mml:mi> </mml:math> is a dimensionless parameter and <mml:math display="inline"> <mml:mi>k</mml:mi> </mml:math> is a wave number. Both curvature functions are solutions of the classical wave equation with wavelength given by the de Broglie relation. This new formula still keeps itself as the inverse square law, and it is like <mml:math display="inline"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> </mml:math> when the dimensionless parameter <mml:math display="inline"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>274</mml:mn> </mml:mrow> </mml:math> and like <mml:math display="inline"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:msub> </mml:mrow> </mml:math> when <mml:math display="inline"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.14198</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>45</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . It was found that the values of the parameter <mml:math display="inline"> <mml:mi>ξ</mml:mi> </mml:math> quantize the formula from which <mml:math display="inline"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> </mml:math> and <mml:math display="inline"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>G</mml:mi> </mml:msub> </mml:mrow> </mml:math> are obtained as particular cases.
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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 | 0.001 | 0.001 |
| 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 it