Relating quantum mechanics with hydrodynamic turbulence
Bibliographic record
Abstract
In this letter we attempt to trace back the origin of quantum uncertainty. We show that the Schrödinger equation can be mapped into the inviscid Favre-Reynolds turbulence equations of classical compressible fluids, albeit in zero temperature. Under this mapping the probability density function becomes the Reynolds time mean density of the fluid, the real and the imaginary parts of the momentum become the mean and turbulent root-mean-square velocities, respectively, where the latter obeys the first Fick law of diffusion and saturates the lower bound of the uncertainty principle. The mean pressure is proportional to the divergence of the turbulent mass flux and is the source for stochasticity. The roles of the pressure gradient force and the Reynolds stress tensor convergence, under this mapping, are illustrated in two well-known systems, namely, the 1 s orbital hydrogen atom and the 1D dynamic Gaussian wavepacket. Finally, we analyze within an independent part of the letter, a conjecture according to which this pressure results from vacuum fluctuations at the zero-point energy, mediated by random collisions of the particle with virtual photons. This suggests that the typical turbulent eddy is of the size of the Compton wavelength corresponding to a Reynolds averaging time scale which is twice the Zitterbewegung period. Moreover, according to this interpretation the quantized characteristics of the particle result from interactions with virtual photons.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".