dorsal/arxiv
View SchemaQuantum Mechanics and the Weak Equivalence Principle
| Authors | Stella Huerfano, Sarira Sahu, M. Socolovsky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606172 |
| URL | https://arxiv.org/abs/quant-ph/0606172 |
Abstract
We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying the strong equivalence principle (SEP) we obtain the Schroedinger equation for a particle in an inertial frame and in the presence of a uniform and constant gravity field. Second, using the associated Feynman propagator, we propagate an initial gaussian wave packet, with the final wave function and probability density depending on the ratio m/hbar, where m is the inertial mass of the particle, thus exhibiting the fact that the weak equivalence principle (WEP) is violated by quantum mechanics. Although due to rapid oscillations the wave function does not exist in the classical limit, the probability density is well defined and mass independent when hbar goes to 0, showing the recovery of the WEP. Finally, at the quantum level, a heavier particle does not necessarily falls faster than a lighter one; this depends on the relations between the initial and final common positions and times of the particles.
{
"annotation_id": "cff3cf7b-bad4-4f12-a1c1-fc00ae0c8f46",
"date_created": "2026-03-02T18:02:27.608000Z",
"date_modified": "2026-03-02T18:02:27.608000Z",
"file_hash": "e384e98c68d06c5e494e432096e9e7d017222ff2f46f7ba4262621ac72adc84c",
"private": false,
"record": {
"abstract": "We use the Feynman path integral approach to nonrelativistic quantum\nmechanics twofold. First, we derive the lagrangian for a spinless particle\nmoving in a uniformly but not necessarily constantly accelerated reference\nframe; then, applying the strong equivalence principle (SEP) we obtain the\nSchroedinger equation for a particle in an inertial frame and in the presence\nof a uniform and constant gravity field. Second, using the associated Feynman\npropagator, we propagate an initial gaussian wave packet, with the final wave\nfunction and probability density depending on the ratio m/hbar, where m is the\ninertial mass of the particle, thus exhibiting the fact that the weak\nequivalence principle (WEP) is violated by quantum mechanics. Although due to\nrapid oscillations the wave function does not exist in the classical limit, the\nprobability density is well defined and mass independent when hbar goes to 0,\nshowing the recovery of the WEP. Finally, at the quantum level, a heavier\nparticle does not necessarily falls faster than a lighter one; this depends on\nthe relations between the initial and final common positions and times of the\nparticles.",
"arxiv_id": "quant-ph/0606172",
"authors": [
"Stella Huerfano",
"Sarira Sahu",
"M. Socolovsky"
],
"categories": [
"quant-ph"
],
"title": "Quantum Mechanics and the Weak Equivalence Principle",
"url": "https://arxiv.org/abs/quant-ph/0606172"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "76cb600f-6ed1-42fc-a8b4-ddc8e6143b9a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}