### Abstract

Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case in which the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.

Original language | English (US) |
---|---|

Pages (from-to) | 5677-5683 |

Number of pages | 7 |

Journal | Classical and Quantum Gravity |

Volume | 21 |

Issue number | 24 |

DOIs | |

State | Published - Dec 21 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Transit time of a freely falling quantum particle in a background gravitational field.** / Davies, Paul.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 21, no. 24, pp. 5677-5683. https://doi.org/10.1088/0264-9381/21/24/001

}

TY - JOUR

T1 - Transit time of a freely falling quantum particle in a background gravitational field

AU - Davies, Paul

PY - 2004/12/21

Y1 - 2004/12/21

N2 - Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case in which the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.

AB - Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case in which the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.

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UR - http://www.scopus.com/inward/citedby.url?scp=10844279059&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/21/24/001

DO - 10.1088/0264-9381/21/24/001

M3 - Article

VL - 21

SP - 5677

EP - 5683

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 24

ER -