The general relativistic interaction of the electric field with the gravitational field may be observable in a charged-particle interferometer containing a suitable arrangement of fields. Observation of the effect in the earth's field would constitute a new laboratory test of the equivalence principle, involving $e$ , $h$ , $c$ , and $g$ . The magnitude of the phase shift induced can be comparable to the Colella-Overhauser-Werner phase shift, for electrons.The general relativistic interaction of the electric field with the gravitational field may be observable in a charged-particle interferometer containing a suitable arrangement of fields. Observation of the effect in the earth's field would constitute a new laboratory test of the equivalence principle, involving $e$, $h$, $c$, and $g$. The magnitude of the phase shift induced can be comparable to the Colella-Overhauser-Werner phase shift, for electrons.

Physical Review LettersMay 30, 19839 citations

Quantum mechanics, matter waves, and moving clocks

Holger Müller

This paper is divided into three parts. In the first (section 1), we demonstrate that all of quantum mechanics can be derived from the fundamental property that the propagation of a matter wave packet is described by the same gravitational and kinematic time dilation that applies to a clock. We will do so in several steps, first deriving the Schroedinger equation for a nonrelativistic particle without spin in a weak gravitational potential, and eventually the Dirac equation in curved space-time describing the propagation of a relativistic particle with spin in strong gravity. In the second part (sections 2-4), we present interesting consequences of the above quantum mechanics: that it is possible to use wave packets as a reference for a clock, to test general relativity, and to realize a mass standard based on a proposed redefinition of the international system of units, wherein the Planck constant would be assigned a fixed value. The clock achieved an absolute accuracy of 4 parts per billion (ppb). The experiment yields the fine structure constant $α= 7.297\,352\,589(15) \times 10^{-3}$ with 2.0 ppb accuracy. We present improvements that have reduced the leading systematic error about 8-fold and improved the statistical uncertainty to 0.33 ppb in 6 hours of integration time, referred to $α$ . In the third part (sections 5-7), we present possible future experiments with atom interferometry: A gravitational Aharonov-Bohm experiment and its application as a measurement of Newton's gravitational constant, antimatter interferometry, interferometry with charged particles, and interferometry in space. We will give a review of previously published material when appropriate, but will focus on new aspects that haven't been published before.This paper is divided into three parts. In the first (section 1), we demonstrate that all of quantum mechanics can be derived from the fundamental property that the propagation of a matter wave packet is described by the same gravitational and kinematic time dilation that applies to a clock. We will do so in several steps, first deriving the Schroedinger equation for a nonrelativistic particle without spin in a weak gravitational potential, and eventually the Dirac equation in curved space-time describing the propagation of a relativistic particle with spin in strong gravity. In the second part (sections 2-4), we present interesting consequences of the above quantum mechanics: that it is possible to use wave packets as a reference for a clock, to test general relativity, and to realize a mass standard based on a proposed redefinition of the international system of units, wherein the Planck constant would be assigned a fixed value. The clock achieved an absolute accuracy of 4 parts per billion (ppb). The experiment yields the fine structure constant $α= 7.297\,352\,589(15) \times 10^{-3}$ with 2.0 ppb accuracy. We present improvements that have reduced the leading systematic error about 8-fold and improved the statistical uncertainty to 0.33 ppb in 6 hours of integration time, referred to $α$. In the third part (sections 5-7), we present possible future experiments with atom interferometry: A gravitational Aharonov-Bohm experiment and its application as a measurement of Newton's gravitational constant, antimatter interferometry, interferometry with charged particles, and interferometry in space. We will give a review of previously published material when appropriate, but will focus on new aspects that haven't been published before.

arXiv:1312.6449Dec 23, 20133 citations

e

h

c

, and

g

. The magnitude of the phase shift induced can be comparable to the Colella-Overhauser-Werner phase shift, for electrons.

α= 7.297\,352\,589(15) \times 10^{-3}

with 2.0 ppb accuracy. We present improvements that have reduced the leading systematic error about 8-fold and improved the statistical uncertainty to 0.33 ppb in 6 hours of integration time, referred to

α

. In the third part (sections 5-7), we present possible future experiments with atom interferometry: A gravitational Aharonov-Bohm experiment and its application as a measurement of Newton's gravitational constant, antimatter interferometry, interferometry with charged particles, and interferometry in space. We will give a review of previously published material when appropriate, but will focus on new aspects that haven't been published before.