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=7.297352589(15)×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.
The standard quantum mechanical description of the motion of a charged particle in the field of a stationary magnetic monopole is notorious for the presence of unnatural singularities in the Hamiltonian operator originating in the vector potential A(r) used to describe the magnetic field of the monopole. In this paper, an elementary quantum mechanical formulation of the problem which involves only the physically observable field B(r) is presented. This is achieved by treating as a fundamental observable of the charged particle its kinetic momentum instead of the linear momentum p . An irreducible representation of the fundamental commutation relations involving the operators and is explicitly constructed. It is shown that the existence of an irreducible representation requires that Dirac’s charge quantization condition is satisfied. Also, it is demonstrated that, from the quantum mechanical perspective, the singularities (appearing when the vector potential is introduced) are in fact properties of coordinate representations of the fundamental commutation relations.
The contemporary comprehension of quantum mechanics and fundamental particles, such as bosons, offers an intriguing perspective to analyze its infinite nature, while the nature of fundamental particles, such as fermions, predicts the finite nature of classical mechanics. It is the act of observation or interaction that changes indeterministic infinite quantum mechanics to deterministic finite classical mechanics. This document explores these concepts by delving into the nature of photons, gravitons, and tachyons, the mathematics of infinities, and the profound implications these have on our understanding of the universe. Particle speed from zero to infinity is the regime of infinite quantum mechanics, while particle speed slower than light speed is the regime of finite classical mechanics. The wave nature of photons is used to create charge, while gravitons use their particle nature to create mass. Gravitons and photons exist together in void levels “n” of quantum mechanics by increasing energy and decreasing entropy as “n” increases. The wave particle duality gives a dual nature to photons and gravitons in the quantum region. The Quantum Field Theory of General Relativity should contain Tensor Fields for both photons and gravitons.