  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 $\alpha = 7.297\,352\,589(15) \times 10^{-3}$ 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 $\alpha$.
  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.
