Using Matrix Theory as a concrete example of a fundamental holographic
theory, we show that the emergent macroscopic spacetime displays a new
macroscopic quantum structure, holographic geometry, and a new observable
phenomenon, holographic noise, with phenomenology similar to that previously
derived on the basis of a quasi-monochromatic wave theory. Traces of matrix
operators on a light sheet with a compact dimension of size R are interpreted
as transverse position operators for macroscopic bodies. An effective quantum
wave equation for spacetime is derived from the Matrix Hamiltonian. Its
solutions display eigenmodes that connect longitudinal separation and
transverse position operators on macroscopic scales. Measurements of transverse
relative positions of macroscopically separated bodies, such as signals in
Michelson interferometers, are shown to display holographic nonlocality,
indeterminacy and noise, whose properties can be predicted with no parameters
except R. Similar results are derived using a detailed scattering calculation
of the matrix wavefunction. Current experimental technology will allow a
definitive and precise test or validation of this interpretation of holographic
fundamental theories. In the latter case, they will yield a direct measurement
of R independent of the gravitational definition of the Planck length, and a
direct measurement of the total number of degrees of freedom.Comment: 19 pages, 2 figures; v2: factors of Planck mass written explicitly,
typos correcte