Holographic Geometry and Noise in Matrix Theory

TL;DR

This paper demonstrates that Matrix Theory predicts a holographic quantum structure and noise in spacetime, which can be tested experimentally through interferometry, providing insights into fundamental holographic degrees of freedom.

Contribution

It introduces a new holographic quantum structure and noise in spacetime derived from Matrix Theory, with testable predictions for current experimental technology.

Findings

Holographic noise exhibits nonlocality and indeterminacy.

Measurements of transverse positions reveal holographic nonlocality.

Experimental tests can measure the fundamental holographic scale R.

Abstract

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.