Statistical model of exotic rotational correlations in emergent space-time

Abstract

A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck information density in invariant proper time determined by the world line of an observer. It describes macroscopic spacelike correlations that appear as observable timelike correlations in phase differences of light propagating on paths that begin and end on the same world line. The model allows an exact prediction for the autocorrelation of any interferometer time signal from the shape of the light paths. Specific examples computed for configurations that approximate realistic experiments show that the model can be rigorously tested, allowing a direct experimental probe of Planck scale degrees of freedom. B. Model assumptionsThe model is based on two principal assumptions: 1. The system has a Planck scale information density, in invariant proper time, on the world line of a measurement.Unlike a classical world line, the information content or bandwidth of a world line, and any measurement, is limited to that of a discrete 1D time series with steps of duration ≈ l P /c in invariant proper time. That limit applies as well to the rotational relationship of its local inertial frame with rest of the universe. The information available to describe directional orientation relative to an interval on a world line matches its duration in Planck units.2. The quantum departure from a classical space-time can be represented by random Planck scale spacelike displacements that exactly preserve classical causal structure defined by the light cones of the world line of the measurement.

Nonlocal entanglement and directional correlations of primordial perturbations on the inflationary horizon

“…Unlike the particle example, geometrical states are universal: they must entangle with all forms of matter and energy on a light cone in all directions, not just a single pair of particles. Their correlations describe the relationship of the local inertial frame of a world line to the rest of the universe [13][14][15].…”

“…This leads to a directional uncertainty relation: from Eqs. (9) and (14) in the limit of l ≈ l i >> 1, orthogonal temporal displacements have a variance about a mean value T given by…”

“…5, and refs. [13][14][15]). Projections of states are directionally antisymmetric on each light cone, like the rotational raising and lower operatorsδ i± , as discussed in the Appendix.…”

Models of exotic interferometer cross-correlations in emergent space-time

“…Roughly speaking, the mean phase differences of N ≈ 10 28 photons with frequency f ≈ 10 15 Hz can On the left, the causal diamond is shown associated with a free spectral range, a complete round trip of light in the arm. The radial separation of a "tracer photon" in the bent arm is shown in the lab frame; see [12] for a more detailed description. The transverse part of light path for one arm, where light does not travel radially, departs from the overall causal diamond.…”

“…a A(⌧ ) as a sum of the rotational components in the two directions, so that to provide projections for autocorrelations of one interferometer [12]. Apart from the addition of new mirrors to bend the light paths, the new system has not been modified from the one that previously measured a null.…”