# Statistical model of exotic rotational correlations in emergent space-time

## Abstract

A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictions for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.

- Authors:

- Univ. of Chicago, Chicago, IL (United States)
- Korea Advanced Institute of Science and Technology, Daejeon (Republic of Korea)
- Univ. of Chicago, Chicago, IL (United States); Univ. of Michigan, Ann Arbor, MI (United States)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1331775

- Report Number(s):
- FERMILAB-PUB-16-264-A; arXiv:1607.03048

Journal ID: ISSN 0264-9381; 1474997

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Classical and Quantum Gravity

- Additional Journal Information:
- Journal Volume: 34; Journal Issue: 13; Journal ID: ISSN 0264-9381

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum geometry; holographic noise; planckian physics; optical interferometry; inertial frames; rotational correlations; quantum observables and statistics

### Citation Formats

```
Hogan, Craig, Kwon, Ohkyung, and Richardson, Jonathan.
```*Statistical model of exotic rotational correlations in emergent space-time*. United States: N. p., 2017.
Web. doi:10.1088/1361-6382/aa73c0.

```
Hogan, Craig, Kwon, Ohkyung, & Richardson, Jonathan.
```*Statistical model of exotic rotational correlations in emergent space-time*. United States. doi:10.1088/1361-6382/aa73c0.

```
Hogan, Craig, Kwon, Ohkyung, and Richardson, Jonathan. Tue .
"Statistical model of exotic rotational correlations in emergent space-time". United States.
doi:10.1088/1361-6382/aa73c0. https://www.osti.gov/servlets/purl/1331775.
```

```
@article{osti_1331775,
```

title = {Statistical model of exotic rotational correlations in emergent space-time},

author = {Hogan, Craig and Kwon, Ohkyung and Richardson, Jonathan},

abstractNote = {A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictions for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.},

doi = {10.1088/1361-6382/aa73c0},

journal = {Classical and Quantum Gravity},

number = 13,

volume = 34,

place = {United States},

year = {Tue Jun 06 00:00:00 EDT 2017},

month = {Tue Jun 06 00:00:00 EDT 2017}

}

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