The Bilateral Cosmos

Note 1. Gaztañaga, E., Kumar, K. S., & Marto, J. (2026). “A new understanding of Einstein-Rosen bridges.” Classical and Quantum Gravity, 43, 015023. arXiv:2512.20691. DOI: 10.1088/1361-6382/ae3044.

Note 2. Barbour, J., Koslowski, T., & Mercati, F. (2014). “Identification of a gravitational arrow of time.” Physical Review Letters, 113, 181101. arXiv:1409.0917. See also Barbour, J. (2020). The Janus Point: A New Theory of Time. Basic Books. Entaxy is introduced in Barbour, J., Koslowski, T., & Mercati, F. (2015), “Entropy and the Typicality of Universes,” arXiv:1507.06498, which describes it as scale-invariant and decreasing as the observable universe evolves away from the Janus point of maximum disorder.

Note 3. Boyle, L., Finn, K., & Turok, N. (2018). “CPT-Symmetric Universe.” Physical Review Letters, 121, 251301. arXiv:1803.08928.

Note 4. Boyle, L. & Turok, N. (2022). “The Big Bang, CPT, and neutrino dark matter.” Annals of Physics, 438, 168767. arXiv:1803.08930.

Note 5. Maldacena, J. & Susskind, L. (2013). “Cool horizons for entangled black holes.” Fortschritte der Physik, 61(9), 781–811. arXiv:1306.0533.

Note 6. Barbour, J., Koslowski, T., & Mercati, F. (2016). “Janus Points and Arrows of Time.” arXiv:1604.03956.

Note 7. Einstein, A. & Rosen, N. (1935). “The particle problem in the general theory of relativity.” Physical Review, 48(1), 73–77.

Note 8. Einstein, A., Podolsky, B., & Rosen, N. (1935). “Can quantum-mechanical description of physical reality be considered complete?” Physical Review, 47(10), 777–780.

Note 9. Coppo, A., Pranzini, N., & Verrucchi, P. (2026). “Quantum model for black holes and clocks.” arXiv:2601.07437. A bipartite quantum system modeling a test particle near a Schwarzschild horizon and Hawking radiation satisfies exactly the Page-Wootters clock conditions.

Note 10. Ladghami, Y., Lobo, F.S.N., Ouali, T. et al. (2026). “Timelike Entanglement Entropy of Hawking Radiation.” arXiv:2602.06833. Reveals periodic “timelike Page times” — transitions in the temporal entanglement structure between a black hole’s interior and its emitted radiation.

Note 11. Egan, C.A. & Lineweaver, C.H. (2010). “A Larger Estimate of the Entropy of the Universe.” Astrophysical Journal, 710, 1825–1834. Supermassive black holes dominate the cosmic entropy budget. At roughly 10¹⁰⁴ k, where k is Boltzmann’s constant, they account for effectively the entire total.

Note 12. Penrose, R. (1979). “Singularities and Time-Asymmetry.” In General Relativity: An Einstein Centenary Survey, ed. S.W. Hawking & W. Israel. Cambridge University Press. The Weyl curvature hypothesis: low Weyl curvature at the Big Bang, increasing via gravitational clumping toward black holes, drives the arrow of time.

Note 13. Castro-Ruiz, E., Giacomini, F. & Brukner, Č. (2017). “Entanglement of quantum clocks through gravity.” Proceedings of the National Academy of Sciences, 117(6), 2890–2895. arXiv:1908.10165. Gravitational time dilation entangles quantum clocks — gravity itself triggers the Page-Wootters mechanism.

Note 14. Pikovski, I., Zych, M., Costa, F. & Brukner, Č. (2015). “Universal decoherence due to gravitational time dilation.” Nature Physics, 11, 668–672. arXiv:1311.1095. Gravitational time dilation universally decoheres composite quantum systems, producing classicality without any external environmental interaction.

Note 15. Susskind, L. (2016). “Computational complexity and black hole horizons.” Fortschritte der Physik, 64, 24–43. arXiv:1402.5674. ER bridge interior growth corresponds to quantum computational complexity growth. Refined by Brown, A.R. et al., Physical Review D 93 (2016): 086006. Extended to the non-perturbative regime by a calculation in Iliesiu, L.V., Mezei, M. & Sárosi, G., JHEP 2022:73.

Note 16. Jacobson, T. (1995). “Thermodynamics of spacetime: The Einstein equation of state.” Physical Review Letters, 75, 1260–1263. Derives Einstein’s field equations from thermodynamics of local Rindler horizons. Updated in Jacobson (2016), Physical Review Letters 116, 201101, using entanglement entropy.

Note 17. Calcinari, A. & Gielen, S. (2025). “Relational dynamics and Page-Wootters formalism in group field theory.” Quantum, 9:1610. Applies Page-Wootters to discrete quantum spacetime and derives an expanding universe from matter-clock correlations, showing that the mechanism can be carried into a cosmological model.

Note 18. Hutsemékers, D. et al. (2014). “Alignment of quasar polarizations with large-scale structures.” Astronomy & Astrophysics, 572, A18. Quasar polarization vectors are aligned with their host large-scale structures over gigaparsec scales (<1% probability of random occurrence), which the authors interpret as the spin axes of the central supermassive black holes lying parallel to those structures. Confirmed at radio wavelengths by Pelgrims, V. & Hutsemékers, D. (2016), Astronomy & Astrophysics, 585, A32.

Note 19. NANOGrav Collaboration (Agazie, G. et al.) (2023). “The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background.” Astrophysical Journal Letters, 951, L8. Stochastic gravitational wave background at nanohertz frequencies from 68 pulsars, consistent with merging supermassive black hole binaries. The EPTA, PPTA, and CPTA arrays report comparable signals.

Note 20. Lee, J. et al. (2019). “Mysterious Coherence in Several-megaparsec Scales between Galaxy Rotation and Neighbor Motion.” Astrophysical Journal, 884, 104. Galaxy rotation correlates with neighbor motions out to 6 Mpc, far beyond the distance at which tidal forces from those neighbors could plausibly set a galaxy spinning.

Note 21. Wang, P. et al. (2021). “Possible observational evidence for cosmic filament spin.” Nature Astronomy, 5, 839–845. Coherent vortical motion in stacked cosmic filaments — the largest known rotating structures. See also Tudorache, M. N. et al. (2025). “A 15 Mpc rotating galaxy filament at redshift z = 0.032.” MNRAS, 544(4), 4306–4316. doi:10.1093/mnras/staf2005.

Note 22. Hutsemékers, D. et al. (2014), quoted in ESO Press Release eso1438. See also Zhao, Y. et al. (2025), arXiv:2503.10841, finding observed filament alignment sometimes exceeds simulation predictions. The excess may reflect systematics or a genuine departure from tidal torque theory.

Note 23. Alternative mechanisms proposed for gigaparsec-scale alignment: Arun, K. et al. (2010), “Cosmic magnetism from electroweak strings,” Physical Review Letters 105, 161301 (primordial magnetic fields); Shurtleff, R. (2018), International Journal of Modern Physics D 27, 1850094 (cosmic string networks); Hutsemékers, D. et al. (2008), arXiv:0809.3088 (pseudoscalar-photon mixing as propagation effect). None is established.

Note 24. Olsen, C. et al. (2021). “Star Formation Histories from Spectral Energy Distributions and Color–Magnitude Diagrams Agree: Evidence for Synchronized Star Formation in Local Volume Dwarf Galaxies over the Past 3 Gyr.” Astrophysical Journal, 913, 45. Thirty-six Local Volume dwarf galaxies show coordinated star formation across several megaparsecs.

Note 26. Müller, O., Pawlowski, M.S., Lelli, F. et al. (2021). “The coherent motion of Cen A dwarf satellite galaxies remains a challenge for ΛCDM cosmology.” Astronomy & Astrophysics, 645, L5. Twenty-one of 28 Centaurus A dwarf satellites share coherent orbital motion (0.2–0.3% probability in simulations). The anomaly is contested. Sawala and colleagues argue that the best-known such plane, the Milky Way’s own, is a transient alignment rather than a stable structure; see Sawala, T. et al. (2023). “The Milky Way’s plane of satellites is consistent with ΛCDM.” Nature Astronomy, 7, 481–491. A rival reading takes the Centaurus A plane’s members to be tidal dwarf galaxies condensed from the debris of the galaxy’s major merger roughly two billion years ago, a merger whose aftermath JWST/MIRI observations resolve in the nucleus (arXiv:2607.04942). Tidal dwarfs would inherit co-rotation from a single debris stream, but standard cosmology expects a large galaxy’s satellites to sit in dark-matter halos of their own, and tidal dwarfs should carry almost none. The rescue replaces one departure from standard cosmology with another. The chapter draws only on the observed coherence; the explanation remains open.

Note 27. Martín-Navarro, I. et al. (2021). “Anisotropic satellite galaxy quenching modulated by supermassive black hole activity.” Nature, 594, 187–190. arXiv:2106.04587. Satellite quenching patterns correlate with AGN activity timing and axis orientation, with effects on satellites outside the direct outflow path.

Note 28. Bennett, M. et al. (2002). “Huygens’s clocks.” Proceedings of the Royal Society A, 458, 563–579. Modern analysis of Huygens’ 1665 observation that pendulum clocks on a shared beam spontaneously synchronize.

Note 31. Minami, Y. & Komatsu, E. (2020). “New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data.” Physical Review Letters, 125, 221301. arXiv:2011.11254. Original detection at 2.4σ; improved to 3.6σ by Eskilt & Komatsu (2022), Physical Review D, 106, 063503; supported independently by ACT at 2.9σ (Diego-Palazuelos & Komatsu, 2025, arXiv:2509.13654), and combining the ACT and Planck data sets gives roughly 7σ. The Chern-Simons coupling explicitly breaks parity; if the field has a time-dependent vacuum expectation value, the violation extends to CPT. See Chapter 12.