References

This page preserves the starting sources from the original formalization.

19. References and starting sources

These are not exhaustive. They are starting anchors for agents.

Core action/phase bridge

• Feynman Lectures, Vol. II, Ch. 19, "The Principle of Least Action": https://www.feynmanlectures.caltech.edu/II_19.html
• Path integral formulation overview: https://en.wikipedia.org/wiki/Path_integral_formulation

GR and Einstein field equations

• MIT OCW, "Einstein's Field Equations": https://ocw.mit.edu/courses/8-033-relativity-fall-2006/02415213222b845bbec6e734c64d1718_fieldeqs.pdf
• MIT OCW 8.962, Lecture 12, "The Einstein Field Equation": https://ocw.mit.edu/courses/8-962-general-relativity-spring-2020/resources/lecture-12-the-einstein-field-equation/
• Stanford Gravity Probe B, "Einstein's Spacetime": https://einstein.stanford.edu/SPACETIME/spacetime2.html

Atomic clocks and gravitational time dilation

• NIST/JILA, "JILA Atomic Clocks Measure Einstein's General Relativity at Millimeter Scale": https://www.nist.gov/news-events/news/2022/02/jila-atomic-clocks-measure-einsteins-general-relativity-millimeter-scale
• NIST educational page, "Einstein's General Relativity and Your Age": https://www.nist.gov/education/resources-for-parents%2C-teachers-and-students/einsteins-general-relativity-and-your-age

Gravitational quantum phase

• Colella, Overhauser, Werner, "Observation of Gravitationally Induced Quantum Interference", Physical Review Letters 34, 1472 (1975): https://link.aps.org/doi/10.1103/PhysRevLett.34.1472
• Pound and Rebka, "Apparent Weight of Photons", Physical Review Letters 4, 337 (1960): https://fisica.unipv.it/percorsi/pdf/rebka_1960.pdf

Quantum clocks and problem of time

• Altaie, Hodgson, Beige, "Time and Quantum Clocks: a review of recent developments", Frontiers in Physics / arXiv:2203.12564: https://arxiv.org/abs/2203.12564
• Gambini, Porto, Pullin, "A relational solution to the problem of time in quantum mechanics and quantum gravity induced by a fundamental mechanism for quantum decoherence", arXiv:gr-qc/0402118: https://arxiv.org/abs/gr-qc/0402118
• Gryb, Thébault, "The role of time in relational quantum theories", arXiv:1110.2429: https://arxiv.org/abs/1110.2429

Quantum clocks, time dilation, and entanglement

• Pikovski, Zych, Costa, Brukner, "Universal decoherence due to gravitational time dilation", Nature Physics 11, 668-672 (2015): https://ucrisportal.univie.ac.at/de/publications/universal-decoherence-due-to-gravitational-time-dilation/
• Castro-Ruiz, Giacomini, Brukner, "Entanglement of quantum clocks through gravity", PNAS 114, E2303-E2309 (2017): https://pmc.ncbi.nlm.nih.gov/articles/PMC5373405/
• Meltzer et al., "Atomic clock interferometry using optical tweezers", Physical Review A 110, 032602 (2024): https://ui.adsabs.harvard.edu/abs/2024PhRvA.110c2602M/abstract
• Giacomini, "Spacetime Quantum Reference Frames and superpositions of proper times", Quantum 5, 508 (2021): https://quantum-journal.org/papers/q-2021-07-22-508/

Equivalence principle tests

• Touboul et al., "MICROSCOPE mission: final results of the test of the Equivalence Principle", arXiv:2209.15487: https://arxiv.org/abs/2209.15487
• Touboul et al., "Result of the MICROSCOPE Weak Equivalence Principle test", arXiv:2209.15488: https://arxiv.org/abs/2209.15488

Emerging quantum-clock / curved-spacetime proposals

• "Probing curved spacetime with a distributed atomic processor", arXiv:2502.12954: https://arxiv.org/html/2502.12954v1
• Gündoğan, Barzel, Rätzel, "Gravitational time dilation in quantum clock interferometry with entangled multi-photon states and quantum memories", arXiv:2601.02470: https://arxiv.org/abs/2601.02470
• Balsells, "Geometry and proper time of a relativistic quantum clock", arXiv:2410.08156: https://arxiv.org/abs/2410.08156

Cosmology / dark sector context

• CERN, "Dark matter": https://home.cern/science/physics/dark-matter/
• Planck Collaboration, "Planck 2018 results. VI. Cosmological parameters", arXiv:1807.06209: https://arxiv.org/abs/1807.06209
• DESI / Lawrence Berkeley National Laboratory, "New DESI Results Strengthen Hints That Dark Energy May Evolve": https://newscenter.lbl.gov/2025/03/19/new-desi-results-strengthen-hints-that-dark-energy-may-evolve/
• Khalife et al., "Review of Hubble tension solutions with new SH0ES and SPT-3G data", arXiv:2312.09814: https://arxiv.org/html/2312.09814v2

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