Physicist: "It Was Hiding in Plain Sight"
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This podcast is about dark matter — and Professor Philip Mannheim thinks it isn't missing at all, just hiding in plain sight as the rest of the visible universe. In his first-ever podcast, on ideas he's pursued since 1972, Mannheim lays out conformal gravity: a theory built on Weyl symmetry rather than Einstein's equations, which explains galaxy rotation curves without dark matter, tames the cosmological constant, and fits the accelerating universe without fine-tuning. With longtime collaborator Carl Bender, he also resolves gravity's infamous "ghost" problem using PT symmetry instead of Hermiticity — suggesting the graviton may not even exist as a particle. I hope you enjoy.
CLARIFICATIONS:
The opening quote refers to the metric being the gravitational field.
At 1:00:08, Mannheim's response to Hobson/Lasenby is GRG 54, 99 (2022): https://arxiv.org/abs/2105.14679
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TIMESTAMPS:
00:00:00 - Einstein's Relativity Foundations
00:05:47 - Riemann Tensor and Curvature
00:11:50 - Flaws in Einstein's Equations
00:17:23 - Quantum Gravity Renormalizability
00:23:28 - Conformal Symmetry Principles
00:30:09 - Dynamical Mass Generation
00:37:08 - Inflation and Horizon Problems
00:43:55 - Renormalization Group Fixed Points
00:51:05 - Composite Higgs Solution
00:57:03 - Weyl Tensor Action
01:03:44 - Solving Dark Matter
01:09:36 - Cosmic Coincidence Problem
01:16:27 - Hubble Tension and Redshift
01:24:31 - PT Symmetry and Ghosts
01:31:21 - Probability Conservation vs. Hermiticity
01:38:13 - CPT Theorem and Fermions
01:45:14 - Quantum Decays and Resonances
01:51:05 - Parity and Right-Handed Neutrinos
01:56:14 - Gravitons and Wavefunction Collapse
02:02:24 - Cyclic Universes and Singularities
02:08:24 - String Theory Fine-Tuning
02:14:45 - Unitarity and Poincaré Stresses
02:21:02 - Gravitational Lensing and Tenure
02:26:55 - Nature and Experimental Data
LINKS MENTIONED:
Philip's Papers: https://inspirehep.net/authors/998943
Newton's Law Of Gravity: https://en.wikipedia.org/wiki/Newton%...
Geodesics: https://en.wikipedia.org/wiki/Geodesi...
Equivalence Principle: https://en.wikipedia.org/wiki/Equival...
Introduction To General Relativity [Book]: https://amazon.com/dp/0070004234?tag=...
Foundation Of The General Theory Of Relativity [Paper]: https://isidore.co/misc/Physics%20pap...
Dynamical Symmetry Breaking As A Bootstrap [Paper]: https://journals.aps.org/prd/abstract...
Dynamics Of The Universe And Spontaneous Symmetry Breaking [Paper]: https://ui.adsabs.harvard.edu/abs/198...
Mass Generation, The Cosmological Constant Problem, Conformal Symmetry, And The Higgs Boson [Paper]: https://arxiv.org/abs/1610.08907
Living Without Supersymmetry [Paper]: https://arxiv.org/abs/1506.01399
Exact Vacuum Solution To Conformal Weyl Gravity And Galactic Rotation Curves [Paper]: https://ui.adsabs.harvard.edu/abs/198...
No-Ghost Theorem For The Pais-Uhlenbeck Oscillator [Paper]: https://arxiv.org/abs/0706.0207
Fitting Galactic Rotation Curves With Conformal Gravity [Paper]: https://arxiv.org/abs/1011.3495
Cosmic Coincidence Problem: https://en.wikipedia.org/wiki/Cosmic_...
Cosmological Perturbations In Conformal Gravity [Paper]: https://arxiv.org/pdf/1109.4119
Implications Of Cosmic Repulsion For Gravitational Theory [Paper]: https://arxiv.org/abs/astro-ph/9804335
Exact Solution To Perturbative Conformal Cosmology [Paper]: https://arxiv.org/abs/2101.02608
CPT Symmetry Without Hermiticity [Paper]: https://arxiv.org/abs/1611.02100
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