Safety, Causal, and Discrete Programs: Evidence, Obstructions, and Status
The programs surveyed here have established complementary regulated calculations, not a common completed theory. Asymptotic safety has persistent fixed-point evidence across many functional truncations; CDT has a defined causal sum and extended phases; causal sets have strong Lorentz-invariant kinematics and discrete operators; tensor models have controlled large- expansions. Each retains decisive continuum, observable, or unitarity obstructions.
Required background. Functional Renormalization Group and Truncation Control, Emergence and Continuum-Limit Tests, and Unitarity, Reflection Positivity, and Causality Checks supply the technical tests.
Helpful background. Canonical and Loop Programs: Evidence, Obstructions, and Current Status supplies a comparison. Evidence Triangulation and Reproducibility constrains synthesis.
Status through August 2026
Section titled “Status through August 2026”| Program | Established evidence | Main unresolved obstruction |
|---|---|---|
| Asymptotic safety | Recurrent non-Gaussian points, selected truncation stability, perturbative interfaces | Regulator-independent observables, Lorentzian positivity, full closure |
| CDT | Causal configuration space, transfer matrix, phase diagram, extended volume and dimensional flow | Critical continuum trajectory and complete low-energy observable recovery |
| Causal sets | Lorentz-invariant sprinkling, dimension estimators, discrete curvature and wave operators | Dynamics favoring manifoldlike causal sets with controlled continuum |
| EDT | Precise Euclidean sum and well-mapped phases | Original phases do not yield an established four-dimensional continuum |
| Tensor models | Gurau expansion, melonic solutions, critical and double-scaling limits | Dominant geometry, causality, and Einstein dynamics |
No entry is an empirical detection of quantum gravity.
Application: three evidence trails
Section titled “Application: three evidence trails”For asymptotic safety, Reuter’s Einstein–Hilbert fixed point is the primary starting result; higher-curvature work supplies a partially independent basis-enlargement test Falls et al. 2018. The contrary control is gauge, regulator, background, and Lorentzian sensitivity—not numerical failure inside one flow.
For CDT, the de Sitter-like volume profile and four-dimensional scaling are primary observables Ambjørn, Jurkiewicz, and Loll 2005. Independent phase and transfer-matrix analyses strengthen the regulated model. The blocker is converting candidate phase boundaries into lines of constant physics with multiple renormalized observables.
For causal sets, the Benincasa–Dowker curvature operator has a controlled sprinkling continuum expectation Benincasa and Dowker 2010. The adversarial fact is that generic large finite partial orders are overwhelmingly nonmanifoldlike; successful sprinkling tests do not show that a proposed dynamics selects them.
These evidence trails share methods but are not statistically independent confirmations of one microscopic theory.
Reproducibility and falsifiers
Section titled “Reproducibility and falsifiers”Release flow equations, regulator choices, projection code, triangulation ensembles, autocorrelation estimates, causal-set seeds, and tensor normalizations. Predeclare observables and fit windows. Material falsifiers include proliferation of relevant directions under convergent truncation enlargement, absence of a suitable CDT critical limit, dynamical domination by nonmanifoldlike causal sets, or tensor continuum observables locked to an unwanted branched-polymer class.
Strongest conclusion
Section titled “Strongest conclusion”Several programs have crossed the threshold from qualitative idea to reproducible nonperturbative calculation. None has yet jointly delivered a regulator-free four-dimensional theory, complete physical observables, controlled unitary causality, realistic matter, and empirical predictions. That conclusion is narrower—and more informative—than either declaring completion or dismissing the concrete results.
The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.
For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.
References
Section titled “References”- Ambjørn, J., J. Jurkiewicz, and R. Loll. “Reconstructing the Universe.” Physical Review D 72 (2005): 064014. DOI.
- Benincasa, D. M. T., and F. Dowker. “The Scalar Curvature of a Causal Set.” Physical Review Letters 104 (2010): 181301. DOI.
- Falls, K. G., C. R. King, D. F. Litim, K. Nikolakopoulos, and C. Rahmede. “Asymptotic Safety of Quantum Gravity beyond Ricci Scalars.” Physical Review D 97 (2018): 086006. DOI.
- Reuter, M. “Nonperturbative Evolution Equation for Quantum Gravity.” Physical Review D 57 (1998): 971–985. DOI.