Dirac's 90-Year-Old "Mistake" Unifies All of Physics

• Causal fermion systems (CFS) is a candidate theory of everything developed over 30+ years by mathematician-physicist Felix Finster, starting from a radical rethinking of the Dirac sea — the idea that negative-energy solutions of the Dirac equation are not mathematical artifacts but a real, physical sea of particles filling the vacuum. From this foundation, spacetime itself is not assumed but emerges as correlations between wave functions spread across a discrete set of abstract points, with no pre-existing geometry, manifold, or metric. The dynamics are governed by a causal action principle — a variational principle that minimizes a non-negative functional defined on families of wave functions — and from this austere starting point, general relativity, quantum field theory, and the Standard Model all arise in appropriate limiting cases.

  • Why this matters: Most approaches to quantum gravity (string theory, loop quantum gravity, etc.) struggle to reproduce the full Standard Model, explain the existence of three particle generations, account for matter-antimatter asymmetry, or resolve the measurement problem. CFS claims to address all of these, while also making the graviton and quantum gravity conceptually well-defined — though not yet in a form the broader community has accepted.

  • The core arc of the episode: Finster traces the intellectual history of the theory from his dissatisfaction as a student with the artificiality of standard quantum field theory, through decades of mathematical development largely carried out in the mathematics community (because physicists were unreceptive to vague new ideas from a young student), to the present moment in 2025 when the theory has matured enough to reproduce known physics and make novel predictions — and is finally receiving wider attention through figures like Sabine Hossenfelder and conferences like the one Finster is organizing in Regensburg.

The Dirac Sea: From Problem to Foundation

• The original Dirac sea (1928): Dirac’s equation has solutions with both positive and negative energy. Dirac proposed that in the vacuum, all negative-energy states are filled — a “sea” of infinitely many particles. This naturally explains antimatter: removing a negative-energy electron leaves a hole that behaves as a positron (positive energy, opposite charge). The idea successfully predicted antimatter but was widely criticized because it implies infinite negative energy density and infinite charge density — seemingly nonsensical infinities.

• Finster’s revival: Rather than discarding the Dirac sea, Finster takes it literally as the fundamental structure of the vacuum. The causal action principle is specifically designed so that these infinities drop out of the equations — the Dirac sea configuration is a minimizer of the causal action, and only deviations from it (particles, antiparticles, excitations) appear as physical sources. This resolves the historical objection while preserving Dirac’s physical insight.

• Connection to the measurement problem: The vacuum’s structure gives rise to stochastic background fields (linearized solutions of the Euler-Lagrange equations that are not determined macroscopically). These fields couple to matter and, combined with the intrinsic nonlinearity of the causal action, produce dynamics resembling continuous spontaneous localization (CSL) collapse models — but with a key difference: the CFS version is non-local in time (smeared over small time strips via “surface layer integrals”) and appears to conserve energy, unlike standard CSL. This offers a dynamical explanation for wave function collapse rather than postulating it.

How Spacetime Emerges

• Starting point: A finite set of abstract points with no geometry, topology, or causal structure. At each point, a spin space (a vector space with an indefinite inner product) is attached. Wave functions are vectors in a Hilbert space that can be evaluated at each point, giving a section of this bundle.

• The causal action principle: A functional is defined on families of wave functions. Minimizing it (subject to constraints) yields the Euler-Lagrange equations — the fundamental physical equations. The wave functions, when in an optimal (minimizing) configuration, induce causal relations, a topology, and geometric structure on the set of points. Spacetime is the web of correlations between wave functions across these points.

• Recovering Lorentz signature without assuming it: There is no Lorentzian metric at the fundamental level. But when one constructs a CFS from standard Minkowski space (using Dirac sea wave functions satisfying the Dirac equation), the resulting causal structure from the CFS coincides with the standard causal structure of Minkowski space. The Lorentzian geometry is thus generalized and recovered, not imposed.

• Recovering Einstein’s equations: Starting from a Minkowski vacuum (a minimizer), one perturbs the system by introducing particles, fields, or metric deformations. The Euler-Lagrange equations are satisfied if and only if the perturbations satisfy the coupled Einstein-Dirac-Maxwell equations (in the appropriate limit). This is called the continuum limit — classical general relativity and classical field theory emerge as the effective description. The full CFS equations are nonlinear and diffeomorphism-invariant, so the recovery holds beyond the linearized level (contrary to some criticism).

• The graviton and quantum gravity: Classical gravity is recovered on the nonlinear level. For the quantum level, Finster’s group has shown that QED (second-quantized bosonic fields) emerges naturally in a limiting case. A similar procedure should in principle work for gravity, but Finster is cautious — it’s not clear what “quantum gravity” even means as a mathematical theory, since the perturbative quantum gravity field theory is non-renormalizable. In CFS, the fundamental equations are well-defined at the Planck scale (spacetime is discrete/regularized), so quantum geometry is described by the causal action principle itself. Whether this matches what loop quantum gravity or other approaches produce remains an open question.

Recovering the Standard Model

• Gauge groups: At each spacetime point, the spin space carries a group of unitary transformations. This local freedom to transform spinors independently at each point gives rise to local gauge invariance. In the continuum limit, this produces the correct Standard Model gauge group — but only if a chiral asymmetry is assumed in the neutrino sector (at least one neutrino generation must be left-right asymmetric, and at least one neutrino must be massive). Chirality is not derived but assumed as a property of the vacuum configuration; once assumed, the gauge groups, couplings, and mixing matrices follow.

• Three generations: The vacuum is built from seven identical sectors (each containing three Dirac seas for three generations) plus one distinct sector for quarks (which has broken chiral symmetry). This gives eight sectors total, which connects to the octonions — an 8-dimensional non-associative division algebra that can be represented by 8×8 matrices acting naturally on these eight sectors. The appearance of octonions is being investigated in collaboration with Tejinder Singh and others; it is not yet fully understood whether the octonionic structure is forced by the mathematics or merely suggestive.

• No supersymmetry: CFS fundamentally distinguishes fermions (the basic constituents that build spacetime) from bosons (effective descriptions of fermion interactions). Supersymmetry, which transforms fermions into bosons and vice versa, is incompatible with this picture. Finster notes that LHC bounds on supersymmetric partners are consistent with this, though he stops short of claiming supersymmetry is ruled out.

• The single parameter κ: The causal action has essentially one free dimensionless parameter κ, related to the ratio of the Planck length to the Compton wavelength. However, this does not mean all Standard Model parameters are derived from κ alone. The vacuum configuration requires specifying particle masses (including three neutrino masses), and the regularization procedure (needed because the Planck-scale structure of spacetime is unknown) introduces additional free parameters. Deriving all ~25 Standard Model parameters from first principles remains a major open problem.

Baryogenesis: Why Matter Exists

• The problem: The universe is made overwhelmingly of matter, not antimatter. The Dirac equation allows pair creation (particle + antiparticle) but cannot create matter without equal antimatter. Some mechanism must have produced the asymmetry.

• CFS mechanism: Start with a completely filled Dirac sea (no matter, no antimatter). As the universe evolves (through inflation, structure formation, etc.), the number of states needed to form the Dirac sea decreases. States that are no longer needed to fill the sea are “left over” and occupy positive-energy solutions — these are the matter particles we observe. This is a purely geometric/dynamical consequence of the causal action principle applied to an evolving spacetime.

• Corrections to the Dirac equation: The causal action principle yields correction terms to the Dirac equation that allow baryogenesis. This has been worked out technically with collaborators Claudio Paganini and Marco Zanetti-Belzerano. The mechanism appears compatible with the Sakharov conditions (though the origin of CP violation in the formalism needs further study). The next step is to compute the baryogenesis rate quantitatively using realistic early-universe metrics and compare with observations.

The Born Rule and Measurement

• Recovering the Born rule: A conserved scalar product is constructed using surface layer integrals — integrals over space and a thin time strip that generalize the notion of a Cauchy surface to discrete or non-smooth spacetimes. This gives a time-independent norm, and the integrand serves as a probability density. The sesquilinear (ψ²-like) form comes from the Hilbert space structure built into the theory from the start.

• Why ψ² and not ψ³ or ψ⁴?: The mathematics of the surface layer integral, rooted in the Hilbert space scalar product, naturally produces sesquilinear expressions. This is not imposed by hand but follows from the structure of the theory. Finster sees the consistency of all these conservation laws as evidence the approach is on the right track.

• Wave function collapse explained: The stochastic background fields from the vacuum (described earlier) couple to matter and, combined with the nonlinearity of the causal action, produce collapse dynamics. This was shown in a 2024 paper with Claudio Paganini and Johannes Kleiner. The collapse is a consequence of the dynamics, not an additional postulate.

Octonions and Algebraic Structure

• Why octonions appear: The eight sectors of the vacuum (seven identical + one chiral quark sector) naturally carry the structure of the octonions (8-dimensional, non-associative). Octonions can be represented as 8×8 matrices acting on these sectors. The connection is being explored with Tejinder Singh (who has his own octonionic Standard Model) and Jose Isidro.

• Why not sedenions or split octonions?: The octonions are the largest division algebra (every nonzero element has an inverse). The sedenions (16-dimensional) are not a division algebra — they have zero divisors. This mathematical property may be why octonions are selected, but this is not yet proven. The connection between octonionic algebraic properties and the specific form of the causal Lagrangian is under active investigation.

Sociological Reflections on Fundamental Physics

• Why the theory was ignored for decades: Finster attributes the resistance to several factors: (1) young students are not taken seriously; (2) the ideas were initially vague and mathematically demanding; (3) physicists demand that any new theory reproduce all known results before they’ll engage — a standard no existing theory of everything meets; (4) the field is dominated by a few large communities (string theory, loop quantum gravity) that self-replicate through hiring and funding decisions made by established figures.

• Mathematics vs. physics culture: Finster found the mathematics community more tolerant — interesting rigorous mathematics is appreciated regardless of physical motivation. In physics, the standard is describing nature, which is harder and leaves less room for speculative exploration.

• The experiment gap: Much of theoretical high-energy physics has become disconnected from experiment. Without experimental guidance, criteria for theory selection become subjective (beauty, elegance, community consensus), which Finster finds problematic. He notes that communities connected to experiments (e.g., collapse model tests at Gran Sasso) are far more open-minded and less dogmatic.

• Advice to young researchers: Do what you truly love, because pursuing new ideas is a long uphill battle requiring deep persistence. Don’t chase fashionable topics (AI, big data) purely for career reasons — motivation will fade. But also don’t give up too early after initial discouragement from professors. Give ideas several years of serious effort before deciding whether to continue.

What Remains to Be Done

• Deriving Standard Model parameters: The regularization procedure introduces too many free parameters. Understanding the Planck-scale structure of spacetime better would reduce this.
• Quantitative baryogenesis: Computing the matter-antimatter asymmetry rate using realistic cosmological metrics.
• Quantum gravity: Making the connection between CFS and other quantum gravity approaches precise; understanding whether the graviton emerges and how.
• Simplifying the mathematics: Making the framework more accessible to physicists who lack deep mathematical training. PhD student Patrick Fisher is working on a more systematic computational framework (analogous to Feynman rules).
• Experimental predictions: Developing the theory to the point where it makes distinctive, testable predictions that could distinguish it from other approaches.