# The Theory of Causal Fermion Systems

## Wave Function Collapse

### Prerequisites

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## Wave Function Collapse

It is an outstanding open problems of contemporary physics to reconcile the linear dynamics of quantum theory with the reduction of the state vector in a measurement process. Different solutions to this so-called *measurement problem* have been proposed, among them Bohmian mechanics, the many-worlds interpretation and objective-collape theories.

In [FKP24] is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. In this way, the measurement problem is solved from first principles starting from a fundamental physical theory.

The causal action principle gives rise to corrections to the linear dynamics of Quantum Theory:

- Nonlinear corrections come about because the Euler-Lagrange equations are nonlinear equations.
- As shown in [F23], the linearized field equations in Minkowski space admit a multitude of solutions (→ construction of linear fields and waves). Describing all the linearized bosonic fields stochastically gives rise to stochastic corrections.

Working out the resulting correction terms in the non-relativistic limit, one gets the followig results: The dynamics of the statistical operator is described by a deterministic equation of Kossakowski-Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale $\ell_{\min}$.

### Felix Finster

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