Chapter 11. Causality in a New Double Slit Experiment and in Epr

Manuel Bernardo Muñoz Bastias

This chapter completes the physical groundwork of the thesis by examining quantum mechanics, the second of the two theories that the following chapters interpret philosophically. Rather than offering an exhaustive mathematical treatment, it selects the concepts required to follow the two transversal principles identified in Chapter 3: causality and the principle of stationary action. It presents the emergence of the quantum of action, the formal structure of the theory (states, observables, Born’s rule, Schrödinger dynamics, superposition and entanglement), the double-slit experiment, the uncertainty principle, the measurement problem, and the sequence formed by the EPR argument, Bell’s theorem and its experimental tests. Using the three senses of causality distinguished in Chapter 3, the chapter shows that Heisenberg’s 1927 attempt to refute the law of causality did not succeed: unitary evolution preserves dynamical determination at the level of the quantum state, while the no-signalling condition and relativistic microcausality preserve causal precedence and causal propagation, even though Bell-local models fail. It then shows that action, present at the very birth of the theory as Planck’s quantum of action, governs quantum dynamics through Feynman’s path integral and Schwinger’s quantum action principle, and that the classical principle of stationary action re-emerges in the classical limit. The principal result, restricted to physics, is that causality and stationary action are transversal to classical, relativistic and quantum physics, although their mathematical formulation changes. Ontological conclusions are reserved for the following chapters.

Raphael Neelamkavil

Raphael Neelamkavil

Tamoor .A Zaidi

Building upon the unified 4D geometry of the Causal Smoothing Framework, this paper resolves three foundational paradoxes of quantum mechanics: wave-particle duality in the double-slit experiment, the measurement problem (wave function collapse), and the origin of particle-antiparticle asymmetry. By defining particles as time-like topological knots (ds² < 0) and quantum fields as the deterministic causal smoothing of vacuum momentum fluxes along the null boundary (ds² = 0), this framework discards probabilistic observer-driven collapse. The double-slit experiment is analyzed under two distinct boundary conditions (continuous emission and single-particle emission), demonstrating that quantum statistics are simply the macroscopic interference of vacuum geometry guiding discrete knots through a chaotic ER=EPR substrate. Furthermore, the framework provides a strict geometric proof for why fermions require distinct antiparticles while gauge bosons act as their own antiparticles, rooted entirely in the chiral phase of the localized metric shear.

Michel Gondran, Alexandre Gondran

We propose a pedagogical presentation of measurement in the de Broglie-Bohm interpretation. In this heterodox interpretation, the position of a quantum particle exists and is piloted by the phase of the wave function. We show how this position explains determinism and realism in the three most important experiments of quantum measurement: double-slit, Stern-Gerlach, and EPR-B. First, we demonstrate the conditions in which the de Broglie-Bohm interpretation can be assumed to be valid through continuity with classical mechanics. Second, we present a numerical simulation of the double-slit experiment performed by Jönsson in 1961 with electrons. It demonstrates the continuity between classical mechanics and quantum mechanics. Third, we present an analytic expression of the wave function in the Stern-Gerlach experiment. This explicit solution requires the calculation of a Pauli spinor with a spatial extension. This solution enables us to demonstrate the decoherence of the wave function and the three postulates of quantum measurement. Finally, we study the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time shows that a causal interpretation exists where each atom has a position and a spin.

Arkady Plotnitsky