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Mordecai Waegell

Local Lorentz-Invariant Quantum Mechanics

Parallel Lives (PL) is an ontological model of nature in which quantum mechanics and special relativity are unified in a single universe with a single Minkowski space-time. Point-like objects called \emph{lives} are the only fundamental objects in this space-time, and they propagate at or below $c$, and interact with one another only locally at point-like events in space-time — somewhat like relativistic billiard balls. The only causes and effects in the universe occur when lives meet locally, and thus the causal structure of interaction events in space-time is Lorentz invariant. Each life traces a continuous world-line through space-time, and each life experiences its own \emph{relative world}, fully defined by the past events along its world-line. Despite the historical choice of the name, lives in PL are not alive in any biological sense, nor do they have any consciousness or decision-making power — they are just points along parallel word-lines. All quantum fields are sliced up into continua of point-like lives throughout space-time, and excitations like particles are the familiar physical systems in the universe — each comprising its own sub-continuum of lives. A pure universal quantum wavefunction tracks the collective behavior of the lives, but not their individual dynamics. There is a preferred separable basis for the Hilbert space of the universal wavefunction, and for a given physical system, each orthogonal term in this basis is a different relative world — each containing some fraction of the lives of the system. Hidden information about entanglement correlations in the universal wavefunction is shared locally by lives at all interaction events and carried in an internal ledger as they propagate. This hidden information governs which lives of different systems will meet during future interactions, and enforces entanglement correlations between the lives of the systems. All entanglement correlations — including Bell violations — are enforced by this local mechanism. The hidden information lives carry is just a local portion of the universal wavefunction, which is thus distributed throughout Minkowski space. As a result, configuration space is not a fundamental part of the PL ontology.

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