Demonstrating the Necessity of Relational Collapse in Viable Interpretations of Quantum Mechanics

Sky Nelson, MS

Independent Researcher in Physics

Wikipedia lists fourteen different “interpretations” of quantum mechanics, all based upon (mostly) the same mathematical axioms. A major unresolved problem in physics is to provide a rigorous reason for choosing one interpretation over the others. This paper shows that any quantum theory which is to be compatible with the basic postulates of special relativity must contain relational collapse of the wavefunction. This effectively rules out about half of the available options, including, notably, the Von Neumann and Copenhagen Interpretations.

Quantum theory limits what we are allowed to say about the “true” state of a quantum system if that system is unobserved. But special relativity relies fundamentally on a universal assumption about what a light particle is doing at ALL times (namely, traveling at speed c relative to any inertial observer, regardless of being observed). This fundamental conceptual gap between the theories is the starting point of the proof.

In resolving this impasse we show that the existence of light (and hence space and time) is not continuous. Since time dilation and length contraction become infinite for a photon, light can have no temporal or spatial interactions (Δt’ = 0, Δx’ = 0). To describe an interaction, the principle of simultaneity can be applied between an inertial observer and a light particle. Although light would register no separation between events, the Lorentz transform implies that the inertial observer measures a separation between those same events of exactly Δt = ΔL/c, a light-like separation. In other words, although light has no passage of time or space itself, light will always be measured by an observer at a position and time exactly as if it had travelled at speed c continuously through the medium. This fits nicely within the limitations set above by quantum mechanics, and leads to the necessary conclusion of relative states.

The author’s preferred interpretations of relational quantum mechanics and consistent histories quantum mechanics will be discussed. It will be pointed out that the relative state interpretation that is proven here is far more friendly to the possible existence of consciousness than its competing interpretations.