Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability

Abstract

The inaccessibility to the experimenter agent of the complete quantum state is well-known. However, decisive answers are still missing for the following question: What underpins and governs the physics of agent inaccessibility? Specifically, how does nature prevent the agent from accessing, predicting, and controlling, individual quantum measurement outcomes? The orthodox interpretation of quantum mechanics employs the metaphysical assumption of indeterminism-'intrinsic randomness'-as an axiomatic, in-principle limit on agent-quantum access. By contrast, ontological and deterministic interpretations of quantum mechanics typically adopt an operational, in-practice limit on agent access and knowledge-'effective ignorance'. The present work considers a third option-'objective ignorance': an in-principle limit for ontological quantum mechanics based upon self-referential dynamics, including undecidable dynamics and dynamical chaos, employing uncomputability as a formal limit. Given a typical quantum random sequence, no formal proof is available for the truth of quantum indeterminism, whereas a formal proof for the uncomputability of the quantum random sequence-as a fundamental limit on agent access ensuring objective unpredictability-is a plausible option. This forms the basis of the present proposal for an agent-inaccessibility principle in quantum mechanics.

Discretization of the Bloch sphere, fractal invariant sets and Bell’s theorem

“…such properties cannot be found by reduced-precision computation. It can be noted that Penrose [30] has for many years speculated that non-computability may play a central role in deterministic reformulations of quantum theory; invariant set theory provides a specific [31] has concluded that the inaccessibility to the experimenter of the complete quantum state may be a consequence of non-computability at some deeper ontological level. Such non-computability is consistent with the fact that by finite precision, it is impossible for an experimenter to determine whether a putative Hilbert state is associated with finite squared amplitudes and phases, or not.…”

Emergent Quantum Mechanics: David Bohm Centennial Perspectives

“…Jan Walleczek advances the concept of agent inaccessibility as a fundamental principle in quantum mechanics, based on the objective uncomputability of quantum processes as a formal limit [ 2 ]. In support of the Bohmian theory, the proposal of an agent-inaccessibility principle presents an alternative position to the standard textbook view of quantum indeterminism.…”