A non-collapse scenario for ``conscious'' selection of a term from a superposition was proposed in quant-ph/0309166: thermally assisted tunneling of neuronal pore molecules. But ``observers'' consisting of only two neurons appear to be at odds with Born's rule. In the present paper, an observer is assumed to possess a large number of auxilliary properties irrelevant for the result of the measurement. Born's rule then reduces to postulating that, prior to the result becoming conscious, irrelevant properties are in an entangled state with maximum likelihood, in the sense that phase-equivalent entanglements cover a maximal fraction of the unit sphere (leading to equal-amplitude superpositions).
A non-collapse scenario for conscious'' selection of a term from a superposition was proposed in quant-ph/0309166: thermally assisted tunneling of neuronal pore molecules. But observers'' consisting of only two neurons appear to be at odds with Born's rule. In the present paper, an observer is assumed to possess a large number of auxilliary properties irrelevant for the result of the measurement. Born's rule then reduces to postulating that, prior to the result becoming conscious, irrelevant properties are in an entangled state with maximum likelihood, in the sense that phase-equivalent entanglements cover a maximal fraction of the unit sphere (leading to equal-amplitude superpositions).
Chapter 3 describes how quantum entanglement leads to probabilities based on a symmetry, but—in contrast to subjective equal likelihood based solely on ignorance—it is an objective symmetry of known quantum states. Entanglement-assisted invariance (or envariance for short) relies on quantum correlations: One can know the quantum state of the whole and use this to quantify the resulting ignorance of the states of parts. Thus, quantum probability is, in effect, an objective consequence of the Heisenberg-like indeterminacy between global and local observables. This derivation of Born’s rule is based on the consistent subset of quantum postulates. It justifies statistical interpretation of reduced density matrices, an indispensable tool of decoherence theory. Hence, it gives one the mandate to explore—in Part II of this book—the fundamental implications of decoherence and its consequences using reduced density matrices and other customary tools.
The quantum measurement problem—why measurement yields a single definite outcome, and why that outcome follows the Born rule P(i)=|c_i|²—has for nearly a century been treated as a postulate rather than a derivable consequence. This paper proposes that measurement is not an extraneous process tacked onto quantum mechanics; it is the natural execution of the settlement operation Ŝ(Θ). The core settlement cost functional is defined as C[ρ]=D_KL(ρ∥ρ_target)+β·Tr(ρH)−η·N(ρ). Three core results are obtained: (1) The Born rule P(i)=|c_i|² is strictly derived as the statistical limit of KL divergence minimization under projective measurement, requiring no additional postulates; (2) Wavefunction collapse is reinterpreted as irreversible settlement commitment. The stochasticity and nonlinearity of collapse originate from discrete Kraus branch selection of settlement operations; (3) A finite non-zero settlement delay τ_settle is predicted, which varies with consciousness parameters C, Q, A, I. High-coherence observers (C>0.8) possess far shorter settlement delay than ordinary humans or electronic detectors. This paper gives the explicit formula τ_setle=1/[η₀·C·Q·(1−A)·I] and designs a delayed-choice Bell experiment based on SPDC entangled photons for experimental verification. Predictions P1 and P3 from the series provide direct experimental channels to test this settlement framework. quantum measurement problem, Born rule, wavefunction collapse, settlement choice, settlement delay, consciousness parameters, two-phase settlement, Ξ-field
If conscious observers are to be included in the quantum mechanical universe, we need to find the rules that engage observers with quantum mechanical systems. The author has proposed five rules that are discovered by insisting on empirical completeness; that is, by requiring the rules to draw empirical information from Schrodinger's solutions that is more complete than is currently possible with the (Born) probability interpretation. I discard Born's interpretation, introducing probability solely through probability current. These rules tell us something about brains. They require the existence of observer brain states that are neither conscious nor unconscious. I call them 'ready' brain states because they are on stand-by, ready to become conscious the moment they are stochastically chosen. Two of the rules are selection rules involving ready brain states. The place of these rules in a wider theoretical context is discussed. Key Words: boundary conditions, consciousness, decoherence, macroscopic superposition, Penrose, state reduction, von Neumann, wave collapse.
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required to engage and interpret the Schrodinger solutions in individual measurements. The rules in this paper (called the nRules) do not include the Born rule that connects probability with square modulus. It is required that the rules allow all conscious observers to exist inside the system without empirical ambiguity, reflecting our own unambiguous experience in the universe. This requirement is satisfied by the nRules. They allow both objective and observer measurements, so state reduction can occur with or without an observer being present. Keywords: brain states, consciousness, decoherence, epistemology, measurement, ontology, stochastic, state reduction, wave collapse.
We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.
Tunnel amplitudes of molecular configurations (like neuronal channel pores) may be very sensitive to thermal vibrations of the barrier width (vibration-assisted tunneling) resulting in pseudo-random spikes of widely varying sizes. An observer who ``lives'' behind the barrier would experience as an ``event'' an accidental minimum of the barrier width, the timing being determined by the microstate of the neuron's heat bath. In two neurons, set to detect a ``left'' or ``right'' state of an object, firing amplitudes typically differ so much as to produce a quasi-selection of one option.