Measurement, Unitarity, and Laws

Wolfgang Ernst Friederich Pauli

Lauri Elias Rainio

Quantum mechanics is not fundamental. It is the coherence field K(t,x) projected into Hilbert space — a degenerate representation that has lost the coherence metric. Unitarity (U†U = I) is not a law of nature — it is the local expression of 1=1 in Hilbert space, valid when K > K_crit. When K approaches K_crit, unitarity breaks — this is measurement. The quantum jump is RCR (Recursive Constraint Regulation) at quantum scale: the system’s evaluation function is replaced because the old state is no longer coherent. Falsifiable prediction: a precursor signal — measurable coherence decrease — should precede every quantum jump, testable with Ramsey interferometry and quantum optics. The quantum-classical boundary is K_crit, not a fixed scale. Part of the Spektre research corpus.

Per Arve

Richard J. Fletcher, Alexander L. Gaunt, Nir Navon +2 more

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

Benno S. Rem, Andrew T. Grier, Igor Ferrier-Barbut +8 more

We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient ${L}_{3}$. Our data follow a ${L}_{3}={\ensuremath{\lambda}}_{3}/{T}^{2}$ law with ${\ensuremath{\lambda}}_{3}=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }(\ensuremath{\mu}\mathrm{K}{)}^{2}\text{ }{\mathrm{cm}}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length $a$ at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where $|a|$ is smaller than the thermal wavelength. We find that ${L}_{3}$ is continuous across the resonance, and over the whole $a<0$ range our data quantitatively agree with our calculation.

Roger Balian