1,504 research outputs found
Linear superposition as a core theorem of quantum empiricism
Clarifying the nature of the quantum state is at the root of
the problems with insight into (counterintuitive) quantum postulates. We
provide a direct-and math-axiom free-empirical derivation of this object as an
element of a vector space. Establishing the linearity of this structure-quantum
superposition-is based on a set-theoretic creation of ensemble formations and
invokes the following three principia: quantum statics,
doctrine of a number in the physical theory, and
mathematization of matching the two observations with each
other; quantum invariance.
All of the constructs rest upon a formalization of the minimal experimental
entity: observed micro-event, detector click. This is sufficient for producing
the -numbers, axioms of linear vector space (superposition
principle), statistical mixtures of states, eigenstates and their spectra, and
non-commutativity of observables. No use is required of the concept of time. As
a result, the foundations of theory are liberated to a significant extent from
the issues associated with physical interpretations, philosophical exegeses,
and mathematical reconstruction of the entire quantum edifice.Comment: No figures. 64 pages; 68 pages(+4), overall substantial improvements;
70 pages(+2), further improvement
The Analysis of Space-Time Structure in QCD Vacuum II: Dynamics of Polarization and Absolute X-Distribution
We propose a framework for quantitative evaluation of dynamical tendency for
polarization in arbitrary random variable that can be decomposed into a pair of
orthogonal subspaces. The method uses measures based on comparisons of given
dynamics to its counterpart with statistically independent components. The
formalism of previously considered X-distributions is used to express the
aforementioned comparisons, in effect putting the former approach on solid
footing. Our analysis leads to definition of a suitable correlation coefficient
with clear statistical meaning. We apply the method to the dynamics induced by
pure-glue lattice QCD in local left-right components of overlap Dirac
eigenmodes. It is found that, in finite physical volume, there exists a
non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at
smaller (fixed) eigenvalues exhibit convex X-distribution (positive
correlation), while at larger eigenvalues the distribution is concave (negative
correlation). This chiral polarization scale thus separates a regime where
dynamics enhances chirality relative to statistical independence from a regime
where it suppresses it, and gives an objective definition to the notion of
"low" and "high" Dirac eigenmode. We propose to investigate whether the
polarization scale remains non-zero in the infinite volume limit, in which case
it would represent a new kind of low energy scale in QCD.Comment: v2: 38 pages, 12 figures, author-preferred version; v3:
journal-preferred versio
- …