A New Field Method for pH Determination

Bell inequalities for random fields

“…which is enough to fix the Wightman functions of the quantum field (by linearity, e iλφ f +iµφg = e iφ λf +µg , which we can use to construct a multivariate characteristic function). Other sectors can be constructed by changing the right-hand side, which, as well as thermal sectors, include "extra quantum fluctuation" sectors [20],…”

“…The algebras of observables are not the same, but the state over the classical algebra is sufficiently similar to the vacuum state over the quantum algebra to make it reasonable to call the random field state a presentation of "quantum fluctuations". Certainly the amplitude of the fluctuations of the random field is controlled byh and the fluctuations are distinct from the thermal fluctuations of a classical Klein-Gordon field, which can be presented as ϕ C (e iλχ f ) = e − 1 2 λ 2 (f,f ) C , with the Lorentz non-invariant inner product This thermal state can be presented either with a trivial commutator [χ f ,χ g ] = 0 or with the commutator [χ f ,χ g ] = (g, f ) C − (f, g) C , depending on whether we wish to use models in which idealized measurements are always compatible or generally not compatible at time-like separation because of thermal fluctuations (see [20]). The difference between quantum fields and random fields can be taken to be only a different attitude to idealized measurements; actual measurements can be described in terms of either.…”