from the point of view of the physical behavior of the detectors. To preserve maximum generality, we adopt a non-factorisable expression of joint detection probabilities (we suspect it is a necessary condition to match quantum correlations, an issue we will examine elsewhere): such non-factorability on (the vacuum amplitudes) is simply an indicator of the need to introduce other (vector of) additional variables in the model, that would possibly correspond to other relevant physical variables related to the laser and the state of the crystal. A conjecture: for the simplest possible model, may possibly correspond to the phase of the laser complex amplitude (or its relative value with respect to ’s). As a correction on initial versions or this paper, such additional -dependence is now introduced directly within the intensities Ii( ) ! Ii(; ) at each (the i-th) detector, which introduces no conceptual change in our initial approach but preserves a reasonable dependence of the probability of detection on the incoming intensity alone: Pi(detj; ) f(I(; )) instead of our former Pi(detj; ) f(I( ); ). For completeness, we also treat some closely related issues, such as: (i) the appearance of (detection probability) enhancement in this framework, (ii) the interpretation of that mysterious \subtraction of the average ZPF intensity at the detector, and (iii) why vacuum uctuations are not directly \observable. Points (i) and (iii) are developed in side-notes [14] and [15], respectively. PACS numbers:
from the point of view of the physical behavior of the detectors. To preserve maximum generality, we adopt a non-factorisable expression of joint detection probabilities (we suspect it is a necessary condition to match quantum correlations, an issue we will examine elsewhere): such non-factorability on (the vacuum amplitudes) is simply an indicator of the need to introduce other (vector of) additional variables in the model, that would possibly correspond to other relevant physical variables related to the laser and the state of the crystal. A conjecture: for the simplest possible model, may possibly correspond to the phase of the laser complex amplitude (or its relative value with respect to ’s). As a correction on initial versions or this paper, such additional -dependence is now introduced directly within the intensities Ii( ) ! Ii(; ) at each (the i-th) detector, which introduces no conceptual change in our initial approach but preserves a reasonable dependence of the probability of detection on the incoming intensity alone: Pi(detj; ) f(I(; )) instead of our former Pi(detj; ) f(I( ); ). For completeness, we also treat some closely related issues, such as: (i) the appearance of (detection probability) enhancement in this framework, (ii) the interpretation of that mysterious \subtraction of the average ZPF intensity at the detector, and (iii) why vacuum uctuations are not directly \observable. Points (i) and (iii) are developed in side-notes [14] and [15], respectively. PACS numbers:
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward "subtraction" of the average ZPF intensity at the Wigner image of the detection process.
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward subtraction of the average ZPF intensity at the Wigner image of the detection process.
Within the Wigner-PDC picture of photon entanglement, detection "errors" are not independent (though they may look, on average), nor can they be controlled by means of a technological improvement on the detectors. Those two elements make possible the interpretation of experimental evidence without the need to exclude local realism: for that reason, we propose the abandonment of the usual (photon, particle-based) description of (PDC-generated) light states, in favour of an also quantum, but field-theoretical description (QED), a description that finds a one-to-one equivalent in the Wigner-PDC approach we have advocated in recent posts.
In this paper, the nexus between the Bell-state measurement and extracting phase information from the zeropoint field is investigated. For this purpose, the Wigner representation in the Heisenberg picture is applied in a Bell-type experiment in which the polarisation-entangled photon pairs generated in a type-II parametric down-conversion do not overlap. The signal intensities at the detectors are calculated in a four-mode approximation, being expressed as functions of the modules and phases of the four zeropoint amplitudes entering the crystal. A general criterion for identifying the correlated detectors is proposed based on the equality of the signal intensities, and without involving the calculation of the joint detection probabilities. In addition, from the analyses in the rectilinear and diagonal basis, it is shown that the distinguishability of the polarisation Bell states, which is in direct correspondence with the joint detection events in each experiment, can be related to the knowledge of the phases of the vacuum field entering the entanglement source, and giving rise to correlated detections. To this purpose, it is conjectured that a detection event is associated with a maximum value of the signal intensity averaged in the modules of the zeropoint amplitudes, as a function of the vacuum phases.
What i Really RepresentsFrom Spacetime Action to Quantum Phase: The Imaginary Unit as aMarker of Action-Phase GeometryPeter Davies, v1.0230th April, 2026AbstractQuantum mechanics differs from classical probability theory by assigning complex amplitudes rather than real probabilities to physical alternatives. The appearance of the imaginary unit i in the Schr¨odinger equation, unitary time evolution, path integrals, gauge transformations, and geometric formulations of quantum mechanics suggests that i is not merely a calculational artifact.This paper argues that i is best understood as the algebraic marker of action-phase geometry: the phase-rotation structure through which action, measured in units of ℏ, becomes a probability-preserving quantum amplitude. In this interpretation, spacetime geometry determines the action accumulated along possible histories, while quantum mechanics maps this action into phase through eiS/ℏ. The constants ℏ and h acquire complementary interpretations: ℏ is action per radian of phase, while h = 2πℏ is action per full phase cycle. Observable probabilities arise only after interference among phase-weighted histories, with the final quadratic product converting the surviving amplitude structure into measurable probability. The paper develops this interpretation through phase gradients, action periodicity, proper-time phase, gauge connections, gravitational phase modulation, light–matter phase matching, and multi-photon interference. The proposed contribution is not a replacement of quantum mechanics, quantum field theory, or general relativity, but a conceptual synthesis: the repeated appearance of i, ℏ, h, action, proper time, and interference may be understood as different aspects of a single action-phase structure linking spacetime and quantum mechanics. The proposal is interpretive rather than a Bell-local hidden-variable completion of quantum mechanics. It does not assign pre-existing local outcome values to measurement events, and it is intended to remaincompatible with the nonclassical correlation structure required by Bell-type results. - Preprint version v1.02. This manuscript presents a conceptual framework and has not yet undergone peer review. Later versions may incorporate corrections, expanded references, and feedback on framing.