The characteristic difference between the paleoquantal calculation (addition of partial probabilities) and the neoquantal one (addition of partial amplitudes) for the correlation of photon polarizations in cascade transitions is derived in terms of elementary trigonometry. This deliberate use of simple formulae aims at a transparent rendering of the change in paradigm required by the so-called EPR paradox (which is truly the 1927 Einstein paradox), namely that 1) the two photons donot possess polarizations of their own when leaving the source C, butborrow onelater, when interacting with the analysersL andN; 2) the die is thus not cast atC, but later, atL andN; 3) the correlation between the measurements atL andN is tied throughC, in their common past. The tight connection between this « Einstein nonseparability » and the nonlocality in Feynman’s « theory of positrons » is demonstrated through an analysis of the e+e+ annihilation into two photons. Thus the Einstein paradoxcorresponds, in the « new wavelike probability calculus », to the Loschmid and Zermelo sort of paradox in the old probability calculus. That is, it contrasts theintrinsic time symmetry existing at the elementary level to thefactlike macroscopic time asymmetry. Our discussion deliberately by-passes the hidden-variable problem, our model in this being Einstein’s by-passing of the mechanical aether when proposing special relativity. We believe that here today, like there in 1905, the problem istayloring the wording after the (operationally good)mathematics. Moreover, that the change in paradigm, which is needed, comes through a victory of formalism over modelism.

Time symmetry and the Einstein paradox

The de Broglie-Bohm theory of motion and quantum field theory

Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.

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Experimental nonlocal and surreal Bohmian trajectories.

The particle internal clock conjectured by de Broglie in 1924 was investigated in a channeling experiment using a beam of ~80 MeV electrons aligned along the 〈110〉 direction of a 1 μm thick silicon crystal. Some of the electrons undergo a rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0° shows a 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which the frequency of atomic collisions matches the electron's internal clock frequency. A model is presented to show the compatibility of our data with the de Broglie hypothesis.

A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling

The fundamental impasses and ruptures in various domains of the canonical, unitary science, or the 'end of science', become the more and more evident. The natural unity of being is recovered within a universal nonperturbative method leading to the dynamic redundance paradigm. It is shown that the unreduced behaviour of any nontrivial (isolated) system includes many equally real, but incompatible dynamic regimes, each of them being roughly equivalent to an ordinary 'complete' solution of the unitary science. Therefore the regimes should 'spontaneously' and randomly replace one another, which provides a universal, purely dynamic origin of randomness. The discovered dynamic redundance leads to the universal, reality-based concept of dynamic complexity and its permanently developing hierarchical structure, alias the world. Its lowest levels give the causally complete mechanics of dynamically quantized elementary fields, extending the double solution found by Louis de Broglie. One obtains a physically complete solution for the 'mysteries' of quantum mechanics, unifyng it with the extended, causal versions of relativity (emergent space and time), quantum and classical gravity (dynamical mass), field theory (electric charge and spin), particle physics, and cosmology. The same key features of the unreduced dynamic complexity determine behaviour of any system at higher levels of complexity described by a case of the single, universal equation in its two related versions, the extended Lagrange-Hamilton (trajectorial) and Schroedinger (distributional) equations. The end of the unitary science opens the renaissance of the ultimately complete and universal understanding initiated by Rene Descartes (but then mechanistically falsified), which is confirmed by many sound, practically important results.

Universal concept of complexity by the dynamic redundance paradigm: Causal randomness, complete wave mechanics, and the ultimate unification of knowledge

L. Morton

Papers

Une Tentative d'Interprétation Causale et non Linéaire de la Mécanique Ondulatoire