A Model of Nonlocal Quantum Electrodynamics; Time's Arrow and Epr-Like Quantum Correlation

Abstract

A recent experiment with squeezed light has shown that two-photon absorption by an atom can occur with a linear intensity dependence. We point out that this result verifies a prediction made by us a decade back from an analysis of a non-local model of Quantum Electrodynamics. This model had earlier been proposed by us in an ad hoc manner to interpret certain features of multiphoton double ionisation and above-threshold ionisation in an atom placed in a strong laser field ; in this paper we show that the model can be obtained field-theoretically by demanding covariance of the field Lagrangian under a nonlocal U(1) gauge transformation. We also show that the model makes direct contact with squeezed light, and thus allows us to describe these two completely different scenarios from a unified point of view. We obtain a fundamentally new result from our non-local model of QED, namely that only the past, but not the future, can influence the present -thus establishing a non-thermodynamic arrow of time. We also show that correlations within a quantum system should necessarily be of the Einstein-Podolsky-Rosen (EPR)-type, a result that agrees with Bell's theorem. These results follow from the simple requirement of energy conservation in matter-radiation interaction. Furthermore, we also predict new and experimentally verifiable results on the basis of our model QED.

Father Time Ii: A Physical Basis Behind Feynman's Idea of (Anti)particles Moving Backward in Time, and an Extension of the CPT Theorem to Include Nonlocal Gauge Fields

“…To make the present paper self-contained, we briefly recapitulate here how the time's arrow appears in the theory as a necessary condition for conservation of energy in the atomic level. (See [1] for details.) A matrix element for matter-radiation interaction with the non-local electromagnetic field potential A(x, x ′ ) where x≡(r,t) is typically of the form…”

“…After Fourier expanding A in two sets of photon modes (see, e.g. [6]), the time integration over dt gives us the energyconserving delta-function δ(E f , E i +hω +hω ′ ) in the correlated two-photon absorption process (see below ; this is one of the new results in [1]). Formally, this time integration runs from t = −∞ to t = +∞.…”

“…We may ask the question from the opposite viewpoint : what happens in a reaction if one or more of the reactants/products travel backward in time ? According to [1], the answer is simple ; energy will not be conserved, hence mass↔energy conversion must occur in such reactions. (Of course, the precise time interval between the "start" of the reaction and the mass↔energy conversion depends on the particular characteristics in the process involved ; for example, positron-electron annihilation can take place either instantaneously or after positronium formation, depending on the collision geometry.…”

“…(This invariance is not quite self-evident, as we remember that the CPT theorem is supposed to be valid for local field theories only ; our work seems to have broadened its scope.) c As shown in [1], however, we have to pay a price for it ; the correlation with the "past" is to be understood in an EPR-like sense and not in a Lorentz invariant sense, if we are to maintain energy conservation. (This serves to remind us that quantum mechanics and special relativity have always been strange bedfellows.)…”

“…Some time ago [1] we obtained a result that matter fields possess a non-local U(1) gauge transformation symmetry that necessitates invoking a non-local electromagnetic field, and that a non-thermodynamic arrow of time at the quantum (atomic) level is enforced upon us as a necessary condition for conservation of energy in matter-radiation interactions. Based upon this result, it was subsequently predicted [2] that the spectrum of a blackbody radiation passing through gaseous matter would show an apparent deviation from the Planck formula.…”