Non-classical correlations in reducible quantum electrodynamics

Abstract

The question is discussed whether the momentum of a photon has a quantum uncertainty or whether it is a classical quantity. The latter assumption is the main characteristic of reducible Quantum Electrodynamics (QED). Recent experiments in Quantum Optics may resolve the question. The non-classical correlation of quantum noise in color-entangled beams cannot be explained by reducible QED without modification of the standing explanation. On the other hand, reducible QED explains uncertainty of the momentum of a single photon when it is entangled with a quantum spin residing in its environment. The explanation of the historical experiment with equally-polarized pairs of photons, showing violation of the Bell inequalities, invokes the argument of collapse of the wave function, also in reducible QED. k k H y = ñ ¢ ¢ | †. The present paper questions whether states of the form (1) or (2) do occur in Nature. If they don't then a modified theory of QED, such as reducible QED, is needed.The original picture behind QED is that Euclidean space is filled with two-dimensional quantum harmonic oscillators the excitations of which are photons. Marek Czachor suggested [11] that the frequency of these oscillators should be quantized as well. Together with his collaborators he developed a non-canonical theory of QED. See [11][12][13][14][15][16][17][18] and references quoted in these papers. One of the main results of the theory is that QED after renormalization is recovered as a limiting case, without the need to fall back on ad hoc procedures like renormalization. On the other hand, an attempt to force the formalism into a mathematically rigorous framework was not successful [19].

Gauge transformations of a relativistic field of quantum harmonic oscillators

“…See [6,7,8,9] and references given there. The present author introduced a simplified formalism [10,11,12]. By starting from gauge transformations, as is done here, the possibility of a rigorously formulated QED can be investigated in a more systematic manner.…”