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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

On velocity and the transverse doppler effect in the six-dimensional space. A hidden-variable model?

P. T. Pappas

Published Jun 1, 1980• 4 citations
Publisher
DOI
10.1007/bf02770199

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We present a three-dimensional theoretical comparison between the radiation-pressure forces exerted on an atom in an isotropic light cooling scheme and in a six-beam molasses. We demonstrate that, in the case of a background vapor where all the space directions of the atomic motion have to be considered, the mean cooling rate is equal in both configurations. Nevertheless, we also point out what mainly differentiates the two cooling techniques: the force component orthogonal to the atomic motion. If this transverse force is always null in the isotropic light case, it can exceed the radiation-pressure-force longitudinal component in the six-beam molasses configuration for high atomic velocities, hence reducing the velocity capture range.
The effects of Doppler broadening on Autler-Townes (AT) splitting in six-wave mixing (SWM) are investigated by the dressed-state model. We analyze the velocities at which the atoms are in resonance with the dressed states through Doppler frequency shifting and find that, depending on the wave-number ratio, there may be two resonant velocities which can originate from resonance with one of the dressed states or from resonance with two different dressed states. Based on this model, we discuss a novel type of AT doublet in the SWM spectrum, where macroscopic effects play an important role. Specifically, the existence of resonant peaks requires polarization interference between atoms of different velocities in addition to a change in the number of resonant atoms involved. Our model can also be employed to analyze electromagnetically induced transparency resonance and other types of Doppler-free high-resolution AT spectroscopy.
According to the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, but we found that the electromagnetic force of the Maxwell's theory can not completely satisfy this orthogonality, this incompletion leads us to find that the electromagnetic force has two independent components in the 4 dimensional space time. A 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the force reduces to 3, while the electromagnetic force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the electromagnetic force. This missing undefined component may serve as a hidden variable which quantum mechanics is eager to find for a long time. The primary purpose of this paper is to strictly proof that the electromagnetic force has two independent components in the 4 dimensional space time. We also briefly discuss the possibility that the undefined component of the electromagnetic force serves as a hidden variable for quantum mechanics.