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Rotation in classical zero-point radiation and in quantum vacuum

Yefim S. Levin
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Abstract

Two reference systems (RS) are defined and used as the basis for investigating thermal effects of rotation through both random classical zero point radiation and quantum vacuum. Both RSs consist of an infinite number of instantaneous global inertial reference frames (RF). The RFs do not accompany the detector and are defined so that at each moment of proper time of the detector there are two RFs belonging with different RSs. These RFs agree momentarily, are connected by a Lorentz transformation with the detector velocity as a parameter, and with origins at the detector location at the same proper time. The two- field correlation functions (CF) measured by the observer rotating through a random classical zero point radiation have been calculated and presented in terms of elementary functions for both electromagnetic and massless scalar fields. If the CFs are periodic with a period of rotation the observer finds the spectrum which is very similar, but not identical, to Plank spectrum. If both fields of such a two-field periodic CF, for both electromagnetic and massless scalar case, are taken at the same point then its convergent part is shown, using Abel-Plana summation formula, to have Planck spectrum with the temperature T= hw/k, where w is an angular velocity of the detector. It is shown that the vacuum of the quantized massless scalar field in rotating RS is not equivalent to the vacuum of the field in the laboratory system because the respective Bogolubov transformation is not a zero.

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Yefim S. Levin. 2006-06-02. Rotation in classical zero-point radiation and in quantum vacuum. https://arxiv.org/abs/math-ph/0606009

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