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Unruh versus Tolman: on the heat of acceleration

Dedicated to the memory of Rudolf Haag

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Abstract

It is shown that the Unruh effect, i.e. the increase in temperature indicated by a uniformly accelerated thermometer in an inertial vacuum state of a quantum field, cannot be interpreted as the result of an exchange of heat with a surrounding gas. Since the vacuum is spatially homogeneous in the accelerated system its temperature must be zero everywhere as a consequence of Tolman’s law. In fact, the increase of temperature of accelerated thermometers is due to systematic quantum effects induced by the local coupling between the thermometer and the vacuum. This coupling inevitably creates excitations of the vacuum which transfer energy to the thermometer, gained by the acceleration, and thereby affect its readings. The temperature of the vacuum, however, remains to be zero for arbitrary accelerations.

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Acknowledgments

We acknowledge stimulating critical comments by S.A. Fulling, G.L. Sewell and W.G. Unruh and an intense exchange with R.M. Wald on our differing views.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Göttingen, 37077, Göttingen, Germany

    Detlev Buchholz

  2. Institute for Theoretical Physics, University of Leipzig, 04009, Leipzig, Germany

    Rainer Verch

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  1. Detlev Buchholz
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  2. Rainer Verch
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Correspondence to Rainer Verch.

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Buchholz, D., Verch, R. Unruh versus Tolman: on the heat of acceleration. Gen Relativ Gravit 48, 32 (2016). https://doi.org/10.1007/s10714-016-2029-2

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