Acceleration and vacuum temperature

The quantum fluctuations of an “accelerated” vacuum state, that is, vacuum fluctuations in the presence of a constant electromagnetic field, can be described by the temperature $T_{\mathrm{M}}$. Considering $T_{\mathrm{M}}$ for the gyromagnetic factor $g=1$ we show that $T_{\mathrm{M}}(g=1)=T_{\mathrm{U}}$, where $T_{\mathrm{U}}$ is the Unruh temperature experienced by an accelerated observer. We conjecture that both particle production and nonlinear field effects inherent in the Unruh accelerated observer case are described by the case $g=1$ QED of strong fields. We present rates of particle production for $g=0$, 1, 2 and show that the case $g=1$ is experimentally distinguishable from $g=0$, 2. Therefore, either accelerated observers are distinguishable from accelerated vacuum or there is unexpected modification of the theoretical framework.

Figure 1

The rate per unit volume of decay of the field $d\Gamma /d^{4}x=2\mathtt{I}\mathtt{m}{V}_{\mathrm{eff}}$ with $\mathtt{I}\mathtt{m}{V}_{\mathrm{eff}}$ given by Eq. (14). The electric field magnitude is normalized to ${\mathcal{E}}_c=m^2/e$ the critical field strength, at which $T_{\mathrm{M}}\to m/\pi$. For $g\ne 2$ the rate of field decay is reduced with the largest reduction for $g=1$. Above ${\mathcal{E}}_c$ we see suppression due to the $g$ factor modifying weights in the sum in Eq. (14).