The quantum formula of the fluctuation dissipation theorem (FDT) was given by Callen and Welton in 1951 [1] for the case of conductors, and then expanded by Kubo in 1966 [2, 3]. The drawback of these quantum relations concerns with the appearance of a zero-point contribution, hω/2 with h the reduced Planck constant and ω the angular frequency of the considered photon, which implies a divergence of the fluctuation spectrum at increasing frequencies. This divergence is responsible for a vacuum-catastrophe, to keep the analogy with the well-known ultraviolet catastrophe of the classical black-body radiation spectrum. As a consequence, the quantum formulation of the FDT as given by Callen-Welton and Kubo introduces a Field Grand Challenge associated with the existence or less of a vacuum-fluctuations catastrophe for the energy-density spectrum. Here we propose a solution to this challenge by taking into account of the Casimir energy that, in turns, is found to be responsible for a quantum correction of the Stefan-Boltzmann law.

卡伦和韦尔顿在1951年给出了波动耗散定理（FDT）的量子公式[1个”，然后由Kubo在1966年[2， 3]。这些量子关系的缺点与零点贡献的出现有关，ω/ 2与 H减小的普朗克常数和ω是所考虑的光子的角频率，这意味着在增加的频率下波动谱的发散。这种差异导致了真空灾难，从而与经典黑体辐射光谱的众所周知的紫外线灾难保持了类比。结果，Callen-Welton和Kubo给出的FDT的量子公式引入了一场场大挑战，与能量密度谱的真空波动灾难的存在或更少有关。在这里，我们通过考虑卡西米尔能量提出了解决这一挑战的解决方案，而卡西米尔能量又被发现负责斯蒂芬-玻尔兹曼定律的量子校正。