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arXiv 0705.2611hep-thgr-qcquant-ph
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卡西米尔能量如何下降?II。量子真空能的引力加速

How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

Kimball A. Milton, Prachi Parashar, K. V. Shajesh, Jef Wagner

摘要:

已经证明,量子真空能量的引力根据等效原理,至少对于有限的卡西米尔能量与完美的导电平行板。在这里,我们通过考虑作用于无质量标量场的平行双透明板,即δ函数势,在由Rindler坐标(tau,x,y,xi)定义的时空中,进一步支持这一结论。在这样的时空中,固定的xi代表均匀加速度。我们计算由一个或两个这样的板组成的系统在固定的xi值上的力。在大Rindler坐标xi的极限下,(小加速度),我们恢复(通过等效原理)弱引力的情况,发现系统所受的引力为Mg,其中g为引力加速度,M为系统的总质量,由各板块的质量分别由各板块的Casimir能量重整化而成,加上板块间卡西米尔相互作用的能量这再现了前面的结果在极限的耦合到δ函数潜力接近无穷大。

英文摘要:

It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. We here add further support to this conclusion by considering parallel semitransparent plates, that is, delta-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (tau,x,y,xi). Fixed xi in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of xi. In the limit of large Rindler coordinate xi (small acceleration), we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just Mg, where g is the gravitational acceleration and M is the total mass of the system, consisting of the mass of the plates renormalized by the Casimir energy of each plate separately, plus the energy of the Casimir interaction between the plates. This reproduces the previous result in the limit as the coupling to the delta-function potential approaches infinity.

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