双光子衰变引力及其量子相干性
Gravity of Two Photon Decay and its Quantum Coherence
摘要：
导出了质量为$M$的粒子衰变为一对零粒子时产生的引力激波的线性解析解。所得到的时空被证明是未扰动和各向同性的，除了一个不连续的扰动球零壳。公式推导出作为极角的函数的扰动，作为测量的观察员在原点观察距离$R$的球体上的时钟。冲击的影响在物理上被解释为冲击通过时钟时在时间和速度上的瞬时位移。的时间位移被证明是各向异性的，占主导地位的四极谐波对齐的粒子衰变轴，与幅度$δτ\sim GM/c^3$，独立的$R$。速度位移是各向同性的。该解被用来导出一个量子态的引力效应，该量子态由大量随机取向的、统计各向同性的粒子衰变叠加而成。这种方法被证明是提供一个良好的控制近似估计系统的引力波动的幅度由点粒子到普朗克能量的因果菱形的持续时间$τ= 2R/c$，以及量子引力波动的黑洞和宇宙学视野。相干大角度量子扭曲的宏观几何从波动到普朗克尺度的增长与持续时间呈线性关系，与方差$\langle δτ^2\rangle\sim τt_P$远远大于模型中产生的因果量子相干性。
英文摘要：
A linear analytical solution is derived for the gravitational shock wave produced by a particle of mass $M$ that decays into a pair of null particles. The resulting space-time is shown to be unperturbed and isotropic, except for a discontinuous perturbation on a spherical null shell. Formulae are derived for the perturbation as a function of polar angle, as measured by an observer at the origin observing clocks on a sphere at distance $R$. The effect of the shock is interpreted physically as an instantaneous displacement in time and velocity when the shock passes the clocks. The time displacement is shown to be anisotropic, dominated by a quadrupole harmonic aligned with the particle-decay axis, with a magnitude $δτ\sim GM/c^3$, independent of $R$. The velocity displacement is isotropic. The solution is used to derive the gravitational effect of a quantum state with a superposition of a large number of randomly oriented, statistically isotropic particle decays. This approach is shown to provide a well-controlled approximation to estimate the magnitude of gravitational fluctuations in systems composed of null point particles up to the Planck energy in a causal diamond of duration $τ= 2R/c$, as well as quantum-gravitational fluctuations of black holes and cosmological horizons. Coherent large-angle quantum distortions of macroscopic geometry from fluctuations up to the Planck scale are shown to grow linearly with the duration, with a variance $\langle δτ^2\rangle\sim τt_P$ much larger than that produced in models without causal quantum coherence.
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