We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10⁻⁶ degree to 10⁻⁴ degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.

我们描述了光子状态的量子力学旋转，即维格纳旋转——一种将参考系的变换与粒子的自旋耦合的量子效应，以研究地球引力场引起的几何相位，供不同轨道上的观察者使用。除了标准名望的旋转之外，我们发现了维格纳旋转角的潜在可测量量子相位，后者被计算并且与大地测量旋转非常吻合。当观察者处于包含非零角动量的圆形或螺旋轨道中时，额外的量子相位贡献 10 ^-6度到 10 ^-4度分别取决于地球轨道的高度。在前一种情况下，附加的量子相位在接近零的经典大地旋转中占主导地位。我们的结果表明，Wigner 旋转代表了量子场论对背景经典引力场的非平凡半经典效应。