相对论天文学III。利用多普勒效应检验狭义相对论
Relativistic Astronomy. III. test of special relativity via Doppler effect
摘要：
“突破摄星”计划在几十年内发送跨相对论探测器前往附近的恒星系统。由于探测器的速度被设计为光速的一个很好的分数，\citet{zha18}最近提出，这些跨相对论探测器可以用来研究天文物体和测试狭义相对论。在这项工作中，我们进一步提出了一些方法来测试狭义相对论和约束光子质量的多普勒效应与天文物体的图像和光谱特征观测的跨相对论探测器。我们引入了更一般的理论来建立检验狭义相对论的框架，包括参量广义多普勒效应和有质量光子的多普勒效应。我们发现，通过比较某个天体的光谱，可以检验洛伦兹不变性和约束光子质量。此外，利用跨相对论探针的成像和摄谱仪功能，可以测试时间膨胀和约束光子质量。对于具有速度$v\sim0.2c$、孔径$D\sim3.5~{\rm cm}$和光谱分辨率$R\sim100$（或$1000$）的跨相对论探测器，我们发现探测器速度不确定度可以被约束为$σ_v\sim0.01c$（或$0.001c$），时间膨胀因子不确定度可以被约束为$Δγ=|\hatγ-γ|\lesssim0.01$（或$0.001$），其中$\hatγ$是时间膨胀因子，$γ$是洛伦兹因子.同时，光子质量限制被设置为$m_γ\lesssim10^{-33}~{\rm g}$，其略低于光学光子的能量。
英文摘要：
The "Breakthrough Starshot" program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Since the probe velocity is designed to be a good fraction of the light speed, \citet{zha18} recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we further propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including a parametric general Doppler effect and Doppler effect with massive photon. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Besides, using imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity $v\sim0.2c$, aperture $D\sim3.5~{\rm cm}$ and spectral resolution $R\sim100$ (or $1000$), we find that the probe velocity uncertainty can be constrained to $σ_v\sim0.01c$ (or $0.001c$), and the time dilation factor uncertainty can be constrained to $Δγ=|\hatγ-γ|\lesssim0.01$ (or $0.001$), where $\hatγ$ is the time dilation factor and $γ$ is the Lorentz factor. Meanwhile, the photon mass limit is set to $m_γ\lesssim10^{-33}~{\rm g}$, which is slightly lower than the energy of the optical photon.
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