利用穆斯堡尔谱测试加速下爱因斯坦的时间膨胀
Testing Einstein's time dilation under acceleration using Mössbauer spectroscopy
摘要：
爱因斯坦的时间膨胀公式在几个实验中得到了验证。为了验证这个公式的正确性，我们用旋转吸收体的穆斯堡尔谱测量了横向二阶多普勒频移。这样的实验也能够测试时间膨胀是否仅取决于吸收体的速度，如爱因斯坦的时钟假设所假设的，或者当前的向心加速度有助于时间膨胀。我们在这里表明，事实上，实验需要$γ$ -射线的发射和检测狭缝的有限大小，吸收线加宽;几何纵向一阶多普勒频移极大。此外，吸收线是非Lorenzian的。对于任意角速度的吸收体，我们得到了吸收线的显式表达式。在以前的所有实验中，没有观察到完整的吸收线本身，对实验结果的分析是错误的，结论是可疑的。唯一合适的实验是由Kündig（Phys. Rev. 129（1963）2371）完成的，他观察到了加宽，但将其与吸收体的随机振动联系起来。建立了穆斯堡尔谱法成功测量横向二阶多普勒频移的必要条件。我们指出，这样的实验结果可以用来验证由于加速度的多普勒频移的存在，并测试爱因斯坦的时钟假设的有效性。
英文摘要：
The Einstein time dilation formula was tested in several experiments. Many trials have been made to measure the transverse second order Doppler shift by Mössbauer spectroscopy using a rotating absorber, to test the validity of this formula. Such experiments are also able to test if the time dilation depends only on the velocity of the absorber, as assumed by Einstein's clock hypothesis, or the present centripetal acceleration contributes to the time dilation. We show here that the fact that the experiment requires $γ$-ray emission and detection slits of finite size, the absorption line is broadened; by geometric longitudinal first order Doppler shifts immensely. Moreover, the absorption line is non-Lorenzian. We obtain an explicit expression for the absorption line for any angular velocity of the absorber. The analysis of the experimental results, in all previous experiments which did not observe the full absorption line itself, were wrong and the conclusions doubtful. The only proper experiment was done by Kündig (Phys. Rev. 129 (1963) 2371), who observed the broadening, but associated it to random vibrations of the absorber. We establish necessary conditions for the successful measurement of a transverse second order Doppler shift by Mössbauer spectroscopy. We indicate how the results of such an experiment can be used to verify the existence of a Doppler shift due to acceleration and to test the validity of Einstein's clock hypothesis.
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