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[小资料，笔记，科普] 爱因斯坦相对论的实验验证

已有 261 次阅读 2024-8-1 22:20 |个人分类:基础数学-逻辑-物理|系统分类:科研笔记

对真理的追求要比对真理的占有更为可贵！The search for truth is more precious than its possession.

我所追求的东西非常简单，我要以我微弱的力量，冒着不讨任何人喜欢的危险，服务于真理和正义。 What I seek to accomplish is simply to serve with my feeble capacity truth and justice, at the risk of pleasing no one.

在真理和认识方面，任何以权威者自居的人，必将在上帝的戏笑中垮台。Whoever undertakes to set himself up as judge in the field of Truth and Knowledge is shipwrecked by the laughter of the gods.

——The New Quotable Einstein 爱因斯坦 - Essay to Leo Baeck (1953)

[小资料，笔记，科普] 爱因斯坦相对论的实验验证

800px-Apsidendrehung-1new_裁剪.jpg

图1 Precession of Mercury's orbit 水星轨道进动

https://physicsinmyview.com/wp-content/uploads/2020/04/800px-Apsidendrehung-1new.png

https://physicsinmyview.com/2020/04/interesting-facts-about-mercury.html

一、狭义相对论、广义相对论的验证：中国大百科全书

1.1 狭义相对论验证

2023-09-08，狭义相对论验证/special relativity verification/张元仲

https://www.zgbk.com/ecph/words?SiteID=1&ID=438956&Type=bkzyb&SubID=198015

①光速不变原理的验证。

②多普勒频移观测验证。

③时间膨胀实验验证。

④运动介质电磁现象验证。

⑤相对论力学实验验证。包括质速关系（惯性质量随物体运动速度的变化）和质能关系（即E=mc 关系）。

⑥光子静质量实验。

1.2 广义相对论验证

（1） 2023-03-10，广义相对论/general relativity/黄超光

https://www.zgbk.com/ecph/words?SiteID=1&ID=59559&Type=bkzyb&SubID=62041

爱因斯坦精确解释了水星近日点的剩余进动，预言了光线偏折、引力红移、引力波等一系列新的物理效应。

广义相对论不断得到实验与天文观测的验证。除最初的水星近日点进动和光线偏折外,雷达回波延迟、引力红移、行星近日点进动、月球测距、引力透镜、引力磁效应等都进一步支持广义相对论。

（2）2023-06-21，广义相对论验证/general relativity verification/张广良

https://www.zgbk.com/ecph/words?SiteID=1&ID=438805&Type=bkzyb&SubID=198015

①引力透镜。

②引力时间延迟。

③等效原理。

④引力红移。

⑤参考系拖拽。

⑥强引力场实验。

⑦对引力波的直接探测。

⑧宇宙学实验。

（3）2022-01-20，广义相对论的天文学验证/astronomical tests of general relativity/周又元

https://www.zgbk.com/ecph/words?SiteID=1&ID=146860&Type=bkzyb&SubID=87380

①引力红移。

②光线偏转。

③行星轨道近日点反常进动。

④雷达回波的延迟。

⑤坐标拖曳效应。

（4）2022-01-20，相对论的天体测量检验/astrometric test of relativity/黄天衣

https://www.zgbk.com/ecph/words?SiteID=1&ID=107747&Type=bkzyb&SubID=150497

广义相对论并不是当今存在的唯一引力理论。一方面是因为实验和观测还不能对理论做出最后的选择，也来自物理理论本身发展的需求。暗物质和暗能量的理论解释，量子引力理论的发展，都使得物理学家认为广义相对论不是最后的引力理论。高精度天体测量是检验引力理论的主要手段。

相对论等引力理论的理论基础是等效原理。它可以分成3个层次，从低到高为：弱等效原理（Weak Equivalence Principle，WEP），爱因斯坦等效原理（Einstein Equivalence Principle，EEP），强等效原理（Strong Equivalence Principle，SEP）。

SEP则将WEP和EEP中的试验体推广到自引力不能忽略的物体，将非引力实验扩展为所有的实验。

WEP和EEP已经有相当坚实的实验验证。主要是地面和空间的物理实验，其中也有一些是天体测量实验。

广义相对论通过了所有的天体测量实验验证，主要在太阳系内。大部分情况下，只是对弱场的1阶后牛顿近似进行了一些验证，需要进一步提高精度，并且通向强场相对论效应的验证。

二、广义相对论验证：一些英文文献

还没有顾上看，好几百页长。

[1] Domenico Giulini, Philippe Jetzer. Current and Future Tests of General Relativity [J]. Universe, 2022, 8(3): 143-143.

doi: 10.3390/universe8030143

https://www.mdpi.com/2218-1997/8/3/143

General Relativity (GR) holds a special place amongst all fundamental theories of physics: on one hand, it is the theory of all gravitational phenomena; on the other hand, it is also a theory of spacetime. However, the structure of spacetime enters all other physical theories of interactions at the most fundamental level. Hence, as a matter of principle, the status of GR cannot be thought of as isolated from the rest of fundamental physics. According to GR, gravity is not just one amongst four independently rooted interactions. If, under certain physical conditions, GR turns out to fail, this will inevitably also effect the rest of physics. Testing GR up to the most extreme conditions imaginable is therefore not just an end in itself, it also means probing the very foundations of physics. For further discussion on the present and future perspectives on gravitation and cosmology, see the Special Issue celebrating the centennial of GR in this journal, in particular [1,2] and references therein.

广义相对论（GR）在所有物理学基础理论中占有特殊地位：一方面，它是所有引力现象的理论；另一方面，它也是一种时空理论。然而，时空结构在最基本的层面上进入了所有其他相互作用的物理理论。因此，从原则上讲，GR的地位不能被认为与基础物理学的其他部分是孤立的。根据GR的说法，重力不仅仅是四种独立相互作用中的一种。如果在某些物理条件下，GR最终失败，这将不可避免地影响其他物理学。因此，在可以想象的最极端条件下测试GR本身不仅仅是一个目的，还意味着探索物理学的基础。有关引力和宇宙学的当前和未来观点的进一步讨论，请参阅本杂志庆祝GR百年特刊，特别是[1,2]和其中的参考文献。

[2] Mustapha Ishak. Testing general relativity in cosmology [J]. Living Reviews in Relativity, 2018, 22(1): Article Number 1.

doi: 10.1007/s41114-018-0017-4

https://link.springer.com/article/10.1007/s41114-018-0017-4#citeas

共计 204 页。

We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.

我们回顾了在宇宙尺度上测试广义相对论（GR）的最新进展和结果。在过去的二十年里，该学科经历了快速发展，旨在解决宇宙加速及其相关的暗能量问题。然而，随着精确宇宙学的出现，它本身也成为了在宇宙尺度上测试引力物理学的积极努力。我们概述了引力的宇宙学探测、在宇宙学尺度上测试GR偏差的形式和参数化、选定的修正引力（MG）理论、引力屏蔽机制以及为这些测试开发的计算机代码。然后，我们总结了最近对MG参数和选定MG模型的宇宙学约束。我们用最近双星中子星合并事件的影响总结来补充这些宇宙学约束。接下来，我们总结了一些在有和没有天体物理系统学的情况下MG参数预测的结果，这些结果将主导不确定性。该综述旨在为有兴趣加入该领域的学生和研究人员提供该学科的总体情况和切入点。它还可以作为在宇宙学尺度上测试重力的最新结果和限制的快速参考。

[3] Emanuele Berti, Enrico Barausse, Vitor Cardoso, er al. Testing general relativity with present and future astrophysical observations [J]. Classical and Quantum Gravity, 2015, 32(24): Article Number 243001.

doi: 10.1088/0264-9381/32/24/243001

https://iopscience.iop.org/article/10.1088/0264-9381/32/24/243001/meta

https://iopscience.iop.org/article/10.1088/0264-9381/32/24/243001/pdf

共计 180 页。

One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

爱因斯坦的广义相对论（GR）在提出一个世纪后做出了卓越的预测，并被证明与所有实验测试都是相容的。这些测试大多在弱场状态下探测理论，有理论和实验理由相信，当引力场强且时空曲率大时，GR应该被修改。探测强场引力的最佳天体物理实验室是黑洞和中子星，无论是孤立的还是在双星系中。我们回顾了考虑GR扩展的动机。我们提出了一个（必然不完整的）修正引力理论目录，对其进行了强场预测计算，并与爱因斯坦的理论进行了对比，我们总结了我们目前对这些理论中紧凑物体结构和动力学的理解。我们讨论了来自脉冲双星和宇宙学观测的修正引力的当前界限，并强调了未来引力波测量的潜力，以告知我们强场状态下引力的行为。

[4] Christopher J. Moore, Eliot Finch, Riccardo Buscicchio, Davide Gerosa. Testing general relativity with gravitational-wave catalogs: The insidious nature of waveform systematics. iScience, 2021, 24(6): 102577.

doi: 10.1016/j.isci.2021.102577

June 16, 2021

https://www.cell.com/iscience/fulltext/S2589-0042(21)00545-9

https://www.cell.com/action/showPdf?pii=S2589-0042%2821%2900545-9

https://linkinghub.elsevier.com/retrieve/pii/S2589004221005459

Gravitational-wave observations of binary black holes allow new tests of general relativity (GR) to be performed on strong, dynamical gravitational fields. These tests require accurate waveform models of the gravitational-wave signal; otherwise waveform errors can erroneously suggest evidence for new physics. Existing waveforms are generally thought to be accurate enough for current observations, and each of the events observed to date appears to be individually consistent with GR. In the near future, with larger gravitational-wave catalogs, it will be possible to perform more stringent tests of gravity by analyzing large numbers of events together. However, there is a danger that waveform errors can accumulate among events: even if the waveform model is accurate enough for each individual event, it can still yield erroneous evidence for new physics when applied to a large catalog. This paper presents a simple linearized analysis, in the style of a Fisher matrix calculation that reveals the conditions under which the apparent evidence for new physics due to waveform errors grows as the catalog size increases. We estimate that, in the worst-case scenario, evidence for a deviation from GR might appear in some tests using a catalog containing as few as 10–30 events above a signal-to-noise ratio of 20. This is close to the size of current catalogs and highlights the need for caution when performing these sorts of experiments.

对双星黑洞的引力波观测允许对强动态引力场进行广义相对论（GR）的新测试。这些测试需要重力波信号的精确波形模型；否则，波形误差可能会错误地暗示新物理学的证据。现有的波形通常被认为对于当前的观测来说足够准确，迄今为止观测到的每个事件似乎都与GR一致。在不久的将来，随着引力波目录的增加，通过同时分析大量事件，将有可能对重力进行更严格的测试。然而，波形误差可能会在事件之间累积：即使波形模型对每个单独的事件都足够准确，当应用于大型目录时，它仍然可能为新物理学提供错误的证据。本文以Fisher矩阵计算的方式提出了一种简单的线性化分析，揭示了随着目录大小的增加，由于波形误差导致的新物理学的明显证据增长的条件。我们估计，在最坏的情况下，使用信噪比为20的目录，在某些测试中可能会出现与GR偏差的证据，目录中只包含10-30个事件。这接近于当前目录的大小，并强调了在进行此类实验时需要谨慎。

[5] 科学网，2021-06-17，当测试广义相对论时，微小建模误差能快速累积

https://news.sciencenet.cn/htmlpaper/2021/10/202110111018314267031.shtm

英国伯明翰大学研究人员表示，当物理学家将多个引力波事件（如黑洞碰撞）结合起来测试爱因斯坦广义相对论时，小的建模误差积累可能会比之前预期的得更快。相关论文6月16日刊登于Cell Press细胞出版社旗下期刊iScience（《交叉科学》）。研究结果表明，如果一个目录中有10到30个事件，而信噪比为20（这对于此类测试中使用的事件来说很典型），就可能产生偏离广义相对论的误导，错误地指向根本不存在的新物理现象。因为这接近于目前用来评估爱因斯坦理论的目录的大小，作者认为物理学家在进行这样的实验时应该谨慎。

三、海交大携手《科学》杂志向全球发布125个科学问题

https://news.sjtu.edu.cn/mtjj/20210412/145693.html

Astronomy 天文学

15. Is Einstein's general theory of relativity correct?

15.爱因斯坦的广义相对论是正确的吗？

https://www.science.org/content/resource/125-questions-exploration-and-discovery

https://www.science.org/do/10.1126/resource.2499249/full/sjtu-booklet-1714066892333.pdf

page 21

Astronomy

Is Einstein’s general theory of relativity correct?

Einstein’s general theory of relativity (GR) successfully describes gravity. Although it has been proven in the local universe in weak-field limits, it remains largely untested in the general strong-field cases. Although Einstein’s theory of gravity has passed all tests thus far, we can’t be sure that it applies everywhere under every condition, and that it extends to the farthest limits of the universe. The largest deviations from GR are expected in the strongest gravitational fields around black holes, where different theories of gravity make significantly different predictions. Now, thanks to the advances in observations such as gravitational-wave detection and the imaging of supermassive black holes, we can test GR in a strong-field regime. It is indeed a timely question.

爱因斯坦的广义相对论正确吗？

爱因斯坦的广义相对论（GR）成功地描述了引力。尽管它已在弱场极限的局部宇宙中得到证明，但在一般强场情况下，它在很大程度上仍未经过测试。尽管爱因斯坦的引力理论已经通过了迄今为止的所有测试，但我们不能确定它是否适用于所有条件下的所有地方，并且它是否延伸到宇宙的最远极限。与GR的最大偏差预计出现在黑洞周围最强的引力场中，不同的引力理论做出了截然不同的预测。现在，由于引力波探测和超大质量黑洞成像等观测技术的进步，我们可以在强场条件下测试GR。这确实是一个及时的问题。