他们被说服了？

戴榕菁

1. 背景

去年底我在academia.edu讨论时间的意义以及为什么引力不可能如广义相对论所说的那样改变时间速率的时候，有一位名为Степан Тигунцев的人在那里与Pound-Rebka实验有关的评论引起了我对那个实验的注意。那是一个在哈菲尔-基廷实验之前的另一个被称为验证了所谓的相对论时间效应的著名的经典实验。今年初我去维基百科查了一下那个实验（见附录），从那里我了解到Pound-Rebka实验的基本内容以及为什么会被认为是验证了相对论的时间效应。当时该网页的更新日期为2022年7月5日。通常来说，维基百科的网页更新的越不频繁就表明相关网页的内容比较没有争议。

Pound-Rebka实验是从一个塔顶向地面的一个接收装置发射光束，发射器内的电子基态振动频率被选为与接受装置里的相同，因此按照爱因斯坦-普朗克的光能公式，如果光束的光子能被接受装置吸收，就表明光子到达接受装置时的频率与光子被发出时的频率一致。Pound和Rebka两个人就让发射器向上运动从而产生红移效应，这样的话，如果在某个红移点上光子最终被下面等着的接受装置吸收了，就表明光束在向下传播的过程中经历了蓝移效应从而使得蓝移与红移相互抵消了。

从上面的描述我们可以看出Pound-Rebka实验实际上比较靠谱地验证了这样两件事：1）光子在地球引力中向下运动时产生了蓝移；2）根据爱因斯坦-普朗克的光能公式，光子在地球引力场中的向下运动使得光子的能量增加。

相对论学者以其向来奇葩的逻辑愣是得出结论说Pound-Rebka实验证明了广义相对论关于引力导致时间变慢的结论，并给这种现象起名为引力红移，这种红移说的不是引力让光线产生红移而是引力让时间变慢。

但实际上，即便是用牛顿定律，只要认为光子有质量，我们同样可以得出引力可以使得向下运动的光子的能量增加的结论。只要承认爱因斯坦-普朗克公式并承认光子有质量，用牛顿定律也可得出引力让光线发生蓝移的结论，因此，别人同样可以说Pound-Rebka实验是验证了光子有质量。当然，相对论学者们不会这样认为。

那么相对论学者是用什么样的逻辑来得出Pound-Rebka实验验证引力让时间变慢的结论的呢？

首先，他们说Pound-Rebka实验验证了广义相对论所说的引力让光线发生蓝移，也就是说频率变大波长变短。从牛顿定律的角度出发，这可以用单纯的波动物理特性的变化来解释。但是，相对论学者是不承认光子有质量的，因此光子是不可能受到任何由质量引起的作用力的，他们非常奇葩地把光子频率之所以会变大的原因解释为时间变慢了。也就是说原来1秒钟变成了现在的0.9秒钟，因而原来每1秒钟变1000次的周期变化，现在成了每0.9秒钟变1000次的周期变化，所以频率就增加了。也就是说，广义相对论学者认为Pound-Rebka实验表明的光子的能量的增加不是因为光子如同伽利略从匹萨塔上丢下的铁球那样受到了重力的吸引，而是因为地球引力改变了时间的速率。。。。对于一般人来说，这个圈子绕的有点大，但对于相对论学者来说这就是他们可以心安理得地接受的逻辑。

当然，相对论学者要想得出上述结论还需要一个对他们来说是至关重要的的法宝，但同时也是他们的致命的照门，就是那个连爱因斯坦本人都犹豫不决的真空中的光速在引力场中不变的前提假设。这是因为如果光速不是不变的，那么由下式（其中f  是频率，λ是波长，而c是光速）：

f  = c/ λ                                 (1)

我们可以知道如果波长保持不变，只要光速上升，频率也可以增大。也就是说只要光子以更快的速度走完同样的距离的话，它的频率也照样可以上升。但按照相对论的光速不变的前提，则只有当波长变短时频率才会增大，而波长与周期之间又有着下面的关系：

λ  = cT                                    (2)

T是周期。这样一来，在c不变的前提下，只要把原本作为运动之物理参数的周期T的变化解释为时间的变化，就可以得出波长变短的结论，然后由(1)就可得出频率变长的结论。（这里的波长变短不是按照洛伦兹的动尺变短的套路来的。这里强调的是引力引起的时间变化而不是速度产生的长度变化，这里如果用洛伦兹变换的话就会出现无限大的洛伦兹因子的问题。）

可见，相对论学者之所以会认为Pound-Rebka实验验证了所谓引力导致时间变慢是以他们的一整套理论为前提的，而不是简单直接的逻辑结论。

2. 他们的变化

当我去年已经用大量的证据论证了真空中的光速不可能如狭义相对论假设的那样对所有的观察者一样（参见【[1]】）的之后，我就知道没有理由认为光速在引力场中一定是不变的，而爱因斯坦本人对于引力场的光速不变假设都出现了自相矛盾的前后摇摆不定的言论更是让我相信假设光速在引力场中不变是没道理的。在光速不是不变的前提下，由上述的讨论可以直接推翻所谓的Pound-Rebka实验验证了引力场导致时间变慢的结论；尤其是在我已经通过讨论时间的意义（【[2]】，【[3]】）来论证了引力和速度都不可能导致时间变化之后，我更是肯定可以轻易地驳倒相对论学者们关于Pound-Rebka实验的结论，只是等待有时间和精力的机会而已。

不久前当我开始推翻那个所谓的一次性验证狭义和广义相对论的哈菲尔-基廷实验时（参见【[4]】），就打算要在解决了哈菲尔-基廷之后，就来解决这个Pound-Rebka实验。但是，当我再次回到今年初查看该实验的相同网页【[5]】时，却发现他们改了。更确切地说，有人对该网页的内容做了大幅修改。特别是增加了下面这段话：

【

The equivalence principle (EP) lies at the heart of the general theory of relativity. Most proposed alternatives to general relativity predict violation of the EP at some level. The EP includes three hypotheses:

1. Universality of free fall (UFF). This asserts that the acceleration of bodies freely falling bodies in a gravitational field is independent of their compositions.
2. Local Lorentz invariance (LLI). This asserts that the outcome of a local experiment is independent of the velocity and orientation of the apparatus.
3. Local position invariance (LPI). This asserts that clock rates are independent of their spacetime positions. Measurements of differences in the elapsed time displayed by two clocks will depend on their relative positioning in a gravitational field. But the clocks themselves are unaffected by gravitational potential.

Gravitational redshift measurements provide a direct measure of LPI. Of the three hypotheses underlying the equivalence principle, LPI has been by far the least accurately determined.

】

如同有关相对论的文章经常出现的别扭情景一样，这面这段话的最后两句在逻辑上是针尖对麦芒的，只是不了解状况的人不容易看出而已。前一句话“Gravitational redshift measurements provide a direct measure of LPI.”听上去象是对广义相对论的肯定，而且还是实验性的肯定，那可是了不起的肯定。但接下来的第二句话“Of the three hypotheses underlying the equivalence principle, LPI has been by far the least accurately determined.”马上就打脸那第一句话。

不夸张地说，上面这第二句甚至可以被看成是用不情愿的口吻以保守的形式来表达了我从去年开始反复强调的论点：所谓的引力改变时间的实验如果没有数据上的造假，那就是引力改变了时钟的周期节奏，而不是引力改变了时间。

特别是他们在前面说了这样一句对于他们来说几乎是胆大妄为的话：

【

In the decade preceding Einstein's publication of the definitive version of his theory of general relativity, he anticipated several of the results of his final theory with heuristic arguments, not all of which were to prove to be correct.

】

这让我顿时有了一种“他们似乎已经被我说服了，这个世道改变了”的感觉。当然，我马上就冷静地告诫自己：世界还未改变，自己尚需努力。

不过，既然他们的语调都变了，我也可以先稍微省点力了。这篇本来可能会更长的文章，就到此为止吧。给他们点时间，看看世界会如何变化。。。。。。

。。。。。。

附录. 2023年初打印的2022年7月版的维基百科关于Pound-Rebka实验的介绍

Pound–Rebka experiment

The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativity by showing that photons gain energy when traveling toward a gravitational source (the Earth). It was proposed by Robert Pound and his graduate student Glen A. Rebka Jr. in1959, and was the last of the classical tests of general relativity to be verified (in the same year). It is a gravitational redshift experiment, which measures the change of frequency of light moving in a gravitational field. In this experiment, the frequency shift was a blueshift toward a higher frequency. Equivalently, the test demonstrated the general relativity prediction that clocks should run at different rates in different places of a gravitational field. It is considered to be the experiment that ushered in an era of precision tests of general relativity.

Overview

 Consider an electron bound to an atom in an excited state. As the electron undergoes a transition from the excited state to a lower energy state it will emit a photon with a frequency corresponding to the difference in energy between the excited state and the lower energy state. The reverse process will also occur: if the electron is in the lower energy state then it can undergo a transition to the excited state by absorbing a photon at the resonant frequency for this transition. In practice the photon frequency is not required to be at exactly the resonant frequency, but must be in a narrow range off requencies centred on the resonant frequency: a photon with a frequency outside this region cannot excite the electron to a higher energy state. Now consider two copies of this electron-atom system, one in the excited state (the emitter), the other in the lower energy state (the receiver). If the two systems are stationary relative to one another and the space between them is flat (i.e. we neglect gravitational fields) then the photon emitted by the emitter can be absorbed by the electron in the receiver. However, if the two systems are in a gravitational field then the photon may undergo gravitational redshift as it travels from the first system to the second, causing the photon frequency observed by the receiver to be different to the frequency observed by the emitter when it was originally emitted. Another possible source of redshift is the Doppler effect: if the two systems are not stationary relative to one another then the photon frequency will be modified by the relative speed between them. In the Pound–Rebka experiment, the emitter was placed at the top of a tower with the receiver at the bottom. General relativity predicts that the gravitational field of the Earth will cause a photon emitted downwards (towards the Earth) to be blueshifted (i.e. its frequency will increase) according to the formula:

where f_r and f_e are the frequencies of the receiver and emitter, h is the distance between the receiver and emitter, M is the Earth's mass, R is the radius of the Earth, G is Newton's constant and c is the speed of light. To counteract the effect of gravitational blueshift, the emitter was moved upwards(away from the receiver) causing the photon frequency to be redshifted, according to the Doppler shift formula:

where v is the relative speed between the emitter and receiver. Pound and Rebka varied the relative speed v so that the Doppler redshift exactly cancelled the gravitational blueshift:

In the case of the Pound–Rebka experiment h ? R; the height of the tower is tiny compared to theradius of the earth, and the gravitational field can be approximated as constant. Therefore, the Newtonian equation can be used:

The energy associated with gravitational redshift over a distance of 22.5 meters is very small. The fractional change in energy is given by δE/E, is equal to gh/c² = 2.5×10⁻¹⁵. As such, short wave length high energy photons are required to detect such minute differences. The 14 keV gamma rays emitted by iron-57 when it transitions to its base state proved to be sufficient for this experiment.

Normally, when an atom emits or absorbs a photon, it also moves (recoils) a little, which takes away some energy from the photon due to the principle of conservation of momentum. The Doppler shift required to compensate for this recoil effect would be much larger (about 5 orders of magnitude) than the Doppler shift required to offset the gravitational redshift. But in 1958 Rudolf Mössbauer reported that all atoms in a solid lattice absorb the recoil energy when a single atom in the lattice emits a gamma ray. Therefore, the emitting atom will move very little (just as a cannon will not produce a large recoil when it is braced, e.g. with sandbags). This allowed Pound and Rebka to set up their experiment as a variation of Mössbauer spectroscopy.

The test was carried out at Harvard University's Jefferson laboratory. A solid sample containing iron(57Fe) emitting gamma rays was placed in the center of a loudspeaker cone which was placed near the roof of the building. Another sample containing 57Fe was placed in the basement. The distance between this source and absorber was 22.5 meters (73.8 ft). The gamma rays traveled through a Mylar bag filled with helium to minimize scattering of the gamma rays. A scintillation counter was placed below the receiving 57Fe sample to detect the gamma rays that were not absorbed by the receiving sample. By vibrating the speaker cone the gamma ray source moved with varying speed, thus creating varying Doppler shifts. When the Doppler shift canceled out the gravitational blueshift, the receiving sample absorbed gamma rays and the number of gamma rays detected by the scintillation counter dropped accordingly. The variation in absorption could be correlated with the phase of the speaker vibration, hence with the speed of the emitting sample and therefore the Doppler shift. To compensate for possible systematic errors, Pound and Rebka varied the speaker frequency between10 Hz and 50 Hz, interchanged the source and absorber-detector, and used different speakers(ferroelectric and moving coil magnetic transducer). The reason for exchanging the positions of the source and the detector is doubling the effect. Pound subtracted two experimental results:

1. the frequency shift with the source at the top of the tower

2. the frequency shift with the source at the bottom of the tower

The frequency shift for the two cases has the same magnitude but opposing signs. When subtracting the results, Pound and Rebka obtained a result twice as big as for the one-way experiment. The result confirmed that the predictions of general relativity were borne out at the 10% level. This was later improved to better than the 1% level by Pound and Snider.

Another test, Gravity Probe A, involving a space-borne hydrogen maser increased the accuracy of the measurement to about 10−4 (0.01%).

This page was last edited on 25 July 2022, at 05:27

(UTC)

注：上述内容是在2023年初于文献【3】完全相同的地址打印下来的。