討論:斐索實驗

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In 1851, Fizeau used a 特殊干涉儀 arrangement to measure the effect of movement of a medium upon the speed of light.

根據當時盛行的理論，光穿過移動介質時會被其拖曳，所以測量出的光速應該是簡單的把光穿過介質的速度加上介質 本身的速度。

菲索確實檢測到了拖曳效應，但是他觀測到的強度比預期的低很多。它的結果看起來支持菲涅耳的以太拖曳假說，這令大部分物理學家大惑不解。

Over half a century passed before a satisfactory explanation of Fizeau's unexpected measurement was developed with the advent of 愛因斯坦的狹義相對論。

實驗裝置

Fizeau Experiment.

A light ray emanating from the source S' is reflected by a beam splitter G and is collimated into a parallel beam by lens L. After passing the slits O₁ and O₂, two rays of light travel through the tubes A₁ and A₂, through which water is streaming back and forth as shown by the arrows. The rays reflect off a mirror m at the focus of lens L', so that one ray always propagates in the same direction as the water stream, and the other ray opposite to the direction of the water stream. After passing back and forth through the tubes, both rays unite at S, where they produce interference fringes that can be visualized through the illustrated eyepiece.

The interference pattern can be analyzed to determine the speed of light traveling along each leg of the tube.

菲涅耳拖曳係數

Assume that water flows in the pipes at velocity v. According to the non-relativistic theory of the luminiferous aether, the speed of light should be increased when "dragged" along by the water, and decreased when "overcoming" the resistance of the water. The overall speed of a beam of light should be a simple additive sum of its speed through the water plus the speed of the water.

That is, if n is the index of refraction of water, so that c/n is the velocity of light in stationary water, then the predicted speed of light w in one arm would be

$w_{+}={\frac {c}{n}}+v\ ,$

and the predicted speed in the other arm would be

$w_{-}={\frac {c}{n}}-v\ ,$

Light traveling against the flow of water should be slower than light traveling with the flow of water.

The interference pattern between the two beams when the light is recombined at the observer depends upon the transit times over the two paths, and can be used to calculate the speed of light as a function of the speed of the water.

Fizeau found that

$w_{+}={\frac {c}{n}}+v(1-{\frac {1}{n^{2}}})\ .$

In other words, light appeared to be dragged by the water, but the magnitude of the dragging was much lower than expected.

The Fizeau experiment forced physicists to accept the empirical validity of an old, theoretically unsatisfactory theory of Augustin Fresnel (1818) that had been invoked to explain an 1810 experiment by Arago, namely, that a medium moving through the stationary aether drags light propagating through it with only a fraction of the medium's speed, with a dragging coefficient f given by

$f=(1-{\frac {1}{n^{2}}})\ .$

In 1895, Lorentz predicted the existence of an extra term due to dispersion:

$V={\frac {c}{n}}+v\left(1-{\frac {1}{n^{2}}}-{\frac {\lambda }{n}}\!\cdot \!{\frac {\mathrm {d} n}{\mathrm {d} \lambda }}\right)$

重複

Albert Michelson and Edward Morley (1886), repeated Fizeau's experiment with improved accuracy. Another experiment was conducted by Zeeman in 1914, who confirmed Lorentz's modified coefficient. In 1910, Franz Harress (1910) used a rotating device and overall confirmed Fresnel's dragging coefficient. However, he additionally found a "systematic bias" in the data, which later turned out to be the Sagnac effect.

爭議

Although Fresnel's hypothesis was empirically successful in explaining Fizeau's results, many leading experts in the field, including Fizeau (1851), Éleuthère Mascart (1872), Ketteler (1873), Veltmann (1873), and Lorentz (1886) were united in considering Fresnel's partial aether-dragging hypothesis to be on shaky theoretical grounds. For example, Veltmann (1870) demonstrated that Fresnel's formula implies that the aether would have to be dragged by different amounts for different colors of light, since the index of refraction depends on wavelength; Mascart (1872) demonstrated a similar result for polarized light traveling through a birefringent medium. In other words, the aether must be capable of sustaining different motions at the same time.

Fizeau's dissatisfaction with the result of his own experiment is easily discerned in the conclusion to his report:

The success of the experiment seems to me to render the adoption of Fresnel's hypothesis necessary, or at least the law which he found for the expression of the alteration of the velocity of light by the effect of motion of a body; for although that law being found true may be a very strong proof in favour of the hypothesis of which it is only a consequence, perhaps the conception of Fresnel may appear so extraordinary, and in some respects so difficult, to admit, that other proofs and a profound examination on the part of geometricians will still be necessary before adopting it as an expression of the real facts of the case.

Despite the dissatisfaction of most physicists with Fresnel's partial aether-dragging hypothesis, repetitions and improvements to his experiment (see section above) by others confirmed his results to high accuracy.

Besides the problems of the partial aether-dragging hypothesis, another major problem arose with the Michelson-Morley experiment (1887). In Fresnel's theory, the aether is almost stationary, so the experiment should have given a positive result. However, the result of this experiment was negative. Thus from the viewpoint of the aether models at that time, the experimental situation was contradictory: On one hand, the Fizeau experiment and the repetition by Michelson and Morley in 1886 appeared to prove the (almost) stationary aether with partial aether-dragging. On the other hand, the Michelson-Morley experiment of 1887 appeared to prove that the aether is at rest with respect to Earth, apparently supporting the idea of complete aether-dragging (see aether drag hypothesis). So the very success of Fresnel's hypothesis in explaining Fizeau's results helped lead to a theoretical crisis, which was not resolved until the development of the theory of special relativity.

洛侖茲的解釋

主條目：Lorentz ether theory和History of Lorentz transformations

In 1892, Hendrik Lorentz proposed a modification of Fresnel's model, in which the aether is completely stationary. He succeeded in deriving Fresnel's dragging coefficient by the reaction of the moving water upon the interfering waves, without the need of any aether entrainment. He also discovered that the transition from one to another reference frame could be simplified by using a auxiliary time variable which he called local time:

$t^{\prime }=t-{\frac {vx}{c^{2}}}$

In 1895, Lorentz more generally explained Fresnel's coefficient based on the concept of local time. However, Lorentz's theory had the same fundamental problem as Fresnel's: a stationary aether contradicted the Michelson-Morley experiment. So in 1892 Lorentz proposed that moving bodies contract in the direction of motion (FitzGerald-Lorentz Contraction hypothesis, since George FitzGerald had already arrived in 1889 at this conclusion). The equations that he used to describe these effects were further developed by him until 1904. These are now called the Lorentz transformations in his honor, and are identical in form to the equations that Einstein were later to derive from first principles. Unlike Einstein's equations, however, Lorentz's transformations were strictly ad hoc, their only justification being that they seemed to work.

狹義相對論的推導

主條目：Special relativity

Einstein showed how Lorentz's equations could be derived as the logical outcome of a set of two simple starting postulates. In addition Einstein recognized that the stationary aether concept has no place in special relativity, and that the Lorentz transformation concerns the nature of space and time. The Fizeau experiment was one of the key experimental results that shaped Einstein's thinking about relativity. Robert S. Shankland reported some conversations with Einstein, in which Einstein emphasized the importance of the Fizeau experiment:

He continued to say the experimental results which had influenced him most were the observations of stellar aberration and Fizeau’s measurements on the speed of light in moving water. 「They were enough,」 he said.

Max von Laue (1907) demonstrated that the Fresnel drag coefficient can be easily explained as a natural consequence of the relativistic formula for addition of velocities, namely:

The speed of light in immobile water is c/n.

From the velocity composition law it follows that the speed of light observed in the laboratory, where water is flowing with speed v (in the same direction as light) is

$V_{LAB}={\frac {{\frac {c}{n}}+v}{1+{\frac {{\frac {c}{n}}v}{c^{2}}}}}={\frac {{\frac {c}{n}}+v}{1+{\frac {v}{cn}}}}$

Thus the difference in speed is (assuming v is small comparing to c, approximating to the first non-trivial correction)

$V_{LAB}-{\frac {c}{n}}={\frac {{\frac {c}{n}}+v}{1+{\frac {v}{cn}}}}-{\frac {c}{n}}={\frac {{\frac {c}{n}}+v-{\frac {c}{n}}(1+{\frac {v}{cn}})}{1+{\frac {v}{cn}}}}$ $={\frac {v\left(1-{\frac {1}{n^{2}}}\right)}{1+{\frac {v}{cn}}}}\approx v\left(1-{\frac {1}{n^{2}}}\right)$

This is accurate when v/c << 1, and agrees with the formula based upon Fizeau's measurements, which satisfied the condition v/c << 1.

Fizeau's experiment is hence supporting evidence for the collinear case of Einstein's velocity addition formula. and the earliest refutation of the emission theory of light.

—以上未簽名的留言由Flamelai（對話｜貢獻）於2012年7月25日 (三) 00:29‎ (UTC)加入。

新條目推薦討論

在候選頁的投票結果

• 阿曼德·斐索在哪次實驗中驗證了菲涅耳關於以太的假說？

  斐索實驗條目由LeoTschW（討論 | 貢獻）提名，其作者非一人主編或主編者非註冊用戶，屬於「experiment」類型，提名於2017年2月24日 02:49 (UTC)。

  • (＋)支持達標物理條目，有趣的物理史。-和平、奮鬥、救地球！（留言）^{歡迎加入維基Telegram群} 2017年2月24日 (五) 04:44 (UTC)
  • (？)疑問，是「部分以太拖曳模型」還是「以太部分拖曳模型」？--Antigng（留言） 2017年2月24日 (五) 11:06 (UTC)
    • (：)回應：多謝您的意見。由於這兩天術語在線那裡不大好用，而用Google也沒有找到比較有參考價值的來源，手頭上也沒有相關的文獻，所以是自己翻譯的。術語原文是「partial aether dragging」，如果字字對譯的話，應該是部分以太拖曳。而「以太拖曳」（aether dragging）是一個連貫的術語，個人覺得不能拆開。如果您能查到相關文獻的話，我會即時糾正的。--LeoTschW（留言） 2017年2月24日 (五) 11:52 (UTC)
      • @LeoTschW：，"部分以太拖曳" 但是除了維基百科，似乎就一個博客這麼翻譯...另外「部分以太拖曳」容易被人誤解為只有一部分以太被動體拖曳。--Antigng（留言） 2017年2月24日 (五) 12:09 (UTC)
        • (：)回應：好的。已改成「以太部分拖曳模型」。--LeoTschW（留言） 2017年2月24日 (五) 12:36 (UTC)
  • (＋)支持，達標條目。--Finblanco（留言） 2017年2月26日 (日) 08:33 (UTC)
  • (＋)支持：符合標準。－hiJK910 _じぇじぇ^じぇ 2017年2月26日 (日) 17:41 (UTC)
  • (＋)支持，符合標準。KSTTK _talk 2017年2月27日 (一) 11:13 (UTC)
  • (＋)支持：符合DYK標準。--Joeinwiki（留言） 2017年2月27日 (一) 18:19 (UTC)