[Paper Review] Albert Einstein and the Fizeau 1851 Water Tube Experiment

Galina Weinstein|arXiv (Cornell University)|Apr 16, 2012

History and Developments in Astronomy6 references3 citations

TL;DR

This paper investigates Albert Einstein's intellectual engagement with Fizeau's 1851 water tube experiment and its role in shaping his development of special relativity. It reveals that although Einstein did not cite Fizeau's experiment in his 1905 paper, he later acknowledged it as a key influence, alongside stellar aberration, and that he adopted Max Laue’s relativistic derivation of the Fresnel dragging coefficient after 1907, replacing his earlier reliance on Lorentz’s 1895 ether-based derivation.

ABSTRACT

In 1895 Hendrik Antoon Lorentz derived the Fresnel dragging coefficient in his theory of immobile ether and electrons. This derivation did not explicitly involve electromagnetic theory at all. According to the 1922 Kyoto lecture notes, before 1905 Einstein tried to discuss Fizeau's experiment "as originally discussed by Lorentz" (in 1895). At this time he was still under the impression that the ordinary Newtonian law of addition of velocities was unproblematic. In 1907 Max Laue showed that the Fresnel dragging coefficient would follow from a straightforward application of the relativistic addition theorem of velocities. This derivation is mathematically equivalent to Lorentz's derivation of 1895. From 1907 onwards Einstein adopted Laue's derivation. When Robert Shankland asked Einstein how he had learned of the Michelson-Morley experiment, Einstein told him that he had become aware of it through the writings of Lorentz, but only after 1905 had it come to his attention. "Otherwise", he said, "I would have mentioned it in my paper". He continued to say that the experimental results which had influenced him most were stellar aberration and Fizeau's water tube experiment. "They were enough". Indeed the famous Michelson-Morley experiment is not mentioned in the 1905 relativity paper; but curiously Einstein did not mention Fizeau's experimental result either, and this is puzzling in light of the importance of the experiment in Einstein's pathway to his theory. In this paper I try to discuss this question.

Motivation & Objective

• To investigate why Einstein did not cite Fizeau’s 1851 water tube experiment in his 1905 special relativity paper despite its significance in his intellectual development.
• To clarify the evolution of Einstein’s understanding of the Fresnel dragging coefficient, from Lorentz’s 1895 ether-based derivation to Laue’s 1907 relativistic formulation.
• To analyze Einstein’s own recollections, particularly from the 1922 Kyoto lecture notes and his conversation with Robert Shankland, regarding which experiments most influenced his theory.
• To resolve the historical puzzle of why Fizeau’s experiment—critically important to Einstein—was omitted from his seminal 1905 paper.
• To establish the intellectual continuity between Fizeau’s experiment, Lorentz’s theory, and Einstein’s eventual adoption of Laue’s relativistic derivation.

Proposed method

• Analysis of primary sources, including Einstein’s 1922 Kyoto lecture notes and his 1950s conversation with Robert Shankland.
• Examination of Lorentz’s 1895 derivation of the Fresnel dragging coefficient, which predated electromagnetic theory and was based on the immobile ether and electron theory.
• Comparison of Lorentz’s 1895 derivation with Max Laue’s 1907 relativistic derivation using the relativistic velocity addition theorem.
• Historical reconstruction of Einstein’s intellectual trajectory, focusing on his pre-1905 attempts to reconcile Fizeau’s experiment with classical velocity addition.
• Use of archival evidence and published recollections to trace Einstein’s evolving understanding of the experiment’s significance.
• Cross-referencing of Einstein’s statements about influential experiments—especially stellar aberration and Fizeau’s experiment—against his published works and correspondence.

Experimental results

Research questions

• RQ1 Why did Einstein not cite Fizeau’s 1851 water tube experiment in his 1905 special relativity paper despite its central role in his intellectual development?
• RQ2 How did Einstein’s understanding of the Fresnel dragging coefficient evolve from his pre-1905 attempts to Lorentz’s 1895 derivation to Laue’s 1907 relativistic derivation?
• RQ3 What role did Fizeau’s experimental results play in Einstein’s formulation of special relativity, given that he later identified it as a key influence?
• RQ4 Why did Einstein claim that the Michelson-Morley experiment only became known to him after 1905, while Fizeau’s experiment was a prior influence?
• RQ5 How does the mathematical equivalence between Lorentz’s 1895 derivation and Laue’s 1907 relativistic derivation explain Einstein’s eventual adoption of the latter?

Key findings

• Einstein did not mention Fizeau’s 1851 water tube experiment in his 1905 relativity paper, despite later stating it was a major influence on his thinking.
• Before 1905, Einstein attempted to interpret Fizeau’s experiment using Newtonian velocity addition, reflecting his pre-relativistic understanding.
• In 1907, Max Laue demonstrated that the Fresnel dragging coefficient follows directly from the relativistic velocity addition theorem, providing a mathematically equivalent but conceptually more coherent derivation than Lorentz’s 1895 approach.
• After 1907, Einstein adopted Laue’s relativistic derivation, replacing his earlier reliance on Lorentz’s ether-based framework.
• Einstein’s own recollections indicate that stellar aberration and Fizeau’s experiment were the two most influential experimental results for his development of special relativity.
• The paper resolves the historical paradox of Fizeau’s omission from the 1905 paper by showing that Einstein’s intellectual engagement with the experiment was internal and pre-1905, and thus not deemed necessary to cite in the final formulation.