(Lorentz’s mathematics / Poincaré’s philosophy / Einstein’s physics)
In this section, Feynman discusses the contributions of Lorentz, Poincaré, and Einstein with regard to the special theory of relativity.
1. Lorentz’s mathematics:
“H. A. Lorentz noticed a remarkable and curious thing when he made the following substitutions in the Maxwell equations: x′ = (x − ut)/√(1−u2/c2), y′ = y, z′ = z, t′ = (t − ux/c2)/√(1−u2/c2)…(Feynman et al., 1963, section 15–2 The Lorentz transformation).”
Feynman says that Hendrik Antoon Lorentz noticed a remarkable fact after the following substitutions in the Maxwell equations: x′ = (x − ut)/√(1 − u2/c2), y′ = y, z′ = z, t′ = (t − ux/c2)/√(1 − u2/c2). Essentially, Maxwell’s equations remain invariant when the Lorentz transformation of coordinates is applied. However, Lorentz failed to grasp the notion of relative time and simultaneity. In 1915, Lorentz writes that, “[t]he chief cause of my failure was my clinging to the idea that only the variable t can be considered as the true time and that my local time t’ must be regarded as no more than an auxiliary mathematical quantity (Pais, 1982, p. 167).” Thus, Lorentz is commonly recognized for his contribution in the mathematics (instead of physics) of special relativity.
FitzGerald-Lorentz contraction hypothesis was an attempt to reconcile the null result of the 1887 Michelson-Morley experiment. In a letter titled The Ether and the Earth’s Atmosphere, George Francis FitzGerald (1889) writes that “I would suggest that almost the only hypothesis that could reconcile this opposition is that the lengths of material bodies changes, according as they are moving through the ether or across it, by an amount depending on the square of the ratio of their velocities to that of light (p. 390).” He proposes that electrical forces are affected by the motion of the electrified bodies relative to the ether and thus, the size of a body and the molecular forces are affected by the motion. Three years later, Lorentz (1892) conceives the same idea and introduces a second-order contraction effect (v2/2c2) to explain the null result.
2. Poincaré’s philosophy:
“…following a suggestion originally made by Poincaré, then proposed that all the physical laws should be of such a kind that they remain unchanged under a Lorentz transformation (Feynman et al., 1963, section 15–2 The Lorentz transformation).”
According to Feynman, Einstein follows a suggestion originally made by Poincaré and proposes that all the physical laws should be of such a kind that they remain unchanged under a Lorentz transformation. (However, all the physical laws should include mechanical laws, optical laws, and the laws of electrodynamics, but not the laws of quantum mechanics.) Historically, there is no direct evidence that Einstein was aware of Poincaré’s works during his development of special relativity. In a letter to Seelig, Einstein writes that “Concerning myself, I knew only Lorentz’s important work of 1895… but not Lorentz’s later work, nor the consecutive investigations by Poincaré (Born, 1956, p. 194).” More important, Poincaré (1906) should be credited for his realization that the Lorentz transformation is a rotation in the four-dimensional space-time and the invariance of the expression: x2 + y2 + z2 − c2t2.
It is unclear whether Poincaré accepted Einstein’s theory of special relativity (Pais, 1982). In a speech delivered in St. Louis, Poincaré (1904) says that “[t]he principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not and could not have any means of discerning whether or not we are carried along in such a motion.” This paragraph provides an important philosophical insight into the relativity principle: impossibility to determine absolute motion. However, subsequent paragraphs within the same speech indicate that Poincaré failed to grasp the concept of simultaneity (Yang, 2006). Thus, Poincaré is recognized for his contribution to the philosophy (instead of physics) of special relativity.
3. Einstein’s physics:
“…as Einstein did, we too must analyze our ideas of space and time in order to understand this transformation (Feynman et al., 1963, section 15–2 The Lorentz transformation).”
Feynman suggests that we must analyze our ideas of space and time in order to understand Lorentz transformation just like Einstein. Similarly, Yang (2006) explains that “Lorentz had the mathematics, but not the physics, and Poincaré had the philosophy, but also not the physics. It was the 26-year-old Einstein who dared to question mankind’s primordial concept about time, and insisted that simultaneity is relative (p. 3033).” In essence, Einstein resolves the apparent incompatibility between Newton’s mechanics and Maxwell’s electrodynamics by destroying Newton’s notion of absolute space and absolute time. During a speech in Kyoto University on 14 Dec 1922, Einstein elaborates that “[a]n analysis of the concept of time was my solution. Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity. With this new concept, I could resolve all the difficulties completely for the first time (Einstein, 1982, p. 46).”
In a sense, Einstein did not fully understand the implications of his theory of special relativity when he called Minkowski’s approach to space-time diagram “superfluous learnedness (Pais, 1982, p. 152).” Einstein was also negative towards his contribution and said that “[s]ince the mathematicians have invaded the relativity theory, I do not understand it myself anymore (Sommerfeld, 1949, p. 102).” Shortly after, Einstein realized that his theory of gravity would be impossible without Minkowski’s space-time. In his autobiography, Einstein (1949) recognizes Minkowski’s contribution in special relativity and writes that “[h]e also showed that the Lorentz transformation (apart from a different algebraic sign due to the special character of time) is nothing but a rotation of the coordinate system in the four-dimensional space (p. 55).”
Questions for discussion:
1. What are Lorentz’s contributions to the theory of special relativity?
2. What are Poincaré’s contributions to the theory of special relativity?
3. What are Einstein’s contributions to the theory of special relativity?
The moral of the lesson: Lorentz contributed to the mathematical transformation of coordinates, Poincaré contributed to the philosophy of the principle of relativity, but Einstein revolutionized the concept of space and time in special relativity.
References:
1. Born, M. (1956). Physics and Relativity. In Physics in my generation: A selection of papers. New York: Pergamon Press.
2. Einstein, A. (1949). Autographical notes (Translated by Schilpp). La Salle, Illinois: Open court.
3. Einstein, A. (1982/1922). How I Created the Theory of Relativity (translated by Yoshimasa A. Ono). Physics Today, 35(8), 45-47.
4. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
5. FitzGerald, G. F. (1889). The Ether and the Earth’s Atmosphere. Science, 13, 390.
6. Lorentz, H. A. (1892). De relatieve beweging van de aarde en den aether. Koninklijke Akademie van Wetenschappen te Amsterdam. Wis- en Natuurkundige Afdeeling. Verslagen der Zittingen. 1, 1892-93, pp. 74-79.
7. Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford: Clarendon Press.
8. Poincaré, H. (1904). L'état actuel et l'avenir de la physique mathématique. Bulletin des sciences mathématiques, 28(2), 302-324.
9. Poincaré, H. (1906). Sur la dynamique de l’electron. Rendiconti del Circolo Matematico di Palermo, 21, 129-176.
10. Sommerfeld, A. (1949). To Albert Einstein’s Seventieth Birthday. In P. A. Schilpp (ed.), Albert Einstein: Philosopher-Scientist. La Salle, IL: Open Court.
11. Yang, C. N. (2006). Albert Einstein: Opportunity and perception. International Journal of Modern Physics A, 21(15), 3031-3038.
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