The relay race towards the Theory of Relativity: Poincaré’s and Einstein’s influences and contributions.

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There has been a long standing debate on who must be given the most credit for the relativity theory. Albert Einstein is considered as its father, but one cannot deny the important discoveries done by Henri Poincaré for the development of the theory. This text’s main goal is to find a middle point conclusion to this debate, acknowledging both men’s contribution to the theory. For this reason, it will begin by analyzing the figure of Henri Poincaré: his influences and his main contributions to the future relativity theory. Secondly, it will look at the main reasons why it is usually considered that Poincaré stayed half way from relativity in relation to Einstein. Finally, the text will give an overview of the context and influences that channeled Einstein into relativity and it will close by looking at the main points of his special relativity theory and its important consequences on the contemporary concept of “time”.

Henri Poincaré: Context and Influences

To analyze Poincaré’s influences, one must consider the his academic and cultural background, in order to see the strong impact that these had on his way of thinking. In Poincaré’s case, following Peter Galison’s detailed study on the subject[1], the environment had a very important role: Not only the educational methodology of the École Polytechnique where he studied, but also his time working as an engineer in the mine at Magny or his periods as head of the Bureau des Longitudes and his direct contact with the bureaucracy surrounding the world’s standardization and conventions on time and space[2], were fundamental to his development.

Among the people that influenced Poincaré in his years as a young student, one must underline the importance of his teacher, the physicist, Alfred Cornu, who introduced Poincaré into a different conception of science and technology; he applied a transverse approach to knowledge aiming at finding a link between the various sciences, from the most abstract physics to their concrete applications on the real world[3]. His future brother-in-law, the philosopher Émile Boutroux, had a similar and reinforcing effect on Poincaré: Boutroux introduced him to a wide group of philosophers who were interested in the unification of the sciences and the humanities; they believed, as Poincaré did, that real knowledge could only be attained through both induction and deduction; through mental theorization linked with an empirical observation of the real world[4].

Last but not least, one must remember a fellow student at the Polytechnique, the philosopher and physicist Auguste Calinon. He injected in Poincaré a dose of skepticism in relation to the attainment of knowledge. He believed that the ‘absolutes’ were unknowable, hence they became unnecessary concepts. Knowledge had to be seen as relative to frames of reference because it was only through these that one could perceive the world. In relation to time, Calinon affirmed that “there was an irreducible choice in the measure of time, one that had to be based on convenience”[5]. With ideas like this one, Calinon had opened a new path that would eventually lead to Poincaré’s new conventionalist conceptions of the world.

Henri Poincaré: Conventionalism

It is with his conventionalist views of time and space that Poincaré approached the frontier of relativity. In few words, he insisted that theories, and men’s application of those theories, were nothing more than what the word implied: ideas created by man, which intend to organize how one conceives the world. They are not absolute truths but merely tools that one can use when they are the simplest and most conventional possibility for solving a problem. The rules that one applies to space or time are nothing more than conventions created by humans in order to understand the world that surrounds them. In Poincaré’s words, “We […] choose these rules, not because they are true, but because they are the most convenient”[6]; with this statement, Poincaré had abolished (at least in theory) the philosophical absolutes.

In his philosophical text “The Measure of Time” (1898), Poincaré affirms that man’s conceptions of space, time, simultaneity and even geometry are all relative to a frame of reference, and it is only through conventions that the formers can acquire actual meaning. Four years later, Poincaré would put these philosophical meditations into the field of mathematics and physics in Science and Hypothesis (1902), confirming in the practice of physics what he had proposed as a philosophical idea: Space is only conceived through relative motion; time can only acquire value through conventions that define it; there is no direct intuition of the simultaneity of two phenomena separated in space; and Euclidean geometry is nothing more than a conventional language[7].

Poincaré had clearly made the first steps towards relativity some years before Einstein had even thought of the idea. What he called ‘the 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 motion”[8],

seems to be the same fundamental principle that Einstein would give in his 1905 paper “On the electrodynamics of moving bodies” to support his new conception of kinematics: “for all coordinate systems for which the mechanical equations hold, the equivalent electrodynamical and optical equations hold also”[9]. So, why is the relativity theory almost unanimously attributed to Einstein, if the fundamental equations and the theoretical reasoning for the theory had been developed by Poincaré years before?

This is mainly due to the fact that Poincaré did not have the courage (nor the intention) of cutting loose from tradition: he did not want to create a “new” theory; his intention was to find solutions to the discrepancies he had seen in the past and correct them while maintaining the fundamental principles of physics untouched. And this is precisely what Einstein did: he broke with the past, he destroyed the old principles and he created a new theory.

Poincaré hands the torch to Einstein

As said before, the fundamental difference between Poincaré and Einstein in relation to relativity was that Poincaré believed in the past, while Einstein was more skeptical of it: “Authority gone to one’s head is the greatest enemy of truth”[10]. But, in what points precisely did they differ? The divergence between them came basically from Poincaré’s stubborn attachment to two concepts: “ether” and “absolute time”.

H. A. Lorentz can be considered a fundamental influence for both Poincaré and Einstein. It can even be said that his theories (the “Lorentz contraction” and “local time”) [11] were the ones that allowed relativity to be born, due to the fact that it was by making corrections to Lorentz’s theories that both Poincaré and Einstein gave the first steps towards relativity. The difference comes from the solutions that each of them took from Lorentz’s texts: Poincaré corrected Lorentz’s equations, but did not risk erasing the concepts of “ether” and “absolute time” from the thesis, remaining tied to Classical physics[12]. On the other hand, Einstein realized that neither of the two above said concepts was necessary (they could even be contradictory) to the relativity principle, so he denied them completely, structuring a theory that had managed to work without those two fossils[13]: “One would think [ether-theory] came from antiquity, its views are so obsolete. It makes one see how fast knowledge develops nowadays”[14].

Albert Einstein: Influences

Apart from the above said Lorentz, it can be considered that Michelson and Morley’s experiment to find ether[15] was another crucial influence on Einstein’s development of the relativity theory because it was a clear example of the need to create a kinematic principle that was not dependent on a phenomenon that could not be proven empirically.

A third influence came from the field of electrodynamics, where he found an “asymmetry” in Faraday’s experiment of the electric field created between a magnet and a conductive wire: in spite of the fact that traditional electromagnetic theory affirmed that only a magnet in motion produced an electromagnetic field, Einstein found that, even when the magnet was at rest and the wire was the one in motion, there was still an electric current passing[16]. Theory had to adjust to empirical evidence and not the opposite; “symmetry in the phenomena should show up as a symmetry in the theory”[17].

As a positive influence, compared to the formers which can be considered more as influences by opposition, one must underline the philosopher-physicist, Ernst Mach, whose criticism of Newton’s Principia created a very strong mark on Einstein and his conception of the “absolutes” in physics. In relation to absolute time Mach said: “absolute time can be measured by comparison with no motion; it has therefore neither a practical nor a scientific value; […] It is an idle metaphysical conception”[18]. He was stating the necessity of eliminating the metaphysical from physics; a physical world required conventions and solutions that could be empirically tested. For Mach, the absolute did not have any space in contemporary physics, and Einstein took good note of this fact.

Albert Einstein: Special Relativity and its consequences on Time

In his fundamental text of 1905 (“On the electrodynamics of moving bodies”), where Einstein laid the basis for the “special relativity theory”, the goal was not to eliminate the concepts of “ether” and “absolute time” that were explained before; this was simply the means by which he could complete his two new principles for kinematics: his “relativity principle”, “according to which the laws of physics are the same in any inertial system; and the principle of the “constancy of the velocity of light” in any given inertial system”[19]. But for these two seemingly contradictory principles to fit together, time had to stop being seen as absolute because if so, light would not be able to travel at the same speed in all inertial systems due to Galileo’s “velocity-addition” principle. But, by eliminating the idea of “absolute time”, the speed of light would depend exclusively on the frame of reference.

As a consequence to this last statement, another of Poincaré’s conventionalist statements would also be confirmed by Einstein: the relativity of simultaneity. If light had the same speed in all frames of reference and the time that defines this velocity is relative to the observer, then simultaneity of two events would only be relative to the above said observer.

An example of the relativity of simultaneity can be seen when one looks at the stars: “the light that we see from distant galaxies left them millions of years ago […]. Тhus, when we look at the universe, we are seeing it as it was in the past”[20]. Simultaneity at long distances cannot be defined directly, but only through convention. Even though one is looking at a star in a specific moment, one can say that the light of the star is simultaneous to one looking at it only relative to the Earth’s frame of reference; if seen from the star’s point of view there would be millions of years separating the observer and the light.

Conclusive statements

Having seen (briefly) the influence that Poincaré had on the mathematical and philosophical development of the relativity theory and, noticing that many of the fundamental problems that covered relativity had already been solved by Poincaré, Lorentz or others, years before Einstein published his paper in 1905, one must ask oneself the question: Why then is the relativity theory acknowledged to Einstein?

Poincaré had already developed the relativity principle; he had already solved the possible inconsistencies in Lorentz transformations and he had already reinterpreted Lorentz’s “local time” in a manner in accordance to relativity. The main equations and mathematical considerations that affected the issue were already contained and resolved in papers submitted by Poincaré a year before Einstein published his famous text[21]. Then, how can one solve the question proposed in the former paragraph? The most valid answer may seem trivial and superficial, but it solves the problem: Einstein, opposed to Poincaré, “dared to reform the concepts of space and time”[22]; he gave the iconoclastic step that Poincaré did not risk to take due to his complete trust on tradition’s firm structure.

It can be affirmed without a doubt that Einstein was not the first contributor to relativity theory. He not only structured his theory on others ideas but he also “partly duplicated results already obtained by Lorentz and Poincaré”[23]. But no one else apart from him had such a strong conviction on the theory as to deny some of the most fundamental principles of modern physics.

Many authors twirl around the question of why did Poincaré not give the last step in his search for relativity? Why did he stop, having had already the answers in front of his nose?[24] But instead of spinning around psychological questions, one may simply affirm that the relativity theory does not rest solely on one man; but it was a construction where many relevant thinkers left their mark and “Poincaré’s introduction of the principle of relativity appears to have been a transitional stage between traditional electrodynamics on the one hand and the fully relativistic theory published by Einstein on the other”[25].  It may be seen as a relay race, where one man runs until he has to hand the torch to the next one and so on until the last runner reaches the finish line for the whole team; in this case, Einstein was the last runner and it was Poincaré who gave him the torch.

Annex I: Einstein and Ether-Theory

James Clerk Maxwell developed in the second half of the nineteenth century a series of equations that intended to predict that radio and light waves traveled at a fixed speed but, due to Newton’s assertion that there was no absolute rest, for this theory to be correct, light would have to travel at a fixed speed relative to a fixed frame of reference. For this reason, it was suggested the existence of a substance that was present everywhere: “Light waves should travel through this ether […] and their speed should therefore be relative to the ether”[26], hence fixed.

Before completely denying the ether, Einstein says that he intended to find the experimental evidence of it in the literature, but without any positive results[27]. And it can be considered that the Michelson-Morley experiment was the turning point. Albert Michelson and Edward Morley stated the hypothesis that

“If the Earth is moving through the aether, with the aether at rest in the universe (or filling Euclidean space), then there should be a constant aether wind blowing towards us in the direction we are moving through it”[28].

So they carried out an experiment that intended to discover the presence of ether. Michelson developed an interferometer that used mirrors to split a beam of light, then take the two consequent beams in different directions and recombine them[29]. Their method was to compare the speed of light in different directions to find interference and find the ether’s presence. But all experiments showed no interference, hence there was no experimental proof of the existence of ether.

It is considered that having known of the negative result of this experiment led Einstein to conclude that it was necessary to find a different solution to the light speed constancy problem: “Soon I came to the conclusion that our idea about the motion of the Earth with respect to the ether is incorrect, if we admit Michelson’s null result as a fact”[30].

Bibliography

Burnett, D. G. & Galison, P. (2003) “Einstein, Poincaré & modernity: a conversation”, Daedalus, Spring, pp. 1-15.

Damour, T. (2010) “Time and Relativity”  Séminaire Poincaré, XV, Le Temps, pp. 1-15.

Derrigol, O. (2005) “The Genesis of the Theory of Relativity”, Séminaire Poincaré, I, pp. 1-22.

Einstein, A. (1905) “On the electrodynamics of moving bodies” in A. Einstein & H. Minkowski, (1920) The Principle of Relativity, M. Saha & S. Bose (trans.), Calcutta: University of Calcutta Press, pp. 1-34.

Einstein, A. (1920) Sobre la teoría de la relatividad especial y general, M. Paredes Larrueca (trans.), Madrid 2008: Alianza Editorial.

Einstein, A. (1922) “How I created the theory of relativity”, lecture in Kyoto, 14 December 1922, in Physics Today, (August 1982), pp. 45-47.

Galison, P. (2003) Einstein’s Clocks, Poincaré’s Maps. Empires of Time, New York: W. W. Norton & Company.

Hawking, S. (1988) “2. Space and Time” in A Brief History of Time, London: Bantam Books, pp. 15-36.

Holton, G. (1988) Thematic Origins of Scientific Thought. Kepler to Einstein, Cambridge: Harvard University Press.

Jammer, M. (2006) Concepts of Simultaneity. From Antiquity to Einstein and Beyond, Baltimore: John Hopkins University Press.

Janis, A. (2010) “Conventionality of Simultaneity” in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (fall 2010 Edition), in <http://plato.stanford.edu/archives/fall2010/entries/spacetimeconvensimul/&gt;.

Mach, E. (1893) The Science of Mechanics, T. McCormack (trans.), Chicago 1919: Open Court Publishing.

Pektov, V. (2008) “Conventionality of Simultaneity and Reality” in D. Dieks (ed.), The Ontology of Spacetime II, Amsterdam: Elsevier Publishing, pp. 175-185.

Poincaré, H. (1898) “The Measure of Time” in G. B. Halsted (trans.), The Foundations of Science, New York 1913: Science Press, pp. 222-234.

Poincaré, H. (1902a) “Non-Euclidean Geometries” in J. Larmor (trans.), Science and Hypothesis, London 1905: Walter Scott Publishing, pp. 35-50.

Poincaré, H. (1902b) “The Classical Mechanics” in J. Larmor (trans.), Science and Hypothesis, London 1905: Walter Scott Publishing, pp. 89-110.

Scribner, C. (1964) “Henri Poincaré and the Principle of Relativity”, American Journal of Physics, 32, pp. 672-678.

Topper, D. R. (2013) How Einstein Created Relativity out of Physics and Astronomy, New York: Springer Science+Business Media.


[1] Galison (2003), “Chapter 2. Coal, Chaos, and Convention” and “Chapter 4. Poincaré’s Maps”.

[2] Ibidem.

[3] Ibid., p. 51.

[4] Ibid., pp. 55-56.

[5] Ibid., p. 189.

[6] Poincaré (1898), p. 234.

[7] Poincaré (1902b), p. 90.

[8] Poincaré quoted in Scribner (1964), p. 673.

[9] Einstein (1905), p. 2.

[10]Einstein quoted in Galison (2003), p. 233.

[11] For details on Lorentz’s work see Galison (2003), pp. 205-211.

[12] Holton (1988), p. 205.

[13] Topper (2013), p. 68. For more information on the “ether-theory” see “Annex I”.

[14] Einstein quoted in Galison (2003), p. 235.

[15] For more information on Michelson-Morley’s experiment see “Annex I”.

[16] Topper (2013), p. 44.

[17] Burnett & Galison (2003), p. 8.

[18] Mach (1893), p. 224.

[19] Derrigol (2005), p. 17; originally in Einstein (1905), p. 2.

[20] Hawking (1988), p. 30.

[21] Derrigol (2005), p. 18; Damour (2010), p. 7.

[22] Derrigol (2005), p. 18.

[23] Derrigol (2005), p. 22.

[24] Scribner (1964), p. 676; Holton (1988), p. 203; Jammer (2006), p. 105.

[25] Scribner (1964), p. 674.

[26] Hawking (1988), p. 20.

[27] Einstein (1922), p. 46.

[28] Topper (2013): 50.

[29] A thorough explanation in Galison (2003), pp. 203-205; Topper (2013), pp. 49-53.

[30] Einstein (1922), p. 46.

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