History of special relativity

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See also: Special relativity

Contents 1 Pre-1900 relativity 2 The formulation of special relativity 3 Einstein's 1905 papers 4 Looking back at special relativity 5 Criticisms of special relativity 6 See also 7 References 7.1 Works by Albert Einstein 7.2 Works by Henri Poincaré

[edit] Pre-1900 relativity

The principle of relativity was introduced by Galileo. Overturning the old absolutist views of Aristotle, it held that motion, or at least uniform motion in a straight line, only had meaning relative to something else, and that there was no absolute reference frame by which all things could be measured. Galileo also assumed a set of transformations called the Galilean transformations, which seem like common sense today. Galileo produced five laws of motion.

In contrast, Newton inferred from the effects of rotation the existence of an "absolute space" -- an absolute reference frame -- on which he based his theory. Thus he constructed an improved set of equations containing only three laws of motion. Nevertheless he kept the principle of relativity for what can be observed -- uniform motion could not detect his absolute space.

The principle of relativity seemed to work well for everyday phenomena involving solid objects, but light was still problematic. Newton believed that light was "corpuscular", but later physicists found that a transverse wave model of light was more useful. Mechanical waves travel in a medium, and so it was assumed for light. This hypothetical medium was called the "luminiferous aether." It seemed to have some conflicting properties, such as being extremely stiff, to account for the high speed of light, while at the same time being insubstantial, so as not to slow down the Earth, which moves through it. The idea of an aether also seemed to introduce the idea of a detectable absolute frame of reference.

In the early 19th century, light, electricity, and magnetism began to be understood as aspects of electric and magnetic fields. Maxwell's equations related the known facts that changes in magnetic fields causes changes in electric fields and vice versa, in such a way that a solution for propagating electro-magnetic waves could be set up. These wave solutions to the equations travel at a constant speed, c, which arises as the ratio of constants in the equations. This turned out to correspond to the speed of light, so that Maxwell identified 'light' to be an electromagnetic aether wave as well.

As the equations referred to light propagation with respect to the hypothesised aether, physicists tried to use this idea to measure the earth's velocity with respect to the aether. The most famous such attempt was the Michelson-Morley experiment. While these experiments were controversial for some time, a consensus emerged that the speed of light does not vary with the speed of the observer, and since -- according to Maxwell's equations -- it does not vary with the speed of the source, the speed of light must be invariant (the same) between reference systems.

Since electromagnetic forces travelling at the speed of light within an object hold an object's atoms together, high speed motion would rearrange these forces, changing the object's shape and causing a shortening. After carefully considering the physics of fast moving objects within an Aether, Hendrik Lorentz proposed a solution in which objects and observers travelling with respect to a stationary aether undergo a physical shortening (Lorentz-Fitzgerald contraction) and a change in temporal rate (time dilation) as well as an offset in time along a moving object (lack of simultaneity).

This theory allowed a conciliation of electromagnetics and Newtonian physics by correcting the Galilean transformations. When the velocities involved are much less than the speed of light, the resulting laws simplify to the Galilean transformations. However, at that point in time Lorentz didn't realise the full power nor all implications of his theory. In addition, he still assumed the existence of an Aether. The theory, today often called Lorentz Ether Theory (LET) was criticized because of its apparently ad hoc nature. For all practical purposes however, it is the same theory as SRT, and he later taught it as such.

[edit] The formulation of special relativity

• In 1889 George FitzGerald published the first known paper about a relativistic effect, claiming that the Michelson-Morley experiment could be explained introducing a length contraction in the direction of the movement.

• In 1895 Hendrik Lorentz published a `first-order' version of the Lorentz transformations, for which electrical and optical phenomena in a moving system were independent of motion if terms of order v² / c² could be ignored. In these transformations he introduced the concept of local time. Simultaneous events in the rest frame (having the same time coordinate t) had different time coordinates .

• In 1898 in a paper called "La Mesure du Temps", Henri Poincare claimed that simultaneity of distant events would have to be established by convention, specifying that lightspeed is taken to be the same in all directions (see relativity of simultaneity).

• In 1899, Lorentz presented a `second-order' version of the Lorentz transformations, which included a time dilation in the moving frame of an undetermined amount. He showed that electrical and optical phenomena in the moving system were independent of motion even if terms of order v² / c² were retained.

• Joseph Larmor published the correct transformations in 1897 and again in a book in 1900 and was the first to predict time dilation [1]. The significance of this work apparently went unnoticed in Europe.

• In 1900 Poincaré published a paper in which he explained that Lorentz's local time arose from a conventional method of synchronising clocks in a moving frame - by exchanging light signals assumed to travel with the same speed relative to the moving frame in both directions. This method is very similar to the one proposed by Einstein ([Sta89, p. 893, footnote 10]). He repeated this explanation in many subsequent `popular science' books. In the same paper he considered radiation as a fictitious fluid with effective mass of m = E / c², as mentioned above [Poi00].

• In 1900 Henri Poincare published a paper in which he said that radiation could be considered as a fictitious fluid with an equivalent mass of m_r = E / c². He derived this interpretation from Lorentz's `theory of electrons' which incorporated Maxwell's radiation pressure.

• In 1902, Poincaré rejected the notion of absolute space and time. The following appeared in his 1902 book La science et l'hypothese ([Poi02]):

1° Il n'y a pas d'espace absolu et nous ne concevons que des mouvements relatifs ; cependant on énonce le plus souvent les faits mécaniques comme s'il y avait un espace absolu auquel on pourrait les rapporter ;

2° Il n'y a pas de temps absolu ; dire que deux durées sont égales, c'est une assertion qui n'a par elle-même aucun sens et qui n'en peut acquérir un que par convention ;

3° Non seulement nous n'avons intuition directe de l'égalité de deux durées, mais nous n'avons même pas celle de la simultanéité de deux événements qui se produisent sur des théâtres différents ; c'est ce que j'ai expliqué dans un article intitulé la Mesure du temps, Revue de Métaphysique et de Morale, t.~VI, p.~1--13 (janvier 1898); voir aussi la Valeur de la Science, chapitre II.;

1° There is no absolute space, and we only conceive of relative motion; and yet in most cases mechanical facts are enunciated as if there is an absolute space to which they can be referred.

2° There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by a convention.

3° Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places. I have explained this in an article entitled " Mesure du Temps."

• In many commentaries on Lorentz's work, 1900-1904, Poincaré used the phrase `the principle of relative motion' a familiar cornerstone of Newtonian mechanics, which he said was called into question by electro-magnetic theory, but apparently salvaged by Lorentz's theory. He expressed some dissatisfaction with Lorentz's theory by claiming it contained `too many hypotheses'.

• In 1904, Lorentz published the correct transformations and derived a number of results from them, such as the variation of mass with velocity, and the inability of electrical or optical experiments to detect motion of the reference frame.

• In Sept 1904, Poincaré spoke at an international conference in St Louis in which he discussed "the principal results" of Lorentz's 1904 paper. Poincaré there spoke of "The Principle of Relativity", which he was now more confident would be true for electrodynamics. Poincaré's version of the Principle of relativity: "The laws of physical phenomena must be the same, whether for a fixed observer, as also for one dragged in a motion of uniform translation, so that we do not and cannot have any means to discern whether or not we are dragged in a such motion." While Lorentz suggested the Lorentz transformation equations, Poincaré pointed out the full observational symmetry that follows from them, recognizing them as a solution for the relativity principle. He expressed unease about the violations of the principle of conservation of momentum and mass in the radiation emission process.

• On 5 June 1905 Poincaré spoke at the Academy of Science in Paris and some days later a five page version of that talk was published in Comptes Rendus de l'Academie des Sciences, v140, pp 1504-08 in which he discussed Lorentz's 1904 paper. He wrote "the results that I have obtained agree on all important points with those of Lorentz; I have been led to only to modify and complete them on some points of detail" (Poincaré 1905). He went on to write "the essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz)". He then wrote the Lorentz's transformations in their modern form, having introduced a slightly different notation from that Lorentz had used, and having re-arranged the equations algebraically. He also gave different expressions from those of Lorentz for the electric charge density and the convection current of an electron moving with respect to the moving frame (and moving with respect to the rest frame), and consequently derived expressions for the electric force on the moving electron which differed "also a little from those of Lorentz" (Poincaré 1905). He said the "ensemble of these transformations together with all rotations of space" form a group (but did not give details of the proof), and connected this group property with the impossibility of measuring absolute motion. Poincaré noted that he was led by Lorentz's results to suppose "that inertia is a completely electromagnetic phenomenon, as it is generally considered to be since the experiment of Kaufmann" (Poincaré 1905).

[edit] Einstein's 1905 papers

In 1905, Albert Einstein published his "Elektrodynamik" paper [Ein05c]. Einstein's paper derived the Lorentz equations from the Principle of relativity and the observed constancy of light speed, without assuming the presence of an aether. (Because the aether was not used in the derivation, many physicists use Ockham's razor to remove it entirely, since, as with Poincaré's formulation, no uniform speed relative to an ether can be detected anyway). Einstein wanted to know what was invariant (the same) for all observers. Some modern derivations use simple geometry, including the Pythagorean theorem.

The original title for Einstein's paper translates from the German as "On the Electrodynamics of Moving Bodies". Max Planck suggested the term "relativity" to highlight the notion of transforming the laws of physics between observers moving relative to one another, and the term 'Special' was later given to it by Einstein in order to distinguish it from the general theory of relativity.

In his September 27, 1905 paper, "Does the Inertia of a Body Depend Upon Its Energy Content?", ("Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?") in Annalen der Physik [Ein05d], Einstein prominently featured the formula E=mc². Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies. He was the first to suggest that when a material body lost energy (either radiation or heat) of amount E its mass decreased by the amount E / c² - generalizing the idea of the mass-energy equivalence from the "fictitious fluid" proposed by Poincaré.

Einstein's Elektrodynamik paper contains no references to other literature. It does mention Lorentz, but only in §9, part II in connection with the treatment of the electromagnetic field. Poincaré is not mentioned.

[edit] Looking back at special relativity

One might ask, "Did the founders of special relativity need to invent new mathematics for the mathematical model that is spacetime theory?" The answer is that today we see special relativity as a corner of applied linear algebra, but at the time Lorentz, Einstein, and Minkowski were doing mathematics, that field was still in its infancy; there were no textbooks on linear algebra as modern vector space and transformation theory, and the matrix notation of Cayley (that unifies the subject) was yet to catch-on. The actual Lorentz transformations are a mapping concept inherent in tessarine multiplication, an idea put forward by James Cockle in 1848. In his short (34 year) life, William Kingdon Clifford used this multiplication with the evocative description "motor algebra". The lecture "The Principles of the Algebra of Physics" by Alexander MacFarlane in 1891 before the American Association for the Advancement of Science marks the beginning of public discussion of this mathematics in the context of academic physics. The talk was published in the Proceedings of AAAS and MacFarlane also promulgated the text in pamphlets.

Minkowski space can be viewed as watered-down hyperbolic quaternions which arise under the premise that every spacetime subplane has a split-complex number structure. This premise, taken from MacFarlane's 1891 lecture, sparked a significant response in the 1890s, and a revision by MacFarlane in 1900.

[edit] Criticisms of special relativity

Criticisms of relativity theory are normally done from a number of different perspectives. Early criticism centered on lack of evidence, but modern evidence is completely overwhelming. Many seem to believe, or perhaps hope, that the world really doesn't work the way an enormous number of experiments show that it does. Most just seem to misunderstand the physics and fail to grasp the theory, or simply disagree with popular interpretation.

Another cause of criticism was the existence of several apparent inconsistencies. Since the works of Herman Minkowski we know that the special theory is equivalent to a four dimensional geometry and therefore self-consistent. For this reason consistency can be assumed and only experimental facts could eventually lead to a rejection of the theory.

Herbert Dingle was a respectable astrophysicist who was initially a supporter and book author of relativity, but his interpretation of special relativity was subtly different than Einstein's. Eventually he decided that the theory was inconsistent, and he began a life-long condemnation of relativity theory in general. His 'proof' that special relativity theory is inconsistent was based on his own interpretation of relativity and was largely rejected by other scientists. Besides, his alternative theory is incompatible with experimental evidence.

One early criticism has been that light travels simply with the Earth in a so-called "co-moving luminiferous aether". The light travels trough its "immedeately surrounding physical reality", and obtains a speed which is different for observers who travel at different speeds relative to each other, as is normal with every other object known to man. The idea was that the Michelson-Morley experiment null result was not the theoretical enigma some scientists believed it to be, and that apparently the then current understanding of light needed to be changed according to this new result: the medium for light was not rigid after all. But science had already concluded on the basis of stellar aberration that there had to be a rigid aether which carried the light as the Earth moved through it. The outcome of the two experiments suggested contradictory conclusions: was the aether local and fluid, or was it universal and rigid? Hendrik Lorentz's solution made the Earth shorter in the direction of travel around the Sun and later also modified the speed of time. This was laughed at by scientists at first, but Einstein's interpretation of it left most scientists speechless, and the press ecstatic. Einstein's interpretation is currently believed by professional scientists to have been correct, though there are still dissenters. Some opponents of Special Relativity suggest that Einstein has gained the mythical status of a super human genius.

[edit] See also

Priority disputes about Einstein and the relativity theories

[edit] References

[edit] Works by Albert Einstein

[Ein05c] 

Zur Elektrodynamik bewegter Körper, Annalen der Physik 17(1905), 891-921. Received June 30, published September 26, 1905. Reprinted with comments in [Sta89], p. 276-306 English translation, with footnotes not present in the 1905 paper, available on the net

[Ein05d] 

Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?, Annalen der Physik 18(1905), 639-641, Reprinted with comments in [Sta89], Document 24 English translation available on the net

[Sta89] 

John Stachel (Ed.), The collected papers of Albert Einstein, volume 2, Princeton University Press, 1989

[edit] Works by Henri Poincaré

[Poi00] 

La Theorie de Lorentz et le Principe de Réaction, Archives neérlandaises des Sciences exactes et naturelles, 2e série, 5(1900), p. 252-278, Recueil de Travaux offert à M. Lorentz à l'occasion du 25e anniversaire de son doctorat, Reprinted in Oeuvres, vol. IX, p. 454-488. An English translation, put into modern notation by V. A. Petrov, is given in [Log05, p. 113-120]

[Poi02] 

La science et l'hypothèse, E. Flamarion, Paris, 1902. Electronic version, English translation thereof.

[Poi04a] 

L'état actuel et l'avenir de la physique mathématique., Bulletin des sciences mathématiques 28(1904), 302-324. Address delivered before the Section of Applied Mathematics of the International Congress of Arts and Science, St. Louis, September 24, 1904

[Poi04b] 

The Present and the Future of Mathematical Physics, Bull. Amer. Math. Soc., 12(1906), 240-260, engl. transl. of [Poi04a] by J. W. Young.

[Poi04c] 

The Present and the Future of Mathematical Physics, Bull. Amer. Math. Soc. (new series), 37(2000), 25-38, reprint of [Poi04b]

[Poi05] 

Sur la Dynamique d'Électron, Comptes rendus de l'Academie des Sciences, 140(1905), p. 1504-1508. Reprinted in Oeuvres, vol. IX, p. 489-493

[Poi06a] 

Sur la Dynamique d'Électron, Rendiconti del Circolo matematico di Palermo, 21(1906), 129-176. Submitted July 23, 1905. Reprinted in Oeuvres, vol. IX, 494-550