Did Albert Einstein discover the

special theory of relativity?

Mr Shane McLean

Beaconhills College Pakenham

James Clerk Maxwell Prior to Einstein and after the Maxwell equations were discovered

electrodynamics consisted of Maxwell’s equations, current and charge densities and a conjecture on the nature of the aether.

Maxwell simplified the aether by no longer having many different possible aethers.

These were distinguished by degree of homogeneity, compressibility and how the earth drags the aether along with it. These different aethers were replaced by one aether for light, heat, magnetism and electricity.

Optical Phenomena in the 19th Century

Lorentz wrote in 1895 about a dynamic derivation of the Fresnel drag in terms of polarisation induced in a medium by incident electromagnetic waves.

The so called Fresnel aether is explicitly postulated throughout this paper.

The concept of an aether at absolute rest was introduced by Fresnel in 1818 where he considered a liquid moving through a tube with velocity v relative to the aether and a light beam traversing the tube in the same direction.

This was used to derive a result for the net velocity of light in a laboratory.

Optical Phenomena in the 19th Century

Fresnel assumed that the light imparted elastic vibrations to the aether that it traverses. There is a drag coefficient 1 – 1/n2 (n the refractive index of the liquid) as the light is partially held back by the aether in the tube.

In 1886 Lorentz commented that “It seems doubtful in my opinion that the hypothesis of Fresnel has been refuted by experiment”.

Electromagnetic theory in the late 19th Century

In an 1892 paper Lorentz used electron theory to explain certain properties of matter such as conduction of electricity and heat and of dielectric behaviour.

Electrons were discovered experimentally by J.J. Thompson in 1897.

Lorentz attempted to explain the mass of the electron as a consequence of their electric charge and the back reaction of the electric and magnetic fields due to the electrons motion. This vision of electromagnetic mass inspired further work by Lorentz and of Henri Poincare, anticipating significant parts of Einstein’s special relativity. Scientific American June 1 2012.

Electromagnetic theory in the late 19th Century

In the 1892 paper on atomistic electromagnetic theory Lorentz becomes concerned about the consequences of the Michelson-Morley experiment.

Lorentz states ‘This experiment has been puzzling me for a long time, and in the end I have been able to think of only one means of reconciling it with Fresnel’s theory”.

Lorentz then goes on to independently introduce the hypothesis of contraction to maintain Fresnel’s aether. This contraction was equivalent to that introduced earlier by Fitzgerald (1889), Lorentz being unaware of this earlier paper. This is referred to as the Fitzgerald or Fitzgerald-Lorentz contraction up to second order in v/c. Given by the equation below.

George Francis Fitzgerald

The Irish physicist George Francis Fitzgerald circa 1889 suggested that the manner in which one was to reconcile the measurements of Michelson and Morley with the hypothesis that the Earth was moving through the aether was to have the following.

“ that the length of material bodies changes, according as they are moving through the aether or across it, by an amount depending on the square of the ratio of their velocities to that of light”

George Francis Fitzgerald

This change was considered to be an absolute change that was real and due to some as yet unmeasured molecular force due to the electrical properties of the substance. This is a dynamic contraction and not a change relative to a given observer at rest.

Heaviside described Fitzgerald soon after his death. ”He had, undoubtedly , the quickest and most original brain of anybody. A great distinction, it was, I think however, a misfortune regarding his scientific fame. He saw too many openings. His brain was too fertile and inventive. I think it would have been better for him if he had been a little stupid, not so quick and versatile. He would have been better appreciated, except by a few”

Hendrik Antoon Lorentz

Born at Arnhem, The Netherlands, on July 18, 1853, as the son of nursery-owner Gerrit Frederik Lorentz and his wife née Geertruida van Ginkel.

“From the start of his scientific work, Lorentz took it as his task to extend James Clerk Maxwell's theory of electricity and of light. Already in his doctor's thesis, he treated the reflection and refraction phenomena of light from this standpoint which was then quite new. His fundamental work in the fields of optics and electricity has revolutionized contemporary conceptions of the nature of matter”

Hendrik Antoon LorentzA life in science

Through Lorentz’s prestige in governmental circles in his own country, he was able to convince them of the importance of science for national production.

“Lorentz was a man of immense personal charm. The very picture of unselfishness, full of genuine interest in whoever had the privilege of crossing his path, he endeared himself both to the leaders of his age and to the ordinary citizen”

“It may well be said that Lorentz was regarded by all theoretical physicists as the world's leading spirit, who completed what was left unfinished by his predecessors and prepared the ground for the fruitful reception of the new ideas based on the quantum theory”

Lorentz was awarded the The Nobel Prize in Physics in 1902 along with Pieter Zeeman.

Hendrik Lorentz died at Haarlem on February 4, 1928.

Hendrik Antoon LorentzThe physics

In 1899 Lorentz wrote down what we now call the Lorentz transformations up to a scale factor ε. He also introduced concepts such as a general time t and a local time t’. Lorentz did however consider there to be only one true time.

In 1904 Lorentz writes down the transformations with the scale factor set to one after considering the equations of motion of an electron in an external field. He attempts to prove Lorentz covariance for the Maxwell-Lorentz equations but makes an error and is only able to obtain covariance to first order in v/c.  

Voigt noted in 1887 that equations of a certain type keep the same form if new space-time variables are introduced. These new space-time variables are the Lorentz transformations up to a scale factor.

Lorentz was aware of Voigt’s work as they corresponded about the Michelson- Morley experiment. He does not however appear to have been aware of these transformations given by Voigt used in his argument for the elastic theory of the propagation of light in an elastic incompressible medium.

The Lorentz Transformations

The Lorentz transformations for relative motion in the x direction

The Lorentz transformations in matrix form

PoincaréThe last polymath

Born: 29 April 1854 in Nancy, Lorraine, FranceDied: 17 July 1912 in Paris, France

Henri Poincaré's father was Léon Poincaré and his mother was Eugénie Launois. Henri was born in Nancy where his father was Professor of Medicine at the University.

Toulouse commented on Poincaré:-

... does not make an overall plan when he writes a paper. He will normally start without knowing where it will end. ... Starting is usually easy. Then the work seems to lead him on without him making a wilful effort. At that stage it is difficult to distract him. When he searches, he often writes a formula automatically to awaken some association of ideas. If beginning is painful, Poincaré does not persist but abandons the work.

Miller notes: Incredibly, he could work through page after page of detailed calculations, be it of the most abstract mathematical sort or pure number calculations, as he often did in physics, hardly ever crossing anything out.

Poincaré Poincaré wrote an article in 1898 ‘La Mesure du Temps’ , he noted that

“we have no direct intuition about the equality of two time intervals. People who believe they have this intuition are the dupes of an illusion”.

Poincaré concludes in this paper that “The simultaneity of two events or the order of their succession, as well as the equality of two time intervals, must be defined in such a way that the statement of natural laws be as simple as possible”.

He does not make remarks about any concerns with electrodynamics. Later in 1900 and 1904 Poincaré does consider the work of Fizeau and Lorentz. In 1904 Poincaré asked the question “What is the aether? how are its molecules arrayed? Do they attract or repel each other?”

https://www.youtube.com/watch?v=sMyahdOOwU4

Poincaré Poincaré also remarked on the idea of an absolute velocity. “If we

succeed in measuring something we will always have the freedom to say that it is not the absolute velocity, and if it is not the velocity relative to the aether, it can always be the velocity relative to a new unknown fluid with which we would fill space.”

He considers clocks that were synchronised using light signals and concluded that “Clocks regulated in this way will not mark the true time, rather they will mark what one may call the local time” and he also points out that ” As demanded by the relativity principle the observer cannot know whether he is at rest or in absolute motion”.

Poincaré

Poincaré suggested that “Perhaps we must construct a new mechanics, in which the velocity of light would be an impassable limit”.

This indicated just how close this is to Einstein’s relativity. Poincaré however requires there to be further hypotheses.

In 1905 Poincaré obtains the correct form of the Lorentz transformations a few weeks after Einstein.

These further hypotheses demonstrate that Poincaré had not discovered the relativity theory of Einstein.

Poincaré In 1909 Poincaré described a new mechanics based on three hypotheses.

Bodies cannot attain velocities larger than the velocity of light.

The laws of physics are the same in all inertial reference frames.

A body in translational motion suffers a deformation in the direction in which it is displaced. Poincaré did not therefore understand as late as 1909 one of the basic traits of Einstein’s theory, that the contraction of rods is a consequence of the first two postulates of special relativity.

Previously in 1904 Poincaré also considered that further hypotheses besides the two stated above were required, namely that bodies in motion suffer uniform contraction in their direction of motion.

Poincaré also did not deduce that the Lorentz transformations implied the contraction of rods.

What Einstein knew in 1905

Einstein considered the Michelson-Morley experiment as the most important one of all the null experiments on the aether drift. Einstein does not make clear in articles written and lectures given between 1907 – 1921 whether he knew about the Michelson-Morley experiment prior to 1905.

Einstein stated that he knew the work of Lorentz up to 1895. He mentions Maxwell, Hertz and Lorentz in his first paper on relativity.

In 1905 Einstein did not know about the Lorentz transformations. Einstein invented these transformations independently.

What Einstein knew in 1905

In 1905 Einstein knew of on Lorentz’s work up to 1895. He was therefore aware of the following:

Most probably Lorentz’s concern about the Michelson-Morley experiment, although this is not clear.

His first order Lorentz transformation. This discussed the relative motion of a coordinate system with respect to a nonmagnetic substance at rest relative to the aether.

First order theorem for optical phenomena, the need to introduce a contraction hypothesis and a new postulate of the Lorentz force.

What Einstein knew in 1905

Michelson-Morley was discussed in Lorentz’s paper and Einstein was familiar with this paper prior to 1905.

In Einsteins first paper on relativity he mentions “the failed attempts to detect a motion of the earth relative to the “light medium”” without actually specifying which particular attempts. Michelson and Fizeau were not mentioned.

The result of the Michelson-Morley experiment did however influence the ideas of H. Lorentz and Fitzgerald as discussed previously.

What Einstein concluded

Einstein rejected the nineteenth century aether as inherently artificial and unconvincing. This was opposed to looking to resolve the conflict illuminated by the Michelson-Morley experiment and the prevalent version of the aether in the late nineteenth century.

Einstein derived what we refer to length contraction as a consequence of the relative motion of an observer. The quantitative nature of this contraction given by the Lorentz transformations which he independently discovered.

Einsteins efforts culminated in 1905 with the following postulates of special relativity or as the first paper on relativity was called. On the Electrodynamics of moving bodies, "Zur Elektrodynamik bewegter Körper".

The laws of physics are the same in all inertial reference frames.

The speed of light in a vacuum propagates with the speed c, regardless of the state of motion of the light source.

Did Einstein discover the special theory of relativity? The answer is yes. The statement below clearly indicates the status of discovery of the

special theory of relativity.

“The solution anticipated by Poincaré was given by Einstein in his memoir of 1905 on special relativity. Einstein accomplished the revolution that Poincaré had foreseen when at the time the development of physics seemed to be at an impasse”.

References

Subtle is the Lord, The science and life of Albert Einstein. Abraham Pais. Oxford University Press 1982.

Scientific American June 1 2012.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1902/lorentz-bio.html

http://www-history.mcs.st-and.ac.uk/Biographies/Poincare.html

Thank you to Beaconhills College, Pakenham for allowing me to present.