The General Theory of Relativity and the “Magnificent Nine” (PART 2)

Gunnar Nordström and his Theory of Relativity

Gunnar Nordström was born on March 12, 1881. He was a Finnish theoretical physicist best remembered for his theory of gravitation similar to Einstein 1912-1913. The equivalence principle was valid in his theory and it also satisfied ‘red shift of the spectral lines from the sun’, such as Einstein's theory; it led to a Perihelion like the one predicted by Newton's law, and, it could not explain the deflection of light near the sun, because in Nordstrom's theory, the velocity of light was constant. Einstein's 1913-1914 theory, the field equations of which were not generally covariant, remained without empirical support. Thus a decision in favor of one or the other theory - Einstein's or Nordstrom's - was impossible on empirical grounds. Einstein began to study Nordstrom's theory from the theoretical point of view and he developed his own Einstein-Nordstrom theory on the basis of his conception of the natural interval. Eventually, in a joint 1914 paper with Lorentz's student Adrian Fokker, Einstein showed that a generally covariant formalism is presented from which Nordstrom's theory follows if a single assumption is made that it is possible to choose preferred systems of reference in such a way that the velocity of light is constant; and it was done after Einstein had failed to develop a generally covariant formulation for his own theory.

In theoretical physics, Nordström's theory of gravitation was a predecessor of general relativity. Strictly speaking, there were actually two distinct theories proposed by the Finnish theoretical physicist Gunnar Nordström, in 1912 and 1913 respectively. The first was quickly dismissed, but the second became the first known example of a metric theory of gravitation, in which the effects of gravitation are treated entirely in terms of the geometry of a curved space-time.

Neither of Nordström's theories are in agreement with observation and experiment. Nonetheless, the first remains of interest insofar as it led to the second. The second remains of interest both as an important milestone on the road to the current theory of gravitation, general relativity, and as a simple example of a self-consistent relativistic theory of gravitation. As an example, this theory is particularly useful in the context of pedagogical discussions of how to derive and test the predictions of a metric theory of gravitation. Gunnar Nordström died on December 24, 1923.

Adriaan Daniel Fokker, Einstein’s Assistant

Adriaan Daniel Fokker was born on August 1, 1887 in Buitenzorg (now Bogor) on Java in Indonesia, then Dutch East India, where his father was a successful businessman. Fokker was educated in the Netherlands as a mining engineer from Delft University of Technology, and as a physicist from the Leiden University. In Leiden he earned his doctorate in 1913. In physics Fokker’s name is best known through the Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation of second order, which describes the time evolution of the probability distribution of a physical variable subjected to a stochastic force, in addition to friction and possibly other driving forces. The prototypical example is Brownian motion. The Fokker-Planck equation was contained in Fokker’s thesis, and was independently derived by Max Planck.

During 1913-14 Fokker worked in Zürich as Albert Einstein’s assistant, and published an article in general relativity with Einstein as coauthor. He kept a lifelong interest in relativity, as witnessed by his 1963 article in the proceedings of the DKNVS. His best known contribution in this field is a determination of the change of direction when a gyroscope (like the Earth) moves in a closed orbit in a gravitational field.

Fokker made several contributions to special relativity, and some less well-known contributions to general relativity, particularly in the area of geodetic precession. The geodetic effect (also known as geodetic precession, the Sitter precession or the Sitter effect) represents the effect of the curvature of space-time, predicted by general relativity, on a vector carried along with an orbiting body.

In 1923 Fokker was appointed professor of physics at Delft University of Technology. However, after five years he preferred to succeed Lorentz as curator at the Teyler Museum in Haarlem, a position that was combined with a special professorship at Leiden University. Adriaan Daniel Fokker died on September 24, 1972.

Hendrik Lorentz: The Nobel Prize Winner

Hendrik Lorentz born in Arnhem Netherlands, on 18 July 1853, his father, Gerrit, was the owner of a successful nursery in the city. Unfortunately, his mother died when Lorentz was four years old.
He pursued his professional studies at the University of Leiden obtaining his bachelor degree in Science with specialization in Mathematics and Physics. After he finished his degree he worked as a teacher, while at the same time continued his research on reflection as well as refraction of light for his thesis.

Lorentz obtained his doctorate in 1875 based on his thesis ‘the reflection and refraction of light’ amplifying Maxwell’s electromagnetic theory.

From 1892 onwards Lorentz worked on the electromagnetism phenomenon in relation to the propagation of light, and his theories included something that was never used in the past; the usage of ‘local time’ implying a time variable. His findings were used by Albert Einstein on his theory of special relativity.

Hendrik is also best known for his work on the FitzGerald-Lorentz contraction. In 1904, he introduced his transformations which basically described the increase of mass, the reduction of length, and the time dilation of a body that is moving at speeds closest to the velocity of light.
This served as the fundamentals of Einstein’s special theory of atoms and theories of relativity. In 1953, Einstein wrote that Lorentz meant more to him than all the others he met on his life’s journey.
He won the Nobel Prize in Physics in 1902 for his work in the Zeeman Effect. In 1917, he won the Franklin Medal Catharina Kaiser and the following year he was awarded the Copley Medal.
Hendrik Lorentz died on February 4, 1928, at the age of 74, in Haarlem.

David Hilbert: A ‘Pure Mathematician’

David Hilbert was born on January 23, 1862, in Königsberg, Prussia, on the Baltic Sea. Prussia later merged into Germany. His father was a judge while his mother’s family were merchants.His mathematics teacher, Hermann Morstein, once wrote “Hilbert has a comprehensive knowledge of mathematics, with the ability to solve problems using his own methods.”

After completing his Ph.D., Hilbert spent winter at the University of Leipzig and then Paris. On 1886, David Hilbert worked at the University of Königsberg, first as a lecturer, then as a professor.
He was a "pure" mathematician. When planning a visit from Bonn, where he was immersed in studying physics, his fellow mathematician and friend Hermann Minkowski joked he had to spend 10 days in quarantine before being able to visit Hilbert. In fact, Minkowski seems responsible for most of Hilbert's physics investigations prior to 1912, including their joint seminar in the subject in 1905.

In 1912, three years after his friend's death, Hilbert turned his focus to the subject almost exclusively. He arranged to have a "physics tutor" for himself. He started studying kinetic gas theory and moved on to elementary radiation theory and the molecular theory of matter. Even after the war started in 1914, he continued seminars and classes where the works of Albert Einstein and others were followed closely.

By 1907 Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years with a confounding problem of putting the theory into final form. By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject. Einstein received an enthusiastic reception at Göttingen. Over the summer Einstein learned that Hilbert was also working on the field equations and redoubled his own efforts. During November 1915 Einstein published several papers culminating in "The Field Equations of Gravitation". Nearly simultaneously David Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations. Hilbert fully credited Einstein as the originator of the theory, and no public priority dispute concerning the field equations ever arose between the two men during their lives.

Throughout this immersion in physics, Hilbert worked on putting rigor into the mathematics of physics. While highly dependent on higher math, physicists tended to be "sloppy" with it. To a "pure" mathematician like Hilbert, this was both "ugly" and difficult to understand. As he began to understand physics and how physicists were using mathematics, he developed a coherent mathematical theory for what he found, most importantly in the area of integral equations. When his colleague Richard Courant wrote the now classic Methoden der mathematischen Physik (Methods of Mathematical Physics) including some of Hilbert's ideas, he added Hilbert's name as author even though Hilbert had not directly contributed to the writing. Hilbert said "Physics is too hard for physicists", implying that the necessary mathematics was generally beyond them; the Courant-Hilbert book made it easier for them.

David Hilbert died on February 14, 1943 in Germany. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries.

The Breeding Ground

One of the interesting historical aspects of the modern relativity is that we cannot give credit to a single individual. Almost every idea and formula of the theory had been anticipated by others scientist.

For example, Lorentz covariance and the inertia of electromagnetic energy were both arguably implicit in Maxwell’s equations. Also, Voigt formally derived the Lorentz transformations; at least for electromagnetism of the wave equation. In the context of electro-dynamics, Fitzgerald, Larmor, and Lorentz had all arrived at the Lorentz transformations by the 1880’s. (At least for electromagnetism. Although they did not understand that these represent the relationships between inertial coordinate.)

The Clouds over Einstein Head

As any other theory, we will always find individuals who claim that other scientists have been part of the formulation of the Relativity Theory. One of the historians of the theory said; “It seemed obvious that the real founder of Relativity was the French scientist Henri Poincaré, and that the text of Einstein was not entirely his creation. It was really difficult to understand how this had been possible for Einstein in the few available weeks he had, especially if we further consider that he had not previously published anything on this subject. Poincaré worked entirely on the theory before 1905 along with scientific texts of lesser importance.”

Detractors also claim that “at the dawn of the twentieth century ‘Mr. Henri Poincaré proved to the science community, that they were working in the wrong direction! Also at the time, Europe and France were just in the middle of the worst pre-war crisis between them. David Hilbert, who was already awfully jealous of Poincaré, decided to react about Mr. Poincaré’s theory. He organized a machination in order to give to Germany the relativistic works of his French rival.

But as risks were high, they were given to a young man that had little to lose, and much to gain.’ ‘Poincaré relativity principle of September 1904 was conceived before "The young Einstein and his advent of Relativity"... however, it was not attributed to Henri Poincaré, which of course was not taken under consideration for political reasons. To ignore systematically the relativistic work of Poincaré and the neighboring works; look for a German who would accept the risks of this manipulation by publishing the Poincaré results under his signature. It was then that Einstein had appeared.

To ask for the help of Max Planck was an infamy. Poincaré’s discovery did appear on a journal, before Einstein’s theory which was then the equivalent of Nature and Science today. Max Planck would have thought, as Europe was at the verge of war, that his duty was to give Germany this major scientific discovery. Let us recognize that many French of great integrity considered, during the Second World War, that their duty was to act at the Germans’ expense each time, when they had an opportunity, at least give them wrong information when they were asking their way...”

Ending Notes

A beautiful theory must be appreciated as a legacy of science to the young physicist who really cares about the theory itself, and not its political or historic implications. As the old saying goes, “History remembers Generals not soldiers”. However, this should not be taken under consideration, especially when many people were involved on the development of this theory throughout history.

A real history investigator will sooner or later find the historic implications and the truth behind the scenes, but under no circumstances will such findings even touch, with a wind of a thought, the extraordinary and beautiful theory which was presented to the world one century ago. This theory was taken in for consideration and development, and under the guidance of a new generation of physicists. Now these young physicists must keep one thing in mind, that is, the advancement of humanity in relation to the reality of the physical world.

“There are two histories: the official and lying history, and the secret history in which are the real reasons of events” – Honoré de Balzac -

Part 2 of 2

Sources:
Tripod.com
Naturecaresmath.com
C. Marshall
Teslasociety.com
Icratt.com
Michaelsierner.com
Citesser.ixt.psu.edu
Booksgoggle,com
Arxiv.org
Wikepedia

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