What’s the source of Einstein’s creativity?
Not his mind — his heart!
In 1641, Dutch philosopher René Descartes declared:
“Mind and body are distinct and separable.”
Since then, scientists are assumed to work mainly through their mind whereas artists depend on their soul, which is in the body, especially in the heart. But that picture is wrong. Without a heart, without feelings, without deep-ingrained intuitive images, no logical work is possible. We shall see it especially pronounced in Einstein’s works.
Above everything, Einstein had a strong sense for democracy. He hated his teachers because of their dictatorial conduct; he hated the military because of their mindless submission; he hated the dictator that soon came to power in Germany; and he hated people that told him what he should or shouldn’t do. For him, everybody was equal to everybody. This emphasis on equality became the second postulate of his special relativity theory (srt), the first being the constancy of light. In srt every observer sees the same as every other observer. Every inertial frame (that is a frame without forces) experiences the same phenomena. Although that got him into trouble — democracy in srt leads to a series of logical problems, known as “paradoxes”, still not satisfactorily solved after more than 100 years.
If you add aesthetics to democracy, you get symmetry. Theoretical physicist James Clerk Maxwell (1831–1879), because of his strong feeling for symmetry, added a “displacement current” to his famous equations to make them symmetric (which they weren’t — the “curl”, depicting rotation, always is asymmetric). There even is a new theory called “supersymmetry”, where every particle has a mirror-particle in another world.
Paul A. M. Dirac (1902–1984) especially valued beauty.
“A physical law must possess mathematical beauty.”
Dirac wrote on the blackboard when he visited the University of Moscow in 1956.
Physicist Hermann Bondi said about Einstein:
“He was convinced that beauty is a guiding principle in the search for important results in theoretical physics.”
In the introduction to his famous treatise (“On the Electrodynamics of Moving Bodies”) from 1905, he writes:
“It is well known that Maxwell’s electrodynamics, when applied to moving bodies, leads to asymmetries that do not seem to be inherent in the phenomena. Consider, for example, the electrodynamic interaction between a magnet and a conductor. The observable phenomenon here depends only on the relative movement of the conductor and the magnet, whereas according to the usual view, the two cases in which one or the other of these bodies is the moving one are to be strictly separated from one another.”
Einstein thus formulated his principle of relativity — every uniform movement is equal — for electromagnetic induction, although he himself knew that the physical states were completely different:
“If the magnet moves and the conductor is at rest, an electric field is created in the vicinity of the magnet, which generates a current at the locations of the conductor. But if the magnet is at rest and the conductor moves, no electric field is created in the vicinity of the magnet, but an electromotive force is created in the conductor, which gives rise to electric currents of the same size and the same course as the electric forces in the first case.”
Again, Einstein’s obsession with symmetry got him into trouble when developing the general relativity theory (grt). This episode from the history of science shows in an exemplary way how the concept of symmetry (often synonymous with “harmony” and “beauty”) drives a physicist (Albert Einstein) into a dead end, whereas a mathematician (David Hilbert) doesn’t care, carrying calculations according to higher principles. For a mathematician, symmetry at most is an aid, not a goal in itself.
To understand Einstein’s difficulties when developing general relativity, look at these two equations:
(1) A = B
(2) A + x = B
Whatever the symbols mean, which one do you like better? Any physicist would say: equation (1), because what’s the point of the stupid x in formula (2)? Einstein thought the same, with fatal consequences. Since the formulation of the special theory of relativity (1905), his goal was to develop a general theory of the world in which reality could be described using the curvature of space, i.e. as an equation:
Mathematics = physics, or more specific:
Curvature of spacetime = matter + energy
Einstein had mastered the mathematical discipline that was used to describe curved spaces, tensor calculus, also known at the time as “Ricci calculus”.
In this calculus there is a quantity Rik, the curvature or Riccitensor, which describes the curvature of space at every point. This gives us the left-hand side. On the right-hand side, Einstein thought of a tensor that contains everything of physical significance (masses, energies, potentials). He called it the “energy-momentum tensor” and denoted it by Tik. He found an equation that, in its simplest form, looks like this:
Rik = kTik
k is a constant for converting mathematical units into physical ones. This formula corresponds exactly to Einstein’s program — only it is wrong. That became apparent when he tried to transfer it to another (arbitrary) coordinate system. His mathematician friend Marcel Großmann could not help him either. The two of them had already been working on the problem for almost 10 years!
In desperation, Einstein went to Göttingen, the capital of mathematical physics, in 1915. He delivered a lecture about his ideas, his plans and problems. Hilbert, one of the greatest mathematicians of the 20th century and always very interested in fundamental questions of physics, listened carefully, then sat down at his desk and — with the help of a mathematical procedure he had refined (a variational principle) — found the correct equation in no time at all. It looked like this:
Rik — ½gikR = kTik
i.e. exactly the form of equation (2) from above. But what was the point of the second term? It didn’t even provide any additional information. R is the total curvature of space, i.e. a kind of average over the Rik, and therefore nothing really new. gik is the so-called metric of space, which is needed to measure distances or to go from one coordinate system to another.
In retrospect, it becomes clear what this term (which could not be guessed) was for: Einstein assumed that his equations were valid in all coordinate systems, and the metric is needed for coordinate transformation. As I said, no one could have guessed that it would appear in this form. But that was no problem for Hilbert: The general equation popped up automatically during his calculations, and its asymmetry did not bother him.
Hilbert had saved Einstein’s program, and Einstein took over the missing term, which led to a short priority dispute. But Einstein admired Hilbert, and Hilbert admired Einstein, so the controversy was settled. Hilbert acknowledged Einstein’s decades-long efforts to find a “TOE”, a “Theory Of Everything”, and that’s the reason the above equation is called “Einstein’s field equation of gravitation.” The associated theory has gone down in history under the name “General Theory of Relativity”, with Einstein as its sole creator.
If you want to know why Einstein departed special and developed general relativity, it is explained here.
