It Is Beautiful, Therefore It Exists

einsteinfieldeqGeneral Relativity is the reason why I decided to study physics many years ago. (Too many to confess here.)

Tomorow is the 100th anniversary of Einstein’s presentation to the Prussian Academy of Science of what are now known as the Einstein field equations(1).

Einstein Field EquationsGeneral relativity has passed every experimental test with flying colours so far, and has become an essential tool in modern astrophysics. Yet it is still not known how it can be reconciled with the other key foundation of modern physics—quantum physics—to produce a complete and self-consistent theory of quantum gravity, and a thorough unification of the physical forces that govern the known physical universe.

Little can be said about general theory of relativity which has not been said before, so I would not even try. I am going to simply wonder how a mind can conceive of something—a theory like general relativity—which anticipates so many new things, out of a couple of simple insights deeply related to mathematical structures.

Starting in 1907, Einstein began trying to broaden special relativity to include gravity. His first breakthrough came when he was working in a patent office in Bern, Switzerland. “Suddenly a thought struck me,” he recalled. “If a man falls freely, he would not feel his weight… This simple thought experiment… led me to the theory of gravity.” He realised that there is a deep relationship between systems affected by gravity and ones that are accelerating.

The next big step forward came when Einstein was introduced to the mathematics of geometry developed by the 19th-century German mathematicians Carl Friedrich Gauss and Bernhard Riemann. Einstein applied their work to write down the equations that relate the geometry of space-time to the amount of energy that it contains. Now known as the Einstein field equations, and published in 1916, they supplanted Newton’s law of universal gravitation and are still used today, nearly a century later. (“General relativity: Einstein’s insight”)

From black holes, to worm holes, and from gravitational lensing to the intriguing possibility of time travel, general relativity has given us not only a lot of food for thought in science. It has also stimulated the imagination of writers and film makers to give us many of the sci-fi icons of 20th century. All of them have been born out of maths and the search for simplicity (beauty).

It is surprising how beauty can propel us faster than light to absolutely remote places. In a great article—and in a recent book—another Nobel Laurate, Frank Wilczek, reflects about this beautiful question: Why is physics beautiful?

The beauty of physical law is too impressive to be accidental. It has led people throughout history to believe that some tasteful higher being created us, and that we inhabit a consciously designed world (…)

The answer likely lies within us. Beautiful things are those in which we find pleasure and seek out. They are, in neurobiological terms, things that stimulate our reward system. That explains why parents tend to find their young children beautiful, and adults are attracted to nubile models and their images. It makes evolutionary sense to reward such feelings.

The evolutionary utility of the beauty of physical laws is somewhat less obvious, but no less real (…)

In short, because evolution predisposes us to find beautiful those things that help us understand the world correctly, it is no accident that we find the correct laws of nature beautiful. Viewed from this perspective, the apparent beauty of the laws of physics – our attraction to their symmetry and exuberance – is not surprising (…)

What remains mysterious is why they are comprehensible. A profound link between beauty and comprehensibility is an increasingly important source of scientific progress. Today’s frontiers of fundamental physics are far removed from everyday experience. They are difficult and expensive to access experimentally, and we cannot rely on our intuition to fill in the blanks (…)

Instead, we reverse the process, using guesswork to motivate experiment. We first construct beautiful equations, then derive their consequences, and, finally, craft experiments to test them. In recent decades, that strategy has proved remarkably successful (…)

we use principles of beauty – vast symmetry and a high ratio of output to input – to enable discovery. When this works, we have an “anthropic” explanation of the laws’ beauty: If they were not beautiful, we would not have found them.

General theory of relativity would have not been found if it not were so beautiful!

I would not have found general relativity if it not were so beautiful!


(1) Einstein, Albert. “Die Feldgleichungen Der Gravitation.” Sitzungsberichte Der Königlich Preu\s Sischen Akademie Der Wissenschaften (Berlin), Seite 844-847. 1 (1915): 844–47.


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