1.2 Truth and Beauty
The theme of unification is an ever-present one in science.
- We see the incredible power of ideas to unify many physical phenomena.
- Scientists throughout history have often remarked on the tension that exists between beautiful ideas and the reality of nature.
Attempts at devising a 'theory of everything' date back to the ancient Greeks.
- The Greeks developed the platonic solids, five geometrical objects representing the elements that made up everything.
- In the late 16th century, astronomer Johannes Kepler took the five platonic solids and fit them together in a specific way. He was able to find (within 5% accuracy) the ratio of the orbits of the planets in our solar system.
- The theory wouldn’t have held up for many reasons; for instance, there were only six known planets at the time. However, Kepler himself disproved his own theory by careful observations, when he discovered that planetary orbits were in fact ellipses.
- Though Kepler thought his theory of elliptical orbits was an ugly one, there is a beautiful mathematical formalism for ellipses as conic sections.
Scientists continued to unify the complex into simple, elegant concepts.
- Newton was truly a unifier of concepts—he unified the everyday physics (the falling apple) with the movement of the planets.
- Another example was Herschel’s discovery of infrared light in 1800, akin to discovering a new particle today. This led to the realization that all kinds of radiation, including visible light, were different manifestations of the same physical phenomena.
- Maxwell and Faraday were largely responsible for unifying the concepts of electricity and magnetism.
- Einstein’s contributions to physics also unified space and time.
Einstein’s unifications are crucial in understanding modern theories of particle physics.
- Time is the fourth dimension we perceive. Objects moving in both space and time create a world line as they travel.
- Physicists look at the world lines as physical reality—the history of a particle’s space and time represented all at once.
- This becomes challenging in modern particle physics. The mathematics underpinning particle behavior was once thought of as a “black box.”
- We can now describe these behaviors with the relatively concise formula for the Standard Model:$$L=F^2+\psi\left(iD +\varphi\right)\psi+\lvert D\varphi\rvert^2 +\left(\lvert\varphi\rvert^2-1\right)^2$$
- Beautiful and elegant (according to mathematicians and physicists), this formula represents many of the physical implications we observe.