# Einstein's amazing theory

Marton Trencseni - Tue 16 February 2016 - Physics

## Introduction

Recently the LIGO experiment reported the measurement and experimental verification of gravitational waves. This is a big deal and should get those involved in the experiment a Nobel prize. Great news for physics and our understanding of nature!

From the press release:

Gravitational waves carry information about their dramatic origins and about the nature of gravity that cannot otherwise be obtained. Physicists have concluded that the detected gravitational waves were produced during the final fraction of a second of the merger of two black holes to produce a single, more massive spinning black hole. This collision of two black holes had been predicted but never observed.

Based on the observed signals, LIGO scientists estimate that the black holes for this event were about 29 and 36 times the mass of the sun, and the event took place 1.3 billion years ago. About 3 times the mass of the sun was converted into gravitational waves in a fraction of a second—with a peak power output about 50 times that of the whole visible universe. By looking at the time of arrival of the signals—the detector in Livingston recorded the event 7 milliseconds before the detector in Hanford—scientists can say that the source was located in the Southern Hemisphere.

This post is about the amazing success of the theory of general relativity, the theory Einstein developed between 1907 and 1916.

## Historical context

Let's start with some history and context. The 100 years between 1850 and 1950 were a tremendously fruitful time for physics. Maxwell wrote down his famous equations, Einstein developed the special and the general theory of relativity, quantum mechanics and then quantum field theories were invented.

It is often said that given the Maxwell equations and its invariant, the Lorentz transformation, somebody would have eventually extracted special relativity from it. The invention of quantum mechanics (QM) came after experimental observations that needed a new theory to explain them. Various frameworks for QM were devised in parallel by a number of physicists (Heisenberg, Schrodinger, Dirac, Pauli, Bohr, Sommerfeld, Einstein, etc.). Quantum mechanics isn’t compatible with special relativity, so a few years later quantum field theories came along (mostly by the QM physicists, plus new kids on the block, like Feynman). QFTs are extensions of QM to take into account special relativity and the creation and destruction of particles and antiparticles. QFTs have predicted the existence of then-unobserved particles, but primarily have been constructed to model experimental observations, and have to be continuously patched and hacked to do so.

## General relativity

Compared to the history of quantum theories, Einstein's invention of general relativity is very different and elevates Einstein into a class by himself. Einstein conducted gedanken experiments and concluded *“this is how the Universe must work”*. Here is a short description of his famous thought experiment involving elevators. His invention of general relativity was completely unexpected because from an experimental viewpoint it was "unnecessary": there were no experiments that needed to be explained. From Wikipedia:

As Einstein later said, the reason for the development of general relativity was the preference of inertial motion within special relativity, while a theory which from the outset prefers no state of motion (even accelerated ones) appeared more satisfactory to him. So, while still working at the patent office in 1907, Einstein had what he would call his "happiest thought". He realized that the principle of relativity could be extended to gravitational fields. Consequently, in 1907 (published 1908) he wrote an article on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a free falling observer the rules of special relativity must apply. This argument is called the Equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation.

Einstein's theory was successful of course, and in the next 100 years turned out to predict, among other things: (i) the accelerating Universe, (ii) black holes, (iii) gravitational lensing and (iv) gravitational waves. The real shocker is to remember that Einstein didn't invent general relativity to explain these things. He didn’t know about these things, they didn't exist at that time!

So how does thinking about inertial reference frames and accelerating observers lead one to come up with a theory that somehow features black holes and gravitational waves? The original thought experiments were “just” arguments about what would happen in an elevator in space, in an elevator in a gravitational field, and so on. Einstein needed a mathematical framework which can be extended with some physics, ie. equations, and a mapping from the mathematical quantities to measurable quantities, and hence a way to connect the math to an understanding of what is being calculated. He found this in manifolds and differential geometry, put the famous Einstein field equations on top, and connected the resulting theory to the real world (eg. in the mathematical framework, what corresponds to a real-world event, world line, how does an observer perceive time, distance, etc). It is this theory—that treats space and time as a combined entity called spacetime, modeled as a manifold—that amazingly predicts (i)-(iv): (i) spacetime is expanding, at an accelerating rate (ii) spacetime can have singularities (iii) spacetime warps near a heavy object, photos follow spacetime, hence an object behind a heavy object appears lensed (iv) ripples in spacetime.

## Conclusion

I’m not sure how successful I was in communicating the amazing fact that Einstein’s theory, developed to explain a very general but simple idea, predicts such a variety of mind boggling phenomena, which are one after the other found to exist in nature. I recommend you to read the book Einstein wrote for the layman to explain the special and the general relativity with his original thought experiments. Read the book, and then think about how given that you could get to gravitational waves!

It is often said that Einstein touched so many areas of physics, he could have received several Nobel prizes. An incomplete list of Einstein's more famous results:

- Brownian motion.
- The special theory of relativity.
- The general theory of relativity.
- His contributions to quantum mechanics.

Einstein did get the Nobel prize in 1922 related to the last item on the list: *“for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect”*.