Einstein's relativity

“The suddenly famous Dr. Einstein”
The standard way of visualizing general relativity is to imagine a flexible sheet stretched out and marked in a standard square grid, and then imagine dropping a bowling ball on the sheet. If you shoot a marble across the distorted sheet, its path will be deflected as it passes near the bowling ball. Newton would say that the deflection was caused by the gravitational attraction of the bowling ball. But Einstein would say that the marble was following the shortest path in a space-time that had been distorted by the presence of the bowling ball’s mass — two different descriptions of the same event.

The traditional way of choosing the right theory in this sort of situation is to find where the two predict different results and then do experiments or make observations to see which one is right. Relativity (both special and general) makes predictions that are basically identical to Newtonian ones except in cases where objects are moving near the speed of light or near large masses.

That makes testing difficult. The first experimental proof of relativity came from detecting light rays deflected by the Sun’s mass in 1919, along with Einstein’s solution to a long-standing problem with the orbit of Mercury. These tests also created what The New York Times called “the suddenly famous Dr. Einstein.” I should point out that the bending of light rays near massive objects is the basic principle behind gravitational lensing, a tool routinely used by astronomers to search for dark matter.

Hunting gravitational waves
Since the early days of relativity, there have been many experimental proofs of both the general and special theories — far too many to list here. Let me mention just one such proof that will be familiar to most readers. It confirms relativity millions of times every day. I’m talking about the Global Positioning System (GPS). The system consists of a suite of 24 orbiting satellites, each of which is equipped with a high-precision atomic clock that compensates for relativity-driven time differences between its orbit and the ground. The GPS receiver in your car can then measure the time it takes satellite signals to arrive and calculate its position on Earth’s surface.

There is, however, one prediction that has eluded confirmation until now — the existence of gravitational waves. The easiest way to visualize gravitational waves is to go back to our example of the bowling ball on a flexible sheet and imagine what would happen if you grabbed the bowling ball and bounced it up and down. If you did this, ripples would go out on the sheet — ripples that would have their own effect on the marbles in the system. These ripples are analogous to gravitational waves.

Calculating gravitational wave properties is complex, but the bottom line is that they occur whenever a mass is accelerated. Once a gravitational wave is produced, it will spread out through the universe for billions of years, barely interacting with matter.

Thus, we should be surrounded by gravitational waves from extreme events like merging black holes or even from the Big Bang itself. Because gravity is the weakest force in nature, however, the effects of these waves are tiny. So, the question is how such waves can be detected.

Detection, of course, depends on what we think the effect of a passing gravitational wave will be. Theory predicts that the wave will change the shape, ever so slightly, of objects it encounters. A basketball will first be stretched into a football in the horizontal direction, then return to being a basketball, then be stretched into a football in the vertical direction, then return to being a basketball, and so on. The challenge for scientists is to detect these tiny changes in shape.

Enter LIGO — the Laser Interferometer Gravitational-wave Observatory. There are two LIGO detectors, one in Livingston, Louisiana, and one in Hanford, Washington. Each consists of an L-shaped apparatus with a vacuum chamber 2.5 miles (4km) long in both arms with mirrors at the ends. A split laser beam is sent down the arms, and when the beams are reflected back to the center, extremely small changes in the relative position of the two mirrors can be detected.

The idea is that you can think of the two LIGO mirrors as being small parts of the surface of the hypothetical basketball described above. As a gravitational wave causes contortions in the shape of this imagined basketball, the laser beams will detect those changes in position. This is not a simple operation, since the expected changes in the mirror’s position from a passing wave are 1,000 times smaller than the nucleus of an atom!

LIGO went into operation in 2002 and collected data for eight years. It detected no waves, but this wasn’t surprising. It would have taken an extraordinary event (something like two black holes colliding nearby) to produce a wave strong enough to trigger the instrument as it was then.

This first run established that the system actually worked. LIGO was recently closed for several years as engineers upgraded to the Advanced LIGO phase. The instrument was re-dedicated in May 2015, and its first observing run took place between September and January 2016. And, just like so many other experiments over the last hundred years, LIGO has proven Einstein correct once again.