1.2 From Einstein to LIGO

summary

Albert Einstein discovered the field equations of general relativity in 1915.

- Before general relativity, gravity was understood in Newtonian terms as an attractive force between two objects. This force is proportional to their masses and decreases with increasing distance between the objects.
- Newton was famously troubled by the problem of instantaneous transmission of the force of gravity. He was right to be worried about this: with Einstein’s proposal of special relativity in 1905 came the so-called “universal speed limit”—the speed of light—which applies to all forms of information and energy, including gravity.
- Einstein’s general theory of relativity, which developed out of special relativity, does not have a gravitational force at all. It is a theory in which space is deformed by mass, and masses move because of the deformations in space.

In 1916 Einstein wrote his first paper on gravitational waves.

- Einstein’s original work on gravitational waves had some errors, including the idea that any moving matter could produce them. It turns out
**only non-spherical motion produces gravitational waves.** - Nonetheless, his original paper made a number of correct predictions about gravitational waves: they are strains in spacetime, they propagate at the speed of light, and they are transverse waves.
- Transverse waves cause distortions perpendicular to their direction of motion. A ripple on a pond is one example—the wave moves out horizontally, causing vertical distortions to the water’s surface.
- Gravitational waves are also quadrupolar, which means that the strain works differently in different directions. One dimension of spacetime experiences compression while the other experiences expansion, and these effects oscillate back and forth in the two dimensions.
- The strain ($h$) is a dimensionless value that relates the change in separation between two points ($\Delta L$) to the total separation between them ($L$) by this equation: $$h = \Delta L/L $$

It takes a tremendous amount of energy to distort spacetime, even by a tiny amount.

- The strain is approximately proportional to the source mass ($m$), the square of the source velocity ($v$), and inverse distance of the measurement from the source ($R$) by the equation: $$ h \approx \frac{Gm}{Rc^{2}} * \frac{v^{2}}{c^{2}} $$
- This equation shows that even an extremely small amount of spacetime strain requires huge amounts of energy. This means that the only viable sources of measurable gravitational waves are astronomical systems, like binary star systems.
- Furthermore, the strains are so small that measuring them is extremely difficult. Certainly in Einstein’s time, measurement of such strains was completely hopeless.

“Gravitational waves move with the speed of thought.”

- Arthur Eddington, who made Einstein famous when he verified general relativity’s prediction about the bending of light around massive objects, found that Einstein’s formulation of gravitational waves was coordinate-dependent. This meant that in a different coordinate system the waves were not present, suggesting that they were simply mathematical artifacts.
- He also found that two stars in a binary system would actually gain energy from gravitational waves, which made no sense and convinced him that they did not exist.
- Einstein himself doubted gravitational waves, and even published a paper in 1936 with Nathan Rosen asserting that gravitational waves do not exist. For the next twenty years gravitational waves languished in the realm of mathematical theory, untouched by physicists.

Gravitational waves were brought out of obscurity in 1957.

- A thought experiment created by Richard Feynman at a 1957 conference in Chapel Hill, North Carolina convinced John Wheeler and Joe Weber that gravitational waves existed and prompted them to consider experimental measurements of these waves.
- Weber designed a device that he thought would be able to detect gravitational waves. The “Weber bar” was an aluminum cylinder that would be stretched by the passing of a gravitational wave; this stretching would cause the bar to ring, indicating a successful detection.
- In 1968 Weber claimed he had used this technology to detect gravitational waves. This set off a flurry of attempted replications that all found nothing, discrediting Weber’s experiment and the field of gravitational wave research generally.

The idea behind LIGO was conceived in the late 1960s.

- Mikhael Gertsenshtein was the first to conceive of the basic technique used today to detect gravitational waves, though it was not pursued and fell into obscurity. It was later discovered again by American and German physicists.
- The idea was to separate two masses, each with a perfectly precise clock. A beam of light is sent from one mass to the other, and the travel time is recorded. When a gravitational wave passes between the masses, the space between them will expand or contract, and the travel time of the light will change.
- This is only a thought experiment (or
*Gedankenexperiment*in German), as no clocks exist that are precise enough to make the measurement. The basic idea, however, is experimentally sound and underlies LIGO’s technology.