Gravitational Waves, Relativity & Photonics

​We have already detected gravitational waves. The rumors of the news were in the air for a few weeks and finally the researchers (from the MIT, Caltech and the LIGO project) have announced their finding

Michelson interferometer (from scienceclarified.com).

​Special Relativity: one century of interferometry

One of the most common ways to introduce special relativity is by describing the interferometry experiment of Michelson and Morley from the late 19th Century. Their negative result was pointing to a fundamental problem in the interpretation of space and time. Even though Albert Einstein didn't use their result to present his special theory of relativity, the experiment was one of the most precise experiments of all times, and it is a pedagogical tool.

Michelson designed an interferometer to measure the drag of the "luminiferous aether" on the speed of light. This aether was a supposed fluid that filled all space and was introduced in order to explain the wave nature of light.

In his experiment, Michelson first and with Morley later, compared the time that light needed to travel along two perpendicular paths, as in the figure. The light was coming from the left (see figure). A beam splitter divided the beam of light into two. One half going to Mirror 2 and the other half to Mirror 1. Then those beams were reflected. They interfered at the beam splitter again and recombined, being sent to the detector. Depending on the difference in time the interference pattern can be different, and from this we can extract the difference in velocity, if any.

As light has undulatory behavior the interference between two pulses or beams of light depends on their relative phases. This phase will depend on the difference of path taken by each beam.

The problem shown in this experiment was that, contrary to the general belief, there was no aether, and the way to explain some contradictory results was to assume that space and time are distorted as seen from different observers that move one with respect to the other: if a traveler flies at very high speeds (comparable to that of light), time for the traveler passes much slowly than for an observer at rest. Also, space seen by the traveler  gets contracted. This is a direct implication of two principles:

- The speed of light is constant (has an absolute value). It is the same for all observers, independently of the velocity of the observer with respect to the source that emitted the light.
- All inertial reference frames (those with constant velocity but no acceleration) are equivalent. We can not design an experiment to tell us if our reference frame is at rest or it moves with uniform motion (constant velocity in magnitude and direction). All the laws of physics are the same for all observers.

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General Relativity

But the Special Theory of Relativity of 1905 didn't account for gravity. After almost a decade later 9in 1915), Albert Einstein presented his general theory of relativity, which described gravity. This theory introduced the idea of curved space-time. Einstein introduced a geometric description of space and time in 1905 and he showed that space and time formed a continuum four dimensional tissue where all matter in the universe is immersed. Matter deforms the space-time fabric and the distortion of space-time shows the matter and light how/where they have to move.

The Universe is full of matter that gravitates and distorts space-time as it flies by. It is like playing bowling in a green that is not uniform, but also, it changes shape as the bowls roll by.

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But an indirect observation of gravitational waves had already been made in the late 1990s. General Relativity predicts that a fast spinning neutron star will emit energy in for of gravitational waves. This lost of energy will be reflected is the rotational energy of the star. Detailed observations through thirty years confirmed that the rotational energy lost was exactly the one predicted by General Relativity to be emitted as gravitational waves.Gravitational waves

All the predictions of general relativity have been confirmed. Gravitational lensing, or how gravity changes the straight lines and makes light travel in curved trajectories. gravitational time dilation, or how gravity makes clocks travel slower, so that a person in a intense gravity field will experience less time lapse than a person far from an intense gravity field. Gravitational redshift, or how light looses energy due to gravity by changing its wavelength.

Gravitational waves was the last prediction to be directly observed. This waves are created when cataclysmic phenomena  happen in the universe, such as collision of black holes or coalescence of neutron stars. Even though the energy released in these phenomena are huge (about two solar masses in the  gravitational waves observed by LIGO), when we detect them (so far away, luckily) they are really tiny.

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Interferometry to the rescue.

​But to measure the Gravitational Waves we need to measure tiny, very tiny variations in the distance between atoms, as the waves traverse them. It is like measuring the distance from the Sun to Proxima Centaury (~4light years) with a resolution of one human hair!

To do this, physicists form the LIGO project have used a Michelson interferometer (yes, again the same experiment Michaelson did in 1887). In this case, though, it was not a tabletop experiment. The two arms of the interferometer were four kilometers long. This has to be this way so that the distance of the mirrors are change enough to be detected (one thousandth of the size of the proton).

In order to be sure that what was measured were really Gravitational Waves, the experiment counted with two different interferometers, one in the state of Washington and the other in the state of Louisiana. They are far enough so that any local perturbation measured in one of them is not detected by the other. Also, the time difference between detections can hive hints on the origin of such waves. In September, 14th, 2015, both interferometers detected the same signal, almost simultaneously. The signal had the specific frequency pattern predicted by General Relativity for two merging black holes, and could not be attributed to any other phenomena.  The first ever Gravitational Wave had been observed.

This detection technique, not only confirms once more Einstein's Relativity, but opens a new window to the Universe. We can now observe it not only with electromagnetic waves, but also with gravity waves.

​In Terrassa (Spain) the Association Planeta da Vinci, together with the Astronomical Association of Terrassa, are organizing the 9th Dissemination Day on Relativity. They have been creating a meeting point between Scientists, Science Communicators and Society since 2008.

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