Gravitational waves in our space-time universe

Einstein predicted in 1916 that important mass accelerations must generate gravitational waves. One hundred years later, the American gravity waves detector LIGO was able to observe such phenomenon. Before presenting these results, the main theoretical steps that led to the existence of gravity waves will be summarized.

The main steps which led to the existence of gravitational waves

Einstein showed in 1905 with his Special Relativity theory that time is relative, and one illustration is that two events that are considered simultaneous by one observer are not considered simultaneous by another observer who is moving relative to the first one. Special Relativity showed that time and distance are closely linked, and they even can be expressed with a single unit (like for instance the light-year); Minkowski deducted that we are in a space-time universe with 4 dimensions, the unitary element being the event having 4 coordinates (3 for the space and 1 for the time). Thus any object is a set of events, and all physics laws explaining the evolution of objects must be written in terms of events. When changing from one inertial frame to another, the coordinates (x,y,z,t) of one event must not any longer be transformed using the classical Galilean transform which assumed time was absolute, but with the Lorentz Transform.

Einstein then addressed the gravity theory which did not fit well with his Special Relativity theory, and he did not want his new theory to be restricted to the field of electromagnetism. Indeed since Newton, it was assumed that gravity produced instantaneous distant interactions, even over huge distances; but Special Relativity showed that no speed, including distant interactions, could be faster than light speed, otherwise the causality principle would be contradicted: a consequence could precede its cause, which is not acceptable! Besides, it is worth noting that even since the beginning of Newton’s Gravity theory, some important issues where left open: for instance, if one moves a big rock on earth, how can the moon immediately know that the center of mass of the earth has changed? More generally, how can the moon know where to fall? Can there be any information transmission without any physical support? Is telepathy possible? All these questions induced Newton to ironically say that one must be mad to believe in his universal gravity theory!

Einstein solved these issues with his General Relativity theory: he first issued in 1907 the “equivalence principle” by which he generalized observations that for a free falling person, for instance if you are inside a free falling lift, there is no gravity effect and all laws of physics are the same as if you were in an inertial frame. This implied that gravity is nothing else but the effects of accelerations, and as Special Relativity showed that we are in a space-time universe, these accelerations could be explained by distortions of our space-time universe, these distortions being generated by masses. The more important is the mass, the more important are the distortions, which progressively fade as the distance to the mass increases. The important issues regarding the instantaneity of distant interactions were solved as Einstein stated that space-time distortions propagate at the speed of light. The subsequent calculations were quite complex and were completed in 1915 with the famous equations of General Relativity. The bending of light in the neighborhood of the sun gave in 1919 a brilliant confirmation of the space-time universe curvature; but even in 1915, a first confirmation of General Relativity was given with the explanation of the enigma of the perihelion of Mercury, and which clearly showed that gravity interactions were not instantaneous:

Mercury perihelion enigma:

Mercury is the only planet which does not strictly follow Newton’s law, as its trajectory is a continuously deviating ellipse as shown in the picture below, and the magnitude of the deviation could not be explained.

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Einstein gave the explanation with his new General Relativity theory showing that at the time when Mercury receives a gravity wave from the sun, the position of the sun indicated by this wave corresponds to the position of the sun at the time when this wave was emitted, but the position of the sun relative to Mercury has changed when the wave arrived. This effect is much more important for Mercury which is the closest planet to the sun, and thus incurs the most important space-time deformations. Einstein later said that when he saw that his calculations gave the correct Mercury’s deviation angle, he remained “speechless with excitement during few days.”

Einstein thus showed that space-time distortions constitute a field, like electromagnetism; this parallel between gravity and electromagnetism was further developed: similarly as the photon is the massless particle associated to a quantum of energy contained by an electromagnetic wave (another finding of Einstein), then the graviton was conceived as the massless particle associated with an elementary gravity wave. Masses are thus supposed to continuously emit gravitons propagating at light speed; however the graviton still is an hypothetical particle.

Pursuing the similarity with electromagnetism, Einstein predicted in 1916 that important mass accelerations must generate gravitational waves, meaning oscillations of the space-time universe, like accelerations of electrical charges generate electromagnetic waves. Both types of waves don’t require any substance to propagate, but gravitational waves modify the very geometry of the space-time universe whereas electromagnetic waves follow the geodesic lines of the existing space-time universe, which are trajectories maximizing the proper times of free falling objects (including photons); they correspond to straight lines in regions where the space-time universe is not curved.

One century after their prediction by Einstein, a direct observation of gravity waves on earth was accomplished.

The first direct observations of gravitational waves

Gravitational waves thus are ripples modifying the very geometry of our space-time universe, and they fade with a ratio of 1/R (R being the distance to their generating point). Hence gravity waves which are big enough to be detectable on earth must have been generated by extremely massive and rapid objects, such as pairs of neutron stars or black holes.

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To illustrate the effects of a gravity wave on earth, a circle appears like an ellipse which successively enlarges and shrinks as the gravity wave passes, as shown in the picture below.

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For the first time in September 2015 gravitational waves were directly detected on earth: the two new American gravitational waves detectors, named LIGO, located one in Hanford (Washington) and the other one in Livingston (Louisiana), had just been brought into operation for their first observing run when a very clear and strong signal was captured by both detectors, with a delay of 7 milliseconds between them corresponding to the propagation time of the gravitational wave.

Remark: The existence of gravitational waves was first demonstrated in the in 1974 J.Taylor, R. Hulse and J. Weisberg who discovered a binary system composed of a pulsar in orbit around a neutron star, and explained the fact that the orbit of the pulsar was slowly shrinking over time by the release of energy in the form of gravitational waves.

Direct detection of gravitational waves on earth is a technological exploit resulting from 40 years of important studies, experiments and the development of a highly sophisticated instruments that are able to detect distance variations in the range of 10-18 meter ! (representing one-ten-thousandth the diameter of a proton !).

The principle of the gravitational waves detector is based on the Michelson & Morley interference lay out (cf. picture below): a gravity wave generates a change in the lengths of the interferometer arms, the arm being more in the direction of the gravity wave incurring a greater length variation; subsequently the phases of the beams will be altered when recombining, and generate changes in the interference pattern at the light detector. However, huge sensitivity improvements are required from Michelson & Morley equipment which had a sensitivity of 10-7 meters (only).

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The great difficulty is to isolate the system from all sources of perturbations on earth, and to reduce all sources of noise and variations that are inherent to any instrument, so that the effects due to the gravity waves can be more important than the remaining noise, perturbations and fluctuations. Hence drastic and expensive measures have been taken in order to increase the signal resulting from the gravity wave and to reduce to the minimum all sources of noise and perturbations; in particular:

  • in order to increase the signal, the interferometer arms are very long: 4 km; moreover, the beams travel a distance of 1120 km by making round trips between the mirrors before combining and interfering, thanks to the use of Fabry Perot cavities;
  • in order to reduce all sources of noise and perturbations, the interferometer arms are built inside tunnels covered with thick concrete framework; the vacuum is done inside the interferometer arms so as to avoid perturbations from the air;
  • the mirrors are suspended and attached via special shock absorbers (seismic isolation);
  • a complex system amplifies the power of the laser, and compensates for its small fluctuations in power as well as in frequency and geometry.

Last but not least, it is important to have two such interferometers separated by a large distance in order to make sure that the observed signal does come from a local source of noise or perturbation, but from a common source: a gravity wave. Besides, the time difference between the signals recived in the two locations gives an indication as to the direction from which the wave came.

Another important accomplishment was on the theoretical side, as the waves generated by the coalescence (merge) a pair of neutron stars or black holes could be modeled and calculated, which involved very complex equations and calculations. According to General Relativity, a pair of black holes orbiting around each other lose energy through the emission of gravitational waves, causing them to gradually approach each other during billions of years, and then extremely rapidly in the final minutes. During the final fraction of a second, the two black holes collide into each other at nearly one-half the speed of light, and form a single more massive black hole, converting a portion of the combined black holes mass into energy; it is this energy which emits a final strong burst of gravitational waves which are detectable on earth by LIGO.

The form of the expected signal was thus known, and reality gave a brilliant confirmation. This form is characterized by a frequency and an amplitude which simultaneously increase, both reaching a maximum at the coalescence between the two great masses; then both the frequency and the amplitude fade. Such frequencies are in the range of 30 Hz to 200 Hz, and the signal lasts about 0,15 seconds.

Thanks to these predictions, LIGO powerful algorithms took only 3 minutes to recognize the coalescence signal after it was detected. LIGO scientists estimate that the event was caused by the coalescence (merge) of a pair of black holes which were about 29 and 36 times the mass of the sun.

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The event took place 1.3 billion years ago, and about 3 times the mass of the sun was converted into gravitational waves in a fraction of a second—with a peak power output of about 50 times that of the whole visible universe. The phenomenon took place in the Southern Hemisphere, as indicated by the time difference in the wave arrival in Livingston and in Hanford.

Gravitational waves detector: a new powerful tool for cosmology

Gravitational waves detection opens a new era of observation of the cosmos. Due to the enormous amount of galaxies (more than 100 billion) and stars (our Galaxy contains 200 billion stars), it has been estimated that the yearly number of events which are comparable to this first one, is between 200 and 400; and indeed LIGO detected a second event, similar to the first one, 3 months later, but without reaching the statistical threshold “5 sigma” required to be sure of a true event (as opposed to perturbations or noise).
One first finding is the very existence of such massive black holes in the range of 30 times the solar mass: the ones that were detected in our galaxy were much smaller, except the one in its center which is extremely huge; it also was the first proof of the existence of merging pairs of black holes. This also provides scientists with means to test General Relativity in “strong field regime”.
Compared with other observational means, gravitational waves give a more direct information as to the mass of the concerned objects. Furthermore, they enable us in theory to detect events that occurred very soon after the big bang (before year 380 000), and which are not detectable by other means because the universe was so hot and dense that photons were rapidly captured by matter (electrons) and thus could not propagate over long distances and ultimately reach us. The big band itself may have generated gravity waves, and also the huge inflation phase that occurred soon after.
The importance of this new observation means has been recognized worldwide: several even more powerful detectors are being implemented worldwide, in particular in Japan where the KAGRA project is expected to be the most sensitive detector in 2018; the European VIRGO project is being implemented in Italy; India is constructing a LIGO clone. All these instruments will enable us to detect more events and to better qualify them. For the longer term, there are plans for launching a laser interferometer in space which would orbit the sun, enabling us to escape from our noisy environment on earth, and to benefit from the possibility to have huge distances between the mirrors, such as one million kilometer!