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GRAVITATIONAL WAVES OUTLINE • historical introduction from Newton to Einstein : why physicists need waves • the revolutionary idea of General Relativity • what are black holes? • what generates gravitational waves? • physical principles of gravitational wave detection • the discovery of 14 September 2015 (announced 11 February 2016) Newton’s theory of gravitation Galileo Galilei (1564-1642) : two important principles • bodies of different masses fall with uniform acceleration MEarth a/ r2 height of the tower • the laws of physics are the same in any system moving at constant speed in a straight line : ‘‘inertial system’’ Newton’s theory of gravitation Isaac Newton (1642-1727) : • the force of gravity is universal : the same force to explain falling objects and planets motion MEarth m2 F2 = m 2 a = G r2 Newton second law He found the proportionality constant! MEarth a=G 2 r Newton’s theory of gravitation • one law that worked very well to explain the motion of planets gravitational field generated by a mass M F g(x) = = m M G 2 r̂ r Newton’s theory of gravitation • one law that worked very well to explain the motion of planets • the same law in every inertial reference system • time is absolute : it is the same in all reference systems Poisson equation @ @ (x) = 4⇡ G ⇢(x) ij @xi @xj ALL VELOCITIES ARE POSSIBLE ! Newton’s theory of gravitation double derivative in space: how the potential varies in space i=j gravitational potential: related to the acceleration (before: a) Newton proportionality constant source: mass density (before: M) @ @ (x) = 4⇡ G ⇢(x) ij @xi @xj EVERYBODY HAPPY… but in the meanwhile… in the meanwhile : ELECTROMAGNETIC WAVES James Clerk Maxwell (1831-1879) in the meanwhile : ELECTROMAGNETIC WAVES James Clerk Maxwell (1831-1879) Equations to describe the propagation of light (EM waves) : 1 @ @ A (x, t) µ c2 @t @t @ @ 4⇡ Aµ (x, t) = Jµ (x, t) ij @xi @xj c double derivative in space: how the potential varies in space i=j gravitational Newton potential: proportionality related to the force constant (before: F) @ @ (x) = 4⇡ G ⇢(x) ij @xi @xj in the meanwhile : ELECTROMAGNETIC WAVES James Clerk Maxwell (1831-1879) Equations to describe the propagation of light (EM waves) : 1 @ @ A (x, t) µ c2 @t @t @ @ 4⇡ Aµ (x, t) = Jµ (x, t) ij @xi @xj c electromagnetic potential (before: gravitational) BRAND NEW TERM ! double derivative in time: how the potential varies in time c : SPEED OF LIGHT another proportionality constant source: charge and current density (before: mass density) in the meanwhile : ELECTROMAGNETIC WAVES James Clerk Maxwell (1831-1879) Equations to describe the propagation of light (EM waves) : 1 @ @ A (x, t) µ c2 @t @t @ @ 4⇡ Aµ (x, t) = Jµ (x, t) ij @xi @xj c • the EM wave propagates at a finite speed km c = 300 000 sec · • the propagation IS NOT INSTANTANEOUS • causality : if the source changes, it takes a finite time for the information to propagate in the electromagnetic potential the problem of action at a distance 1. event : turn on light bulb 3. event : light arrives (x1 , t1 ) (x2 , t2 ) x2 x1 = c (t2 t1 ) 2. EM waves propagate… BUT THE SAME PROBLEM IN GRAVITATION THEORY GOES : 1. event: the Sun disappears (sudden change in mass) @ @ (x) = 4⇡ G ⇢(x) ij @xi @xj MISS TERM IN THE EQUATION: NO WAVE TO PROPAGATE… 3. the Earth feels it immediately ! the problem of action at a distance 1. event : turn on light bulb Newton theory of gravitation is not causal ! 3. event : light arrives (x2 , t2 ) (x1 , t1 ) x2 x1 = c (t2 t1 ) 2. EM waves propagate… BUT THE SAME PROBLEM IN GRAVITATION THEORY GOES : 1. event: the Sun 3. the Earth @ @ disappears(big disaster feels it (x)a= physicist) 4⇡ G ⇢(x) for ij @xi @xj (sudden change in immediately ! mass) MISS TERM IN THE EQUATION: NO WAVE TO PROPAGATE… The revolution by Einstein 1. event : two black holes inspiral and merge somewhere in the universe and a very long time ago x2 t2 x1 = 1.26 · 1022 km 9 t1 = 1.3 · 10 years 3. on Earth, now, the LIGO detector measures GW : therefore it detects the event ‘‘black hole merger’’ 2. Gravitational waves propagate at the speed of light… Two new theories: special and general relativity Albert Einstein (1879-1955) • there is a maximal speed: the speed of light c • it is the same in all reference frames • time is not absolute: it depends on the reference frame • for Newton space and time were different; for Einstein there is a unique entity, spacetime MAXIMAL VELOCITY c ! Two new theories: special and general relativity SPACETIME : time trajectory of a light beam space Two new theories: special and general relativity Albert Einstein (1879-1955) • gravitation is no longer seen as a force, like in Newton theory, but as a property of spacetime • the presence of energy bends spacetime emptiness : flat spacetime (also called metric) Two new theories: special and general relativity Albert Einstein (1879-1955) mass is energy : it bends spacetime (space is curved, time flows slower) Two new theories: special and general relativity Albert Einstein (1879-1955) mass bends spacetime : new explanation of orbits of planets objects move on trajectories determined by the geometry of spacetime Two new theories: special and general relativity Albert Einstein (1879-1955) mass bends spacetime : new explanation of orbits of planets objects move on trajectories determined by the geometry of spacetime even light is deflected! Two new theories: special and general relativity Albert Einstein (1879-1955) bigger masses induce bigger curvature in spacetime Two new theories: special and general relativity Albert Einstein (1879-1955) Black hole: the mass is so big that spacetime is infinitely curved what is a black hole ? • region of space of infinite curvature: nothing can escape, not even light (event horizon) • for an observer far away, time becomes infinite nearby a BH • BH arises because of the compression of mass into a tiny space 2G M Rs = 2 M = 2.95 km c M M = 2 · 1030 kg R = 690· 000 km for the Earth to be a black hole : it should be compressed into 8 mm • a black hole can arise after the collapse of a big star : tenths of solar masses • or it can be formed at the center of a galaxy : millions/billions of solar masses SAGITTARIUS A at the center of the Milky Way M = 4· 000· 000 M · · Rs = 12 000 000 km Two new theories: special and general relativity Albert Einstein (1879-1955) gravitational waves are SMALL PROPAGATING RIPPLES IN SPACETIME Two new theories: special and general relativity Albert Einstein (1879-1955) gravitational waves are SMALL PROPAGATING RIPPLES IN SPACETIME 1 @ @ h (x, t) µ⌫ c2 @t @t time derivative : propagation at speed of light @ @ hµ⌫ (x, t) = ij @xi @xj ‘‘wavy’’ component of metric - spacetime (before : gravitational potential) Transverse-traceless, spin 2 16⇡G T (x, t) µ⌫ c4 yet another proportionality constant source: time-varying energy momentum tensor ?? Two new theories: special and general relativity Albert Einstein (1879-1955) gravitational waves are SMALL PROPAGATING RIPPLES IN SPACETIME generated by a TIME DEPENDENT (MOVING) QUADRUPOLAR DISTRIBUTION OF MASS NO SPHERICAL SYMMETRY such as a deformed rotating neutron star Two new theories: special and general relativity Albert Einstein (1879-1955) gravitational waves are SMALL PROPAGATING RIPPLES IN SPACETIME generated by a TIME DEPENDENT (MOVING) QUADRUPOLAR DISTRIBUTION OF MASS such as two black holes orbiting around each other MOVIE https://www.youtube.com/watch?v=1agm33iEAuo How to detect gravitational waves ? it is very difficult, because GW have very small amplitude and interact very weakly METHOD ONE : INDIRECT DETECTION • GW carry away energy from the binary system • therefore the radius of the orbit of the two compact objects gets smaller with time because of this energy loss • one could measure the rate of shrinking of the orbit • and then compare with what predicted by the theory • if they agree… proof of existence of GW ! • but which astronomical object can be used for that ? certainly not black holes… How to detect gravitational waves ? METHOD ONE : INDIRECT DETECTION • • • • binary of neutron stars emitting beamed EM waves detected by a radio telescope at very precise time intervals from the rate of the pulses infer the rotation period does the orbit shrink? How to detect gravitational waves ? METHOD ONE : INDIRECT DETECTION method used with the Hulse-Taylor binary pulsar · d = 21 000 ly M = 1.44 M first indirect evidence of GW NOBEL PRIZE IN 1993 TO HULSE AND TAYLOR still, it’s not the GW that directly interacted with a detector…. prediction of GW emission from general relativity How to detect gravitational waves ? METHOD TWO : DIRECT DETECTION what is the effect of a GW passing perpendicularly through a ring of test masses ? two independent propagation modes, called polarisations how can one measure the displacement in the masses ? How to detect gravitational waves ? answer : using a laser between massive mirrors interferometer LIGHT IN THE DETECTOR NO LIGHT IN THE DETECTOR How to detect gravitational waves ? answer : using a laser between massive mirrors interferometer Advanced LIGO interferometers 4 km armlength, laser power 125 W, beam radius 6 cm, test masses 40 kg sensitive to length differences L ⇠ 2 · 10 18 m size of a molecule with respect to the solar system! pictures of the VIRGO interferometer in Pisa comparable performance, 3 km arm length, start operating for 2017 observation run pictures of the VIRGO interferometer in Pisa pictures of the VIRGO interferometer in Pisa pictures of the VIRGO interferometer in Pisa pictures of the VIRGO interferometer in Pisa Gravitational wave detectors worldwide • we need many detectors to distinguish the signal from the noise (earthquakes, atmosphere, passing trucks… ) • the same signal should be seen after a time interval d=c t about 7 msec for the two LIGO detectors • three detectors to localize the source and measure the polarization 14/9/15 : the first direct detection by the two LIGO interferometers (7 msec later) 14/9/15 : the first direct detection by the two LIGO interferometers HOW DOES IT SOUND LIKE ? https://www.youtube.com/watch?v=TWqhUANNFXw 14/9/15 : the first direct detection by the two LIGO interferometers M1 = 36 ± 5 M M2 = 29 ± 4 M Mfim = 62 ± 4 M Rs ' 210 km x2 t2 x1 = 1.26 · 1022 km 9 t1 = 1.3 · 10 years what next ? a new window on the universe ! • Nobel prize for this discovery • only 16 days of data : many more events expected • when VIRGO joins in, better sky localization : EM follow-up with telescopes • beginning of the era of GW astronomy : many new informations on objects that generate GW • new tests on general relativity • maybe an unattended signal (from the early universe?) • launch of a GW interferometer in the sky, called eLISA