Gravitational Waves their discovery and significance Lecture to WEA Sydney 21 August 2016 Ian Bryce BSc(physics) BE(Hons) ianrbryce@gmail.com
Contents 1. What are waves? 2. Theories of gravitation 3. Sources of Gravitational Waves 4. Finding GW – detectors 5. What it means for science
1. What are waves?
Waves in air - compression
Krakatoa explosion 1883. Was clearly heard 3,000 miles away.
Waves in water Diffraction – physics experiments
Can pass through each other - choppy
Can travel from Fiji to Bondi Cyclone Winston February 2016
Through the ground
Waves in a slinky toy Demonstration
Light waves
Radio waves
We have seen some waves… what are some common features?
We have seen some waves… what are the common features? 1. A travelling disturbance 2. Not involve the transport of matter 3. Sometimes in a medium (air, water, earth) 4. Sometimes not – in a vacuum 5. Inverse square law
A wave can be any shape, eg a single pulse… or a periodic sine wave Pulse Has a duration Sine wave Has a wavelength
Students learn to apply Newton’s Laws for waves in a rope (or slinky) Curvature leads to acceleration Wave Velocity from force of tension, and density
…Wave Velocity from force of tension, and density For a guitar string… What determines the pitch (frequency)? Tension and density! Q: Why are some guitar strings wound?
Waves are now used for exercise
Non-waves There are other forces-at-a distance in physics • Electrostatic attraction • Magnets • wind These weaken rapidly with distance – 1/r 3 , 1/r 4
But waves are special Two parameters which regenerate each other: • Sound: pressure and velocity • Ground vibrations (earthquakes): shear stress and strain • Water waves: height and velocity • Light: Electric field and Magnetic field
This makes waves special When spreading out from a point source: The disturbance weakens with distance only as 1/r The energy carried is 1/r 2
So waves are special • Once launched, a wave can travel independently of its source • Carrying energy • In a particular direction.
2. Theories of gravitation
2. Advances in gravitation Newton – gravity, motion Lorentz etc – special relativity Einstein – general relativity Gravitational waves
1. Isaac Newton ~1687 Calculus - relation between position, speed and acceleration Law of motion - F = m a Local gravity - falling apple Celestial gravity - the orbiting moon, inverse square law
“Local gravity” experiments - Newton’s country house with apple tree
Local experiments - Uniform Gravity Hold an object - can feel Observe falling objects, measure the “force” position, apply calculus to find acceleration Sit an object on a weighing device - can Conclude: Objects accelerate measure the “force” downwards, g = 9.8 m/s2 Relate force and acceleration Horizontal force-motion experiments F = ma
Newton stitched together…
Newton continued Law of Universal Gravitation Given the observed motions and distances of moons and planets, The law of motion now enabled Newton to estimate the forces acting on them. Combining data from apples, moons and planets eventually led him to: Where G = universal constant G M m M = mass of attracting body F g 2 r m = mass of satellite r = distance
Today we describe this as Sources, fields, and forces 1. Newtonian gravity FORCE SOURCE FIELD Causes satellite Eg mass Eg gravity orbit density
Measuring Gravity Directly
Modern apparatus A modern apparatus is shown here. Despite this, G is the least accurately known physical constant, to only 4 significant digits (0.01%) 1970: G = 6.68 x 10 -11 2010: G = 6.72 x 10 -11 As accuracy improved.
Groundwork for Relativity • Bernhard Riemann, German 1850 • Edwin Christoffel, German, 1869 • Hendrik Lorentz, Dutch, 1899 • Hermann Minkowski, Polish, 1900 • Albert Einstein, German, 1905 • Q: Why is Albert’s bike leaning? Newton would know!
What are the limitations of Newton? A. Static or slow-moving bodies. B. Only weak gravity.
• If one body moves away…?
Cartesian co-ordinates X, Y, Z Add Time Four-vector Opens the way to Three-vector relativity
Momentum (3-vector) con be combined with energy, to make a 4-vector. 4-vectors need to be manipulated with tensors,
Space-time deformed by matter The maths - Manifolds
Sources, fields, and forces In Relativity become: EINSTEIN “FORCE” SOURCE CURVATURE Path is a Eg mass, Distortion of geodesic - energy, space-time appears curved momentum
Sources, fields, and forces 2. General Relativity Curvature Source tensor tensor 4 x 4 4 x 4
Source term : Stress-energy tensor 16 elements We will tease this out shortly… But first the big picture
Curvature term : Stress-energy tensor 16 elements
Matter causes the space-time around it to curve; the curvature of space-time determines how objects move… …insofar as freely falling objects follow geodesics (paths which are locally straight) …If there are non -gravitational forces, eg electromagnetic (materials) then they will still accelerate.
Source term in detail : Stress-energy tensor 16 elements Newton’s gravity needs only the first element
Complete source term. What are the other elements?
Sponge demonstration - The Source term
A Mechanical Engineer would recognise the 3 x 3 block – stresses in an element of material
< wing bending in flight Tensile testing of a specimen The stress engineer’s job is to ensure the stresses in flight are less than the strength of the material For each and every part of the airplane
Show bracket
Sources, fields, and forces 3. Gravitational waves WAVES IN APPARENT SOURCES THE METRIC ACCELERATIONS Mass flows, Propagating Mirrors move acceleration distortion
Gravitational Waves • We have seen what properties of matter distort the fabric of space-time - massive objects. • For GW – need movement of masses – apple demonstration. • Need to increase the effect
3. Sources of Gravitational Waves
Sources of Gravitational Waves The experimenters need to know what to look for. The theoreticians have suggested several candidates.
1. Stochastic: Big Bang… or rather the inflation period We might hope for some kind of map This is the cosmic microwave background
Next candidates - dense and compact bodies
2. Orbiting bodies – eg neutron stars Expect constant frequency
3. Colliding compact bodies – sudden impact followed by brief ringing
4. Inspiralling and coalescing black holes Should increase frequency – a chirp! Recognisable signature – makes detection easier. This is what they found on 14 September 2015. And a second similar event on 26 Dec 2015
4. Finding GW – the detectors
4. Finding GW – detectors 1. Principle 2. WA 3. LIGO 4. LISA
The Principle: Two-arm interferometer Switch back and forth between these two slides
The Principle: Two-arm interferometer
Demonstration Mirrors and elastic spacetime OK so spacetime expand and contracts in a gravitational wave… But so does any ruler. And even the wavelength of light! So the change would not be measurable. Need two mirrors suspended free from the earth… They appear to wobble!
AIGO - David Blair’s detector in WA
LIGO – two detectors in USA Laser Interferometer Gravitational-wave Observatory
LIGO – two detectors in USA
Inside… with air let in of course!
One of the mirrors and its suspension system
And this is what they found! Play video • Two black holes – 30 solar masses each • Each 90 km diameter (event horizon) • 350 km apart and inspiralling • 0.3 speed of light • At centre of chirp – 0.5 seconds… • Radiated 3 solar masses of energy in GW • Cyclic, 15 hertz • Movement of the mirrors = 0.02 penta metre • Similar signal both detectors • 7 ms time difference (10 ms max)
Next generation - LISA – planned Laser Interferometer Space Antenna
The two sites detected similar waveforms. There was a 7 millisecond delay. This enablesd an estimate of the direction of arrival… To a cone. A third LIGO will allow location in the sky! Approved for India. Can then correlate with other observations eg light, radio, particles.
LISA – planned next generation Laser Interferometer Space Antenna Not funded yet A set of 3 satellites orbiting the sun 5 million km apart Sensitive to length changes of less than a proton diameter! Will look for GW at lower frequencies 0.01 Hz
5. What it means for science
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