Gravitational Waves their discovery and significance Lecture to - - PowerPoint PPT Presentation

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Gravitational Waves their discovery and significance Lecture to - - PowerPoint PPT Presentation

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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.

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Gravitational Waves

their discovery and significance

Lecture to WEA Sydney 21 August 2016 Ian Bryce BSc(physics) BE(Hons) ianrbryce@gmail.com

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Contents

  • 1. What are waves?
  • 2. Theories of gravitation
  • 3. Sources of Gravitational Waves
  • 4. Finding GW – detectors
  • 5. What it means for science
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  • 1. What are waves?
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Waves in air - compression

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Krakatoa explosion 1883. Was clearly heard 3,000 miles away.

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Waves in water

Diffraction – physics experiments

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Can pass through each other - choppy

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Can travel from Fiji to Bondi

Cyclone Winston February 2016

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Through the ground

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Waves in a slinky toy Demonstration

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Light waves

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Radio waves

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We have seen some waves… what are some common features?

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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
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Pulse Has a duration Sine wave Has a wavelength A wave can be any shape, eg a single pulse… or a periodic sine wave

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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

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…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?

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Waves are now used for exercise

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Non-waves

There are other forces-at-a distance in physics

  • Electrostatic attraction
  • Magnets
  • wind

These weaken rapidly with distance – 1/r3, 1/r4

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But waves are special

Two parameters which regenerate each

  • ther:
  • Sound: pressure and velocity
  • Ground vibrations (earthquakes):

shear stress and strain

  • Water waves: height and velocity
  • Light: Electric field and Magnetic

field

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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/r2

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So waves are special

  • Once launched, a wave can

travel independently of its source

  • Carrying energy
  • In a particular direction.
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  • 2. Theories of

gravitation

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  • 2. Advances in gravitation
  • Newton – gravity, motion
  • Lorentz etc – special relativity
  • Einstein – general relativity
  • Gravitational waves
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  • 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

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“Local gravity” experiments - Newton’s country house with apple tree

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Local experiments - Uniform Gravity

Observe falling objects, measure position, apply calculus to find acceleration Conclude: Objects accelerate downwards, g = 9.8 m/s2 Hold an object - can feel the “force” Sit an object on a weighing device - can measure the “force” Horizontal force-motion experiments Relate force and acceleration F = ma

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Newton stitched together…

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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: Newton continued Law of Universal Gravitation

2

r m M G Fg 

Where G = universal constant M = mass of attracting body m = mass of satellite r = distance

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Today we describe this as Sources, fields, and forces

  • 1. Newtonian gravity

SOURCE Eg mass density

FIELD Eg gravity

FORCE Causes satellite

  • rbit
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Measuring Gravity Directly

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Modern apparatus A modern apparatus is shown here. Despite this, G is the least accurately known physical constant, to

  • nly 4 significant digits

(0.01%) 1970: G = 6.68 x 10-11 2010: G = 6.72 x 10-11 As accuracy improved.

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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!

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What are the limitations of Newton?

  • A. Static or slow-moving bodies.
  • B. Only weak gravity.
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  • If one body moves away…?
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Cartesian co-ordinates X, Y, Z Add Time

Four-vector Opens the way to relativity Three-vector

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Momentum (3-vector) con be combined with energy, to make a 4-vector. 4-vectors need to be manipulated with tensors,

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The maths - Manifolds

Space-time deformed by matter

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Sources, fields, and forces

In Relativity become: SOURCE Eg mass, energy, momentum EINSTEIN CURVATURE Distortion of space-time “FORCE” Path is a geodesic - appears curved

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Sources, fields, and forces

  • 2. General Relativity

Curvature tensor 4 x 4 Source tensor 4 x 4

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Source term: Stress-energy tensor 16 elements

We will tease this

  • ut

shortly… But first the big picture

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Curvature term: Stress-energy tensor 16 elements

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Matter causes the space-time around it to curve; the curvature of space-time determines how

  • bjects 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.

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Source term in detail: Stress-energy tensor 16 elements

Newton’s gravity needs

  • nly the first

element

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Complete source term. What are the other elements?

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Sponge demonstration - The Source term

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A Mechanical Engineer would recognise the 3 x 3 block – stresses in an element of material

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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

< wing bending in flight Tensile testing of a specimen

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Show bracket

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Sources, fields, and forces

  • 3. Gravitational waves

SOURCES Mass flows, acceleration WAVES IN THE METRIC Propagating distortion APPARENT ACCELERATIONS Mirrors move

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Gravitational Waves

  • We have seen what properties of matter

distort the fabric of space-time - massive

  • bjects.
  • For GW – need movement of masses –

apple demonstration.

  • Need to increase the effect
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  • 3. Sources of

Gravitational Waves

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Sources of Gravitational Waves

The experimenters need to know what to look for. The theoreticians have suggested several candidates.

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  • 1. Stochastic: Big Bang… or rather

the inflation period We might hope for some kind of map

This is the cosmic microwave background

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Next candidates - dense and compact bodies

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  • 2. Orbiting bodies – eg neutron stars

Expect constant frequency

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  • 3. Colliding compact bodies – sudden

impact followed by brief ringing

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  • 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

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  • 4. Finding GW

– the detectors

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  • 4. Finding GW – detectors
  • 1. Principle
  • 2. WA
  • 3. LIGO
  • 4. LISA
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The Principle: Two-arm interferometer

Switch back and forth between these two slides

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The Principle: Two-arm interferometer

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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!

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AIGO - David Blair’s detector in WA

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LIGO – two detectors in USA

Laser Interferometer Gravitational-wave Observatory

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LIGO – two detectors in USA

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Inside… with air let in of course!

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One of the mirrors and its suspension system

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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)
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Next generation - LISA – planned Laser Interferometer Space Antenna

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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

  • ther observations eg light,

radio, particles.

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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

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  • 5. What it means

for science

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What it means for science

A new window on the universe, after: 1. Material eg meteorites 2. Optical 3. Radio 4. Gamma rays etc 5. Particles eg protons 6. Gravitational waves!

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What can GW potentially do for science? A means of:

  • Testing hypotheses and theories of the

Big Bang and Inflation period

  • Testing General Relativity
  • Observing Black holes, Wormholes
  • Illuminating dark matter
  • Explaining Dark energy

WATCH THIS SPACE!

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End

PS: You asked for a joke…

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A group of physicists were driving across the USA. A cop pulls them over, and asks Heisenberg "Do you know how fast you were going?" Heisenberg replies, "No, but we know exactly where we are!" The officer looks at him confused and says "you were going 108 miles per hour!" Heisenberg throws his arms up and cries, "Great! Now we're lost!" The cop adds “You know you went through a red light back there”. Doppler explains “At high speed, the Doppler Shift turns red into green”. The cop is triumphant “Then I’ll book you for speeding.” The officer looks over the car and asks if the men have anything in the trunk. "A cat," Schrödinger replies. The cop opens the trunk and yells "Hey! This cat is dead." Schrödinger angrily replies, "Well he is now, damn you."