Einsteins Legacy: Exotic Relativistic Objects in the Universe

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Einsteins Legacy Exotic Relativistic Objects in
the Universe
Sharon Morsink, Department of Physics, University
of Alberta
Alberta Physics Teachers Conference, U of A, Dec
9, 2005
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Einsteins Revolutionary Ideas

• No absolute definition of space or time
• Energy and mass are not distinct concepts
• Gravity isnt really a force after all

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Exotic Relativistic Objects?

• The Sun
• White Dwarf Stars
• Neutron Stars
• Black Holes
• Gravitational Lenses
• The Earth

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Equivalence of Mass and Energy

• After publishing his seminal 1905 paper on
  relativity, Einstein suddenly realized that it
  also implied mass and energy are equivalent
  through the equation
• E m c 2
• Because c (speed of light) is so large, small
  amounts of mass can be converted to large amounts
  of energy.

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1919 Francis Aston invented the mass spectrometer

• Astons invention allowed him to measure the mass
  of Hydrogen and Helium very precisely. (1922
  Nobel Prize in Chemistry)
• Aston found that the mass of one Helium atom is
  only 99.3 of the mass of 4 Hydrogen atoms.

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1920 Eddingtons Hypothesis about the Source of
the Suns Energy

• Eddington proposed that the Suns energy results
  from the nuclear fusion reaction 4
  H ? He
• Every time this reaction takes place 0.7 of the
  original mass of the Hydrogen is lost.
• This lost mass can be converted to energy through
  Emc2
• Unfortunately, at this time astronomers thought
  that the Sun was composed of Iron.

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1925 Cecilia Paynes PhD Thesis

• Her calculations showed that the Sun must be
  composed of about 75 Hydrogen and about 23
  Helium.
• This meant that Einsteins equation Emc2 does
  explain the Suns energy.

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Hydrostatic Equilibrium

• In a star, the inward force of gravity is
  balanced by a net outward effective force caused
  by gas pressure.
• In a regular star the gas pressure is due to the
  input of heat from nuclear reactions.
• What happens when the star runs out of nuclear
  fuel?

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Pressure in a T0 Gas

• In classical physics a zero temperature gas has
  zero pressure.
• Quantum mechanics gives us the Heisenberg
  Uncertainty Principle
• Even at T0 fermions (electrons, neutrons, etc)
  have a speed

?x
Degeneracy Pressure results when a gas has low
temperature and high density.
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White Dwarf Stars

• The end-state of a low mass star (like the Sun)
  is a white dwarf star.
• A white dwarf star is composed of Carbon ions and
  electrons
• Typical Mass Suns Mass
• Typical Radius Earths Radius
• No nuclear reactions
• Degeneracy pressure (due to electrons) keeps a
  white dwarf from collapsing.

Until 1930 it was thought that all stars ended up
as white dwarf stars.
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The Chandrasekhar Limit

• In 1930 Chandrasekhar realized that the equation
  for the electron velocity in a white dwarf star
  is fatally flawed

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Einsteins Special Relativity limits White Dwarf
Stars!

• Einsteins Special Relativity tells us that
  electrons cant travel faster than light speed.
• But in order for a high mass white dwarf star to
  exist, ultra-high density and faster than light
  speeds are required.
• High mass stars cant end their
• lives as a white dwarf.
• High mass stars must end their life in a
  complete gravitational collapse!

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The Discovery of Neutron Stars

• 1967 - Jocelyn Bell (while working on her PhD)
  discovered radio pulses that repeated every
  second.
• Best explanation the pulsars are rotating
  neutron stars
• Neutron stars also must have a maximum mass
• The discovery of neutron stars made it seem more
  likely that black holes could exist.

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1915 Einsteins General Relativity

• In 1905 Einstein realized that Special Relativity
  is incompatible with gravity, and that there are
  problems with Newtons theory of Gravitation.
• Einsteins theory of General Relativity is an
  improved description of gravity that includes the
  concepts of special relativity.
• The calculations were so hard that it took
  Einstein 10 years to figure it out.

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Whats the problem with Newtons theory of
gravity?

• Important results from special relativity
• massive particles must travel slower than light
• massless particles (like light) must travel at
  the speed of light
• information cant travel faster than light
• Suppose that the Sun were moved.
• Light from the Sun takes 8 minutes to travel to
  the Earth,
• so it takes 8 minutes for us to learn about the
  change.
• But in Newtons Gravity, the gravitational force
  between the Earth the Sun changes
  instantaneously we would get
• information about the change faster than light
• Einsteins new improved gravity theory allows
  for changes in the gravitational field to emit
  gravitational radiation which communicates
  information about the changes at the speed of
  light.

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Principle of Equivalence
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Gravity as Geometry

• In Einsteins general relativity, gravity isnt
  really a force!
• The mass of a planet (or star) causes a curvature
  of spacetime and satellites move on curved paths
  due to the curvature.

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A Dark Star

• In order for any object (rocket, baseball, etc)
  to escape from a planets gravitational
  attraction, it must be launched with a minimum
  speed called the escape velocity.
• 1783 John Michell Pierre-Simon Laplace
  postulated that if a stars escape velocity were
  the speed of light then the star would appear to
  be dark.

3km
A star with the same mass as the Sun, but with a
3km radius would be a dark star.
Mass of Sun 2 x 1030 kg Radius of Sun 7 x 105
km
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A Black Hole

• In 1916 Karl Schwarzschild found the first
  solution to Einsteins equations of general
  relativity.
• Schwarzschilds solution is now understood to
  represent a black hole.
• When a star (with the same mass as the Sun) gets
  compressed to the size of a Dark Star, it cant
  resist gravitational collapse.
• There is no hard surface inside a black hole.

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Black Holes are Simple!

• 1967 Werner Israel, professor at U of Alberta
  proved that a non-rotating black hole is very
  simple
• A black holes properties are independent of what
  stuff went into it.
• (Werner Israel is now retired and lives in
  Victoria.)

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How do you detect an invisible object?

• Black holes in binary systems are detected by
  looking for the motion of the companion.
• If an accretion disk forms around the black hole
  X-rays are emitted by the disk.

Cygnus X1
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Gravitational Deflection of Light

• In 1917 Einstein predicted that light from
  distant stars would be deflected by the Suns
  gravity.
• In 1919 Arthur Eddington measured the effect
  during a solar eclipse, verifying Einsteins
  theory.

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Gravitational Lensing
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The Einstein Ring
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Gravitational Lensing by Clusters of Galaxies
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Detection of Black Holes
Or Black hole
The MACHO project monitored millions of stars in
the Centre of our Galaxy to look for brief
brightening events caused by gravitational
lensing by an invisible object. A few black holes
were detected.
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Rotational Effects in Gravity

• In Einsteins theory of gravity, all forms of
  energy are sources of gravity (not just mass)
• Rotational Kinetic energy also is a source of
  gravity!
• Einsteins theory predicts that all rotating
  objects drag reference frames around them.
• Joseph Lense and Hans Thirring first pointed out
  this effect in 1918, so this is sometimes called
  the Lense-Thirring Effect

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• The frame-dragging effect causes a gyroscope
  orbiting a rotating object to precess.
• Although the effect due to the Earth is tiny, the
  Earth is the closest rotating astronomical
  object!
• Gravity Probe B is designed to measure this
  precession very accurately in order to test the
  frame-dragging effect.
• The Gravity Probe B experiment finished taking
  data earlier this year.
• Within a year their results will be announced.

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Conclusions

• Einsteins contributions to astronomy are
  indirect, but numerous!