Beyond Astronomy

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Beyond Astronomy
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The Theory of Relativity

• Albert Einstein surprised the world in 1905 when
• he theorized that time and distance can not be
  measured absolutely
• they only have meaning when they are measured
  relative to something
• Einstein published his theory in two steps
• special theory of relativity (1905)how space
  time are interwoven
• general theory of relativity (1915)effects of
  gravity on space time
• What is relative in relativity?
• motionall motion is relative
• measurements of motion (and space time) make no
  sense unless we are told what they are being
  measured relative to
• What is absolute in relativity?
• the laws of nature are the same for everyone
• the speed of light (in a vacuum), c, is the same
  for everyone

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What is Relative?

• A plane flies from Nairobi to Quito at 1,650
  km/hr.
• The Earth rotates at the equator at 1,650 km/hr.
• An observer
• on the Earths surface sees the plane fly
  westward overhead
• at a far distance sees the plane stand still and
  the Earth rotate underneath it

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A Good Paradox

• Paradoxis a situation that seems to violate
  common sense or contradict itself.
• the paradox is resolved when the rules of nature
  are better understood
• Ideas consequences of relativity are not
  evident in everyday life.
• we do not experience the extreme speeds gravity
  required
• so we have no common sense about relativity

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The Up Paradox

• In childhood, we regard up as a single
  direction above our head.
• When we realize that people in Australia do not
  stand upside-down
• we revise our common sense
• up is defined relative to the center of the
  Earth

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Reference Frames

• Two or more objects which do not move relative to
  each other share the same reference frame.
• they experience time and measure distance mass
  in the same way
• Objects moving relative to the other are in
  different reference frames.
• like the plane and ground below
• they experience time and measure distance mass
  in different ways

• Since ground observers see light move at c, the
  plane passenger is always slower.

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Time Dilation

• To an observer outside the train, the ball
  appears to move faster.
• makes common sense
• Now lets consider Jackie moving by at close to
  the speed of light .
• she bounces light instead of a ball

• The outside observer can not see the light moving
  faster than c.
• yet the light does travel a longer distance as
  seen by the observer
• so time must run more slowly for Jackie!

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Ticket to the Stars

• Although we can not travel faster than the speed
  of light
• special relativity will make the journey seem
  shorter if we can travel close to the speed of
  light

• Time moves more slowly for the space traveler.
• The distance to be covered is contracted.
• Space travelers can reach distant stars in their
  lifetimes.
• Their friends and family will not be there to
  greet them when they return home to Earth.

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Order or Simultaneity of Events

• The red green flashes occur simultaneously for
  you.
• Jackies fast motion causes the green light to
  reach her first
• you both agree on that
• But Jackie considers herself stationary in her
  reference frame.
• she sees both lights travel the same distance at
  velocity c
• yet she sees the green light first
• so the green flash occurs before the red flash in
  her reference frame

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Length Contraction

• As Jackie moves past you at high velocity
• she tries to measure the diameter of your ship
• but time moves more slowly for her
• so she measures a shorter length than you do
  (distance velocity x time)
• Objects appear shorter to you in the direction
  which they are moving.

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Mass Increase

• As Jackie moves by at high speed, you give both
  her her identical sister a push.
• time runs more slowly for Jackie, so she feels
  the push for a shorter time
• Jackie accelerates less than her sister does
• Newtons 2nd Law (F ma) says if F is same,
  Jackies mass must be greater
• Objects moving by you have a greater mass than
  when at rest.

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The Topic is Gravity

• Albert Einstein stunned the scientific world
  again in 1915
• with publication of his general theory of
  relativity
• it is primarily a theory of gravity
• Isaac Newton saw gravity as a mysterious force.
• he could explain its actions, but not how it was
  transmitted through space
• Einstein theorized that the force of gravity
  arises from distortions of space (or spacetime)
  itself!
• spacetimethe 4-dimensional combination of space
  time that forms the very fabric of the Universe
• matter shapes and distorts spacetime
• space(time) itself can be curved
• you may think you are traveling a straight line
• but your motion is actually curved

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Matter Distorts Spacetime

• Matter distorts spacetime like weights on a taut
  rubber sheet.
• The greater the mass, the greater the distortion
  of spacetime.

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Accelerated Motion

• The special theory of relativity states that all
  motion is relative
• for objects moving at a constant velocity with
  respect to each other
• everyone (every reference frame) can claim to be
  stationary
• What if you fire your rockets and move away from
  Jackie?
• your velocity increases 9.8 m/s every secondyou
  are accelerating
• you feel a force (1 g) which pushes you to the
  floor of your ship

• Jackie sees you moving away from her stationary
  position.
• you claim that Jackie is moving away
• but she sees you pinned to the floor while she is
  still floating
• this proves you must be accelerating
• you are feeling a force she is not
• Apparently we can distinguish between motion
  non-motion.

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The Equivalence Principle

• This scenario bothered Einstein.
• his intuition told him that all motion should be
  relative
• until he had a revelationthe idea for the
  equivalence principle
• The effects of gravity are exactly equivalent to
  the effects of acceleration.

• Suppose you were in a closed room.
• whether on Earth or accelerating through space at
  9.8 m/s2
• you would never know the difference
• your weight would be the same

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Accelerated Motion or Standing Still?

• Nowback to Jackie!
• because you are feeling a force, she claims that
  you are accelerating
• she is the stationary one
• But the equivalence principle of general
  relativity tells us that
• you can legitimately consider this force to be
  the weight of gravity
• you are firing your rockets in order to remain
  stationary (to hover)
• the weightless Jackie is in free-fall
• General relativity makes all motion relative
  again!

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Dimensions
dimension an independent direction of possible
motion

• A point (0?D) moved in one direction creates a
  line (1?D).
• A line moved in a direction 90º to itself creates
  a plane (2?D).
• A plane moved in a direction 90º to itself
  creates a space (3?D).
• A space moved in a direction 90º to itself
  creates a 4?D space.
• we can not perceive this hyperspaceany space gt
  3?D

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Spacetime for All

• The reality of spacetime is the same in all
  reference frames.
• we can not visualize the 4?D spacetime since we
  cant see through time
• we perceive a 3?D projection (view) of spacetime
• while spacetime is the same for all observers,
  their 3?D perceptions of it (e.g. space time)
  can be very different

• By analogy
• we can all agree on the shape size of this book
  in 3 dimensions

• But
• the following 2?D projections (views) of the same
  book all look very different

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The Rules of Geometry

• The geometry you know is valid when drawn on a
  flat surface.
• The rules change if the surface is not flat.

spherical (curved-in) geometry
flat (Euclidean) geometry
saddle-shaped (curved-out) geometry
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Mass and Spacetime

• According to Newton, all bodies with mass exert a
  gravitational force on each other.
• even Newton had problems accepting this concept
  of action at a distance
• General relativity removes this concept.
• mass causes spacetime to curve
• the greater the mass, the greater the distortion
  of spacetime
• curvature of spacetime determines the paths of
  freely moving objects

• Orbits can now be explained in a new way.
• an object will travel on as straight a path as
  possible through spacetime

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The Strength of Gravity

• The more that spacetime curves, the stronger
  gravity becomes.
• Two basic ways to increase gravity/curvature of
  spacetime
• increased mass results in greater curvature at
  distances away from it
• curvature is greater near the objects surface
  for denser objects
• for objects of a given mass, this implies smaller
  objects

• All three objects impose the same curvature at a
  distance.
• White dwarf imposes steeper curvature at Suns
  former position.
• Black hole punches a hole in the fabric of
  spacetime.
• Nothing can escape from within the event horizon.

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Gravitational Time Dilation

• We use the equivalence principle to study the
  effect of gravity on time.
• You Jackie in the ship have synchronized
  watches
• the ship accelerates
• the watches flash

• Moving away from Jackie, you see larger time
  intervals between her flashes.
• time appears to be moving slower for her
• Moving towards you, Jackie sees shorter time
  intervals between your flashes.
• time appears to be moving faster for you
• you both agree
• So, in the equivalent gravitational field
• time moves more slowly where the gravity is
  stronger

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Gravitational Lensing

• Light will always travel at a constant velocity.
• therefore, it will follow the straightest
  possible path through spacetime
• if spacetime is curved near a massive object, so
  will the trajectory of light

• During a Solar eclipse in 1919, two stars near
  the Sun
• were observed to have a smaller angular
  separation than
• is usually measured for them at night at other
  times of the year
• This observation verified Einsteins theory
• making him a celebrity

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Gravitational Lensing

• Since that time, more examples of gravitational
  lensing have been seen.
• They usually involve light paths from quasars
  galaxies being bent by intervening galaxies
  clusters.

an Einstein ring galaxy directly behind a galaxy
Einsteins Cross
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Gravitational Redshift

• If time runs more slowly on the surface of stars
  than on Earth
• spectral lines emitted or absorbed on the
  surfaces of stars
• will appear at a lower frequency (cycles/s) than
  measured on Earth
• the length of 1 second is longer on the stars
  surface than on Earth
• This gravitational redshift has been observed.

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Gravitational Waves

• General relativity also predicts that
• rapidly accelerating masses should send ripples
  of curvature through spacetime
• Einstein called these ripples gravitational waves
• similar to light waves, but far weaker
• they have no mass and travel at the speed of
  light
• They have not yet been directly observed.
• but the loss of energy from binary neutron stars
• the Hulse-Taylor binary
• is consistent with the energy being emitted
• as gravitational waves

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Science Fact or Fiction?

• Do the theories of relativity prohibit
  interstellar travel?
• we can not travel faster than the speed of light
• but what if we made the distance to our
  destination shorter?

• We might tunnel through hyperspace in a wormhole.
• A wormhole connects two distant points in the
  Universe.
• Or perhaps we could warp spacetime so that two
  locations of our choosing could touch momentarily.

• None of these ideas is prohibited by our current
  understanding of physics.
• Most scientists are pessimistic about the
  possibilities.
• wormholes would also make time travel possible,
  with its severe paradoxes
• For the moment, the Universe is safe for science
  fiction writers!

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Quantum Mechanics

• At the same time Einstein was developing the
  principles of relativity, our theory of the very
  large
• Physicists were developing new theories of the
  very small.
• 1905 Einstein shows light can behave like a
  particle
• 1911 Rutherford discovers atoms consist mostly
  of empty space
• 1913 Bohr suggests that electrons in atoms have
  quantized energies
• They called this new discipline quantum
  mechanics.
• it has revolutionized our understanding of
  particles forces
• it has made possible our modern electronic devices

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Fundamental Particles

• The most basic units of matter, impossible to
  divide, are called fundamental particles.
• Democritus of ancient Greece thought they were
  atoms
• physicists of the 1930s thought they were
  protons, neutrons, electrons
• the advent of particle accelerators has given us
  a zoo of new particles
• Murray Gell-Mann in the 1960s proposed a standard
  model where all these particles could be built
  from a few fundamental components

Fermilab particle accelerator in Illinois
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Basic Properties of Particles

• Important basic properties of a subatomic
  particle
• mass
• charge
• spin angular momentumor spin
• All particles of the same type have the same
  spin.
• but they can have two possible orientations up
  down

• Particles do not really spin like a top.
• the term describes angular momentum
• which is measured in units of h
• Particles having half integer spin are called
  fermions.
• particles of which matter is composed
• Particles having integer spin are called bosons.
• such photons, gluons, other exchange particles

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The Building Blocks of Matter

• Protons neutrons, which are more massive than
  electrons
• are themselves made up of less massive particles
• we call these particles quarks
• quarks come in six flavors
• protons neutrons consist of different
  combinations of two of these flavors

• the up quark (2/3)
• the down quark (?1/3)
• Particles made from quarks (hadrons)
• can contain 2 or 3 quarks
• a quark never exists alone

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The Building Blocks of Matter

• The electron is not made up of lighter particles.
• it is fundamental
• it is one of six particles called leptons
• leptons do exist by themselves
• Here are the six flavors of quarks six leptons

• Quarks leptons are the fundamental particles of
  which all matter is made.
• Quarks leptons are all fermions.
• All of these particles have been experimentally
  verified.

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Antimatter

• Every quark lepton has its own antiparticle.
• when two identical particles of matter
  antimatter meet
• they annihilate each other into pure energy (E
  mc2)
• When conditions are right (like immediately after
  the Big Bang)
• collision of two photons can create a particle
  its antiparticle
• we call this pair production

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Forces of Nature

• Natural forces allow particles to interact and
  exchange momentum.
• mass is always positive, allowing gravity to
  dominate on large scales
• each force is transmitted by exchange particles
• exchange particles are all bosons
• the graviton has not yet been detected
• The EM Strong forces are aspects of the same
  electroweak force.
• physicists are trying to unify all of the natural
  forces (GUT)

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Heisenberg Uncertainty Principle

• The more we know about where a particle is
  located
• the less we can know about its momentum
• The more we know about a particles momentum
• the less we can know about its position
• We can not know the precise value of an object's
  position momentum (or energy time at which it
  has that energy) simultaneously.

x location p momentum h 6.626 x 1034
joule x sec
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Electron Clouds

• As a consequence of the uncertainty principle
• if we locate the precise position of an electron
• we have no idea of where it will go next
• it appears in different locations over time, it
  is thus smeared out
• we can calculate the probabilities of where it
  could be located

electron probability patterns for several energy
levels of Hydrogen
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Wave-Particle Duality of Matter

• If we think of the electron as a wave, it has a
  well-defined momentum.
• but a wave has no single, precise location
• it is spread out over a volume, like an electron
  cloud
• electrons bound in atoms can be described as
  standing waves
• Just like light, all matter has a wave-particle
  duality.
• in different situations, it is more convenient to
  describe it as one or the other

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Pauli Exclusion Principle

• Two fermions of the same type cannot occupy the
  same quantum state at the same time.
• Quantum state specifies the location, momentum,
  orbital angular momentum, spin of a subatomic
  particle
• to the extent allowed by the uncertainty
  principle
• Each of these properties is quantized.
• they can take on only particular values

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Consequences of the Exclusion Principle

• In an atom
• electron in lowest energy level
• has a certain orbital angular momentum
• a restricted range of locations
• quantum state is determined, except for spin
• two electrons can fit in this level
• a third must go to a higher level

• This creation of higher energy levels makes
  chemistry possible.
• Although atoms are mostly empty space, the
  solidity of matter is explained.
• uncertainty principle ensures electrons are not
  packed into very tiny spaces
• exclusion principle ensures that each electron
  gets to have its own space
• These principles govern the sizes of nuclei.

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Quantum Tunneling

• Uncertainty principle also states
• product of uncertainties in time energy are
  constant
• the shorter the time, the greater the range of
  probable energies
• a particle could briefly have enough energy to
  overcome a barrier (like escaping from a cell)
• this will not violate conservation of energy if
  stolen energy is returned before it is noticed
• Quantum tunneling can explain how two protons can
  fuse.
• protons can instantly overcome EM repulsion

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Virtual Particles

• Matter-antimatter pairs of particle can pop into
  existence.
• if they annihilate before the uncertainty time,
  they go unnoticed
• If one particle is lost to the event horizon of a
  black hole
• the other stays in existence
• it will eventually annihilate with another
  stranded particle
• we would observe Hawking radiation emitted just
  outside the event horizon

• Ultimate source of this radiation is the
  gravitational potential energy of back hole
• The black hold would eventually evaporate.
• This effect has not yet been observed.

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Summary

• The view we have of the Universe is very limited.
  It skews our perspective and common sense.
• When dealing with objects that are very small,
  very fast or very massive the results are
  non-intuitive.
• In order to understand the extremes in space and
  time, astronomers turn to advanced physics,
  chemistry and mathematics.
• Our advanced theories explain the Universe we
  observe, but interpreting the results can often
  border on philosophy.
• We will continue to learn more about the nature
  of the Universe as we continue to explore and
  probe its mysteries.