Einsteins Theories of Relativity

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Einsteins Theories of Relativity

• inertial reference frame an arena for doing
  physics, built out of meter sticks and clocks, in
  which Newtons first law is obeyed
• Newtons first law ? law of inertia if no force
  is acting, an object at rest stays at rest an
  object in motion continues in that state of motion

• this excludes accelerating frames speeding up,
  or rotating, in which an object at rest would
  appear to magically start moving without a force!
• Special relativity laws for space and time in
  inertial frames
• General relativity laws for space and time in
  non-inertial frames, and in the presence of
  gravitational force
• E mc2 equivalence of mass and energy is common
  theme

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The special theory of relativity velocity

• basic laws of physics are the same in all
  inertial frames
• speed of light is c 3.0 x 108 m/s in all
  inertial frames
• space and time get intermingled in this theory
• consider superposition of velocity weird!!
• Arthur sits in the bleachers, Esther is running
• if Esther throws a ball at 5 m/s, and is running
  at 3 m/s, Arthur will say the ball is moving at 8
  m/s, right???
• just about but if Esther shines a light while
  running at .67 c 2.0 x 108 m/s, shell claim
  light travels at c. So does Arthur say the light
  travels at 1.67 c 5 x 108 m/s? NO!!

Galileo u v w (velocities merely add
obvious!!)
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The special theory of relativity space and time

• an event is an occurrence something happens at
  a point in space x at a moment in time t
• A E in frames A (no primes) and E (use primes)
  measure the spacetime coordinate of two events I
  II.
• event I occur at both origins, and event II
  occurs at (x,t) (x,t)
• a CLOCK is a pair of events that occurs at the
  same place, at different times
• a LENGTH is a pair of events that occurs at the
  same time, at different places
• time dilation moving clocks run slow
• A says that Es clock is moving, and her ticks
  occur too slowly
• length contraction moving rulers are
  shortened
• A says that Es ruler is moving, and her ruler
  is too short
• OF COURSE Esther says exactly the same things
  about Arthur ...

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Fig.20.22
Spacetime diagrams plot ct against x

• units of ct are meters, just like units of x
• if something moves at c, x ct 45º line

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Fig.20.22
How does length contraction work?

• event I occurs at origins for A and E
• events I II are length measurement of As
  ruler
• events I III are length measurements of Es
  ruler

ct
ct
Green are worldlines of As ruler. E sees it
shortened!!
III
x
Blue are worldlines of Es ruler. A sees it
shortened!!
I
x
II
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The Redshift Parameter z and the Radial Velocity v

• the redshift number z gives the relation between
  z and the observed and actual wavelengths lobs
  and lrest

• Einsteins relativistic doppler shift for
  frequency shift is (converted to wavelength
  language)

• combining and rearranging gives

• a formula for v in terms of z, at least
  indirectly... let

• then one can easily show

• note that v is radial velocity (perpendicular to
  proper motion)

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Fig.20.23
One cannot exceed c (we think)
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The General Theory of Relativity

• basic laws of physics are the same in all frames
• acceleration is indistinguishable from gravity
  effects gut feeling!
• matter curves spacetime, so even light falls
  toward a mass
• so gravity is not really a force it is an
  explanation for the way things move through
  curved spacetime, as in Newtons first law!!
• principle of equivalence inertial m is same as
  gravitational m

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Fig.20.27
Fun with non-Euclidean geometry

• on a flat space, angles in a triangle add to
  180º
• on positive curvature (a lump), angles add to
  more than 180º
• on a negative curvature (a saddle), angles add
  to less than 180º

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What is a black hole?

• so much mass accumulates that neutron degeneracy
  pressure cant hold off gravity mass collapses
  to a point singularity
• the Schwarzschild radius RSchwarschild 3 km
  (M/MS)
• at this radius there is an event horizon there
  is no returning
• A would say that for E to fall through event
  horizon takes an infinite amount of time to reach
  black hole
• E would disagree it only took a finite amount
  of time
• black holes evaporate because quantum theory
  allows particle-antiparticle pairs to
  spontaneously be created if one falls in, its
  counterpart can be emitted, so they radiate
  energy
• smaller evaporate more quickly!!
• we dont know ANYTHING about the singularity.
• black holes exert gravity on their surroundings,
  so we can observe their effects just like
  ordinary masses

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A black hole sucks matter from a star
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A wormhole can connect separated regions of
spacetime
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Approaching the black hole
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/rsgro
w.mpg
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Circling a Black Hole at some distance see the
two Orions?
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/cirbh
.mpg
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Approaching the photon sphere
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/gotop
s.mpg
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Circling the black hole at the photon sphere
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/pscir
c.mpg