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1
Einsteins Happiest Thought

• I was sitting in a chair in the patent office at
  Bern when all of a sudden a thought occurred to
  me
• If a person falls freely he will not feel his
  own weight...
• I was startled. This simple thought made a deep
  impression on me. It impelled me towards a
  theory of gravitation.

2
General Theory of Relativity (1915)

• Presented a series of lectures in which he
  described his theory of general relativity.
• The final lecture climaxed with his introduction
  of an equation that replaced Newton's law of
  gravity.
• In general relativity, gravity is no longer a
  force (as it is in Newton's law of gravity) but
  is a consequence of the curvature of space-time.

3
(True) Gedanken 4
If there were no windows in the elevator,
Einstein would not be able to tell whether he is
at rest on Earth or accelerating at a constant
rate through space.
4
General Theory (cont)

• Gravity can be cancelled by acceleration.
• In fact, artificial gravity can be created by
  acceleration.
• Space Time are no longer independent.
• We talk about SPACETIME.

5
General Theory of Relativity

• Theory says space is curved (or warped).
• This curvature is the reason for gravity.

6
General Theory (cont)

• Gravity is described as spacetime curvature (not
  a force).

7
General Theory of Relativity
8
General Theory (cont)

• Scientists were skeptical because the theory was
  derived by mathematical reasoning and not by
  experiment.
• In 1919, predictions made were confirmed by Sir
  Arthur Eddington's measurements (during a solar
  eclipse), of how much the light emanating from a
  star was bent when it passed close to the Sun.

9
General Theory of Relativity

• Light is still traveling in a straight line
  SPACE is curved and light just follows space

10
General Theory of Relativity

• On November 7, The London Times reported the
  confirmation.
• Headline
• Revolution in Science.
• Newtonian Ideas Overthrown.
• Overnight, Einstein became a legend.

11
General Theory of Relativity

• Science fiction ???
• Spacetime continuum
• Warped space
• Time travel
• Wormholes
• Alpha Omega of the Universe
• Fact or Fiction ?
• Serious scientists want to know

12
General Theory of Relativity
Kip S. Thorne developed the idea of wormholes for
the movie Contact
Can take a short-cut easily go great distances.
13
General Theory of Relativity

• Is there any every day applications of
  relativity???
• Yes, absolutely (ha ha)

14
GPS

• You can purchase hand-held GPS navigation units
  that will give you your position on the Earth
  (latitude, longitude, and altitude) to an
  accuracy of 5 to 10 meters that weigh only a few
  ounces and cost around 100.

15
Current GPS

• 24 orbiting satellites 12,500 miles high
• An orbital speed of about 8700 miles/hour
• At least 4 satellites are always visible from any
  point on the Earth at any time.
• Each satellite carries with it an atomic clock
  that "ticks" with an accuracy of 1 nanosecond (1
  billionth of a second).

16
Current GPS

• An orbital speed of about 8700 miles/hour
• Special Relativity predicts that the atomic
  clocks LOSE about 7 microseconds per day because
  of the slower ticking rate.
• 24 orbiting satellites 12,500 miles high
• General Relativity predicts that the atomic
  clocks GAIN about 45 microseconds per day.

17
Current GPS

• A GPS receiver determines its current position by
  comparing the time signals it receives from the
  satellites (usually 6 to 12) and triangulating on
  the known positions of each satellite.
• Pretty cool

18
But

• Clocks accuracy MUST be 20-30 nanoseconds.
• An observer on the ground sees the satellites in
  motion relative to them, Special Relativity
  predicts that we should see their clocks ticking
  more slowly.
• The satellites are in high orbits, where the
  curvature of spacetime due to the Earth's mass is
  less than it is at the Earth's surface, so
  General Relativity predicts we should see their
  clocks ticking faster..

19
But

• Clocks accuracy MUST be 20-30 nanoseconds.
• Satellite clocks tick faster than ground clocks
  by about 38 microseconds per day (45-738).
• There are 1000 nanoseconds in a microsecond.
• Without relativistic corrections, GPS readings
  are false after only 2 minutes,
• You accumulate an error of about 6 miles, daily.
• After a week, you could be off hundreds of miles
  

20
But

• Special Relativity predicts that the atomic
  clocks LOSE about 7 microseconds per day because
  of the slower ticking rate.
• General Relativity predicts that the atomic
  clocks GAIN about 45 microseconds per day.

21
But

• Satellite clocks tick faster than ground clocks
  by about 38 microseconds per day (45-738).
• There are 1000 nanoseconds in a microsecond.
• Without relativistic corrections, GPS readings
  are false after only 2 minutes,
• You accumulate an error of about 6 miles, daily.
• After a week, you could be off hundreds of miles