Special Relativity

1
Special and General Relativity Einsteins
Physics

• Special Relativity
• and
• General Relativity

2
Michelson-Morley Experiment

• James Clerk Maxwell (1860) light is e/m waves
  traveling at c.
• Waves require a medium, light must travel through
  an ether.
• Michelson and Morley (1880s) looked for the
  ether using an interferometer.

3
Concept of the Interferometer

• Two boats will travel 24 m forward and back at 4
  m/s. The river current is 2 m/s eastward.
• North-South blue route (24 m / 4 m/s) x 2 12
  s.
• East-West red route (24 m / 6 m/s) (24 m / 2
  m/s) 16 s.
• Blue boat wins!
• But, if the river flows northward, the red boat
  would win.

4
Michelson-Morley Experiment

• As the earth moves through the ether, the wind
  acts like the river current, affecting the motion
  of the light waves.
• Rotating the experiment will cause the
  interference fringes to change, proving the
  existence of the ether.

5
Michelson-Morley Experiment

• When they conducted their experiment, no fringes
  were observed to change.
• No ether exists!
• A secondary outcome of the experiment was that c
  is always 3.00 x 108 m/s.
• Lorenz proposed that the ether wind affected the
  distance between the mirrors by a factor of

6
Einsteins Question

• Light propagates through space by changing
  electric and magnetic fields.
• As a student, Albert Einstein wondered what would
  happen if you could travel along with a light
  wave?
• Einstein devoted his life to understanding light.

Hmm...
7
Einsteins Postulates of Relativity

• All the laws of nature are the same in all
  uniformly moving frames of reference. You cannot
  detect absolute uniform motion (no ether for
  reference).
• The speed of light equals c and is independent of
  the speed of the source or the observer. C is
  absolute.
• The evidence for 2

g
g
detector measures energy
detector measures SAME energy
pion
g
g
pion moving at 0.99c
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Simultaneity

• Einstein imagined lightning hitting two poles.
• A stationary observer midway between the poles
  sees the light hit the two poles simultaneously.
• A moving observer midway between the poles sees
  the light hit the pole that he is moving toward
  first, and the other pole afterwards.
• The two observers cannot agree on the order of
  events
• Time is relative! Only the speed of light is
  absolute!

9
Space-Time

• speed distance / time.
• Applied to light, c d / t. If c is absolute,
  and time is relative, then distance (space) must
  be relative too.
• Einstein reasoned that the concepts of space and
  time are woven together into what he called
  space-time.

Think about it any event takes place at a
specific time and a specific place
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Traveling in Space-Time
time
We travel mostly through time, but not through
much space.
A fast-moving spacecraft travels through more
space and thus through less time.
As an object approaches c, it travels mostly
through space and through little time.
space (distance)
slope t/d, and 1/v t/d. As velocity goes up,
slope goes down
11
Time Dilation
Imagine two scientists measuring a light-pulse
inside a moving spaceship. One is inside the
spaceship, the other is outside the spaceship
to proper time
Time and distance measured by observer inside the
spaceship.
Time and distance measured by observer outside
the spaceship.
t dilated time (or td)
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Time Dilation
c t
c to
v t
t is dilated time, clock in motion with respect
to events to is proper time, clock at rest with
respect to events
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Calculating Time Dilation

• Proxima Centauri is the closest star to our solar
  system. If a spacecraft were sent to Proxima
  Centauri traveling at 75 of the speed of light
  (0.75 c), the trip would take 3.72 years
  according to the clocks onboard the ship. How
  long would the trip take according to people on
  Earth?

14
Time Dilation The Evidence

• In 1971, two atomic clocks were placed on
  commercial jets and two reference atomic clocks
  were placed in a building. The clocks were
  synchronized.
• The jets traveled around the world twice (once
  east, once west)
• The clocks that traveled through more space (in
  jets) recorded less time than the stationary
  clocks, as predicted by Einstein.

15
The Twin Paradox

• One twin travels at relativistic speeds away from
  the earth, turns around, and returns at
  relativistic speeds.
• She will be younger than her twin brother!
• The twin brother experiences the dilated time.

16
Twin Paradox The Evidence

• 1976 at CERN
• Muons normally decay in 2.2 ms (to) A muon
  should only be able to make 15 revolutions around
  the accelerator in this time.
• When traveling at 0.9994 c, a muon will make 432
  revolutions and decay in 63.5 ms (td), outlasting
  a twin stationary muon by a factor of 29.

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Length Contraction

• length contraction moving objects appear to
  contract along the direction of motion.
• Looking at a clock and meter-stick inside the
  spaceship, you would see less time pass for a
  beam of light to travel one meter since c d/t,
  distance must be less.

Lo proper length
LC contracted length
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Length Contraction Calculation

• All distances are contracted when you travel at
  relativistic speeds. Thus, Pluto, which is 39 AU
  away, would be closer if you traveled at 0.95
  c. What is the contracted distance?

19
Relativistic Momentum
Newton p mv
true only at non- relativistic speeds
Einstein p gmv
particle accelerator data supports Einstein
What is the momentum of a proton (1.67 x 10-27
kg) traveling at 0.999c (2.997x108 m/s)
according to Newton? What about to Einstein?
measured value Einsteins value
20
Relativistic Dynamics

• Why cant v gt c?
• As v ? c, p ? 8
• Impulse-momentum theorem
• FDt mDv Dp
• If p ? 8, either F ? 8 or Dt ? 8
• It either takes an infinite force or a finite
  force applied for an infinite period of time to
  reach the speed of light!

Einstein p gmv
Momentum (p)
Newton p mv
Speed (v) c
The answer to Einsteins question it is not
possible to ride a light beam, so there is no
paradox.
21
Eo mc2

• rest energy the energy an object possesses due
  to its mass
• mass frozen energy
• objects gain/lose mass when they absorb/emit
  energy
• The sun converts 4 billion kg/s into energy
  through the process of nuclear fusion (4 H ? He
  energy)
• E mc2 (4 x 109 kg)(3 x 108 m/s)2
• 3.6 x 1026 J each second!
• 360 heptillion W light bulb

22
General Relativity
23
Equivalence Principle

• Einsteins happiest thought was that you dont
  feel the force of gravity when you fall.
• But artificial gravity exists in an accelerating
  spacecraft.
• Gravity and acceleration are equivalent.
• An experiment done on earth or done when
  accelerating at g in a spacecraft will yield the
  same results! (general relativity).

24
Light and the Equivalence Principle

• A scientist in an accelerating spacecraft
  observes a horizontal beam of light to curve
  downward.
• According to the equivalence principle, gravity
  should curve light in a similar manner.

Sun
gravity
Astronomical observations after WWI showed that
the sun did indeed bend starlight, supporting
Einstein.
acceleration
25
Curved Space
If mass bends light, and light moves in a
straight line, then mass must warp or curve
space.
Newtons laws could not fully explain the orbital
motion of Mercury however, Einstein used his
general theory to properly calculate the orbit.
26
Warped Space and Orbital Motion
Newton (Law 1) said that an object will move in
straight line unless acted on by unbalanced
force. Einstein suggested that the object moves
in a straight line through curved space!