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RELATIVITY
IN EVERY INERITAL REFERENCE FRAME,
THE SPEED OF LIGHT IS A CONSTANT
BUT WHAT DOES THIS MEAN?
SPEED OF LIGHT
LIGHT TRAVELS QUICKLY, AND UNTIL 1676
WAS ASSUMED TO BE INSTANTANEOUS.
SPEED OF LIGHT
1676 OLE ROEMER: noticed a 20 min difference in the
transit time of Jupiter’s moons, depending on where earth
was in its orbit. He challenged Cassini to predict the
appearance of Io on Nov 9. It was 10 minutes late.
Earth’s orbit
Orbit of Jupiter’s moon, Io
Jupiter
2AU
Calculated c= 132,000 mps (30% low)
SPEED OF LIGHT (2)
1728 BRADLEY: WAS MEASURING THE DISTANCE
TO NEARBY STARS BY PARALAX.
Motion of earth around sun
distant
stars
Earth’s orbit
nearby star
Aberration
Vertical
rain drops
Stationary
umbrella
Moving umbrella
SPEED OF LIGHT (4)
1728 BRADLEY: WAS MEASURING THE DISTANCE
TO NEARBY STARS BY PARALAX.
Calculated c= 176,000 mps (only 5% too low)
Angle of aberation
distant
stars
Earth’s orbit
nearby star
DIRECT MEASUREMENT of
SPEED of LIGHT
1849 FIZEAU
light
rotation
5 miles
mirror
Knowing the speed of rotation and the
separation of the slots, calculate
c= 196,000 mps (high by 5%)
ANOTHER ATTEMPT
FOUCAULT 1862
2
screen
1
mirror
.
rotation
C= 185,000 mps (0.7% low)
66 feet
ANOTHER MEDIUM
FOUCAULT 1862
2
screen
1
mirror
.
Tube filled with H2O
rotation
C= 138,000 mps (75% as fast as in air)
66 feet
SPEED OF LIGHT
MICHELSON 1878 Repeated Foucault’s experiment
with rotating mirror, but passed the beam back and
forth between two mirrors for a total distance of
22 miles. C= 186,295 mps in air (0.007% too high)
When Michelson evacuated the tube, and set up a
beam length of 10 miles.
c= 186,271 mps (0.006% too low)
TODAY WE DO IT
DIFFERENTLY
We know frequency x wavelength = speed
We can measure the frequency of a laser, and its
wavelength and multiply to get speed of light.
1972 Nat’l Bureau of Stds c= 186,282.3959 mps
in SI: 299,792.4562 km/sec; or close to 3 x 10 8 m/s;
or 1 billion kph; or around the world 7.5 times per second
One light-year is 1 x 10 13 km; or 6 trillion (1012)miles
HOW FAST IS LIGHT?
MACH 1:
MACH 20:
MACH 70:
SPEED OF SOUND
SPEED OF THE SPACE SHUTTLE
SPEED OF THE ASTEROID THAT
KILLED OFF THE DINOSAURS
MACH 900,000: SPEED OF LIGHT
SPECIAL RELATIVITY
THE LAWS OF PHYSICS ARE THE SAME
IN ALL INERTIAL REFERENCE FRAMES
vT
c
The speed of light is c whether you are on the train
or on the platform of the station
CLOCK PARADOX
To the observer on train
time of flight is t=2L/c
d=vTt’
A’
A
vT
L
D
D
mirror
To the observer on the platform
distance traveled is 2D=ct’
time of flight is t’=2D/c
Since D>L and t=t’, the speed of light must be different
depending on your reference frame. NO!!
CLOCK PARADOX
d=vTt’
vT
D
L
D=ct’/2
L=ct/2
D2=L2 + (vTt’/2)2
Pythagorus Theorem
D
(ct’)2 - (vTt’)2 =(ct)2
t’ = t[1-(vT2/c2)]1/2
That means for large velocities the moving clock must run slow
The length of a moving body is L’=L [1-(v2/c2)]1/2,
I.e., it gets shorter as the velocity increases.
CLOCK PARADOX
Clock paradox was predicted by theory and
confirmed by experiment.
An atomic clock was put aboard a satellite and
it lost precisely the amount of time predicted.
RELATIVISTIC
ENERGY AND MOMENTUM
P = mov
[1-(v2/c2)]1/2
E = moc2
[1-(v2/c2)]1/2
Where v<<c
p= mov
E = moc2 + 1/2 mov2
E=moc2 is rest energy even when
the object is not moving
ASIMOV’S
LAWS OF ROBOTICS
• A ROBOT MAY NOT INJURE A HUMAN BEING,
OR, THROUGH INACTION, ALLOW A HUMAN
BEING TO COME TO HARM
• A ROBOT MUST OBEY THE ORDERS GIVEN IT BY
HUMANS EXCEPT WHERE SUCH ORDERS WOULD
CONFLICT WITH THE FIRST LAW.
•A ROBOT MUST PROTECT ITS OWN EXISTENCE
AS LONG AS SUCH PROTECTION DOES NOT
CONFLICT WITH THE FIRST OR SECOND LAW.