# RELATIVITY by dffhrtcv3

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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

nearby star
Earth’s orbit
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

nearby star
Earth’s orbit
DIRECT MEASUREMENT of
SPEED of LIGHT
1849 FIZEAU
5 miles
light                                           mirror

Knowing the speed of rotation and the
separation of the slots, calculate
c= 196,000 mps (high by 5%)
rotation
ANOTHER ATTEMPT
FOUCAULT 1862                         mirror
2 screen
1

.
rotation      C= 185,000 mps (0.7% low)

66 feet
ANOTHER MEDIUM
FOUCAULT 1862                            mirror
2 screen
1

.
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:    SPEED OF SOUND
MACH 20:   SPEED OF THE SPACE SHUTTLE
MACH 70:   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
To the observer on train
d=vTt’
time of flight is t=2L/c
A                     A’
vT
L             D            D
To the observer on the platform
distance traveled is 2D=ct’
mirror            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!!
d=vTt’
D=ct’/2
vT
L=ct/2
D2=L2 + (vTt’/2)2
Pythagorus Theorem
D   L      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 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               E = moc2
[1-(v2/c2)]1/2        [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.

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