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RELATIVITY

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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
          CLOCK PARADOX
                                          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!!
            CLOCK PARADOX
                 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

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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posted:5/25/2013
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