Chapter 37: Relativity

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Chapter 37 Relativity
Flashback Newton said that space is infinite and
uniform, and time is the same for all observers
at all points in time
37.1 Einsteins postulates
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Einsteins first postulate
The laws of physics are the same in every
inertial frame of reference (what is an
inertial frame of reference???)
If Maxwells equations are valid in all inertial
frames, then the speed of light must be the same
in all frames
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Einsteins second postulate
The speed of light is the same in all inertial
frames it is independent of the motion of the
source. He had no clue what that speed was!!! It
didnt matter. gt An observer cannot travel
at c !!
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Describing the position of particle P in two
different frames of reference, S and S
S is the rest frame S is moving at velocity v
w.r.t. S
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Galilean transformation
x x ut dx/dt dx/dt u vx vx u But c
c, not c u Which means that t does not
t x does not x v dx / dt
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• Question You are on a spaceship that is flying
  at v 0.8 c. A light pulse is emitted in all
  directions from a point source on the ship. What
  is the shape of the wave that you observe?

0.8c
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• Question You observe a spaceship pass you at
  0.8c. A light pulse is emitted in all directions
  from a point source on the ship. What is the
  shape of the wave that you observe?

0.8c
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This is what you see as the spaceship zooms by
0.8c
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Given enough power, can the spaceship keep up
with the wavefront, from your (stationary) point
of view? 1. Yes 2. No
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37.2 Relativity and simultaneity
He sees everything happen at the same time. Does
she?
She is moving toward light wave B
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37.3 Relativity of time intervals
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Time dilation is not caused by signals travel to
the stationary observer
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Proper time there is only one frame of
reference for which a clock is at rest.
Dont worry about time delay for the light to
reach the observer.
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Twin paradox
One twin leaves on a spaceship and travels at 0.8
c. The other remains home. They each see the
other as moving at relativistic speeds, so both
assume the other is not aging as fast. Which one
really is younger?

• Neither
• The one who stayed home
• The one who took the trip

The one who took the trip is in a non-inertial
frame, and has experienced acceleration relative
to original frame.
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37.4 Relativity of length
Proper length l0 length of object when it is
at rest
2 l0 / c ?t / ?
Round-trip time in rest frame (Mavis) S t
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? gt 1
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37.5 The Lorentz Transformations
The moving frame has velocity u dx / dt
For low speeds, x x - ut and t t S is
moving to the right at speed u compared to frame
S The origins O and O coincide at t t 0
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Some algebra and taking derivatives gives
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Homework problem about simultaneity
Newtonian 2 observers see A happen at same time
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Relativity 2 observers see A happen at different
times
Minkowski diagrams Check wikipedia!
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Skip 37.6
37.7 Relativitistic momentum
v is now the speed of a particle compared to its
rest frame
Where m is the rest mass the mass of the
particle as seen from the frame in which the
particle (not YOU) is at rest
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• The problem with relativistic speeds is
• Momentum still has to be conserved
• We have to use Lorentz transformation to find
  speeds, but then momentum p mv will not be
  conserved.

Take derivative of this
Constant force no longer causes constant
acceleration!
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As a particle moves at high velocities, any given
force is less effective at accelerating it.
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Relativistic mass mrel g m Where m the
rest mass (the mass when the particle is at v0
in its own reference frame)
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Problem on relativistic momentum Calculate the
force required to give a 0.145-kg baseball a
1.00 m/s2 when the ball has a velocity of 0.900
c, if a and F are to v.
What if a and F are to v ?
A force to v cannot do any work (W
F.d) KE and speed v are constant F dp/dt d/dt
(gmv) gm dv/dt g ma.
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37.8 Relativistic work and energy
Where F is based on the relativistic p
energy
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Einsteins famous equation E mc2
Equivalence of matter and energy A particles
rest energy rest massc2
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The KE of a particle is the difference between
its rest mass and the total energy it has because
it is moving
Rest energy
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Massless particle (photon) still has momentum
energy E pc
Often, masses are given not as kg, but as
MeV/c2
1 eV energy given to an e- by accelerating it
through 1 V
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Problem on relativistic momentum and energy
Through what potential does an electron have to
be accelerated (starting from rest) to reach v
0.980 c? What is its KE at this speed?
So U1 K2
From EM K1 U1 K2 U2
U qV K
V q / K where q e
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37.9 Newtonian Mechanics and relativity General
relativity
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