Chapter 37 Special Relativity

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Chapter 37 Special Relativity
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37.2 The postulates
Validity of Maxwells equations
The Michelson-Morley experiment
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37.2 The postulates, The Ultimate Speed
The speed of light in vacuum has been defined to
be exactly c 299 792 458 m/s. It is found to
be the ultimate speed.
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37.3 Measuring an Event

• An event is something that happens, and every
  event can be assigned three space coordinates and
  one time coordinate.
• The Space Coordinates. We imagine the observers
  coordinate system fitted with a close-packed,
  three-dimensional array of measuring rods, one
  set of rods parallel to each of the three
  coordinate axes. These rods provide a way to
  determine coordinates along the axes.
• The Time Coordinate. For the time coordinate, we
  imagine that every point of intersection in the
  array of measuring rods includes a tiny clock,
  which the observer can read because the clock is
  illuminated by the light generated by the event.
• The Spacetime Coordinates. The observer can now
  assign spacetime coordinates to an event by
  simply recording the time on the clock nearest
  the event and the position as measured on the
  nearest measuring rods. If there are two events,
  the observer computes their separation in time as
  the difference in the times on clocks near each
  and their separation in space from the
  differences in coordinates on rods near each.

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37.3 Measuring an Event
Synchronization of all clocks is needed and
achievable.
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37.4 The Relativity of Simultaneity
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37.4 The Relativity of Simultaneity, A Closer
Look
Fig. 37-4 The spaceships of Sally and Sam and the
occurrences of events from Sams view. Sallys
ship moves rightward with velocity, v . (a) Event
Red occurs at positions RR and event Blue occurs
at positions BB each event sends out a wave of
light. (b) Sam simultaneously detects the waves
from event Red and event Blue. (c) Sally detects
the wave from event Red. (d) Sally detects the
wave from event Blue. With the postulate of
constant speed of light, Sally would say event
Red happens earlier.
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37.5 The Relativity of Time
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37.5 The Relativity of Time
In the previous case, Sally measures a proper
time interval, and Sam measures a greater time
interval. The amount by which a measured time
interval is greater than the corresponding proper
time interval is called time dilation. g is
called the Lorentz factor.
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Example, Time dilation of spacecraft which
returns to Earth
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Example, Time dilation and travel distance for a
relativistic particle
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37.6 The Relativity of Length
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37.6 The Relativity of Length, Proof
Consider that both Sally, seated on a train
moving through a station, and Sam, again on the
station platform, want to measure the length of
the platform. Sam, using a tape measure, finds
the length to be L0, a proper length, because the
platform is at rest with respect to him. Sam also
notes that Sally, on the train, moves through
this length in a time Dt L0/v, where v is the
speed of the train. Therefore, For Sally,
however, the platform is moving past her. She
finds that the two events measured by Sam occur
at the same place in her reference frame. She can
time them with a single stationary clock, and so
the interval t0 that she measures is a proper
time interval. To her, the length L of the
platform is given by Therefore,
and finally,
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Example, Time dilation and length contraction
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Example, Time dilation and length contraction as
seen in outrunning a supernova
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37.7 The Galilean Transformation
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37.7 The Lorentz Transformation Equations
Based on the constancy of the speed of light in
all inertial frames
The Lorentz transformation equations are
(The equations are written with the assumption
that t t 0 when the origins of S and S
coincide.)
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37.7 The Lorentz Transformation Equations
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37.8 Some Consequences of Lorentz Transformation
Equations Simultaneity
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37.8 Some Consequences of Lorentz Transformation
Equations Time Dilation
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37.8 Some Consequences of Lorentz Transformation
Equations Length Contraction
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37.9 The Relativity of Velocities
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37.10 The Doppler Effect of Light
The Doppler effect is a shift in detected
frequency for traveling waves. The Doppler
effect for light waves depends on only one
velocity, the relative velocity, v, between
source and detector, as measured from the
reference frame of either. Let f0 represent the
proper frequency of the sourcethat is, the
frequency that is measured by an observer in the
rest frame of the source. Let f represent the
frequency detected by an observer moving with
velocity relative to that rest frame. Then, when
the direction of is directly away from the
source, For low speeds (b 1), this equation
can be expanded in a power series in b and
approximated as
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37.10 The Doppler Effect of Light, Astronomical
Effect
Red shift and blue shift
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37.10 The Doppler Effect of Light, Transverse
Doppler Effect
The transverse Doppler effect. In terms of
period of oscillations, Where To is the proper
period.
The Doppler effect of light in general
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37.11 A New Look at Momentum
momentum conservation in danger with the old
definition p mv concept of four vectors,
proper time as a scalar
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37.11 A New Look at Energy, Total Energy
In a system undergoing a chemical or nuclear
reaction, a change in the total mass energy of
the system due to the reaction is often given as
a Q value. The Q value for a reaction is obtained
from the relation
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37.11 A New Look at Energy, Kinetic Energy
For v ltlt c
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37.11 A New Look at Energy, Momentum and Kinetic
Energy
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37.11 A New Look at Energy, Mass Energy
An objects mass m and the equivalent energy E0
are related by This energy that is associated
with the mass of an object is called mass energy
or rest energy. Masses are usually
measured in atomic mass units, where 1 u 1.660
538 86 10-27 kg, and energies are usually
measured in electron-volts or multiples of it,
where 1 eV1.602 176 462 10-19 J.
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Example, Energy and momentum of a relativistic
electron
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Homework Problems 14, 20, 32, 38, 58