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Special Relativity
Chapter 7
Einstein’s revolution  rethink the meaning
of space and time
Published “Special Theory of Relativity” in
1905 followed by “General Theory” in 1916
which incorporates gravity
He began with the postulate that
the laws
of physics should be independent of the
velocity of the observer
Foundations
Apply this to Maxwell’s theory of EM
radiation  requires there to be a
solution to the equations that is
constant in time (for someone moving
at speed
c
) but sinusoidal in space  not
possible!
Thus, speed of light must be the same
for all observers, independent of their
motion
(EM waves are different from
mechanical waves).
How can velocity of light be constant?
Velocity measurement depends on
distance and time interval  could these
quantities depend on the motion of the
observer?
See
ht p:/ www.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htm
for a discussion of the weirdness of the invariance of the speed of light!
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Simple experiment shows that
simultaneity is not absolute.
Thus, time is not absolute.
Einstein then investigated how
different types of situations
appear to observers with
different velocities (inertial
reference frames).
Einstein’s postulate could be
stated “There is no experiment
we can perform to tell us which
inertial frame is moving and
which is at rest.
There is no
‘preferred’ inertial frame.”
Absolute time
→
absolute simultaneity
The constancy of the speed of light is paradoxical
The postulate that the speed of light is the same in any inertial frame leads
immediately to a paradox.
Imagine the red dot emits a
flash of light and the blue dot is
moving away from Red at about
half the speed of light.
Red
thinks she is at the centre of the
expanding sphere of light.
But,
says special relativity, Blue also
thinks that the light moves
outward at the same speed in all
directions from him. So Blue
should be at the centre of the
expanding light sphere too. But
he's not, is he. Paradox!
(
http://casa.colorado.edu/~ajsh/sr/paradox.html)
Challenge
Can you figure out Einstein's solution to the paradox? Somehow you
have to arrange that both Red and Blue regard themselves as being in
the centre of the expanding sphere of light.
In a spacetime diagram, the units of space and time are chosen so that
light goes one unit of distance in one unit of time, i.e. the units are such
that the speed of light is one, c = 1. Thus light moves upward and
outward at 45 degrees from vertical in the spacetime diagram.
The lines along which Red and Blue move through spacetime are called
their
worldlines
. Each point in 4dimensional spacetime is called an
event. Light signals converging to or expanding from an event follow a
3dimensional hypersurface called the
lightcone
. In the diagram, the
sphere of light expanding from the emission event is following the future
lightcone. There is also a past lightcone, not shown here.
This is a
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 Spring '08
 Sarajedini
 Space, Special Relativity

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