Lecture 19: Special
Relativity
Readings: Section 24-1 and
Box 24-1
Framework
Postulates
Facts assumed
to be true
Example: the speed
of light is the same for all observers
Consequences
What happens when
moving quickly or in strong gravitational fields
Example: moving
clocks run slow
Tests
Observational proof
Example: the bending
of light by the Sun
Relevance
When special or
general relativistic equations must be used
Example: Special Relativity –
fast
General
Relativity – strong gravitational fields
Key Ideas for Special
Relativity:
Central Postulates:
The laws of physics
are the same for all uniformly moving observers
The speed of light
is the same for all observers
Consequences
Different observers
measure different times, lengths, and masses
Only spacetime
is observer independent
Tests
Michelson-Morley
Experiment
Muon
decays
E=mc2
Many,
many particle accelerator experiments
Relevance
When an object is
moving close to the speed of light relative to you
When very accurate
results are required
NewtonÕs Universe
In NewtonÕs view:
The Universe keeps
absolute time
Objects move through
absolute space
Universe
looks the same to all observers, regardless of how they move through it.
Result:
A set of laws formulated from
the perspective of an absolute ÒGodÕs Eye ViewÓ of the Universe.
EinsteinÕs Challenge
1905: Einstein challenged NewtonÕs view:
We cannot take a
ÒGodÕs eye-viewÓ of the Universe
We can only compare
our view with that of other observers
All information we
have is carried by light
But, light moves at
a finite speed.
Result
Introduces
an irreducible relativity to our physical perspective of the world.
Seeing the World
All information about the
Universe is carried by light.
Speed of Light: c=299,792.458 km/s
Compared to everyday
scales
65 mph=0.028
km/s=9.3 x10-8 c
light travels across
this room in ~30 nanoseconds
human reflexes: ~0.1
sec (108 nanoseconds)
Postulates
Definition of a postulate: An idea that is assumed to
be true.
Not just observed to be true in experiments. A
fundamental statement about the way the world has to be.
If a postulate is proven to be untrue, then large
parts of theory can be put in doubt.
Many experimental tests of the postulates have been
done.
1st Postulate of
Relativity
The laws of physics are the same
for all uniformly moving observers.
(ÒUniformlyÓ = Òwith a
constant velocityÓ)
Implications:
No such things as
Òabsolute restÓ
Any
uniformly moving observer can consider themselves to be Òat restÓ
Uniformly moving observers
(examples)
Traveling on a
moving sidewalk
In an airplane or
car moving smoothly
Laws of Physics are the same
A
game of pool played in your house, on the moving sidewalk, or in the place
would be the same. The laws of physics (conservation of momentum, F=ma, etc)
will work both places as will an observer watching the pool game go by on the
moving sidewalk.
Counterexample:
accelerating in a car or plane. Here the laws of physics, in particular
NewtonÕs Law of Inertia, does not appear to hold. All the balls will appear,
without an outside force, to rush to one end of the table.
Every
observer would agree about the laws of physics in every frame.
No
experiment you can perform can tell you whether you are in the stationary or
the moving frame.
The Laws of Physics are
Universal
One of the great advances of
Galileo/Newton was to expand the reach of the laws of physics.
The power of physics comes
from its universality. ÒLawsÓ that only work on the third Thursday of the month
in MP 4025 are pretty useless.
2nd Postulate of
Relativity
The speed of light in a
vacuum is the same for all observers, regardless of their motion.
Implications:
The speed of light
is a Universal Constant
We cannot send or
receive information faster than the speed of light
Cosmic speed light
Experimentally verified in
all cases
Reminder: Light is an
Electromagnetic Wave
Traveling Waves
Waves on Earth travel in a
medium
Water waves: water
Sound waves: air
Earthquakes: earth
No medium, no wave
By moving through the medium
yourself, you can experience a different speed for the wave. Example: running
into or away from ocean waves.
But what is the medium that
light travels in?
Thought to be the ÒetherÓ, a
medium that was at absolute rest
Motion through the ether
would affect the speed of light.
Michelson-Morley Experiment
A really cool experiment to
test whether the ether existed and whether it affected the speed of light.
It used the motion of the
Earth through the ether to test its effect.
Analogy: swimming
perpendicular or parallel to the ocean shore.
It found no difference in the
speed of light going with the motion of the Earth through the ether vs. the
speed of light going perpendicular to the ether. Ether does not exist! Light
does not need a medium to travel in.
The Consequences of the
Constancy of the Speed of Light
Unlike waves that travel in a
medium, we cannot change the observed speed of light.
Therefore we can only change
the length and time we observe
Leads to
Length
contraction
Moving
objects are shorter
Time dilation
Moving clocks run slow
Essential Relativity
Two observers moving relative
to each other experience the world differently:
Both measure the
same speed of light
Both find the same
physical laws relating distance, time, mass, etc.
But, both measure different
distances, times, masses, etc. when applying those laws.
The key is the role of light.
How do you measureÉ..?
Time: it is not absolute. You
need to define how you measure it precisely. The period of a pendulum? The
return of a light beam?
Length: it is not absolute
either. At rest, measuring length is easy: compare it with a yardstick, etc.
How do you measure something moving? Example: time it takes to pass you x the
speed it is traveling.
Implication: A Real Speed
Limit
Imagine that you start
running at the same time your friend turns on a flashlight. You are racing a
beam of light. Can you win?
NO! You can view this as you
are standing still and the whole world is running past you. And the speed of
light you measure is always the same = faster than you standing still.