Topic
2. The speed of light
Note: the fact that light has a unique speed was not
obvious at the beginning – particles normally don’t have a unique speed, and it
was not obvious in the time of Galileo that light was not a stream of particles.
At that time, the real questions were:
1. Is
the speed of light infinite or finite?
2. If
the speed is finite, is it variable or a constant?
a. The general method: speed= distance/time = x/t
Everyday experience suggests
that speed is very great and might be infinite.
The difficulty: when speed is
very great, distance must be large and/or clock must have lots of resolution.
1. Galileo tries in about 1610 using terrestrial path and fails:
distance not long enough, clocks not good enough.
Same method was
tried in 1667 after Galileo’s death. Doesn’t work then either – same problem.
2. Olaf Roemer tries in 1676: Method: Use a very long distance so
that timing requirement will be easier.
Orbital period of innermost
moon of Jupiter is about 42.5 hours; period of Jupiter about 12 years;
interval between eclipses
varies due to changing distance to Earth.
Maximum difference is about 1000 s when light
travels completely across the orbit of the Earth; Jupiter doesn’t move much in
6 months.
Experiment has a number of technical problems that
can be addressed (at least to some extent) by increasing the number of
observers and the length of the observation.
Measuring elapsed time
difference between eclipses is easy, but how do you measure the distance?
Geometrical method compares
radius of orbit to diameter of the Earth
How do you measure diameter
of the Earth?
How well can you do all of
this?
3. Fizeau in 1849; Michelson, 1878; Anderson, 1937. Method: Use a moderate
terrestrial distance with a much better clock
Fizeau: clock is toothed wheel; result= 315,000 km/s
Michelson: clock is
rotating mirror wheel; result= 299,774 km/s
Anderson: clock is
fast electro-optic switch; result=299,773 km/s
Direct measurements limited
by uncertainty in the path length; becomes more and more serious as clocks
improve
Percent difference
between Michelson and Anderson = (1/299773.5) ´ 100 = 0.0003%
This could be explained by an error of only 0.13 m in
a path length of 40 km. (6 inches in the distance between Boulder and Denver)
How do you measure long
paths with high accuracy?
How can you relate those
measurements to the standards of length and time?
General requirement: percent uncertainty in measurements
of path length or elapsed time result in same percent uncertainty in the
computed speed of light.
These questions become more and more difficult to
answer as the required accuracy of the experiment increases.
The most difficult part is generally measuring the
distance – clock technology has improved much faster than techniques for the
precise measurement of lengths.
b. Indirect measurements (several
techniques). Measure frequency and wavelength of same signal – product is speed
of light
Current value= 299,792.458
km/s= 299,792,458 m/s. Usually rounded to 300,000 km/s = 3x105 km/s
= 3x108 m/s
Be careful when using a numerical value to be sure that you have the proper units.
Measurement of the path length in terms of the
standard meter was still the weakest link in all of experiments – even those
that used a number of clever indirect methods. Therefore, current practice is
to define the speed of light as the value specified above and use a measurement
of the speed of light to define the standard for length. In other words, the
meter is currently defined as the distance that light travels in vacuum in a
time of 1/299,792,458 seconds. The effect of this definition is to connect the
meter to the definition of the second.