Particle Model of Light Reading 2: Determining the Speed of Light

Particle Model of Light Reading 2:
Determining the Speed of Light
Anyone who has experienced a lightning storm intuitively knows that sound and light do not
travel at the same speed. A flash of lightning is seen before thunder is heard, unless one is
unfortunate enough to be very close to the location of the strike. It is obvious that sound travels
at a finite speed. But what about light Do any readily observable phenomena suggest that light
has a finite speed Light a candle or flip a light switch and light seems to instantly fill a
darkened room. It is no surprise that in Galileo's day most thinkers believed that light had
infinite velocity. Galileo, however, was not convinced of this.
Galileo believed that light traveled at a finite speed, though he understood from observations of
cannon fire that light traveled much faster than sound (the fiery blast of a cannon can be seen
from a distance before it is heard). In fact, the speed of sound had been measured with relative
accuracy in Galileo's day by observing cannons fired from a distance and timing the delay
between the appearance of fire from the end of the cannon and the arrival of the cannon's sound.
Galileo attempted to determine the speed of light in a similar fashion by attempting to measure
the time it takes for light from a lantern he uncovered to travel to an assistant and back again.
The assistant would signal the arrival of Galileo's lantern light by uncovering a lantern of his
own. In the end, Galileo succeeded only in roughly measuring human reaction times. Even
when distances of a mile or more separated the experimenters, it was obvious that light traveled
too quickly to be measured in this fashion. Many in Galileo's day continued to believe that light
propagated instantaneously.
In the 17th century, the triumph of Newton's Law of Universal Gravitation and of Kepler's Laws
of planetary motion allowed astronomers to make extremely accurate predictions of planetary
motions and positions. The four largest moons of Jupiter, which Galileo had discovered with a
simple telescope, were no exception. Periodically, these moons would disappear behind Jupiter
and not be visible from Earth. The timing of these eclipses was observed carefully and very
accurate timetables were established. Galileo had even suggested that the motion of Jupiter’s
moons could be used as a universal timekeeping mechanism because the eclipses would occur at
the same time from any vantage point on Earth, which is not the case for phenomena associated
with the sun, moon, or stars.
One Danish astronomer, Olhaus "Ole" Roemer, made repeated observations of the eclipses of
Jupiter's moons.
“As the moon moves around Jupiter, there is a place
(A to B) when the moon is in Jupiter's shadow - in
other words, it is eclipsed as far as observations from
the Earth are concerned. The Earth observations might
be made from positions 1 and 2 of Earth's orbit about
the sun; Jupiter's moon would therefore be seen to
enter the shadow at A and emerge at B.
“Roemer noticed that the time between eclipses
(NOT the eclipse time) was 42 ½ hours when
observed from points X or Y; that is, when the Earth
was neither moving away from, or toward, Jupiter.
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“But when the Earth was moving away from Jupiter (position 2) he noticed that the period was
14 seconds longer. He deduced that light had to have a finite speed, because the 14 second lag
indicated that the light had to "catch up" with the Earth (go a larger distance). Observations were
made from many points on Earth's orbit. The details are more complex, but a summary of his
observations is that he estimated that the time needed for light to travel a distance equal to the
diameter of Earth's orbit was 22 minutes (the modern value is 17 minutes).” 1
The value that Roemer obtained was about 2.4 x 10 8 meters per second (150,000 miles per
second). This is approximately eighty percent of the currently accepted value. Given the
relative simplicity of Roemer's equipment, his calculations of the speed of light were remarkable.
Newton used Roemer's method to make calculations of this own, though his calculations were
not much more accurate than Roemer's (Newton's values were actually slightly higher than the
currently accepted value). In the very least, Roemer's work offered strong evidence for the fact
that light, like sound, has a finite velocity.
Other significant efforts to measure the speed of light were conducted in the decades after
Roemer. It wasn't until the late 19th century, however, that significant improvements in the
accuracy of measurement took place. An American astronomer, Alfred Michelson, used a
different method than Roemer's. Simply summarized, his experiment used an eight-sided
rotating mirror to reflect a light pulse toward a flat mirror located on a mountaintop 35 km (22
miles) away. When the mirror rotated at the appropriate rate, the pulse of light reflected from the
rotating mirror to the distant mirror, and the back to the rotating mirror and into an eyepiece of a
telescope through which Michelson could look for the pulse. The light pulse is visible only
when the eight-sided mirror rotates one-eighth of a turn between the initial reflection and the
final reflection into the telescope. If the mirror rotates too fast or too slow, the pulse of light
would reflect to one side of the eyepiece or the other and would not be seen. Because the
distance between mountaintops was known, and the time for one-eighth of a rotation at the
correct speed could be measured, the speed of the light pulse could be calculated.
1
This information was taken from Holton & Roller, Foundations of Modern Physical Science,
Addison-Wesley Publishing Company, pages 551-552 (1958). H & R point out that "some of
Roemer's contemporaries attacked his result as implying a ridiculously large speed...others
continued to believe that the speed of light is infinite." Joseph R. Biegen
http://web.sunybroome.edu/~biegen_j/phys2/light/jupiter.htm
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During the decades in which Michelson carried out his research, he was able to obtain
increasingly accurate measurements of the speed of light using this and other ingenious methods.
One of these experiments included the use of a mile-long vacuum tube that was intended to
eliminate the effects of dust and other interfering factors in the atmosphere. Michelson was able
to arrange mirrors in the tube so that a pulse of light traveled a total of ten miles back and forth
in the tube before being observed.
The currently accepted value for the speed of light is 2.99 x 10 8 meters per second, which is
often rounded to 3.0 x 10 8 m/s. Michelson was eventually able to show (using a different
experimental setup) that the speed of light is constant, even when the light source or the observer
is moving. Though Michelson doubted the results of these experiments, his work measuring the
speed of light was an important piece of evidence shaping Einstein's theory of special relativity.
The fact that light travels at a constant speed for all observers regardless of their motion became
an axiom of Einstein's theory.
There are still numerous questions aimed at understanding exactly why light propagates at a
specific velocity and why that particular velocity seems to be the cosmic "speed limit" for matter
and energy in the universe. Is it possible, even for an individual photon, to travel faster that the
speed of light What would one experience traveling at such great speeds As is the case with
many light related phenomena, deeper thinking about such curiosities leads to a host of
surprising conclusions and even more intriguing questions.
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