3. Sight, c, and light goes in straight lines
Imagine
seeing in a world where light travels in loops and zigzags rather than
straight lines. It would be impossible to find your car keys or read books,
as the photons entering your eyes would not necessarily be coming from
the direction of the source. All you would see is a blur of color.
Now imagine a world where light travels at various speeds – some much slower than the conventional speed of light and some much faster. It would be impossible to determine the time of an event because its photons would be hitting your eyes for several seconds. Even if light traveled in straight lines, motion would be extremely blurry.
QED allows for both of these possibilities! Why then, can we see?
Light
travels in straight lines because the probabilities for weird-shaped paths
cancel out. For instance, the blue path has a length so its stopwatch
points left. The nearby red path, however, has a significantly different
length so its stopwatch points right. Adding the arrows results in a probability
amplitude very near zero, so light won’t travel these paths.
But
if light traveled in straight lines, or near straight lines, their stopwatches
would be pointing in nearly the same direction. When
light strays too far from the straight line path, it takes exponentially
more time and the arrows will cancel out with other paths. Most of the
contribution to the final probability comes from paths near the path of
least time -- in this case, a straight line.
This
result is fortunate, because otherwise it would be difficult to see this
picture of my calculus teacher and laugh at it.
In
a similar fashion, light has an amplitude to travel at speeds other than
c = 299,792,458 m/s. However, over long distances, the amplitude
to travel slower than the speed of light cancels out with the amplitude
to travel faster. As a result, Einstein's postulate that the speed of
light c is constant agrees with experiment in most cases.
This is also fortunate for our society, as photons which sometimes travel at 40 m/s would spell certain doom for Major League Baseball. Except for the pitchers.
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"Mirrors and reflection"