The other morning over coffee my
colleagues and I started talking about measurements, and it occurred
to us that we could express our heights (or lengths) differently. All
we needed were constants that would allow us to convert our commonly
expressed height, in meters, into something else. Of course, we
immediately thought of c, the
speed of light in a vacuum, as one such constant.
Light
is one of those intriguing things because its speed is a constant –
no matter where you are in the universe, no matter how fast your are
moving, within your (inertial) reference frame, you will always
measure the same speed for light. This doesn't hold true for most
other items that we measure: Sound, objects: the speed of each is
always relative to our speed when we measure them. This makes light
unique.
The
International Bureau of Standards has defined the speed of light to
be exactly 299,792,458 meters per second. As Neil Degrasse-Tyson
wryly observes* 'if improvements to our means of measuring the speed
of light lead to refinements, it is the length of a meter that will
change, not our expression for the speed'.
So,
taking my commonly expressed height in meters and dividing by c,
(meters per second), the meters cross out, and you are left with a
value of just seconds. 1.74 meters / 299,792,458 meters / second
gives us the value of 5.8 nanoseconds (billionths of a second). This
represents the time it would take a photon of light to travel from my
head to my feet (or how much older my feet are by the time I observe
them with my eyes.)
But,
is it valid to express my height thus? I think so. Light is the only
entity that moves with constant speed, and, in recognition of this
fact, we are constantly redefining our other expressions of
measurement from the various facets of light (we use the number of
wavelengths emitted by a cesium atom to determine time, for instance,
emitted wavelengths being the inverse of the speed of light and the
energy of the particular atom). So, although not common, expressing
my height in seconds isn't ambiguous, which is what we would want to
avoid.
It is
also nice in that it gives us a reminder of just how fast light
moves, but that it isn't instantaneous. We could apply this to other
items as well: An average 6th
grader is 5.1 nanoseconds tall, a 1st
grader almost 4.1 nanoseconds. An Olympic Swimming pool is 167
nanoseconds, a soccer field twice that.
Hoover
Dam is 221 meters tall, or 737 nanoseconds tall. So, the splashes of
water you see while standing on top of the dam occurred, literally,
737 nanoseconds before you see them, and have already changed shape
and location by the time you become conscience of them!
Henceforth,
I am 5.8 nanoseconds tall – How tall (in seconds) are you?
*
Tyson. 'Death By Black Hole and other Cosmic Quandaries'