Fun With Units (or I am 5.8 nanoseconds Tall)

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 6^th grader is 5.1 nanoseconds tall, a 1^st 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'