Light Pulses and A Magic Spacecraft #2

by Whabby

Welcome to the second installment of "Whabby Wednesday" This week I’m going to start us out with a very simple “thought experiment”, which is quite apropos, since thought experiments were one of Einstein’s favorite investigative tools. Suppose you suddenly became obsessed (I mean seriously obsessed) with measuring how long it takes events to occur (in other words, you got seriously into measuring time). To satisfy your new obsession, you construct a rather special spaceship, shaped like an enormously long, thin cylinder. For reasons that will become clear shortly, you specify that the cylinder must be precisely 300,000 kilometers (186,000 miles) long, not a foot more or less! The floor of your ridiculously elongated spacecraft is quite snug, just large enough to hold one passenger and a strong directional searchlight, just like the ones they use to aim beams of light into the sky at gala movie premieres and the like. This searchlight, though, is a customized beast in the sense that it is bidirectional: it sends a light beam both straight up and straight down through the spacecraft’s floor. That’s possible because the floor of your spacecraft is made of a layer of glass, strong enough to support a human passenger and the searchlight, but completely transparent, so that somebody directly beneath the spacecraft can easily see the light coming from the searchlight.

The roof of your spacecraft, 300,000 kilometers above the floor, is a carefully polished, perfectly reflective, mirror. That mirror is there for one purpose: to assist you to make very precise measurements of the time it takes for a brief flash of light to travel from the floor of the spacecraft to the top, reflect off the mirror, and travel back down the length of the cylinder to the floor. With that goal in mind, you enter the spaceship and lie down on the glass floor, facing straight up. Right beside you is the bi-directional searchlight. When it is powered on, the light it produces goes straight up the shaft, toward the ceiling of the spacecraft, and gets reflected straight back down. When the light pulse reaches the floor, it is still plenty strong enough for you to see as an unmistakable flash, like a lightning bolt.

Now, how do you set about making measurements of how long it takes the flash to travel to the roof and back? Still lying flat on the floor, you carry out two tasks in quick succession. The first task is to toggle the searchlight on and off as quickly as you can, creating the light flash. In your other hand, you hold a standard stopwatch used to time foot races and the like; you know, the kind you both start and stop by pushing the same button on the top of the watch. At exactly the same time as you flick the switch, releasing the pulse of light from the searchlight, you press that button to start the stopwatch. Then, when you see the light flash on its return journey from the ceiling, you press the button on the stopwatch again. Finally, you look at the amount of time showing on your stopwatch, and record that value in a log or a spreadsheet. Voila: You’re measured the duration of our event of interest.

So, how long WOULD it take to see the flash of light? The figure below illustrates the situation and provides the straightforward answer. Since the cylinder is exactly 300,000 kilometers long, the mirror in the ceiling is 300,000 kilometers away. By astonishing coincidence, light happens to travel at a speed of almost exactly 300,000 kilometers per second; rather fast, in other words. The flash of light takes precisely one second to travel up to the mirror, and another second to make the return journey, for a total round-trip time of two seconds. Two seconds is the value you’d expect to see on your stopwatch.

So far, there’s nothing very complicated about this thought experiment, is there? As we all know, the time to complete a journey is simply the distance traveled divided by speed. The total distance up and down the cylinder is 600,000 kilometers; light travels at 300,000 kilometers a second, so the total travel time is two seconds.

Of course, human physiology does enter the picture, and complicates the interpretation of the value that shows up on your stopwatch. As you do the measurement over and over and write down the result in your logbook, you quickly come to see that the average of all those times is a little more than two seconds. This is because, before you can press the button to stop the stopwatch, your eye has to be stimulated by the light flash, and your brain has to respond to that stimulation by issuing a command to your finger to press the button. These brain activities would delay your button presses by a slightly different amount each time you repeat the measurement. On average, though, the delay would be about two-tenths of a second (trust me on this… remember, I’m a psychologist)! If, every time, you subtracted that 0.2 seconds from the value showing on the stopwatch, you would be left with the real two seconds of time it took for the flash to complete its journey and reach your eyes.

From now on, let’s imagine that the stopwatch is a smart device, smart enough to automatically subtract this “brain processing” time from the value that shows when you hit the “stop” button. That way, you get a really pure measure of the time it takes the light pulse to travel.

Next week we’ll extend the thought experiment in a way that I hope will pique your interest. Until then, Owls, in the words of Star Hustler Jack Horkheimer: Keep…. Looking….. Up……. (to the roof of your spacecraft… LOL)! And feel free to speculate, if you like, on where this thought experiment is going. Hint: You’ve deliberately put your measurement apparatus in a spaceship!