Tripping the light fantastic with Shirley

In this second installment, let’s plunge right into a  “thought experiment”, shall we, which is quite apropos since thought experiments were one of Einstein’s favorite investigative tools.  Suppose you all suddenly became obsessed (and I mean seriously obsessed) with measuring precisely how long it takes events to occur (in other words, you went seriously crazy over measuring time).  To satisfy this new interest, you construct a rather unique spaceship, shaped like a thin cylinder fully 300,000 kilometers (186,000 miles) in length.  A structure of that length is kind of hard to imagine, I know.  With the floor of the ship resting on the earth’s surface, the top is way out in space, about two thirds of the way to the moon.  Nevertheless, because we can imagine anything in a thought experiment, please imagine that you manage to build it.  Once construction is complete, you christen your ship “Shirley”, after a friend of mine in Nova Scotia.

Compared to the incredibly long distance from floor to ceiling, Shirley isn’t very wide: her rounded floor is just large enough to hold one passenger and a strong directional searchlight, like the ones used to send beams of light dancing across the sky at movie premieres. Imagine further that the floor is made of a layer of thick glass, fully strong enough to support a human passenger and the searchlight, but completely transparent (hint: the floor is glass so that somebody lying directly beneath the spacecraft can easily see the light from the searchlight.  But I’m getting ahead of myself). Shirley’s searchlight is bidirectional, by the way: When switched on, it sends a beam of light both straight up and straight down through the floor.

300,000 kilometers above the floor, Shirley’s roof consists of a fully reflective mirror. The mirror is there for one purpose: to enable you to measure how long it takes for a brief flash of light, emitted by the searchlight, to travel the distance from the floor of the cylinder to the top, reflect off the mirror, and travel back down to the floor. With this goal firmly in mind, you proceed to enter Shirley and lie down on the glass floor, facing straight up.  Right beside you is the bi-directional searchlight.  At risk of belaboring the obvious, when the searchlight is powered on, the light it produces will travel in a perfectly straight line up the length of the cylinder, reflect off the mirror, and come straight back down.  When the flash returns to the floor, it is still plenty strong enough to see the reflection.

You measure the light’s travel time by performing two simple tasks in quick succession.  First, using your left hand, you toggle the searchlight on and off, creating just a brief flash of light.   In your right hand, you hold a standard stopwatch, the kind that you start and stop by pushing the same button on the top.  Now (we’ll assume you get a lot of practice at this) at exactly the same time as you flick the searchlight on, you press the button to start the stopwatch.  Then, when you see the light flash reflected from the ceiling, you press the button again.  Voila: the amount of time showing on your stopwatch is the journey time for the light!  Quite excited at your own cleverness, you perform this little experiment over and over, entering the result from your stopwatch in a spreadsheet each time.

 

So what do you find?  The figure to the right illustrates the situation and provides the straightforward answer. The mirror in Shirley’s ceiling is 300,000 kilometers away from you and the searchlight.  By astonishing coincidence, light happens to travel at a speed of almost exactly 300,000 kilometers per second (or about 650 million miles per hour; rather fast, in other words).  Therefore, 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.  In the figure, notice that the light pulse (the red squiggly line) spreads out slightly on its way up, so it reflects off of every part of the mirror.  Thus, you see part of the reflection on the way down.  And when you look at the stopwatch, two seconds is the value you should register.

So far, there’s nothing very complicated about this thought experiment, is there?  The time to complete a journey by anything, light included, is simply the distance traveled divided by the speed of the thing doing the traveling.  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 600,000 divided by 300,000, or exactly two seconds.

Of course, human physiology enters the picture and muddies the waters a little bit.  As you do the measurement over and over and write down the result in your spreadsheet, you quickly come to see that the values differ by small amounts, and 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 activities have a variable duration, so they delay your button press by a slightly different amount each time you repeat the experiment.  If you are like most people though, on average, the delay will be about two-tenths of a second (trust me; I’m a psychologist)!  

Suppose that you were able to subtract the physiological delay from the value showing on your stopwatch.  You would be left with the actual two seconds of time it took for the flash to complete its journey and return to Shirley’s floor.  From now on, let’s imagine that the stopwatch is actually a pretty smart device, smart enough to automatically compute your “brain processing” time and subtract it from the value showing.  That way, you always get a pure and totally accurate measure of the time it takes the light pulse to travel up and down Shirley’s shaft. 

Are you with me so far? That is, have you got Shirley’s dimensions, and the path taken by the light pulse, so firmly established in your head that it is quite obvious why the pulse is taking exactly two seconds to complete its journey?

Excellent!  In the next blog, we’ll take the thought experiment in a direction that I hope will pique your interest.  Until then, feel free to speculate in the comments section on what you think I’m going to do next. 

Hint: You’ve deliberately put your measurement apparatus inside a spaceship!