Introducing Astronaut George!

So, have you been doing your homework, faithful Whabblog readers? Have you been performing the thought experiment repeatedly, and always getting the same two second result (once your smart stopwatch automatically subtracts your “brain processing” time)?  If you have, then chances are you’ve gotten thoroughly sick and tired of the whole, dare I use the word, tedious, activity, because the outcome is always the same!  Your spreadsheet never shows anything but two-second entries.

To spice things up a little, you decide to hire an astronaut accomplice.  Since “accomplice” kind of sounds like you’ve decided to rob a bank or something, perhaps “collaborator” or even “confederate” is a better label.  Your “confederate”, who for entirely pernicious reasons is actor George Clooney, agrees to lie on the floor of the spacecraft in your stead.  Therefore, it is now Astronaut George who toggles the searchlight on and off, and measures how long it takes to see the pulse of light on its return from the ceiling.  When George does this, he gets the same two-second result you did (of course, his stopwatch is smart enough to automatically subtract his brain-processing time, too).

Meanwhile, where have you gone?  Not far, because you want to continue to measure the travel time of the light flash right along with Astronaut George.  Therefore, you arrange for Shirley to be tethered just a couple of feet off the ground – just high enough that you can lie flat on the ground underneath the transparent floor, and stare straight up through the floor in the direction of the ceiling (just like George is doing inside Shirley).  And just like George, you’re going to start your stopwatch at the exact point when he flicks the searchlight on (remember, the searchlight is bidirectional, so you immediately see the light coming through the floor), and you’re going to push your stopwatch again, halting it, when you see the return flash.  Of course, when the reflected flash reaches Shirley’s transparent floor, it only has to pass through the glass and travel another couple of feet to reach you – a negligible distance.  Thus, not only do you both start your stopwatches at the same time, you stop them at the same time, too.  Both stopwatches register exactly the same two-second duration for the light pulse to complete its journey.

Still, now it’s both of you, not just you yourself, who keep getting the same result, and two people are now getting restless and bored. The thought experiment, with its predictable two-second result on both stopwatches, is still rather tedious. This is all fine and dandy, you’re probably beginning to think, but what about Einstein?

Relax.  It’s always darkest just before the dawn!  Shirley is a spaceship, remember, so why not repeat the identical experiment with you remaining motionless in the same position on the ground, but with Shirley now in motion?  To accommodate this slightly more complex situation, you and Astronaut George work out the following arrangement.   Lying on the ground, you stretch your arms straight out to your left and right, so your body forms the shape of a cross.  George takes control of Shirley and, still hovering at the same short distance above the ground from you, maneuvers her to a point over on your left, directly along the line formed by your outstretched left arm.  Next, George accelerates Shirley to a constant speed, so that she (and he) move steadily towards you along the straight line.  Still holding the same constant speed, Shirley passes right over top of you and then continues down the line formed by your outstretched right arm.

For your first time measurement experiment with Shirley in motion, you decide to have her move at a steady one-kilometer per second along the line.  Although that’s actually pretty darn fast, about the speed of a supersonic military jet, it pales in comparison to the speed of the light itself:  One kilometer per second is only 1/300,000 of THAT ridiculous speed!  Still, it’s fast enough that Astronaut George has to take great pains to toggle the searchlight on and off at the exact instant Shirley passes over you.  That way, you still see the flash of light through the floor of the spacecraft when George toggles the searchlight on, and you both START your stopwatches in unison.

But do you both still see the light flash return to the spacecraft floor at the same time? Do you both stop your stopwatches together, and measure the same two seconds for the event to happen?  That is the question I’ll tackle in the next blog.  In the meantime, feel free to speculate on the answer!