From Accomplices to Confederates: What’s in a name? #3

by Whabby

Good morning, owls! Well, we’ve made it to the third blog in this little series. I can only trust that you were doing your homework over the past week, performing the time measurement experiment over and over again, and always getting the same two second value (once your smart stopwatch automatically subtracted your “brain processing” time). In fact, you’ve probably gotten thoroughly sick and tired of the whole, dare I use the word, tedious, activity, because the outcome is always the same!

To spice things up a little, you decide to hire an accomplice. Since “accomplice” kind of sounds like you’ve decided to rob a bank or something, perhaps “collaborator” or even “confederate” is the preferred label. Your “confederate” agrees to sit on the floor of the spacecraft instead of you, and to toggle the searchlight on and off, and measure how long it takes to see the pulse of light on its return from the ceiling. Of course, when he does this, he gets the same two second result that you did; his stopwatch is smart enough to automatically subtract his ‘brain time” too.

But where have you gone? Not far! Not far at all! You want to continue to measure the travel time of the light flash right along with your confederate. Thus, you arrange for your spacecraft to be tethered just a couple of feet in the air - 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 your confederate does right above you). And just like him, you’re going to start your stopwatch at the exact point when he flicks the searchlight on (remember, the searchlight is bidirectional, so you can 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 hits the transparent floor, it only has to pass through and travel another couple of feet to reach you – a negligible distance. Thus, not only do you 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 this event.

But where’s Einstein, you’re beginning to wonder? Now it’s two of you, not just you yourself, who keep getting the same result, and are getting restless and bored. The thought experiment, with its predictable two-second result on both stopwatches, is still tedious.

But it’s always darkest just before the dawn! Like a bolt out of the blue, you both get an idea for how to stir things up. Your cylinder is a spaceship, after all, so why not repeat the experiment with you remaining in the same position on the ground, but with the spacecraft in motion? To accommodate this slightly more complex condition, you and your confederate engineer the following situation. Lying on the ground, you stretch your arms straight out to the left and to the right, so your body forms a cross. Your confederate takes control of the spacecraft and, still hovering at the same short distance above the ground from you, flies it to a point directly down the line formed by your outstretched left arm. Next, your confederate accelerates the spaceship quickly to a constant speed, so that it (and he) is moving steadily towards you along the straight line formed by your outstretched left arm. Eventually, still holding the same speed, the spacecraft passes directly over top of you, and continues down the line formed by your outstretched right arm.

Initially, you decide you want the spacecraft to move at a steady one kilometer per second. 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, your confederate now has to take great pains to toggle the searchlight on and off at the exact instant that the spacecraft passes over you. That way, you still see the flash of light through the floor of the spacecraft at the same time that your confederate toggles the searchlight on; therefore, you both still START your stopwatches in unison.

But do you both still see the light flash RETURN to the spacecraft floor at the same time, STOP your stopwatches together, and measure the same amount of time for the event to happen? That, owls, is the question for next week. In the meantime, feel free to speculate on the answer!