A Baseball... and a Terrible Accident

We’ve arrived at the penultimate time dilation blog, faithful readers!  Having explained the nuts and bolts of the phenomenon already, this time I’m going to feast on some of the implications of the effect, such as the solution to the conundrum I posed yesterday.  Before we get to that, though, I’d like to take care of an important piece of unfinished business. I want to be sure you understand that time dilation is not confined to the duration of events involving light pulses; it occurs for any and all events on board Shirley. 

What is an “event”, when you really think about it?  My definition is pretty simple: anything that has a beginning and an end, and takes a measurable amount of time to occur, qualifies as an event.  We’ve discovered that when an event occurs in a frame of reference that’s moving relative to you, during the time that separates the beginning of the event from its end, the objects involved travel farther in your frame of reference than in theirs.  Since Shirley is moving at the same speed in both frames of reference, the only way that she can possibly cover more space for you than for George is for the event to take more time.

To appreciate the point further, let’s return to yesterday’s version of the thought experiment.   Shirley was revved up to very close to the speed of light, and the critical event (the light flash traveling up and down her shaft) took almost 13 minutes (as measured by you).  Now, suppose you and George decide to do something completely different.  Ignoring the searchlight, George stands up on Shirley’s floor with a baseball in his hand.  At just the point where Shirley passes over you (still traveling at the same 299,999 kilometers per second) George lofts the baseball straight up in the air, with just enough speed that it travels upwards for exactly one second, and back down for another second.

Suppose also that a closed-circuit television lets you watch the baseball go up and down from your location on the ground.  What would you see?  Well, the television signal is a form of light that also travels at 300,000 kilometers per second.  Since the television signal is beaming directly from the floor of the spacecraft to your television set, what you see is determined by how far the signal has to travel, which, in turn, is dependent on how far away Shirley is when the images are emitted (these days, about 120 images are emitted every second).   We saw last time that in two seconds, extra space is being created at a furious rate by Shirley’s high speed (the distance along Line B is stretching out quickly).  This means that each successive television image of the baseball has to travel a longer and longer distance, which means a successively longer delay between when the onboard television camera records the image of the baseball, and when you see that image on your screen.  The net result is that you would see the ball moving very slowly upwards, as if you were watching film of the moving baseball in slow motion.  As time continued to pass, the movement of the ball would slow down more and more, until it became imperceptible.

The baseball wouldn’t stop moving entirely, though, and if you took a break and went to the bathroom, when you came back you would see that the ball had shifted position.  13 minutes after George released the baseball, you would finally see it return to his hand, and the event would be over.

Actually, in 13 minutes you could take a lot of breaks from watching your television.  You could go to the bathroom, have a brief conversation with your neighbor, watch the Kentucky Derby, and read a Whabblog.  Meanwhile, George would have no time to do any of these things; he would be fully occupied by throwing the ball up and catching it almost immediately.  A text from him to you might say something like: “Really, really rushed!  Just barely had time to throw the ball up before I had to catch it again!”

Not so for you, and not so for everyone sharing your frame of reference (which is everybody on the Earth).  Imagine all the things that happen across the world in 13 minutes.  Thousands of people die; thousands more are born; thousands exchange wedding vows; thousands get notices of a hiring or a firing; and there’s a distinct possibility that a big natural disaster like an earthquake occurs (and the first reports about it came in on CNN).  In short, a busy little chunk of everyday life, full of scores of individual events, passes by.

What would happen if you didn’t stop Shirley after the ball-throwing task (or the light pulse measurement task)?  Suppose you just let her continue moving at the same speed for, say, two weeks of ship time? You would just go about your normal daily activities during that period, and so would George onboard.  What would your texts to each other look like at the end of the period?

When you and George were doing the light-pulse measurement, it took about 775 seconds for you to see the light pulse return to Shirley’s floor, versus a paltry two seconds for him.  Thus, for every second of time that was passing for George, approximately 387 seconds pass for you.  That same multiplier works for any time scale.  Thus, while only two weeks of time are passing for George, 775 weeks of your life unfold.

775 weeks is almost 15 years!  At the end of George’s two weeks, if you could exchange photos along with your text messages, he would look identical to before; nobody ages noticeably in only two weeks!  But you… you would look noticeably older; depending on how well he knew you, George might even have trouble recognizing you for a moment.  And imagine all the pages and pages of news you could put in your text message to him, with 15 years worth of your life to draw from!

If we extended Shirley’s trip a little longer, to say a month, almost 30 years of your life would pass.  While George would hardly have time to age at all, there would be a nontrivial possibility that you would have grown old enough to die.   And in fact, if you cranked Shirley up even more, to more than 299,999 kilometers per second, the time dilation would grow so extreme that in the month George spent on board Shirley, many thousands of years would pass here on Earth.  When he returned, you would be just a distant memory.   Shirley would have turned into a very effective time machine.

I told you time dilation was a really freaky phenomenon, didn’t I?  But there’s one last aspect to it – the answer to yesterday’s paradox – that may be freakiest of all.  Let’s return to our regular thought experiment with the light pulse.  From George’s point of view, in the two seconds it took for the light pulse to go up and down Shirley’s cylinder, she covered exactly 599,998 kilometers.  That’s not a trivial amount, granted: it’s about 1.5 times the distance from the Earth to the Moon.  But 600,000 kilometers or so is utterly insignificant from your point of view, because for you, Shirley has traveled 236 million kilometers, about a third of the way to the planet Jupiter!  By virtue of traveling so far, she and George could well have collided with an asteroid, ending both the time measurement experiment and poor George’s life.  Meanwhile, from George’s perspective, nothing of the sort would have happened.

One afternoon last spring, while pondering this conundrum during an afternoon run on Stevens’ Creek trail, I had an “aha” experience, and the last piece of the time dilation puzzle finally fell into place.  The light pulse moving up and down Shirley’s shaft is the same event for you and George; therefore, it has to have the same history in both frames of reference.  So how do we get around the “asteroid collision” paradox?  There’s only one way.  Shirley, George, and the light pulse have to be at the identical location in the solar system at every point along the pulse’s journey, both in your frame of reference, and in theirs’.  That way, if George and Shirley meet with an asteroid along the way, they do so in both frames of reference.

Let’s assume George and Shirley have the good fortune to avoid any asteroids, and the light pulse reaches the floor of Shirley’s shaft quite safely.  The speed of light is constant, so according to Shirley’s odometer, she has to have moved exactly 599,998 kilometers to your right when the light flash reaches the floor.  The only way to reconcile that fact with Shirley being all the way out in the asteroid belt is if, from George’s point of view, space itself is compressed – literally, scrunched - in the direction of Shirley’s movement.  That is the simple, but astonishing truth, folks: Space actually shrinks along Shirley’s direction of motion, by exactly the same factor that George’s time expands for you.  In other words, at a speed of 299,999 kilometers per second, everything in Shirley’s path, including her final destination out in the asteroid belt, becomes 387 times closer than it is for you here on Earth.  That’s why, from George’s perspective, it only takes two seconds to reach it!

We just saw that if you are part of a frame of reference that moves at a sufficiently high rate of speed relative to the Earth, you become a time traveler, able to take a very short trip and yet return many years in the future.  Spatial compression is the amazing flip side to this phenomenon; it means that, within your lifetime, you could travel to very remote destinations in the universe, including other stars and even other galaxies, which to us on Earth are so far away that they remain forever out of reach. 

You could argue that it’s totally absurd to have gone to all the trouble of exploring and explaining a phenomenon that never actually happens, because nothing ever goes that fast.  Not true, however.  There are actually things in our universe that move at close to the speed of light, and experience significant time dilation.  I’ll reveal what those things are in tomorrow’s blog.