Time Dilation and Space Compression #9

by Whabby

Well here we are, owls: The penultimate time dilation blog! This week we’re going to feast on some of the implications of the effect, such as the solution to last Wednesday’s conundrum. Before we get to that, though, I want to take care of an important piece of unfinished business. I want to be sure you understand that time dilation is all-encompassing: it occurs for any and all events on board Shirley, not just the movement of the light pulse up and down Shirley’s shaft.

What is an “event”, when you really think about it? My definition is pretty simple: An event is anything that has a beginning and an end, and takes a measurable amount of time to occur. What about when an event happens in a frame of reference that’s moving relative to you (like an event onboard Shirley)? We’ve discovered that, during the time that separates the beginning of the event from its end, the moving object covers a greater distance in your frame of reference than it does in its own frame of reference. Shirley is moving at the same finite speed in both frames of reference (in both cases, she covers exactly the same distance per unit of time). Therefore, the only way that she can possibly cover more space for the stationary observer (you) than for an observer (naked George) onboard is for the event in question to take more time.

To further appreciate this point, let’s return to last week’s version of the thought experiment. Shirley was revved up to very close to the speed of light, and the critical event (that light flash traveling up and down her shaft) took almost 13 minutes (as measured by you). Now, suppose you and naked George decide to do something completely different for a change than tracking a light flash. George proceeds to stand up (still erect, of course) with a baseball in his hand. At just the point where Shirley passes over you, traveling at that same 299,999 kilometers per second, George throws the baseball straight up in the air, with just enough force that it travels upwards for 1 second, and back down to his hand for one second.

Suppose also that you have a closed-circuit television that lets you watch the baseball go up and down. What would you see? Well, a television signal is a form of light, so it 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 that make up the view on your television are emitted (typically, about 120 images are created every second). We saw last week 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 is traveling 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 start to see the ball moving very slowly upwards, like your television was showing film of the event in slow motion, and 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 moved. 13 minutes after George released the baseball, you would finally see it return to George’s hand, and his new throwing event would be over.

Actually, you could take a lot of breaks from watching your television in 13 minutes. You could go to the bathroom, have a brief conversation with your neighbor, perhaps watch the entire Kentucky Derby if it happened to be on, and even read an Owl’s Nest blog. Meanwhile, George would have no time to do any of these things; he would be fully occupied with throwing the ball up and catching it right away. All his concentration would be on that one very short event, and he’d have no time to do anything else. A text from him might say something like: “I was really rushed! I 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 else 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 from traveling at 299,999 kilometers per second after the two seconds it took for George to complete the ball-throwing task (or the light pulse measurement task)? That is, what would happen if you just let Shirley 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. But, what would your texts to each other look like at the end of the two weeks?

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

But 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 what he did 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. Again, George would not have aged at all, not really, but there’d be a nontrivial possibility that you would have grown old enough to die. And in fact, if you cranked Shirley up even more, to faster 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.

In just one short month, George could transport himself far, far into our future. Shirley would have become 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 last week’s paradox – that may rank as the freakiest of all. Let’s go back to our standard thought experiment with the light pulse. Remember from last Wednesday’s blog that, from George’s point of view, in the two seconds it took for the light pulse to go up and down her cylinder, Shirley had traveled exactly 599,998 kilometers down the line? That’s not a trivial amount, granted; it’s about 1.5 times the distance from the Earth to the Moon. But it is trivial from your point of view, because for you, Shirley 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 George’s life. Meanwhile, from George’s perspective, nothing of the sort would have happened.

One afternoon this spring, while pondering this conundrum during my afternoon run on Stevens’ Creek trail, I had an “aha” experience, and the last piece of the time dilation puzzle finally fell into place for me. The light pulse moving up and down the shaft of Shirley 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. The light pulse has to be at the identical location in the solar system at every point along its journey to the top of Shirley, and back down to her bottom, for both you and George. That way, if George and Shirley meet with their doom along the way, they do so both in your frame of reference, and in George’s.

Let’s assume George and Shirley have the good fortune to avoid all 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 gets compressed – literally, scrunched - in the direction of Shirley’s movement. And that is the simple, but astonishing truth, owls: space actually shrinks along that direction of motion, by exactly the same factor as George’s time expands for you. In other words, when Shirley is traveling at 299,999 kilometers per second, everything in her path, including that 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 were part of a frame of reference that moves at a sufficiently high rate of speed relative to the Earth, you would become a time traveler, able to take a very short trip and yet return to Earth years in the future. Spatial compression is the amazing flip side to this; 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 as to be forever beyond our reach.

Even though this is mind-boggling stuff to me, you may have one final “so what” reaction. 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 actually ever goes that fast. But you know what? Actually, some things in the universe do move at close to the speed of light! What those things are is the topic of next week’s final blog.