Help me explain time-dilation to my 13 year old.

Factual Questions
1

My 13 year old son has taken an interest in all things science (so his future as an NBA superstar may now be in jepordy) seriously, he just learned about blackholes in his science class and he’s asking alot of questions about cosmology. I have a smattering of knowledge and many books but there’s nothing like a kid asking you a simple question to point out how little you actually know.

While engaged the other night in our usual talk about the universe and space-travel. I mentioned time-dilation and it’s effect on travelling at near light-speed. His little brain almost popped! He could not grasp it, it also was brought to me that I, myself, could not really explain why it happens. It doesn’t cut any ice with him to merely say “It happens, trust me.”

So can anyone put forth an explanation in simple terms how it happens? I’m not sure that “A Brief History of Time” as a bedtime book would suffice.

Thanks.

Brian

2

Get “The Elegant Universe” by Brian Greene. Take it slow, draw pictures (some are included in the book, but I find it easier to get the picture, so to speak, with a physical drawing). It is possible to understand relativity but it requires some face squinching.

Just wait until he asks about Quantum Theory.

Said by Richard Feynman (quite possibly the finest teacher of advanced physics that ever lived)…or this one from Niels Bohr (one of the central pioneers of quantum theory)

3

How about The Theory of Relativity (In Words of Four Letters or Less)?

4

You could pick up a copy of “The Elegant Universe.” IIRC, a chapter in that book explains it as such:

Imagine you have a long, wide stretch of concrete, like a long dragstrip. You have a car at one end, and drive 100 mph in a straight line to the other end of the strip. It takes 10 seconds. Now imagine if you drive 100 mph diagonally across the strip. It will take longer, as some of your speed is “used” to travel side to side as well as forward. Pretty basic, right?

Time is a dimension, too. There are three spatial dimensions, like X, Y, and Z, and a time dimension. Einstein theorized that everything moves through spacetime at the speed of light. Since we know that we move pretty slowly through space, of course not even approaching the speed of light, most of our “movement” then is through the time dimension. Now imagine the race car again. Once the race car started travelling diagonally–travelling faster in that dimension–it had to travel slower in the other dimension (“straight” down the track), and took longer to get from one end to the other. Our “speed” is shared between all the dimensions in which we travel. When you go faster in one dimension, it slows your progress in another. So if you take off at the speed of light in a spatial dimension, your speed must decrease in one of the other dimensions, including time.

That’s the basic gist, the part that people probably have the hardest time understanding–why is there time dilation. The author of the book goes into lots of detail about the actual “relativity” of it, about how the position and speed of the observer is important. There’s a neat illustration that explains how or why a simple theoretical clock would tick slower as it moves faster through space, too. Great book.

5

If he’s had algebra, get him Einstein for Beginners, if you can find it. It’s an old book (I read it when I was in high school), but it derives time dilation in a way that you can actually follow it.

6

I’m not surprised. No-one knows why it happens. We just know that it does. Much like gravity.

7

I think the explaination troub posted is probably the easiest way to think of it. It sort of takes some of the mystery out of time by allowing the reader to think of it as a spatial dimension which is easier to digest.

8

Don’t use this if it’s going to get confused with troub’s explanation, but wee physics majors learn time dilation using a light clock, which is just a photon bouncing between two mirrors.

To a person on the spaceship, it takes some time for the photon to bounce between the mirrors, and the photon just seems to bounce perpendicular to the mirrors.

But to a person watching the spaceship move by (such that its motion is perpendicular to the photon’s motion), the mirrors are the same distance apart, but they are moving, so the photon must travel a diagonal path, and therefore has a longer distance to travel between the two mirrors.

For both people, the speed of the photon is the same ©. So for the person watching the moving spaceship, the ticks of the clock seem too long; time is dilated.

Here’s a page with an animation of moving and non-moving timeclocks:
http://casa.colorado.edu/~ajsh/sr/time.html

9

Wow! Thanks all of you for your responses.

I’m grateful for the links. (The ‘moving clocks’ is particularly helpful to me because I think in pictures).

This board is the greatest.

10

I’m really impressed with the way troub explained it. I’ve always understood the moving clocks analogy, but didn’t care for it much.

I had never thought of imagining a total speed © being shared across spatial and temporal dimensions. But I like it a lot.

Bravo!

11

So… if for us (matter) the rough equation is:

Vspace + Vtime = c

Then for light, where Vspace = c, what is Vtime? Do photons experience no motion through time? Or do they have diffrent end totals than c?

12

Time Compression Experiment:

Corollary 1: Moving is fun.

Corollary 2: The fun increases the faster you go.

Corollary 3: Time flies when you are having fun.

Experiment: Drive real fast.

Result: It seemed like the time just flew by.

Deduction: At nearly the speed of light time will fly even faster.
Time Expansion Experiment:

Corollary: Marijuana causes time to get all messed up.

Experiment: Get the kid high and have him sit through an episode of “Still Standing.”

Result: He will notice the program lasts nearly forever.

Deduction: There isn’t enough dope in the world to make “Still Standing” funny.

13

It’s:
η[sub]0[/sub][sup]2[/sup] - η[sub]1[/sub][sup]2[/sup] + η[sub]2[/sub][sup]2[/sup] + η[sub]3[/sub][sup]2[/sup] = c[sup]2[/sup]

In your notation this would be (taking the direction of motion as an axis):

v[sub]time[/sub][sup]2[/sup] - v[sub]space[/sub][sup]2[/sup] = c[sup]2[/sup]

Photons don’t have a rest frame, so you cannot talk about how they experince time.

14

You might want to check out one of Hawking’s other works “Black Holes and Baby Universes.” I read it when I was about your son’s age and I believe one of the essays was on time dilation. It’s been a while since I’ve read it, though.

I seem to remember a really good example about how a clock on Earth and a clock on a spaceship traveling close to the speed of light would show different times, I think it was somewhere in that book.

15

I’ve got an explanation I picked up in college, but have sucessfully taught it to middle schoolers. It requires some graph drawing, but no more math than that.

If you tried to graph the movement of a car along a highway over time, you might draw a graph that has distance as the x axis and time as the y axis. Maybe each tick of graph paper in the x axis is 50 miles and each tick in the y axis is 1 hour. You could then draw a diagonal line describing the speed of the car. A line going at a 45 degree angle would represent a car going 50 miles per hour. A line that’s nearly vertical would be snail speed, and a line that’s almost horizontal is going way too fast.

Now instead of using miles, we’ll use “light-hours”. It’s just like light-years only shorter. A light-hour is the distance light travels in one hour. (670 million miles or so, if you’re wondering.) A beam of light, then, would be a 45 degree line on the graph paper. Light only travels at this speed, no matter what. One light-hour per hour. Anything that goes slower than light, on this scale, will be a steeper line. (Even something going the speed of the space shuttle would give you a nearly vertical line on this scale!) Anything (hypothetically) going faster than light would be a shallower (more horizontal) slope than 45 degrees.

[sub](Actually, it doesn’t matter what units you use, light-hours, light-minutes, whatever. In fact, it’s easier to forget all about the units and just remember you’re using a scale where light-speed is 45 degree angles.)[/sub]

Now imagine that the Federation Starship Boobyprize is moving at, say, space shuttle speed, on a journey from Earth to Uranus. Go ahead and draw a vertical line for its path. Let’s say that the Captain is about to go take a nap. After all it’s going to take a long time at space shuttle speed to get to Uranus, he’s got time to spare. For some reason he decides he has to inform his superiors about his decision, both at Starfleet Command at Earth, and the Uranus orbital space station. So he sends out a signal, at light speed, to both places. Pick a point along the starship’s path, and draw a pair of 45-degree lines, starting at that point.

Thirty minutes later he wakes up, and again informs Earth and Uranus about it. So a little higher up on the starship’s path (later in time, that is) draw another pair of 45 degree lines. It’ll look like this:

link

(Red represents the path of the barely-moving starship. Yellow is signal number one, and blue is signal number two. The grey lines represent Earth and Uranus, which aren’t moving much, either. In physics lingo, these are all called “world lines.”

In the picture I made, the starship is a little closer to Uranus than Earth, so Uranus gets the signal a little bit before Earth does. But in both cases, the signals appear 30 minutes apart - the length of the Captain’s nap.

Starfleet tells the Captain to increase speed to 10% the speed of light. So we’ll draw the picture again:

link

This time, the folks at Uranus think the Captain has taken a pretty short nap, but the folks at Earth think the Captain is taking a really long nap.

Now the same picture if the Starship travels at light speed (assuming for the moment it was physically possible to do so):

link

Earth thinks the Captain is taking an even longer nap, but whoops! Uranus station sees that the Captain took a nap so short that he woke up exactly the same time he fell asleep. Not only that, but he did it at the precise moment he arrived at Uranus!

One more picture, this time with the ship going faster than light:

link

This time, the captain arrives at Uranus first. Then they recieve the signal that he’s woken up. Then finally the signal that he’s about to go to sleep.

The moral is, things get really weird when you get close to the speed of light.

16

Drewbert,

Thanks for a super set of pictures.

17

I love you people. Wondered about this for years, always just accepted it. Thanks, everyone.

18

Actually, drewbert’s explanation is flawed. Time dilation isn’t just based on when the different observers receive the messages. Both Earth and Uranus know how far away the Captain is, at the time of each of his transmissions, so they can figure out when he sent his messages, not just when they were received. And if they do this, then Earth and Uranus will agree on how long the Captain’s nap was. But here’s the thing: Earth and Uranus still won’t agree with the Captain on how long the nap was.

The analogy I prefer to use for time dilation/space contraction is rotation. Basically, an observer moving at some speed is similar to an observer who is rotated. for instance, suppose I have a meterstick, and I’m holding it straight up. It’s 1 meter tall, but it’s not very wide. Let’s suppose that it’s a perfectly thin stick, so it has zero width. Now, I look at that same meterstick sideways, and I measure that it has zero height, but now it has a width of one meter. Or, I could look at it at an angle, such that it has a width of .6 meters and a height of .8 meters. So, the height of the meterstick depends on how I’m measuring it, and the width of the meterstick also depends on how I measure it. But the two are related, in just such a way that the distance from one end of the meterstick to the other is always exactly 1 meter, no matter how I look at it. In other words, if I take w[sup]2[/sup] + h[sup]2[/sup], I’ll always get the same result.

Time dilation and length contraction work the same way. If I’m moving at some speed, and observe a pair of events, then the space distance I measure between them will depend on my speed, and the time distance between them will also depend on my speed, but the total “distance” between two points will be the same, no matter what speed I’m going at when I measure them. The only catch is that time works a little differently than space, so instead of the constant distance being given by x[sup]2[/sup] + t[sup]2[/sup], it’s x[sup]2[/sup] - t[sup]2[/sup]