Is my explanation of the relativity of time accurate enough for a 9 year old?

Factual Questions
1

My 9 year old is becoming interested in relativity, and he’s been asking me questions like how time moves more slowly (relative to a stationary observer) depending on how fast one is traveling. As in the well-known theoretical example of 20 year old twins, one of whom is an astronaut who goes on a 50-year round-trip mission traveling close to the speed of light. When the astronaut twin returns, he’s just a couple years older, and his earth-bound brother is a 70 year old man.

So this is how I’ve always understood it as a layman who did not do well in high school physics, and how I explained it to my son:

Say someone is standing in an open boxcar on a fast-moving train, dribbling a basketball. To the guy on the train, the basketball is traveling straight up and down. But to a guy on the ground watching the train go by, the basketball is taking a long diagonal route up and down. So to him, the basketball travels farther, and therefore takes longer, than to the guy on the train dribbling the ball. Of course at that speed the time difference is infinitesimally small, but on a theoretical spaceship at near-light speeds the difference becomes extreme, and everything, including blood pumping through veins, electrical impulses traveling through brains, etc., is taking much longer from the perspective of a stationary observer. Yet seems normal speed to the astronauts on the spaceship.

I’m sure that’s much more simplified than what’s actually happening, but is it reasonably accurate in a dumbed-down way, or am I way off-base in my understanding? Inquiring 9 year old minds want to know!

2

I assume your explanation includes the difference between basketballs which can vary in speed, and light, which doesn’t?

Because with the basketball the two observers will just agree that in one reference frame it moves in a slow bounce, and in another it moves mostly in the same direction as the train, and at the same speed, with the small addition necessary to go up and down.

That’s Newtonian relativity. Einsteinian relativity comes into play at high velocities, because light doesn’t obey Newtonian relativity. It always moves at the speed of light. And for that to work the two observers can’t agree on time.

3

For a 9 year old, that’ll do. You can add in the subtlety later, or just drop it into the conversation.

Then come back and ask us their next question"Why is c always c?". The answer “Because if it wasn’t it wouldn’t be” should be lots of fun to try and explain.

4

I think that’s a reasonably good start, and accurate as far as I can tell. In trying to explain anything, I always try to tell a story around it instead of just laying out the facts, because of how humans relate to stories more than facts.

I’d start with your basketball idea, pointing out how to an observer on the ground it appears to be going much faster, and we all take it for granted that the guy on the ground has the “correct” perspective.

Now 150 years ago, people were wondering how this would happen with light. We had measurements and calculations that gave us the speed of light, but relative to what exactly? If instead of a basketball, there was a pair of mirrors and a light beam bouncing back-and-forth on a really fast train, what reference frame would the known speed of light be correct for? Most people figured there must be a preferred reference frame in the universe, and since light acts like a wave, and waves in their experience were some other stuff moving (like water waves are just water moving), then there must be something out there doing the waving. They called this stuff the ether.

So some really smart guys figured out a way to measure the speed of light on something moving really fast - the Earth is going 60,000 mph around the sun - what if we measured it one direction, and then months later measured it when the Earth was headed the other way? 60,000 mph is not that close to the speed of light, but with really sensitive measurements, it should be enough to see the difference. And they did this setup, but guess what? There was no difference! How could that be?

So now they were stuck. It seemed clear that, like the basketball on the train, you’d have to see a difference in its speed when it’s moving different directions.

This is where Einstein comes in. He was brilliant enough to not just assume that it had to act like the basketball, and didn’t take for granted that time itself is the same for everyone. What if, instead of going farther in the same time equals faster speed, we take the speed as constant, and time itself slows down? How would that work? You can probably see that the math of it would be really complicated, but Einstein was smart enough to work through it all and figure out the whole system where everything made sense now, as long as you ditch that idea that time has to be the same for everyone.

But was it right? Others went to work on it, and came up with certain predictions that this idea would make, which wouldn’t happen in the old system, in particular some very accurate measurements of the orbit of the planet Mercury around the Sun, that could show the difference. The idea of time itself being relative (“relativity”) has withstood every test that anyone has devised to put it to. So far.

5

Just a nitpick, I believe the main experiment actually compared, at the same time, the speed of light in the direction the Earth was going with the speed of light sideways to that direction.

It’s much easier to put two things right up against each other and see if there’s a difference, than it is to measure them separately. You can notice much smaller differences with a direct comparison.

6

Relativity in words of four letters or less.

Relativity in one syllable words.

7

also make sure to distinguish what examples, metaphors and analogies are.

when are you talking about some science phenomena/fact and when are you talking about some illustration of a small part of some science phenomena/fact.

ball and stick models of molecules convey some valuable information yet it is a mistake to think molecules are like that.

you can find on forums where someone trys to explain something by relating that to a car or something that might also happen also when in a car. soon someone is talking about cars and they don’t act that way.

8

I’d argue strongly that the basketball example is no good on its own. It is wrong, and the last thing you want is to train your son to nod in agreement at something that doesn’t sound quite right (in this case, because it isn’t).

In particular:

Correct, but…

…is a false implication. The “therefore” implies that the extra distance has something to do with it taking longer. It doesn’t. The trip is longer, yes, but that’s just Galilean relativity. The time spent taking that longer trip in Galilean relativity is the same for both observers, and the distance/time discrepancy is accounted for exactly by the speed of the train. No Einsteinian special relativity is involved.

This is still a good example to start with, to contrast with a follow-up special relativistic example. It isn’t sufficient, though, to jump immediately to:

If your son tries to extend the basketball example into this conclusion, he won’t be able to convince himself of it (at least not correctly), because it isn’t true. Essentially, the content is an empty assertion of “yeah, time slows down”, only now with the added baggage of an incorrect reasoning.

So, I’d start with the basketball example, and then change the basketball to light bouncing up and down, and then point out that nature, it seems, has made it such that light is always observed at the same speed. Thus, the distance/time discrepancy that was explained by a different observer velocity in the basketball case has to be made up for here by a difference in the flow of time for the light case, given the assumption of equal-speed for the light. You could then explain that light and other special cases are extreme examples but that the time slowing effect is still present for other things, even the basketball and heart beats and all that. But keep it clear that it’s a separate, additional phenomenon from the Galilean effect that you get just with balls bouncing.

As I like to say: if you can do it with bullets and trains, it’s not special relativity.

9

That’s correct. What they actually did was arrange a beam splitter, using a partially silvered mirror so that one beam went up and back and the other side to side. Then, in order to take account of the possible inaccuracies in measuring the distances involved (only a few meters), they rotated the whole apparatus and did it again with the same result. They were called Michaelson and Morley and the experiment is famous.

Unfortuately, the Newtonian relativity of the OP will not give rise to the twin paradox; only Einsteinian relativity will and I don’t know how to explain that to a 9 year old. I suppose you could start with the basketball and then say that, bizarrely, the speed of light is always the same no matter how fast the train goes and the only way to explain that seems to be that time actually slows down. After that it is just geometry.

10

The simplest explanation I can give:

Hold up a stick vertical to the floor (a meterstick or other ruler would be ideal, but any stick will work). Ask him how tall it is. Now tilt it a bit, and ask how tall it is now: It’ll be somewhat shorter. But the fundamental length of the meterstick hasn’t actually changed at all. And if you know that fundamental length, and the angle by which you tilt it, you can mathematically calculate the new height. Alternately, if you know the height, the width, and the depth, you can calculate the fundamental length, and so on.

Well, time dilation or length contraction is just like that tilted stick. The fundamental length is something called the “proper interval”, and can be calculated from other things. The angle by which you’re tilting it is equivalent to the speed. And the length we measure in three dimensions, or the time interval between events, can vary with speed, just like the height of that stick varies with angle, and given the speed, we can calculate those things mathematically.

11

I’d agree with this.

My 12-year son recently wrote an (English) paper on relativity. He had a lot of difficulty with the time dilation, and needed a lot of help to get this right. I’m pretty sure he still does not have a secure grasp of this (I should quiz him!). That’s okay- sometimes stuff has to be presented a few times to a person for it to sink in.

I hate to shove my oar in here, but I think you also have to tell him the other startling things about time dilation. My son did seem to quickly understand that we see the clock run slower on the speeding spaceship. It was harder to get him to understand that TIME was actually going slower (rather than slower aging). It was still harder to get across that the guy on speeding spaceship sees our clock running slower (at the same time we see his clock running slower).

12

Are the twins’ names Stella and Terence?