## Ask Professor Puzzler

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Jakob saw a multiple choice question on a website, and was surprised by the answer. He was curious to know what Professor Puzzler thought.

Here's the question: You have an iron rod which is 1 light year in length. You push one end of the rod. How long does it take before the other end moves? The options are:

A: Immediately

B: 1 week

C: 1 year

D: at least 1,000 years.

The "instinctive" answer is to say A - the moment you move one end is the moment the other end moves. And, as you might guess, from the fact that we're being asked to explain it, A is *not **correct*.

To help understand what's happening here, I'd like you to imagine that the rod is *not *made of iron. I want you to imagine instead that it's made of marshmallow. Yes, that's right - one single marshmallow that's 1 light year tall.

Now imagine what happens when you push one end. Can you visualize it? As you push, the marshmallow rod compresses (squishes) right by where you pushed it. Of course, it won't *stay *compressed, and since it can't "rebound" to its original position (your hand is in the way, and you're still pushing), the compressed section will decompress by pushing the compression down the length of the rod. In other words, you'll create a *wave* of compressed marshmallow that will travel the length of the rod.

"Ah, yes," you might say, "but that's marshmallow. A marshmallow is squishy. An iron rod isn't squishy. It's rigid."

Well, yes and no. It's kind of like "The Princess Bride," where Miracle Max concludes that "mostly dead is partly alive." Iron is "mostly rigid," and mostly rigid is partly squishy. It *will* compress. The motion of the rod is actually a wave of motion, just like with the marshmallow. The other end of your rod will move *after *you've pushed your end.

How much after? Well, that's a good question. And I don't know the answer. But I do know this: the speed of that wave is significantly *slower* than the speed of light. And how long does it take light to travel the length of the rod? Since the definition of a "light year" is "the distance light will travel in a year," we can conclude that light takes a year to travel the length of the rod. And therefore, the amount of time it takes for the other end of the rod to move is more than a year. If you look at your possible answers, D is the only one that is more than a year. Therefore, if *any *of the answers are correct, D must be the one!

It seems counter-intuitive; when you are dealing with much smaller "mostly rigid" objects, it appears to you as though the other end moves simultaneously with the end you pushed. The key is the word "appears." There is actually a tiny, tiny delay, which is so short you couldn't possibly measure it. But when you are dealing with such an astronomical distance (the length of your rod is 63 thousand times the distance from the earth to the sun!), that tiny, tiny delay is suddenly not tiny any more!

Incidentally, I hope you're planning to push *very very *hard, if you intend to move that rod of yours any significant distance. If we assume that the radius of the rod is 1 centimeter, its mass is about 23 quadrillion kilograms, which would make for a decent sized asteroid, if it wasn't so oddly shaped!