Relativity can be riveting

Looking back a long (long) way to my physics degree, special relativity was one of my favourite subjects. It's weird and wonderful enough to be amazing, but (unlike general relativity) the maths is relatively easy. Don't worry though, I'm not going to throw equations at you - I just wanted to share one of the remarkable paradoxes of relativity.

I've seen paradoxes defined as contradictions that can't be true, but I think a much more appropriate definition for physics is situations that appear to involve a mind-boggling contradiction, that the physics tells us really is the way things are. And special relativity is full of them.

This particular one below I hadn't seen before, and I picked up from Andrew Stearne's book The Wonderful World of Relativity. (This sounds like a children's book, but actually it's a relativity primer that is probably best appreciated by those about to start a physics course at university, as it's a bit too textbooky for the general reader.)

Here's the scenario. We've got a table with a 10mm deep hole in it. At the bottom of the hole a beetle is happily beetling about, unaware that we are about to fire a rivet into the hole. The good news is that the shank of the rivet, the bit that will go into the hole, is only 8mm long, leaving room for our (rather small) beetle to feel safe and snug.

Unfortunately, though, the rivet is fired towards the table at a fair percentage of the speed of light. It's somewhat typical of this book that all it tells us about the speed is that γ is 2, which doesn't really give you an idea of how fast the rivet is going, but if my back of an envelope calculations are right, this is around 0.87 times the speed of light. Quite a fast rivet, then.

Now one of the weird effects of special relativity is that an object moving at high speed is squashed up in the direction of travel as seen by an observer. So from the bug's viewpoint the rivet won't by 8mm long, it will be just 5mm long. 'Wow,' thinks the bug, 'what was I worried about?' But before it sits back and starts reading the newspaper, there's something it needs to consider. Relativity works both ways. From the rivet's viewpoint, it's not the rivet that's moving, it's the table. This means from the rivet's view it remains 8mm long - but the hole is contracted and is now only 5mm deep. Squish goes bug.

So what really happens? (I use 'really' loosely. Let's face it, Wickes does not sell a 0.87 times the speed of light rivet gun.) Is the beetle somehow both live and dead, in the manner of the famous quantum cat? Sadly no. It's squish all the way.

Let's follow the event from the beetle's viewpoint. Down comes the rivet and slams into the table. At the moment before the impact the rivet is still just 5mm long as far as the bug is concerned. But here's the thing. Just because the head of the rivet has come to a sudden stop doesn't mean the whole rivet does. A wave has to pass along the rivet to its end saying 'Stop!' The end of the rivet will just keep on going until this wave, typically travelling at the speed of sound, reaches it. That fast-moving end will crash into the beetle long before the wave arrives. It will then send a counter wave back up the rivet and after a degree of shuddering will eventually settle down as an 8 mm rivet in a 10 mm hole. Too late, though, for that bug.

Isn't physics great?


  1. Reading your article in the WSJ 03 DEC 2011, made me recall Robert A. Heinlein's 1956 book "Time For The Stars". In it he explores relativity in an enjoyable story.

    Jerry Munger

  2. Thanks for your comment, Jerry. I was a big Heinlein fan when I was younger and read Time for the Stars - but it has been a long time, and I don't really remember it. Must dig out a copy!


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