Throwing Cats Into Water
Yeeey, we’re back with another edition of throwing cats!
Last week, I showed you what happens when you throw a cat out of an airplane. Today, you will find out what happens when you throw a cat into water!
Please note that this time we’ll be using an idealised mathematical cat. It’s going to stay floating on the surface of the water without moving around, instead of freaking out, shooting out of the water like a bullet and spending years plotting a revenge masterplan against you, like a real cat would. (So don’t try this at home.)
Oh, and in addition to a cat, we’re going to use a dog! Weeee!
Which route will the dog take?
Imagine we’re on a beach. We throw the cat into the water, and then yell “Fetch!”. The dog will start running to fetch the cat. But what’s the best route for him? He can run on the sand a lot faster than he can swim in the water…
If he goes in a straight line, he’s going to be swimming unnecessarily long. Or he could run straight to the point on the sea edge that’s closest to the cat, to minimize the time he spends swimming. Or maybe somewhere in between?
The answer is: somewhere in between. In fact the answer is exactly analogous to light refraction. Light travels faster in air than inside a crystal. So if you shine a light on a crystal, the light will not go in a straight path. Instead, it will go in the path that minimizes the time taken.
This was a big “Ah-ha!” moment for physicists. When they first discovered photons, they thought they travel through the shortest DISTANCE between two points. But they don’t. They take the route that will guarantee the shortest TIME between the two points! It’s almost like photons can THINK!
Some people also propose a theory that dogs can’t really think about the route they’re taking. These people claim the dogs simply run along the beach because they don’t want to get wet, and then jump into the water when staying dry is no longer an option. But there’s a fatal flaw in these people’s claims – we can refute them experimentally! And as a bonus, the experiment shows that dogs are smarter than photons!
How dogs are smarter than photons
The experiment is very simple. Just place the dog in the water. Then throw the cat in the water far away from the dog, and tell the dog to fetch. Which path will he follow?
That’s right, he’ll follow the quickest path! That means getting out of the water, running along the beach, and then getting back in the water! (This was shown by experiments using a stick, because the experimenters couldn’t find an idealized mathematical cat.)
A photon faced with the analogous problem won’t be that smart. If you shine a light inside a crystal and try to find out how it gets to another point inside the same crystal, it will always be in a straight line. The photon isn’t smart enough to get out of the crystal, fly along the edge, and then re-enter when it’s convenient.
And that’s all I have to say about throwing cats into water! It’s probably also the end of my short series about throwing cats. I really don’t think I can frame my next blog post to include throwing cats (well, I could call it “Throwing cats on a bus”, that would be really pushing it).
(Hmmm. Last week I used a cat to illustrate air drag. Today I used a cat and a dog to illustrate refraction. The way this is going, next week I will probably explain the origins of the universe using a giraffe, an elephant, and a duck-billed platypus.)
February 11th, 2009 at 5:29 pm
[...] Update: The next (and probably final) edition of throwing cats is up! You can now find out what happens when you throw a cat into water! [...]
February 12th, 2009 at 8:57 am
Great blog! Where’s the RSS feed?
February 12th, 2009 at 12:54 pm
@fairyhedgehog:
I now added a link to the RSS feed in the sidebar. Cheers!
February 19th, 2009 at 4:25 am
Cool. Did you know about the electrons diffraction through 2 slits experiment? When you try and ‘see’ which way each electron goes (which slit it goes through out of 2) the electrons behave like particles and produce 2 lines on the wall. When you don’t look for where they are going, i.e. don’t try and detect… they behave like a wave, producing a diffraction pattern instead. Are they alive or something? Aware of our intentions perhaps? Anyway, that photon analogy made me think of it, so thought i’d share with you.
February 19th, 2009 at 9:38 am
@James:
Yeah, I know that experiment! I think I first read about it in a book by Richard Feynman.
It still amazes me every time I think about it