Our neighbours have a dog – one of those small, yappy, pointless pooches with an excessive bark-to-weight ratio. It runs about their garden, keeping our cat out and gets very loud when I venture over to the compost bin. The neighbours’ garden is fortunately well-fenced, meaning the creature thankfully can’t invade our side.
So, imagine my surprise, when I discover yesterday evening that one of our chickens is over on the dog’s side of the fence. (It appeared the neighbours and the dog were out at this time). How did she get there? There’s no obvious gap in the fence – there’s even a mesh at the bottom of the fence presumably put up to stop the pesky canine from burrowing under (I mean, being the size of a rabbit it might start behaving like a rabbit). Hyacinth is only fourteen weeks old, and her ability to achieve flight is somewhat limited. She flaps her wings a lot, sometimes, but has shown little ability to rise more than a couple of centimetres in the air.
I had to go over to the other side to rescue the very agitated chook, who was trying to squeeze through gaps in the fence that were way too small.
How did she get there? Sherlock Holmes remarked that, when you have eliminated the impossible, whatever remains, however improbable, must be the truth. In which case there is just one option: quantum tunnelling.
This is the phenomenon in which small particles can traverse through barriers that you wouldn’t think they could get through on energy grounds alone – it arises from the probabilistic nature of quantum mechanics. It’s a real effect, and can be seen with electrons. For example, the tunnel diode relies on this effect to function.
It’s quite straightforward to estimate the probability of Hyacinth performing such a task. Using Schrodinger’s equation, we can estimate the chance of an object tunneling as ‘e’ to the power of minus (square root of (8 m V) ) times x divided by hbar), where ‘e’ is the base of natural logarithms, 2.71828…, m is the object’s mass (say around 1 kg), V is the potential energy of the barrier, x is the thickness of the barrier and hbar is Planck’s constant divided by 2pi, or about 10^(-34) Joule seconds.
Estimating the fence to be about a metre high, so the 1 kg chook needs a potential energy of about 10 J to get over it, 1 cm thick, gives us an estimate of ‘e’ to the power of minus 10 to the power of 32. Approximately. Simplifying a little, its about 10 to the power of minus 3 times 10 to the power 32, or:
0.000……..0001, where the dots hide a few zeros. Just how many zeros between decimal point and the ‘1’? Approximately 300 000 000 000 000 000 000 000 000 000 000 of them, which explains why I cheat and use the dots. It’s a small number.
With no disrespect for Sherlock, I think that it might be prudent to think about other possibilities for Hyacinth’s excursion next door. Such as maybe there is a gap in the fence that I’ve missed, or she’s a better flyer than she lets on, or that those plums I had eaten were hallucinogenic and I’ve imagined the whole episode. Even that last one is more likely that quantum tunnelling.
So why does tunnelling work for electrons, but not for chickens? Fundamentally, it’s because electrons are very, very, very small. You’d need about ten to the power 30 electrons to have the same mass as a chicken.
[2 February 2012 – Problem Solved? Last night I watched as the cat sneaked up on the chickens and then jumped at them from short range. In the general squarking and intense flapping of wings that followed, Hyacinth got at least a metre in the air. Brigitte, the other chook, stayed rather more terrestrial. His fun over, pussycat trotted away looking very smug.]