Phil Plait of Bad Astronomy is having some issues with squirrels attempting to defeat quantum mechanics.

But I think this requires a closer look and a bit more physics.

In his first picture (Squirrel Wavelength), we see the squirrels would travel with approximately 1/4 a fence-length wavelength. We’ll call this a wavelength of 0.25.

In the newer picture, taken at a lower temperature, we can estimate a wavelength of roughly 0.1 (it’s a little shorter but that’s not too much of an issue).

Phil’s concern is that quantum mechanics predicts that as temperature decreases, wavelengths increase. However, by demonstrating this relationship, these squirrel’s have disproved quantum mechanics!

Now, one commenter suggests that this could be due to multiple squirrels superimposing their tracks, or even one squirrel that crossed the fence multiple times, however, this explanation is just not fun enough for these sorts of exercises.

The general relationship for energy and wavelength is given by E = hc/?, where E is the energy, h is Planck’s constant, c is the speed of light and ? is the wavelength. Energy is proportional to temperature, so wavelength is inversely proportional to temperature.

But there’s a problem here: the squirrel’s aren’t moving at c (roughly 300 000 km/s), they aren’t even moving at a constant velocity!

If we assume that the frequency of the squirrels, f=v/? where v is the velocity of the squirrel, is constant (a safe assumption for most waves), then we can figure out a relationship for the squirrels velocity with respect to temperature.

So since the squirrel’s wavelength decreases with temperature, to maintain the constant frequency relationship, we must infer that the velocity increases with decreasing temperature!

Basically, the little buggers move faster because it’s really cold.

This relationship will have to be further developed as it only takes into account non-relativistic squirrels, and the relationship would seem to imply that as the temperature continually dropped, the squirrels would approach near infinite speeds!

There’s a caveat here though: at a finite temperature the body functions of the squirrel will shut down and kill the vermin, thereby preserving the laws of physics for us all.

Should we call this the Ultra Squirrel Catastrophe?

I think we need a large cryostat to empirically determine this transition temperature into the “dead vermin” regime. And we also need to know what properties this “dead vermin” regime has. What is its entropy? Specific heat capacity? Elastic constants, conductivity, etc… Do all of these properties diverge at the transition temperature, Tvermin, as well as the squirrel velocity?

The one problem I see with this experiment is the fact that we can only pass through the transition temperature from one direction, and we can’t reproduce the same results from the same sample….unless these squirrels really do violate some laws of physics…now that would be cool!