Monday, October 25, 2010

Why Pigs Don't Diffract Through Doorways

Some of you may remember Dr. Mason at BYU, and some of you may have had him for a class or two (I had him for three classes...). There was one problem in particular that I remember solving in his quantum mechanics class. It went something like this:

Q: Figure out how slow a 75 kg pig needs to be going in order for it to diffract by a minimum of 1 meter through a door way 1 meter wide into a 10 meter wide room.

I will now solve this problem and demonstrate why pigs do not diffract through doorways.

First we have to find the de Broglie wavelength (Note: de Broglie is pronounced "duh Broy" not "Dee Brog-lee-ay" as I learned from a certain Belgian professor). Knowing the width of the slit (the door) and the distance the pig travels (10 m) before it is observed (hits the opposite wall), we can solve for the wavelength of the pig as it diffracts into the room. First we use simple trigonometry to find the angle of diffraction:
Using the fact that the room is 10 m wide and we expect a maximum in the diffraction pattern 1 m from directly opposite the door we set the opposite side of the triangle to 1 m and the adjacent side to 10 m. This gives us an angle α = 5.71°. Using this angle we then go to the equation for diffraction through a single slit:
Given the angle and the width of the slit (1 m) and the fact that we are finding the first maximum (n = 1) we can then find the wavelength of the particle necessary to do this. A simple calculation gives us a wavelength of 0.0995 meters. Assuming this wavelength represents the de Broglie wavelength of the pig we can then use de Broglie's equation,
to find the velocity needed in order for the pig to diffract through the door way. Using the fact that the pig has a mass of 75 kg and Planck's constant we can find the velocity needed. With this we find that the pig needs to be going slower than 8.88 e -35 m/s in order for the pig to diffract significantly through the doorway. But at this speed the pig will take a phenomenal 1.13 e 35 seconds or 3.57 e 27 years or 2.6 e 17 times the age of the universe, to cross the room. And that my friends, is why pigs do not diffract through doorways.

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