Quantum Christmas

Well, I hope you have been enjoying your winter weather, your holiday festivities, and your holiday-related comics. I certainly have (except the weather lately has been a bit cold... )

Holiday-related comics, you ask? Yes, they are all over the place. But holiday- and physics-related comics, they are harder to come by. xkcd has a good one here. Check it out - being sure to hover your mouse over the comic for the second punchline - then come back and hear my rant :)

This xkcd comic is very funny (as xkcd comics so often are), and even better, it makes an error about quantum mechanics that I can rant about!

The claim is that the only way to keep from changing Christmas is not to observe it (love the pun!) This joke refers to quantum-mechanical event called the collapse of the wavefunction that occurs when a system in a superposition state is observed.

For example, if a particle is in a superposition of the ground state and the first excited state, and you measure its energy, you will find either the energy of the ground state or the energy of the first excited state. If you find the energy to equal the energy of the ground state, then the particle will now be in the ground state; it will no longer be in a superposition of the ground state and the first excited state. Therefore its state has been changed by your measurement! This change of the wavefunction upon measurement (which, by the way, is random and unpredictable) is called the collapse of the wavefunction. Similarly, if an electron is in a superposition of spin-up and spin-down, and you measure its spin, it will collapse to a state of purely spin-up or purely spin-down.

So far it looks like measurements do change the state of a system ... but not so fast. Suppose our particle were already in the ground state and we measured its energy. We would find the energy to be equal to the ground-state energy, and the particle would still be in the ground state - its state will remain unchanged. Similarly an electron with spin-down will still be spin-down after a spin measurement.

What is special about the cases in the last paragraph, so that the state is unchanged by measurement? In these cases, the system is in an eigenstate of the quantity you are measuring, which means it has a definite value of that quantity (not a superposition of values with uncertainty).

So, if you don't want to change Christmas, you need to find out what Christmas is in an eigenstate of, and observe it in that way. I humbly suggest that Christmas is in an eigenstate of generosity, what do you think?

_{Image by Alaina Orwitz. See her art page.}