illuminating science

Guest poster Brett sent me this a little while ago, regarding free will - not just about whether we have free will, but whether that means that particles do too! There’s a little bit of higher level physics here, but you should be able to get the gist of it regardless. Food for thought indeed!

Often when science and philosophy collide, we get out something that is truly remarkable for both sides. Like when we showed that regular
objects like tables, chairs and people were actually composed of tiny particles, it raised questions of “Well, what does it mean to be me? I
feel like I’m different from tables and chairs, but on the atomic level, I’m not!” And let’s not even start with astrophysics and genetics colliding with certain religious beliefs.

Recently, Princeton mathematicians John Conway and Simon Kochen proposed a startling new theorem: “The Free Will theorem”. In general, provocative terms, it says that if you take as axioms stuff that most scientists believe, then if scientists have free will, then so do the particles that they measure. This is an interesting new form of a “No Hidden variables” theorem.

Specifically we suppose that:

• If two particles have total angular momentum 0, and one has angular momentum s, then the other must have angular momentum -s,
• If you measure the squared spin of a spin-1 particle in three mutually orthogonal directions, you will get two ones and one zero, in some
  order.
• There is a finite upper limit to the speed at which you can transmit information.

The first two assumptions (called TWIN and SPIN) have been experimentally verified, and the last one (called FIN) is readily
believable (Einstein’s relativity says that this limit is the speed of light, but this axiom needs only some limit, not specifically
that one).

Then what Conway and Kochen have shown is that if you (as a scientist) have some ability to freely choose which directions you want to
measure the spin of a particle, the particle has exactly the same kind of choice of the value of spin in those directions! This is rather
remarkable. Interestingly, if you don’t like this result, then you must have a problem with one of the three assumptions given
above. Since two of these results are experimentally verified, and the third seems rather reasonable (especially if you like relativity), you
need to do a lot of work to get around this “free will” problem if you don’t like it.

The details are a little technical, but you can check them out here.
The Daily Princetonian has a good article on it as well.