Sunday, August 17, 2008

'Highly Regarded' Mathematicians

Do subatomic particles have free will? ask two 'highly regarded' Princeton Mathematicians.

Yes. Obviously.

Seriously though, it's nice that people are independently coming to my conclusions.
"indeterminacy is inherent in the world itself"
It's nice to be right.

The exact reason is that
"They used a pure mathematical argument to show that there is no way the particle can choose spins around every imaginable axis in a way that is consistent with the 1-0-1 rule."
Although, journalists suck.
"The particle, Kochen and Specker showed, is like a cheating player. They found it out by showing that no single object satisfies all the “questions” (or all 33 axes) at once."
The particle isn't very much like a cheater at all. The particle is being prodded, and that prodding changes its internal state. As a result, it's not surprising at all that it 'decides' its spins ad hoc.

Incidentally, I exactly mean that
"the best way out of this paradox is to accept that the particle’s spin doesn’t exist until it’s measured. "
Something I'm glad I read the article for:

"Conway and Kochen say that they have now proven that particles’ responses can’t be pre-determined, even within this possible interpretation. “We can really prove that there’s no algorithm, no way that the particle can give an answer that is unique and can be specified ahead of time,” Conway says. “I’m still amazed that we can actually manage to prove that.”"

Notice that this means it was, up until now, unproven.

"Kochen and Conway say the best way out of this paradox is to accept that the particle’s spin doesn’t exist until it’s measured. But there’s one way to escape their noose: Suppose for a moment that Alice and Bob’s choice of axis to measure is not a free choice. Then Nature could be conspiring to prevent them from choosing the axes that will reveal the violation of the rule."

(Edit for clarity: the particle's spin or any rule whereby the particle's spin will be determined.)

The paper also beautifully shows how determinism and free will, while supposedly very different, have the exact same consequences. The mathematicians have found that either entanglement is exactly what it's thought to be, or else determinism is strictly true. In other words, that either free will or determinism are true but it works out to the same experimental results.

I also just realized another level of this logical structure. Compatibilism is false, but the consequences of compatibilism - that determined humans are morally responsible - is true.

(Which incidentally is a good example of the fact that you should ask what your philosophy is for. It's very very likely that what's true will also serve that purpose, and then you can stop being wrong without having to completely rearrange your life.)

I've noticed something else. Journalists suck again, though at least only slightly; the article references the "Kochen-Specker paradox" which, if you want to look up, is actually called a theorem.

On the other hand, journalists do have an actual job. Check out La Wik and decide for yourself whether Julie Rehmeyer's hand could do good things there.

I guess to be precise, journalists suck as writers. Their literary and logical skills are weak, because they spent all their time developing the ability to communicate the ideas they're given.

Addendum, from the reddit title: "Two mathies prove that if humans have even the tiniest amount of free will, particles behave unpredictably."

Something I had especial difficulty with.

"But Conway and Kochen have shown this scenario is impossible for particles that are incommunicado. They invoked the old Kochen-Specker paradox to show that if the spin 1 particle’s behavior is pre-determined so that it isn’t allowed to “change its animal,” it won’t be able to give answers that are consistent with the 1-0-1 rule. So if Alice and Bob are lucky in how they choose their axes, they should be able to force the particles either to disagree or to violate the 1-0-1 rule — contrary to experimental evidence."

That phrase there, "change its animal" needs to be clarified. The mathies have actually proven, in a general sense, that Alice and Bob can force the particles to change the rules under which they decide their spins. (Just like the infinite-series-of-averages, this only works in a finite universe.)

In other words, they must be stochastic. There is no other interpretation, unless determinism is strictly true. (Read a fantasy book where the character tries to outsmart prophecy for more illustration.)

No comments: