Saturday, April 04, 2009

Free Will and Quantum Mechanics

John Conway and Simon Kochen recently wrote a paper with a mathematical proof showing that particles exhibiting quantum mechanical behavior can be shown to demonstrate free will. John John Conway gave a lecture at Princeton University explaining the significance of their theorem and proof.

The idea of quantum mechanics as a proof for free will is not new with Conway and Kochen. This idea has been debated as a product of quantum mechanics since these theories were first discovered. I remember Cleon Skousen talking about this in his controversial talk where he mentions quantum mechanics and free will but falsely concludes that God has to appease the intelligences. Nevertheless, this new proof of free will has profound theological and philosophical implications.

What is all this about? Well, I am not going to pretend to understand quantum mechanics completely but there are few basics ideas I picked up along the way. Before Einstein's relativity and quantum mechanics were discovered, most every behavior of matter was described by classical Newtonian physics. Apples falling from trees and bowling balls rolling down inclines, etc. In fact, the laws of classical physics don't just explain these behaviors but they are also predictive. By applying these laws you can in fact precisely tell the future and the past. However, as our society advanced technologically and astronomers began to look out into the universe at really big things moving very fast like stars, and planets etc., and physicists started looking at really small things like electrons and atoms, there began to arise many instances when classical Newtonian physics failed to predict physical behavior.

Quantum Mechanics came about because of Newtonian physics failing to account for black body-radiation, the emission spectrum of hydrogen, and the photoelectric effect. Relativity was discovered to explain the behavior of light in interferometers and laser gyroscopes, gravitational lensing, and moving clock desynchronization. However, the failure of classical physics for big things and small things is for different reasons. While the new equations of relativity allow us to explain and predict behavior of matter moving at or near the speed of light, quantum mechanics does not completely predict the behavior of individual particles like electrons around an atom. Heisenberg's uncertainty principle states that if you want to know the position and the momentum of an electron around an atom, the more precisely you measure one, the less precisely you can know the other because the act of measuring changes the system.

The consequences of relativity are such because it turns out that nothing can move faster than the speed of light or 3x10^8 m/s. According to Newton, if you were driving 2 m/s in a car and you turned your headlights on then the light exiting the lights would appear to be traveling 3x10^8 m/s + 2 m/s to a stationary observer. But it turns out that isn't the case. The experimentally proven reality is that the speed of light remains constant independent of reference frame. All the crazy equations are derived from this and similar observations.

For example, because of time dilation, if you have a set of twins and you keep one on Earth and send the other away on a space ship at near the speed of light and then turn around and come back to Earth, the twin who stayed at home would have aged more then the one who left home. Similar laws and equations that account for relativistic phenomenon such as length contraction and time dilation explain how fiberoptic laser gyroscopes work and allows us to keep the atomic clocks in the GPS satellites from becoming desynchonized.

However, quantum mechanics doesn't work that way. It is inherently unpredictable. Consequently, physicist talking in terms of quantum mechanics routinely use terms such as probability and spacial density to talk about the behavior of whatever particle they are describing. Entanglement helps by associating two or more particles by the laws of the conservation of momentum and then interrogating them separately in different rooms. They will always give the same story (opposite spin state). However, these experiments only get us closer to the Heisenberg's limit but not beyond it.

An example of what I am talking about is explained by another thought experiment by Erwin Schrödinger known as Schrödinger's cat. This thought experiment calls attention to our inability to predict certain things like the spin state (1/2 or -1/2) of an electron around a nucleus. Schrodinger described a situation where you had an atomic atom in a box that would eventually radioactively decay giving off an alpha particle. Also in the box was a Geiger counter connected to a contraption holding a vial of poison. And in addition to the radioactive atom, the detector, and the vial of poison was Schroeder's cat. If the atomic atom decayed, the Geiger counter would detect it, releasing the poison and killing the cat. The question being asked is whether the cat is alive or dead. Ramifications of this scenario are that, only opening the box can reveal the answer, the answer will either be one or the other, and it doesn't make sense to talk about the cat as being half dead and half-alive. It has to be one or the other.

Now is where it gets weird. You would think Entanglement would solve the Heisenberg dilemma. So, if you had a radioactive pion decay giving two electrons (A and B), to conserve angular momentum, one electron (A) would have a positive spin and the other would have a negative spin (B). And If you wanted to measure the spin state along several axis (x,y,z); while you can measure the spin in the x-axis in electron A and correctly infer the spin in electron B, you cannot then measure the y-axis spin in electron B and infer the spin in electron A with any more precision than what Heisenberg's principle allows. Somehow, electron B knows that you have already measured electron A.

I wonder if this is something like the Lets Make a Deal/Monty Hall Principle. After picking one of three doors on the show, only one with a big prize behind it, The Show Host opens up one of the doors that he knows doesn't have the prize behind it and asks you if you want to switch doors. Some may think to tell you to stay with your first choice. But statistics demonstrates that your odds increase from 33% to 66% by always switching your choice. Somewhat counter-intuitive but check out an online simulator and verify it for yourself. Nevertheless, switching doors doesn't make it 100%.

So, in this paper, Conway and Kochen suggest that the spin states don't exist until the point they are measured. Then the particle is free to "decide" which state it will adopt at the moment of measurement. They begin with the assumption that there is at least one being or experimenter in the universe with free will. Then by applying the following axioms they derive their conclusion. The TWIN axiom states that when dealing with entangled particles that while you cannot predict their individual states before measurement, the states between both particles do correlate with one another. The MIN axiom states that is the future cannot change the past, that the past cannot determine the future. The FIN axiom states that information cannot be transmitted faster than the speed of light. And the SPIN axiom says that the three perpendicular spin states (x, y, z) commute to always equal 2 or (101). However, the Kochen-Specker Paradox says that these states don't exist before being measured because a solution does not exist when measuring all 33 axis of a sphere superimposed on a cube. All of this result in the conclusion that the particle being measured by the experimenter also exhibits free will.

I don't really understand the math part of it, but they seem to be saying the math proves that there is nothing deterministic about which way the spin will be. There are no hidden or unaccounted for variables. Or in other words, whether a butterfly flaps its wings in Kansas does not result in thunderstorms in Tokyo verses sunny skies. The paper makes a point to say that they make no attempt to comment on probability and uncertainty. However, an important assertion that Dr. Conway makes using this theorem and proof is to explain randomness in the universe. Dr. Conway is quoted in a lecture in Auckland New Zealand as saying his Theorem could also rightly be named the "Free Whim Theorem." So, in a nutshell this theorem seems to be trying to explain how God plays dice with the Universe despite Einstein's objection to that idea.

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