Re: John Conway, "Free Will Theorem"

[George Levy]

Hi Pete and Russell While it may be true that the propagation of the wave equation (and the consequent branching pattern) is deterministic, the actual branch in which one instance of us finds itself in the Multiverse, is random. I agree with Russell that free will occurs only in irrational cases: when the choice is clear and rational there is no free will; when the situation is so clouded and uncertain that we are teetering between alternatives then irrationality comes into play and we might say that we exercise free will. The problem is what may be irrational for one person may be perfectly rational for another. We are led to another concept. The relativity of information According to Shannon the amount of information in data communicated to a receiver is a function of how much the receiver already knows. Extending Shannon's concept we find that information is relative. At the macro level, choices which may appear clear to one person may not be clear to another, possibly because of different degrees of intelligence or different knowledge bases.  At the micro level, if we can extending Shannon's mutual information concept to Quantum Mechanics, we find that there is an eerie analogy with entanglement. Two entangled particles maintain a constancy in their relative states. Thus entanglement may be viewed as a relative state between two particles. However, a  more interesting theoretical and philosophical situation occurs when observer A states become entangled with a particle P that he observes while oberver B remains unentangled with either A or P. In this case A observes that the state of P depends on his own state. This situation is theoretical at the microscopic level because at this point in time, there is no practical means as far as I know, to construct a lab so well isolated that we can get A entangled to P without also entangling B. To go back to the idea that > the "Free Will Theorem", saying basically that > particles must have as much "free will" as the experimenters who are > deciding which directions to measure the |spin| of a spin-1 particle > in. It is possible to devise a macroscopic experiment simulating entanglement between experimenter and particles by monitoring brainwaves (or implenting electrodes in subject's brains) to correlate the behavior of motorized objects to people's thoughts. For example, an interesting experiment would be to ask a volunteer to catch a motorized object placed on a table, when the object has been programmed to avoid the hand of the experimenter at the slightest thought of him grabbing the object. As soon as the volunteer thinks of exercising his free will, the object will automatically move away.  How would you catch this object? Russell Standish wrote: The Multiverse is a deterministic framework for quantum mechanics. It is completely compatible with it. A paradox can only occur if you think the single world universe of our senses is deterministic - which it clearly isn't. My "definition" of free will is "the ability to do something completely stupid" - ie related to irrationality. A perfectly rational being would be completely deterministic, and in my mind has no free will. This certainly appears to be compatible with Conway's use of the term. It is usual to equate the choice of measurement by the experimenter as "free will". It is also certainly true that fixing the QM state vector, as well as the choice of measurement does not determine the outcome of the measurement. To say that the observed system has free will in deciding the outcome of the experiment is certainly a provocative way of putting it, but I think it is perfectly reasonable to ask the question of why we use the term "free will" to refer to conscious entities making indeterminate choices, and not for non-conscious entities. On an interesting segue on this matter is found in Roy Frieden's book "Physics from Fisher Information", where he talks about measurement as being a game in which the experimenter attempts expose as much information as possible about reality, and reality attempts to hide that information. The minimax principle this generates can be used to derive all sorts of fundamental equations, including the Klein-Gordon equation, a relativistic version of Schroedinger's equation. Cheers On Thu, Apr 07, 2005 at 01:30:00AM -0700, Pete Carlton wrote: Greetings, I recently attended a talk here in Berkeley, California given by John Conway (of 'Game of Life' fame), in which he discussed some of his results with Simon Kochen, extending the Kochen-Specker paradox. He presents this as the "Free Will Theorem", saying basically that particles must have as much "free will" as the experimenters who are deciding which directions to measure the |spin| of a spin-1 particle in. --I would replace his words "free will" with "indeterminacy", but there is still an interesting paradox lurking there. A good online writeup is here: http://www.cs.auckland.ac.nz/~jas/one/freewill-theorem.html I wrote up my brief take on it, necessarily from a more philosophical angle, here: http://homepage.mac.com/pmcarlton/iblog/C1074759898/E263558720/ index.html and here: http://homepage.mac.com/pmcarlton/iblog/C1074759898/E688049825/ index.html. I have the intuition that a multiverse approach very readily dissolves his mystery, but am not quite sure how to formally work it out. I thought some people on this list might be interested, or have a ready answer in hand - in particular, I'd like to know if this 'paradox' really is a paradox in one or more of the multiverse conceptions discussed here. thanks and best regards, Pete