## Comments about "Free will theorem" in Wikipedia

This document contains comments about the article Free will theorem in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles.
There are many problems with this sentence.
• Generally speaking the behaviour of (elementary) particles has nothing to do with how humans behave
• If our choices are a function of the past (yes or not) has nothing to do how particles behave
See also Reflection 1

### 1. Axioms

The proof of the theorem as originally formulated relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin".
IMO the sentence "The proof of the theorem" should be "The rules of the experiment rely on three axioms"
1 Fin: There is a maximum speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
2 Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).
3 Twin: It is possible to "entangle" two elementary particles, and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions.
The sentence is rather flimsy. IMO a better on is:
3 Twin: It is possible to create in a reaction two elementary particles, and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. Such particles are called entangled.
However and that is important this has to be verified 1000 times.

### 2 The theorem

The free will theorem states:
Given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments.
IMO the sentence "Given the axioms" should be: Given an experiment (following the rules as described in the axioms).

### 3. Reception

According to Cator and Landsman, Conway and Kochen prove that "determinism is incompatible with a number of a priori desirable assumptions." They demonstrate that in certain experiments, "the choice an experimenter makes [about what to observe] is not a function of the past."
Such a sentence requires a rather elaborate explanation.
How can you demonstrate that something is not 'a function of the past'?
The philosopher David Hodgson supports this theorem as showing determinism is unscientific, that quantum mechanics allows observers (at least in some instances) the freedom to make observations of their choosing, and so leaves the door open for free will.
This whole issue has nothing to do of what we call: a free will.
The next sentences are also not very clear.

### 4. See also

Following is a list with "Comments in Wikipedia" about related subjects

### Reflection 1 - No choice experiments

The issue as discussed is very much related to what extend humans are involved in the outcome of certain experiments. The answer is generally speaking: No.
A different issue is to what extend humans can predict the outcome of certain experiments. Generally speaking the answer is Yes. But this always requires previous knowledge That means you always have to perform the same or almost the same experiment before.
This is also the case in quantum mechanical experiments. For example in the case of quantum mechanical experiments you must know that there is a clear correlation between the experimental result at the left side (up) and the result at the right side (down). That being the case and you measure in one instance "up" at the left side, you will immediate know that the result at the right side will be "down".

However, and this is important, this has nothing to do with the concept of Free will

### Reflection 2 - Choice experiments

In reflection 1 a 'no choice experiment' was discussed. That means in a situation were you could measure in 3 directions always on both sides the same direction is selected. For example on both sides you measure in the X direction. In such a case it is easy to establish a possible correlation, meaning that when observer 1 measures a photon in the +X direction, observer 2 will measure a photon in the -x direction. The cause is in the reaction.

In the same experiment if both observers have a choice the outcome is completely unpredictable, even if the photons are correlated. The issue is if observer 1 measures photon 1 in the x direction there is a 50% chance that the outcome is +x (and 50% -x). To demonstrate this rule you have to perform the experiment 1000 times.
If observer 2 measures photon 2 in the y direction there is a 50% percent chance he will measure a +y. Also here you have to test this 1000 times and also test if there is any difference what observer 1 does. There will be none.
The only thing you 'know' that in a particular case if observer 1 measures +x and observer 2 measures +y that photon 1 moves in the direction (+x,-y) and photon 2 in the direction (-x,+y).

### Reflection 3 - General

The majority of the text is not very clear.
General speaking physical experiments have nothing to do with my free will nor with any human behaviour. Exceptions are test where you want to tests human responds on external simulations.
Tests were you allow humans to make selections also have in general nothing to do with the outcome of the experiments. Typical experiments were this is the case are all LHC experiments. A typical test in reality is the Schrodinger Cat experiment. The importance of this test is the half-life time of the radioactive element used. If this is 1 second you can be sure that the cat is dead when you perform the experiment for 1 hour. Humans, including my free will, have nothing to do with that, except if I have more cats, to select the cat which will undergo this experiment.

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Created: 4 April 2018

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