Core Concepts
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Free Choice
"Free choice" is an important term in the debates about quantum mechanics and physical reality. It was introduced by Niels Bohr in his response to Albert Einstein's famous challenge to the "completeness" of quantum mechanics.
Einstein's first objections were at the 1927 Solvay conference on "Electrons and Photons." These problems were instructively commented upon from different sides at the Solvay meeting, in the same session where Einstein raised his general objections [about completeness]. On that occasion an interesting discussion arose also about how to speak of the appearance of phenomena for which only predictions of statistical character can be made. In 1935, Einstein, with his Princeton colleagues Boris Podolsky and Nathan Rosen, claimed that their EPR experiment requires the addition of further parameters or "hidden variables" to restore a deterministic picture of the "elements of reality." In classical physics, such elements of reality include simultaneous values for the position and momentum of elementary particles like electrons. In quantum mechanics, Bohr and Werner Heisenberg claimed that such properties could not be said to exist precisely before an experimenter decides to make a measurement. This "freedom of choice" of the experimenter includes the freedom of which specific property to measure for. If the position is measured accurately, the complementary conjugate (and noncommuting) variable momentum is necessarily indeterminate. For many years, Heisenberg and Bohr described the reason for this as "uncertainty," as in Heisenberg's famous "uncertainty principle." Uncertainty was initially believed to be an epistemological problem caused by the measuring apparatus "disturbing" a particle in the act of measurement. The thought experiment Heisenberg's Microscope showed that lowenergy longwavelength photons would not disturb an electron's momentum, but their long waves provided a blurry picture at best, so they lacked the resolving power to measure the position accurately. Conversely, if a highenergy, short wavelength photon was used (e.g., a gammaray), it might measure momentum, but the recoil of the electron would be so large that its position became uncertain. Bohr abandoned this "disturbance" explanation after Einstein's EPR challenge, which showed that quantum mechanics requires a fundamental "indeterminacy" that is ontological, a characteristic of the wave function whether or not it is observed. The experimenter can get different results, depending on the choice of measurement apparatus and the property or attribute measured.
EPR argued (mistakenly) that entangled particles could be regarded as separate systems, and since they could choose which type of measurement to make on the first system, it would make an instantaneous difference in the state and properties of the second system, however far away, violating special relativity. We see therefore that, as a consequence of two different measurements performed upon the first system, the second system may be left in states with two different wave functions. On the other hand, since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system. This is, of course, merely a statement of what is meant by the absence of an interaction between the two systems. Thus, it is possible to assign two different wave functions to the same reality (the second system after the interaction with the first). In his 1935 reply to Einstein, Podolsky, and Rosen, Bohr denied that the limitations on simultaneously measuring complementary properties implied any incompleteness: My main purpose in repeating these simple, and in substance wellknown considerations, is to emphasize that in the phenomena concerned we are not dealing with an incomplete description characterized by the arbitrary picking out of different elements of physical reality at the cost of sacrificing other such elements, but with a rational discrimination between essentially different experimental arrangements and procedures which are suited either for an unambiguous use of the idea of space location or for a legitimate application of the conservation theorem of momentum.In his long 1938 essay on "The Causality Problem in Atomic Physics" Bohr again emphasizes the "free choice" of an experimental procedure in his solution to the EPR paradox. the paradox finds its complete solution within the frame of the quantum mechanical formalism, according to which no well defined use of the concept of "state" can be made as referring to the object separate from the body with which it has been in contact, until the external conditions involved in the definition of this concept are unambiguously fixed by a further suitable control of the auxiliary body. Instead of disclosing any incompleteness of the formalism, the argument outlined entails in fact an unambiguous prescription as to how this formalism is rationally applied under all conceivable manipulations of the measuring instruments. The complete freedom of the procedure in experiments common to all investigations of physical phenomena, is in itself of course contained in our free choice of the experimental arrangement, which again is only dictated by the particular kind of phenomena we wish to investigate. To be sure, those quantum events that are "measured" in a physics experiment which is set up to measure a certain quantity are dependent on the experimenter and the design of the experiment. To measure the electron spin in a SternGerlach experiment, for example, the experimenter is "free to choose" to measure, for example, the zcomponent of the spin, rather than the x or ycomponent. This will influence (but not determine) quantum level events in the following ways:
On the other hand, we could not create the particular value for the position. This is a random choice made by Nature, as P. A. M. Dirac put it.
Bell's Theorem and Free Choice
In all the recent EPR experiments to test Bell's Inequalities, "free choices" of the experimenters are needed when they select the angle of polarization. Note that what determines the second experimenter's results in these tests is simply the first experimenter's measurement, which instantaneously collapses the superposition of twoparticle states into a particular state that is now a separable product of independent particle states. Bell inequality investigators who try to recover the "elements of local reality" that Einstein wanted, and who hope to eliminate the irreducible randomness of quantum mechanics that follows from wave functions as probability amplitudes, often cite "loopholes" in EPR experiments. For example, the "detection loophole" claims that the efficiency of detectors is so low that they are missing many events that might prove Einstein was right. Most all the loopholes have now been closed, but there is one loophole that can never be closed because of its metaphysical/philosophical nature. That is the "(pre)determinism loophole." If every event occurs for reasons that were established at the beginning of the universe, then the experimenters lack any and all the careful experimental results are meaningless. John Conway and Simon Kochen have formalized this loophole in what they call the Free Will Theorem. Conway and Kochen assume three axioms, which they call "SPIN", "TWIN" and "FIN". The spin and twin axioms can be established by entanglement experiments. Fin is a consequence of relativity theory. The formal statement of the Free Will Theorem is then If the choice of directions in which to perform spin 1 experiments is not a function of the information accessible to the experimenters, then the responses of the particles are equally not functions of the information accessible to them.Conway and Kochen say: Why do we call this result the Free Will theorem? It is usually tacitly assumed that experimenters have sufficient free will to choose the settings of their apparatus in a way that is not determined by past history. We make this assumption explicit precisely because our theorem deduces from it the more surprising fact that the particles’ responses are also not determined by past history. The theorem states that, 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. [See the discussion of the EPR experiments to see that "free choices" of the experimenters are needed when they select the angle of polarization in tests of Bell's Inequalities Note that what determines the second experimenter's results is simply the first experimenter's measurement, which instantaneously collapses the superposition of twoparticle states into a particular state that is a product of independent particle states.] Since the theorem applies to any arbitrary physical theory consistent with the axioms, it would not even be possible to place the information into the universe's past in an ad hoc way. The argument proceeds from the KochenSpecker theorem, which shows that the result of any individual measurement of spin was not fixed (predetermined) independently of the choice of measurements. Conway and Kochen describe new bits of information coming into existence in the universe, and we agree that information is the key to understanding both EPR entanglement experiments and human free will. They say ...there will be a time t_{0} after x, y, z are chosen with the property that for each time t < t_{0} no such bit is available, but for every t > t_{0} some such bit is available.Their anthropomorphization of the universe as "taking a free decision" is too simplistic, but it is essential to solutions of the problem of measurement to recognize that the "cut" between the quantum world and the classical world is the moment when new information enters the universe irreversibly. In "The Strong Free Will Theorem," Conway and Kochen replace the FIN axiom with a new axiom called MIN, which asserts only that two experimenters separated in a spacelike way can make choices of measurements independently of each other. In particular, they are not asserting that all information must travel finitely fast; only the particular information about choices of measurements made by the two experimenters. Although Conway and Kochen do not claim to have proven free will in humans, they assert that should such a freedom exist, then the same freedom must apply to the elementary particles. What they are really describing is the indeterminism that quantum mechanics has introduced into the world. While indeterminism is a necessary precondition for human freedom, it is insufficient by itself to provide free will. See also the free will axiom
