Free Choice of the Experimenter
"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 The question was whether, as to the occurrence of individual effects, we should adopt a terminology proposed by Dirac, that we were concerned with a choice on the part of "nature" or, as suggested by Heisenberg, we should say that we have to do with a choice on the part of the "observer" constructing the measuring instruments and reading their recording. Any such terminology would, however, appear dubious since, on the one hand, it is hardly reasonable to endow nature with volition in the ordinary sense, while, on the other hand, it is certainly not possible for the observer to influence the events which may appear under the conditions he has arranged. To my mind, there is no other alternative than to admit that, in this field of experience, we are dealing with individual phenomena and that our possibilities of handling the measuring instruments allow us only to make a choice between the different complementary types of phenomena we want to study. 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 non-commuting) 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 low-energy long-wavelength 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 high-energy, short wavelength photon was used (e.g., a gamma-ray), 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 well-known 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 Any remaining appearance of arbitrariness concerns merely our freedom of handling the measuring instruments characteristic of the very idea of experiment. In fact, the renunciation in each experimental arrangement of the one or the other of two aspects of the description of physical phenomena, - the combination of which characterizes the method of classical physics, and which therefore in this sense may be considered as complementary to one another, - depends essentially on the impossibility in the field of quantum theory, of accurately controlling the reaction of the object on the measuring instruments, i.e., the transfer of momentum in case of position measurements, and the displacement in case of momentum measurements. Just in this last respect any comparison between quantum mechanics and ordinary statistical mechanics, - however useful it may be for the formal presentation of the theory, — is essentially irrelevant. Indeed we have in each experimental arrangement suited for the study of proper quantum phenomena not merely to do with an ignorance of the value of certain physical quantities, but with the impossibility of defining these quantities in an unambiguous way. The last remarks apply equally well to the special problem treated by Einstein, Podolsky and Rosen, which has been referred to above, and which does not actually involve any greater intricacies than the simple examples discussed above. The particular quantum-mechanical state of two free particles, for which they give an explicit mathematical expression, may be reproduced, at least in principle, by a simple experimental arrangement, comprising a rigid diaphragm with two parallel slits, which are very narrow compared with their separation, and through each of which one particle with given initial momentum passes independently of the other. If the momentum of this diaphragm is measured accurately before as well as after the passing of the particles, we shall in fact know the sum of the components perpendicular to the slits of the momenta of the two escaping particles, as well as the difference of their initial positional coordinates in the same direction; while of course the conjugate quantities, i.e., the difference of the components of their momenta, and the sum of their positional coordinates, are entirely unknown.* In this arrangement, it is therefore clear that a subsequent single measurement either of the position or of the momentum of one of the particles will automatically determine the position or momentum, respectively, of the other particle with any accuracy; at least if the wave-length corresponding to the free motion of each particle is sufficiently short compared with the width of the slits. As pointed out by the named authors, we are therefore faced at this stage with a completely free choice whether we want to determine the one or the other of the latter quantities by a process which does not directly interfere with the particle concerned. Like the above simple case of the choice between the experimental procedures suited for the prediction of the position or the momentum of a single particle which has passed through a slit in a diaphragm, we are, in the "freedom of choice" offered by the last arrangement, just concerned with a discrimination between different experimental procedures which allow of the unambiguous use of complementary classical concepts. In fact to measure the position of one of the particles can mean nothing else than to establish a correlation between its behavior and some instrument rigidly fixed to the support which defines the space frame of reference. Under the experimental conditions described such a measurement will therefore also provide us with the knowledge of the location, otherwise completely unknown, of the diaphragm with respect to this space frame when the particles passed through the slits. Indeed, only in this way we obtain a basis for conclusions about the initial position of the other particle relative to the rest of the apparatus. By allowing an essentially uncontrollable momentum to pass from the first particle into the mentioned support, however, we have by this procedure cut ourselves off from any future possibility of applying the law of conservation of momentum to the system consisting of the diaphragm and the two particles and therefore have lost our only basis for an unambiguous application of the idea of momentum in predictions regarding the behavior of the second particle. Conversely, if we choose to measure the momentum of one of the particles, we lose through the uncontrollable displacement inevitable in such a measurement any possibility of deducing from the behavior of this particle the position of the diaphragm relative to the rest of the apparatus, and have thus no basis whatever for predictions regarding the location of the other particle. From our point of view we now see that the wording of the above-mentioned criterion of physical reality proposed by Einstein, Podolsky and Rosen contains an ambiguity as regards the meaning of the expression "without in any way disturbing a system." Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system. Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete. On the contrary this description, as appears from the preceding discussion, may be characterized as a rational utilization of all possibilities, of unambiguous interpretation of measurements, compatible with the finite and uncontrollable interaction between the object and the measuring instruments in the field of quantum theory. In fact, it is only the mutual exclusion of any two experimental procedures, permitting the unambiguous definition of complementary physical quantities, which provides room for new physical laws the coexistence of which might at first sight appear irreconcilable with the basic principles of science. It is just this entirely new situation as regards the description of physical phenomena that the notion of complementarity aims at characterizing. 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 Stern-Gerlach experiment, for example, the experimenter is " free to choose" to measure, for example, the z-component of the spin, rather than the x- or y-component. This will influence (but not determine) quantum level events in the following ways:
Bell's Theorem and Free ChoiceIn 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 two-particle 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.
1. SPIN: Measuring the square of the component of spin of certain elementary particles of spin one, taken in three orthogonal directions, results in a permutation of (1,1,0). 2. TWIN: It is possible to "entangle" two elementary particles, and separate them by a significant distance, so that they give the same answers to corresponding questions. The squared spin results are the same if measured in parallel directions. If the first experimenter A (on Earth) performs a triple experiment for the frame (x, y, z), producing the result x → j, y → k, z → l while the second experimenter B (on Mars, at least 5 light minutes away) measures a single spin in direction w, then if w is one of x, y, z, its result is that w → j, k, or l, respectively. 3. FIN: There is a finite upper bound to the speed with which information can be effectively transmitted. Conway and Kochen say this is a consequence of "effective causality." [But the collapse of the probability amplitude wave function is instantaneous and not so limited. ]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. Thus the theorem asserts that if experimenters have a certain property, then spin 1 particles have exactly the same property. Since this property for experimenters is an instance of what is usually called “free will,” we find it appropriate to use the same term also for particles.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 two-particle 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 Kochen-Specker theorem, which shows that the result of any individual measurement of spin was not fixed (pre-determined) 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 t0 after x, y, z are chosen with the property that for each time t < t0 no such bit is available, but for every t > t0 some such bit is available. But in this case the universe has taken a free decision at time t0, because the information about it after t0 is, by definition, not a function of the information available before t0!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 space-like 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