The two theories that revolutionized physics in the twentieth century, relativity and quantum mechanics, are full of predictions that defy common sense. Recently, we used three such paradoxical ideas to prove “The Free Will Theorem” (strengthened here), which is the culmination of a series of theorems about quantum mechanics that began in the 1960s. It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if (...) the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. Our argument combines the well-known consequence of relativity theory, that the time order of space-like separated events is not absolute, with the EPR paradox discovered by Einstein, Podolsky, and Rosen in 1935, and the Kochen-Specker Paradox of 1967 (See [2].) We follow Bohm in using a spin version of EPR and Peres in using his set of 33 directions, rather than the original configuration used by Kochen and Specker. More contentiously, the argument also involves the notion of free will, but we postpone further discussion of this to the last section of the article. Note that our proof does not mention “probabilities” or the “states” that determine them, which is.. (shrink)

Quantum indeterminism may make available the option of an interactionism that does not have to pay the price of a force over and above those forces that are acknowledged in physics in order to explain how intentions can be physically effective. I show how this option might work in concrete terms and offer a criticism of it.

Conway and Kochen have presented a “free will theorem” [4, 6] which they claim shows that “if indeed we humans have free will, then [so do] elementary particles.” In a more precise fashion, they claim it shows that for certain quantum experiments in which the experimenters can choose between several options, no deterministic or stochastic model can account for the observed outcomes without violating a condition “MIN” motivated by relativistic symmetry. We point out that for stochastic models this conclusion is (...) not correct, while for deterministic models it is not new. In the way the free will theorem is formulated and proved, it only concerns deterministic models. But Conway and Kochen have argued [4, 5, 6, 7] that “randomness can’t help,” meaning that stochastic models are excluded as well if we insist on the conditions “SPIN”, “TWIN”, and “MIN”. We point out a mistake in their argument. Namely, the theorem is of the form deterministic model with SPIN & TWIN & MIN ⇒ contradiction , (1) and in order to derive the further claim, which is of the form stochastic model with SPIN & TWIN & MIN ⇒ contradiction , (2) Conway and Kochen propose a method for converting any stochastic model into a deterministic one [4]. (shrink)

One has it that earlier circumstances and the laws of nature uniquely determine later circumstances, and the other has it that past present and future all exist tenselessly in a ‘block universe,’ so that the passage of time and associated changes in the world are illusions or at best merely apparent.

I am very grateful to the commentators for their consideration of my target article. I found their comments thought-provoking and challenging, but I am not persuaded that any substantial departure is required from the views I expressed in the article. I will respond to each comment in turn, and then I will briefly review how my nine propositions have fared.

Libertarians claim that human behaviour is undetermined and cannot be predicted from knowledge of past history even in principle since it is based on the random movements of quantum mechanics. Determinists on the other hand deny thatmacroscopic phenomena can be activated bysub-microscopic events, and assert that if human action is unpredictable in the way claimed by libertarians, it must be aimless and irrational. This is not true of some types of random behaviour described in this paper. Random behaviour may make (...) one unpredictable to opponents and may therefore be rational. Similarly, playing a game with a mixed strategy may have an unpredictable outcome in every single play, but the strategy is rational, in that it is meant to maximize the expected value of an objective, be it private or social. As to whether the outcome of such behaviour is genuinely unpredictable as in quantum mechanics, or predictable by a hypothetical outside observer knowing all natural laws, it is argued that it makes no difference in practice, as long as it is not humanly predictable. Thus we have a new version of libertarianism which is compatible with determinism. (shrink)

Arguments pertaining to the mind-brain connection and to the physical effectiveness of our conscious choices have been presented in two recent books, one by John Searle, the other by Jaegwon Kim. These arguments are examined, and it is explained how the encountered difficulties arise from a defective understanding and application of a pertinent part of contemporary science, namely quantum mechanics. The principled quantum uncertainties entering at the microscopic levels of brain processing cannot be confined to the micro level, but percolate (...) up to the macroscopic regime. To cope with the conflict between the resulting macroscopic indefiniteness and the definiteness of our conscious experiences, orthodox quantum mechanics introduces the idea of agent-generated probing actions, each of which specifies a definite set of alternative possible empirically/experientially distinguishable outcomes. Quantum theory then introduces the mathematical concept of randomness to describe the probabilities of the various alternative possible outcomes of the chosen probing action. But the agent-generated choice of which probing action to perform is not governed by any known law or rule, statistical or otherwise. This causal gap provides a logical opening, and indeed a logical need, for the entry into the dynamical structure of nature of a process that goes beyond the currently understood quantum mechanical statistical generalization of the deterministic laws of classical physics. The well-known quantum Zeno effect can then be exploited to provide a natural process that establishes a causal psychophysical link within the complex structure consisting of a stream of conscious experiences and certain macroscopic classical features of a quantum mechanically described brain. This naturally created causal link effectively allows consciously felt intentions to affect brain activity in a way that tends to produce the intended feedback. This quantum mechanism provides an eminently satisfactory alternative to the classical physics conclusion that the physical present is 1 completely determined by the physical past, and hence provides a physicsbased way out of the dilemma that Searle and Kim tried to resolve by philosophical analysis.. (shrink)