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From my understanding, a Mixed Quantum State defines the set of all probable outcomes for a system, but isn't there still only one outcome determined through the succession of factors leading up to it (i.e., we may not be able to measure the absolute outcome of a system, but this still wouldn't deny the fact that it has an absolute outcome).

I understand that the state may not be calculated before hand due to various reasons, but does that not change the fact that there is only one definite outcome? In the end, there will only be one outcome for the system?

One of the main arguments that I've been confronted with is one stating that due to the unmeasurable aspects of a Quantum System, free will is plausible. To me, this seems like a major misinterpretation.

If free will were possible, wouldn't it require the ability for an event to occur without a predecessor, thereby violating causality?

  • I agree with @mixedmath. Quantum mechanics seems to be - as for most of interpretations - indeterminist in its core and that does leave an opening for free will. It doesn't mean that free will exists - perhaps it's all just random -, it just means that it is not ruled out. Just for the sake of example, we could state a dualistic soul able to change the probabilities associated with a particle and therefore change its state without being part of the causality chain in the material world. – Koeng Dec 16 '13 at 14:38
  • Related, see my answer here philosophy.stackexchange.com/a/31834/1547 – ThisIsNotAnId Jan 30 '16 at 18:18
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Certainly. Simply because one cannot both know position and velocity through measurement, for example, doesn't prevent the idea that if one did know both, then they could present with certainty the outcome. One might suggest a metaphor: if you were trying to aim a cannon and you measured exactly one of the angle of inclination or the amount of powder in the cannon, you would be presented with a range of possibilities and it might seem random. But if you did know both the angle and the powder, then you could predict the behavior of the shot with great accuracy. In the context of quantum mechanics, these theoretical additional pieces of information are called hidden variables.

Of course, this is a flawed metaphor. It happens to be more common for physicists to not believe this, or rather that it does not make sense to talk about both the position and the velocity of a particle with certainty, and instead you must think of them stochastically. Focusing on smaller subsystems causes certain parts to suddenly be more in focus and others collapse entirely. This is referred to as wave function collapse, and it seems to be at the core of both indeterminism in measurement and the indeterminism of a system. If we followed the heart of the argument, it might actually be the case that inability to measure things precisely is exactly what leads to quantum indeterminism, but I must admit that I do not know this.

There is some confusion on this, and this talked about at physics.se several different times (clicking on the related links on those is a good avenue for further exploration). There are even different interpretations of the same sets of facts.

Perhaps most important here is Bell's Theorem, which says roughly that a theory incorporating local hidden variables will never agree fully with quantum mechanics (note the local bit here). So following our local model of quantum mechanics, it truly does not make sense to talk about knowing both the position and the velocity (for example) of a particle, and thus wave function collapse is inevitable. And this brings us back to the Measurement problem.

So in short, the fact that we can't measure all quantities arbitrarily well leads to indeterminism, which leaves room for free will.

On the other hand, if we were capable of measuring all quantities arbitrarily well, and if the resulting model were completely deterministic (which it might be, as then there would be no need for wave function collapse), then it might not make sense to talk about free will. And thus much of what your physicist friends have said have a kernel of truth to them.

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    Good answer (+1), though I feel compelled to note that there is not very much room since there seems no place for will to intervene causally. – Rex Kerr Dec 16 '13 at 19:33
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    The situation is more trickier than that. In particular, consider that randomness is as different from free will as determinism. For example, if one can compute that the probability of a certain quantity X having values x1 and x2 is 0.5 each, that would reject the free will in selection of x1 versus x2 just as apriori knowledge that the value is x1 would. – Michael Dec 16 '13 at 22:52
  • I guess this is a problem that will continue to trouble humanity for a very long time. Maybe it is best left unknown. Thanks for taking the time to help with my problem! – John LaMontagne Dec 16 '13 at 23:31
  • Relating quantum to free will always strikes me as a composition fallacy – Sam Dec 18 '13 at 19:56
  • Position and velocity do not determine quantum state, so measuring them with any precision wouldn't make any difference for determinism. Quantum indeterminism has nothing to do with precision of measurements, it is inherent in the collapse process. Thinking of it "stochastically" is also erroneous, as shown exactly by the Bell theorem. "Positions", "velocities" and "particles" are labels in quantum mechanics assigned to items that have little to do with their classical counterparts, so discussion of determinism in such terms is not just misleading, but meaningless. – Conifold Jun 21 '15 at 20:53
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There is quite a lot involved here, and a simplistic answer would necessarily be misleading. Let me start though on a few points.

The first thing is not specific Quantum Mechanics, it's more about the false dichotomy between Determinism and Free Will. There are things that are not deterministic, random, but that randomness have nothing to do with free will. Imagine a perfectly random coin flip; does the lack of determinism in the way the coin lands refers to anybody's free will? Can you will the coin to land head up?

The second thing here is the distinction between quantum states and observables, which is at the heart of Quantum Mechanics. Although observables are not deterministic, and one often talks about expectations of observables, the dynamics of states in quantum mechanics is in fact deterministic. In Classical Mechanics the states (the parameters of Nature) and observables (what you can measure) coincide. In Quantum Mechanics the observables are largely inherited from Classical Mechanics (distance, velocity), but the setting of the dynamics, where the parameters on Nature lie, is different. That leads to measurable quantities being determined not by what things are at the moment (which is the current state of Nature), but with the average over all apriori possible state of nature relative to the observable being measured. This leads to a certain degree of randomness in the expected values of observables.

The third ingredient here stems from the intrusive nature of measurements. As Shakespeare would put it, "All the world's a stage, And all the men and women merely players". QM rejects the separation between the experimented and the experiment, makes sure that the men and women are parts of the World, not just the detached observers. Does it make QM more free will friendly? I think not: if you are a part of the Nature that is deterministic at quantum states level that would make your behaviour deterministic as well - perhaps not at the level of observables (how you act), but at the more basic level (why you act the way you act).

Overall, I don't see QM as the cause for celebration for the triumph of Free Will over Nature.

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    I wouldn't really say that a coin flip is random. The outcome of the coin flip is completely determined by factors that alter the coin during its 'trip' through the air. It may seem random to us due to the fact that we don't have the necessary information required to account for all of the different variables that are affecting the coin flip. – John LaMontagne Dec 16 '13 at 23:30
  • Is there more physics based literature that describes this view in more (mathematical) detail? – Dave Jun 19 '15 at 14:50
  • @Dave, there is another very interesting viewpoint on this in "Fabric of Reality" by David Deutsch. I enjoyed that very much. – Michael Jun 19 '15 at 15:54
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The experimental results relating to Bell's inequalities and Leggett inequalities rule out a wide class of "realist" physical theories; including ideas along the lines of "there [is] still only one outcome determined through the succession of factors leading up to it". All of the physical evidence is consistent with the idea that the quantum mechanical description, and it's intrinsic probabilistic nature, are all that there is.

The picture one can draw is that "quantum wierdness" (really a description of the world in terms of quantum fields) is the fundamental description of reality; the "normal" world of classical causation is just a collective epiphenomenon that "falls out" of the quantum mechanical description when you're dealing with macroscopic phenomenon. There's no point/value in trying to force the emergent property of (macroscopic) causality/determinism down to that level. I found this talk to be useful in clarifying this view.

I'm not sure if there is any relationship to be made between the indeterminacy of quantum mechanics and free will, but appealing to a hidden variable theory in the course of the philosophical discussion, without being knowledgeable about how these theorems and experiments severely constrain the possibilities, puts you on very shaky ground.

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