We are living in interesting times:

Here we present a novel argument, showing that a subjective interpretation of the wave function can be ruled out as a consequence of the completeness of quantum theory. This allows us to establish that wave functions are physical properties, using only minimal assumptions. Specifically, the (necessary) assumptions are that quantum theory correctly predicts the statistics of measurement outcomes and that measurement settings can (in principle) be chosen freely.

Bold by me, of course. From arxiv.

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.

Bold by me. Also in arxiv.

Also from that article:

The third assumption is that measuring devices respond solely to the physical properties of the systems they measure. We do not assume underlying determinism.

Bold by me. Of course.

I’m not sure I understand the significance of the passages you cite to free will. Perhaps you can elaborate?

dougsmith - 08 December 2011 05:53 AM

I’m not sure I understand the significance of the passages you cite to free will. Perhaps you can elaborate?

I am still reading the articles myself with an open mind

I’ll come back to it later. (I am enjoying my day off because of the Immaculate Conception...)

In my humble opinion, quantum uncertainty has nothing to do with free will. By definition, it isn’t even close. If our wills were governed with quantum rules, we would have absolutely no control at all, being thrown every possible concevable direction at complete random. This is not ‘free’ in the least sense of the word. Free will is being able to do what I want when I want. That’s pretty much the complete opposite of quantum uncertainty; in fact, if free will were governed by quantum uncertainty, even the will itself would jump around at random in addition to the ability to act on it - the ability to act on our wills and to actually achieve them would be so infitessimal as to be literally nil.

In the first article I find:

- Freedom of choice: The measurement A can be chosen to be independent of any preexisting value, and hence in particular of Γ  (We note that, in [17], this assumption corresponds to the requirement that a quantum system can be freely prepared according to one of a number of predefined states.)

[17] is the other article, which states:

The second assumption is that it is possible to prepare multiple systems such that their physical properties are uncorrelated. Experimentalists aim to achieve this either by building and operating different copies of the same experimental apparatus, or by reusing the same apparatus after a sufficient time period has elapsed that they are confident the later run is independent of the earlier.

In other words, the observer can choose what to measure independent of what happens in the system under scrutiny.

However, the first article states:

The freedom of choice assumption is more difficult to probe experimentally, since it is stated in terms of Z, which is information in a hypothetical higher theory.  Nevertheless, it would be possible to falsify the assumption in specific cases, for example using a device capable of predicting the measurement settings before they were chosen.
(...)
the experimenter can freely choose his measurements (in a deterministic world, all measurement outcomes together form a complete list of physical properties that does not include the wave function, as argued above).

I read this as that any entanglement between system and observer has been dissolved. For that, compatibilist freedom is enough, as it is defined a few levels above the levels where quantum effects play any role.

TromboneAndrew - 08 December 2011 08:33 AM

In my humble opinion, quantum uncertainty has nothing to do with free will. By definition, it isn’t even close. If our wills were governed with quantum rules, we would have absolutely no control at all, being thrown every possible concevable direction at complete random. This is not ‘free’ in the least sense of the word. Free will is being able to do what I want when I want. That’s pretty much the complete opposite of quantum uncertainty; in fact, if free will were governed by quantum uncertainty, even the will itself would jump around at random in addition to the ability to act on it - the ability to act on our wills and to actually achieve them would be so infitessimal as to be literally nil.

Fully agree. But that is not exactly the point here. Freedom of choice is here an essential assumption for a kind of quantum realism, in the sense that the wave function’s statistical nature is not an expression of our lack of knowledge (called ‘subjectivism’ here), but is essential in nature.

GdB - 08 December 2011 09:09 AM

Fully agree. But that is not exactly the point here. Freedom of choice is here an essential assumption for a kind of quantum realism, in the sense that the wave function’s statistical nature is not an expression of our lack of knowledge (called ‘subjectivism’ here), but is essential in nature.

Oh.

So how does this relate to human free will, again? I note that you use the phrase ‘freedom of choice’ and I have no idea why you’re applying this term to quanta.

TromboneAndrew - 08 December 2011 01:08 PM

So how does this relate to human free will, again? I note that you use the phrase ‘freedom of choice’ and I have no idea why you’re applying this term to quanta.

Well, I am not applying it, the authors of the articles did, and therefore it got my interest. To broaden the whole question on physical laws in general:

How can we find out that laws of cause and effect, i.e. laws of nature hold? Just observation often is not enough. In experiments we change input parameters in a controlled way, and see how the output varies. But to be sure that we find laws of nature, i.e. laws that hold independent of our way of observing, it is necessary that we can change the input parameters freely. If the ‘observing system’ and the ‘observed system’ have dependencies, then we cannot be sure that we are influenced in such a way that we find something that looks like a law of nature, but in fact isn’t, because we cannot observe the system independently. So the interesting conclusion is that to be able to find laws of nature that are what they are independentof any observer, it presupposes free will from the side of the observer.

(As an aside: this point is forgotten by all neurologists who say we have no free will. At least they have free will, otherwise they can never be sure about their ‘causal findings’. And as a second aside: the societal justification for science is the promise of technology. Technology is applying laws of nature. It increases our ability to act, i.e our free will. Without technology science would have a similar status as art in our society, and would not get so much money as it gets today.)

Now quantum mechanics is at first sight a different case, as it seems the observer plays a more important role. Depending on the experiment I am measuring waves or particles. As a consequence, predictions using QM get statistical character. Now classically speaking, if my predictions have statistical character, these predictions show a lack of knowledge. Take weather predictions: it is my lack of knowing all details (every molecule in the air, the sea, the flux of the sun radiation etc etc) that I cannot make exact predictions. In both articles, such predictions are said to be subjective. The statistical character of the predictions is not an aspect of reality, but of the observer. Now the question posed in both articles: what is the case with the wave function? Is its statistical character subjective, or is it objective?

Both articles prove, based on a minimal set of assumptions, that the statistical character of the wave function is objective. And in both articles free will is one of these assumptions. But free will has an operational definition, exactly like I described in the first paragraph: that the observer can change its input parameters independent of the observed system. (In the first article, the only other assumption is that the predictions of QM are correct.)