I have never heard of any axiom of free will in quantum mechanics.

I think it is important to point out that no classical or modern theory gives us a good account of initial conditions of the past.
Not GR or the standard model.
If they did, then sure you could claim they were deterministic.

But GR and the standard model do not predict the past initial conditions, we still cannot claim to know nor do we have a complete account of the initial conditions.

So again, even if we take GR and SM to be fundamental theories, these theories are not sufficient to validate the claim that the universe is deterministic because these theories fall to predict what are the exact initial conditions of the past which have produced the universe and it's present state.

I have never heard of any axiom of free will in quantum mechanics. — m-theory

In Bell's ow words:

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the “decision” by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already “knows” what that measurement, and its outcome, will be.

Often the Free Will Axiom is called the "free will loophole", or the "free choice of detector orientations".

I think it is important to point out that no classical or modern theory gives us a good account of initial conditions of the past.
Not GR or the standard model.
If they did, then sure you could claim they were deterministic. — m-theory

I think you are missing the point. Given the conditions now, the past can be calculated by physical laws. This is how we know the big bang happened. Both General Relativity and the Standard Model have time reversal operators.

But GR and the standard model do not predict the past initial conditions, we still cannot claim to know nor do we have a complete account of the initial conditions. — m-theory

Umm, so why did we ever look for CMB?

Often the Free Will Axiom is called the "free will loophole", or the "free choice of detector orientations". — tom

You are misunderstanding Bell's statement. Bell's theorem is derived from the assumption of local hidden variables. Hence, if experiments show Bell's inequalities to be violate (as indeed Alain Aspect was the first to show experimentally) then it follows that either there a no hidden variables, or, if there are hidden variables, then measurement on one member of an entangled pair has a causal effect on the other element, and this causal effect is transmitted faster than light in violation of the special theory of relativity (and in violation of "local realism"). The assumption of superdeterminism -- that, somehow, the orientations of the measurement apparatuses as well as the measurement results all are predetermined in accordance with the statistical predictions of QM (an hypothesis rather akin to Leibniz's preestablished harmony) is one way to save local variables consistently with the predictions of QM, albeit a metaphysically extravagant and rather gratuitous way to do so.

Bell, like many physicists, also takes for granted that determinism and free will are incompatible and hence views the denial of determinism as being tantamount to the denial of human free will. He just assumes incompatibilism.

In summary, the "free will axiom" only is required provided "free will" is understood to mean "indeterminsm", which therefore excludes supercompatibilism. Since few physicists endorse superdeterminism (because they don't care for hidden variables or for local realism) they take QM to be an indeterministic theory, and, in this sense only, they are endorsing the "free will axiom" (a phrase that is almost never used in the literature).

"why did we ever look for CMB?"

To find out more about the early universe. The account that is obtained by studying the CMB is neither complete, nor is it of initial conditions. Rather it is a coarse-grained - ergo incomplete - account of conditions around the time of last scattering, which is some time after the earliest modelled time.

She can sit there all day saying she shouldn't have had that last sip of coffee or she should have had the right fare ready for the bus but she did and she couldn't not have. — Barry Etheridge

Pure supposition on your part.

You are misunderstanding Bell's statement. Bell's theorem is derived from the assumption of local hidden variables — Pierre-Normand

What are the axioms of Bell's Theorem?

Assume that "X" refers to a real thing. Now assume that John defines "X" as being Y, that Jane defines "X" as being Z, and that the real thing referred to by "X" cannot be both Y and Z. In this context it makes sense to argue that either John or Jane are wrong in their account of what it means to be an X. John is wrong if the real thing referred to by "X" isn't Y and Jane is wrong if the real thing referred to by "X" isn't Z. — Michael

That could be the case, but it could also be the case that x is both Y and Z, with John simply choosing to focus on Y in his concept and Jane choosing to focus on Z. (And by the way, for whatever reasons it became a trend, the convention is to use small letter x's, y's, etc. for individual entity variables, and capital letter Fs, Gs, etc. for property variables. But I'll stick with your letters so it's not confusing.)

Now assume that "X" doesn't refer to a real thing. Does it make sense to argue that either John or Jane are wrong in their account of what it means to be an X? Given that there is no real thing referred to by "X", there is no fact of the matter. — Michael

I'd not say that they're wrong, but they could be departing from a convention. For example, there's no real Sherlock Holmes. But if John says Sherlock Holmes lives at 22 Main Street, John is departing from the fictional conventions about where Sherlock Holmes lives.

It's not wrong to depart from a convention, but it's also not the case that there are no conventions just because we're talking about something with no real extension.

And after all, moral stances, definitions of terms, concepts, and all sorts of things have no real extensions. (I'm using "real" in the scholastic sense of "extramental" here, by the way.)

Of course, John could be wrong about something like the following: if he says, "In A. Conan Doyle's Sherlock Holmes stories, Holmes lives at 22 Main Street." In that case, he simply has a fact incorrect.

Likewise if someone were to say, "In most cultures, it is considered morally acceptable to commit murder."

In those cases, the proposition in question is about how someone thought or thinks about something, and there are facts about that.

Unless the term "free will" already refers to a real thing it doesn't seem to make sense to argue that one or the other is wrong in their account of what it means to have free will. The same is also true of the terms "choice" and "moral responsibility". — Michael

So from what I said above, we can see that people can't be wrong about what a term "means" (I'd say "how to define a term," as in my view, we can't literally share meaning, but that's another issue). However, people can match or not match a convention about the definition of a term, and they can be wrong or right about what a particular dictionary gives as a definition, or how a particular person defines a term, etc.

In the free will debate, some people seem to clearly be arguing from a position that's based on a very unconventional definition of "free will."

So if John defines "free will", "choice", and "moral responsibility" in such a way that they don't refer to real things, and if Jane defines "free will", "choice", and "moral responsibility" in such a way that they do refer to real things, what would John mean if he were to argue that Jane's account of what it means to have free will, choice, and moral responsibility are wrong? — Michael

Usually what people are getting at there is that the one person, so Jane in the scenario above, is using the terms unconventionally. Again, there is nothing wrong with using terms unconventionally, being unconventional, etc. It's just that in this case they'd be talking about different things, and Jane may not be engaging in the discussion as it had been previously established at all. She might basically be co-opting the terms to talk about something else instead (something that she believes is real contra views that she sees as mistaken).

It's certainly not the case that her account fails to describe the real things referred to by these terms. I — Michael

So, if Jane is using the terms unconventionally, where the convention is to refer to things that are fictional, she may be using the terms to refer to real things, but it's important to note that she's not using the terms to refer to what they really refer to or something like that. That's because there is no real reference. Again, reference is one of those things that does not occur extramentally, so there is no real reference. Jane can't be right that the terms refer to such and such, whereas John is wrong about the terms referring to such and such. There is no right or wrong there. Just conventional and unvonventional.

Of course, I don't agree with Wittgenstein, and I think that what's usually going on in these sorts of discussions isn't simply using words in different ways, but disagreements about just what is real.

Also, I'm an incompatibilist, for example (and an incompatibilist who believes that there is free will). I can never make any sense of compatibilism unless someone is redefining the terms so that we're not even talking about the same thing any longer.

I addressed all that at the end:

And if John were to say that Jane's "free will" isn't really free will, isn't he just saying that Jane's "free will" isn't what he (and, for the sake of argument, most others) mean by "free will"? If so, is this significant?

What makes the conventional sense of free will more important than the compatabilist sense? What makes the conventional sense of choice more important than the compatabilist sense? What makes the conventional sense of moral responsibility more important than the compatabilist sense?

And if the conventional sense of these things isn't more important than the compatabilist sense then why does it matter if we don't have the conventional sense of these things?

What makes anything more important than anything else is that the individual in question cares about it more. They can care about something more for innumerable reasons, and also for physical reasons that are not rational or sententially statable. "More important" is always to someone.

Also, I'm an incompatibilist, for example (and an incompatibilist who believes that there is free will). I can never make any sense of compatibilism unless someone is redefining the terms so that we're not even talking about the same thing any longer. — Terrapin Station

I had an interesting conversation the other day with someone who claimed to be a compatibilist, but after a rather uncomfortable exchange, he denied that we have free will. It was really strange. After my conversation with him, I feel I need to ask all compatiblists, "are you a compatibilist who accepts free will, or do you deny that we have free will?"

Are you sure he wasn't just denying libertarian free will?

If he was, he didn't make that clear. But that reminds me of the debate I had with another fellow who is convinced that both Dennett and Harris actually accept that free will is the case. I believe the main gist of that particular fellow's argument is that Harris just denies libertarian free will.

Harris actually makes it very clear that he believes free will is incompatible with determinism. Harris believes we are living in a strictly deterministic universe, and he clearly denies that we have free will (although he does suggest that all people need to act as if they have free will).

Care definitely should be taken when denying free will. I'm imagining someone who never had the courage to stand up for himself, and as an adult never moves out of his parent's house. He hears "we don't have free will", and thinks to himself, "oh, yeah, that explains it... where are those Cheetos?"

What are the axioms of Bell's Theorem? — tom

Bell's theorem just is the statement that the statistical predictions of QM are inconsistent with all local hidden variable theories. Since superdeterminism provides a loophole for the local hidden theorist who wants to hold fast to both QM and to local hidden variables, then you may say that the denial of superdeterminism is an axiom of Bell's theorem. What else you consider to be an axiom would depend how you are formalizing Bell's argument (in support of his conclusion) and what commonly agreed presupposition(s) you are attempting to question.

But you are ducking my main point that the denial or affirmation of superdeterminism has very little bearing on the issue of the freedom of the human will when you consider that there are compatibilist accounts of free will, on the one hand, and also that quantum indeterminacies are commonly regarded not to provide the sort of leeway that ascription of human freedom and responsibility require, on the other hand. Human freedom from predetermination isn't the freedom to behave in accordance to the result of God's dice throws on almost all accounts (if you would except accounts such as Robert Kane's quite sophisticated QM dependent version of libertarianism).

Bell's theorem just is the statement that the statistical predictions of QM are inconsistent with all local hidden variable theories. — Pierre-Normand

Since you refuse to provide the axioms of Bell's theorem, allow me:

1. Freedom of choice. The freedom to choose which experiment to perform independently of the object to be measured. i.e. The Free Will of the Experimenter

2. Measurement Independence. Future outcomes do not influence past settings - i.e. causality.

3. Locality.

4. Counterfactual Definiteness.

1. Freedom of choice. The freedom to choose which experiment to perform independently of the object to be measured. i.e. The Free Will of the Experimenter — tom

You are paying no attention whatsoever to the ongoing argument or to the philosophical issue about free will and determinism. Merely using bold characters doesn't validate your assumption of a crude equivalency between the affirmation of free will and the denial of superdeterminsm. What is assumed in order to derive the validity of Bell's theorem is that superdeterminism is false, not that human beings have free will. But the falsity of determinism just is generally assumed to be part of the standard understanding of QM; and if determinism is false then, a fortiory, so is superdeterminism. Superdeterminism just is an extravagant metaphysical doctrine devised as a loophole in order to save QM together with local hidden variables. What is assumed -- your so called "free will axiom" -- in order for Bell's argument to go through merely is that the setup of the measuring apparatus (e.g. the determination of which of two conjugate variables are being measured) together with the result of the measurement aren't predetermined.

In summary again, (1) since most physicists don't care at all for local hidden variables, they don't care for superdeterminism either. And (2) since the question of the compatibility of free will and determinism is central to the philosophical debate you can't crudely equivocate between "free will" and "indeterminism" without begging the question.

Since you refuse to provide the axioms of Bell's theorem, allow me:

1. Freedom of choice. The freedom to choose which experiment to perform independently of the object to be measured. i.e. The Free Will of the Experimenter

2. Measurement Independence. Future outcomes do not influence past settings - i.e. causality.

3. Locality.

4. Counterfactual Definiteness. — tom

I'm confused by this. Isn't Bell's theorem supposed to show that 1., 3., and 4. cannot all be true?

I'm confused by this. Isn't Bell's theorem supposed to show that 3. and 4. cannot both be true? — Michael

Not quite. It is rather supposed to show that those assumptions are jointly incompatible with the statistical predictions of QM. If you then accept the conclusion of "Bell's Theorem" (i.e. this statement of incompatibility) and wish to save the empirically verified predictions of QM (as you probably should) then you have to question at least one of those assumptions. (And keep in mind that "free will" in Tom's statement of the first "axiom" only refers to the lack of predetermination of the setup of the measurement apparatus.)

So I'm right to be confused with the claim that these are axioms of the theory?

So I'm right to be confused that these are all supposed to be axioms of the theory? — Michael

Yes it is confusing because Bell's theorem isn't a theory but rather a statement of incompatibility between a set of assumptions. Physicists who endorse the empirical and theoretical validity of QM seldom endorse assumptions (3) and (4) in Tom's table. (Those rather are consequences of local hidden variable theories that aim at reconciling QM with the intuitive "realist" assumptions of classical physics). So, to suggest that (1) is an "axiom" of QM just because it is an "axiom" of Bell's theorem is not just misleading, but confused.

As I have pointed out more than once, the free will axiom is implicit in all of science, and is made explicit in quantum mechanics, particularly Bell's theorem and the various other no-go theorems. It is just as much an axiom of QM as are states in (projective) Hilbert Space.

The simple fact is that of the four axioms of Bell's theorem that I gave, the first two are regarded as unquestionable by the majority of physicists, therefore it can *only* be the last two that provide the contradiction.

There are notable exceptions to this view. Gerard 't Hooft (if you don't know him, he is a Nobel Prize winning physicist, father of the Standard Model, and of the same stature as Hawking) takes the view that freedom and counterfactual definiteness are wrong. Here's a book he wrote on the subject:

https://arxiv.org/pdf/1405.1548v3.pdf

A more accessible blog on the matter is by Sabine Hossenfelder.

http://backreaction.blogspot.co.uk/2016/01/free-will-is-dead-lets-bury-it.html

Now, counterfactual definiteness can be a surprisingly slippery notion. My view is that when it is expressed in terms of possible measurements, then that statement is incompatible with the absence of free will.

So, what Bell's theorem purports to show is that local counterfactual definiteness is forbidden by quantum mechanics, while the axioms of freedom and causality are protected.

There is of course another way of rendering Bell's theorem impotent - the Everett Interpretation.

So I'm right to be confused with the claim that these are axioms of the theory? — Michael

There is a contradiction produced by accepting the 4 axioms. The solutions are:

1 Axiom 4 is wrong, leading to Copenhagen or Many Worlds.

2. Axiom 3 is wrong, leading to bizarre non-local contrivances.

3. Axiom 2 is wrong, leading to Transactional interpretation??????

4. Axiom 1 and 4 are wrong, leading to Superdeterminism or Many Worlds

Yes it is confusing because Bell's theorem isn't a theory but rather a statement of incompatibility between a set of assumptions. Physicists who endorse the empirical and theoretical validity of QM seldom endorse assumptions (3) and (4) in Tom's table. — Pierre-Normand

Quantum field theory is explicitly local. Copenhagen is local. Many Worlds is local. As a matter of fact it has been proved that QM is a local theory. No sane physicist gives up (3)(or 2)!

One positive aspect of super-determinism is that it brings QM into compatibility with General Relativity.

Quantum field theory is explicitly local. Copenhagen is local. Many Worlds is local. As a matter of fact it has been proved that QM is a local theory. No sane physicist gives up (3)(or 2)! — tom

What about last year's loophole-free Bell test that apparently supports quantum nonlocality?

What about last year's loophole-free Bell test that apparently supports quantum nonlocality? — Michael

Does it really? How?

Huh? How can a statement forming part of the exposition of the argument of a notional third party (in this case an extreme determinist) be a supposition on my part?

I don't know how, but that's what the scientist in charge said it did.

I don't know how, but that's that the scientist in charge said it did. — Michael

That's why I gave the axioms I listed earlier their proper name - axioms! Unfortunately the term "loophole" is used in two ways - to refer to the axioms themselves and to refer to the experimental difficulties.

The importance of the experiment you refer to, is that it closed two loopholes - i.e. two experimental difficulties were overcome. They were able to guarantee no-faster-than-light-communication (i.e. they closed the locality loophole) and they closed the "detection loophole", which is an experimental loophole relating to photons.

The experiment does not "support quantum nonlocality".

The importance of the experiment you refer to, is that it closed two loopholes - i.e. two experimental difficulties were overcome. They were able to guarantee no-faster-than-light-communication (i.e. they closed the locality loophole) and they closed the "detection loophole", which is an experimental loophole relating to photons.

The experiment does not "support quantum nonlocality". — tom

It does support non-locality, as Dr. Hanson says:

“These tests have been done since the late ’70s but always in the way that additional assumptions were needed,” Dr. Hanson said. “Now we have confirmed that there is spooky action at distance.”

Non-locality is not the same as faster-than-light communication. I'm sure you know that, which is why I don't know why you equated them above.

It does support non-locality, as Dr. Henson says: — Michael

Yes it does, but the mention of an "action at a distance" is misleading. Nonlocality has long been seen as a consequence of QM (ever since Niels Bohr replied to the paper by Einstein, Podolski and Rosen) and is commonly seen as having been demonstrated by the empirical verification of the violation of Bell's inequalities. However, this non-locality of QM must be understood merely as the denial of local realism and it doesn't entail "action at a distance" where such a phrase is meant to imply that there is a causal interaction taking place at a speed exceeding the speed of light.

See also the first answer to the question How to understand locality and non-locality in Quantum Mechanics?