I Is Free Will a Foundational Assumption in Quantum Theory?

[Elias1960]

These local hidden variable theories aka determinism have gone out of favour since the ever growing efficency of the experimental setups has eliminated more than 99% of loopholes of Bell tests ...

So what if there are deterministic interpretations that violate Einstein causality (named "nonlocal" even if they are local but with higher maximal speed of information transfer)?

 

[EPR]

So what if there are deterministic interpretations that violate Einstein causality (named "nonlocal" even if they are local but with higher maximal speed of information transfer)?

This is specultaive. Relativity already showed that there is no observer independent object length or mass, distance, time, etc. so the concept of immaliable space is weakened if not downright eliminated. I don't think it makes sense to treat space as something fundamental - there are good indications that it is not. It’s very likely not a deep feature of reality.
Why are there nonlocal correleations in 4D spacetime?

 

[EPR]

'Einstein never got very far. Even today there are almost as many contending ideas for a quantum theory of gravity as scientists working on the topic. The disputes obscure an important truth: the competing approaches all say space is derived from something deeper—an idea that breaks with 2,500 years of scientific and philosophical understanding.'

https://www.scientificamerican.com/article/what-is-spacetime/

 

[Misty Rose]

I think Free Will only exists in a closed environment where no other factors can be introduced. Otherwise you are subject to outside influences. But life just isn't like that. In the game of Othello the black disk will remain black unless someone or something flips one and then all in it's path will flip at same time. Leaving no free will. There are so many outside factors that it makes it hard to imagine Free Will realistically. We are all pushed along and carried with the flow of everyday life. If you were to stop life would continue washing over you like waves. I suppose life is deffinately a force to be reckoned with for indeed time waits for no man. I suppose this is why Jesus claimed that some seed would fall between the cracks or be eaten by birds or burned by the sun while others would flourish in rich fertile soil.

 

[Elias1960]

This is specultaive. Relativity already showed that there is no observer independent object length or mass, distance, time, etc. so the concept of immaliable space is weakened if not downright eliminated. I don't think it makes sense to treat space as something fundamental - there are good indications that it is not.

This is also speculative. There is the straightforward, initial interpretation of relativity, where the ether distorts clocks and rulers and in this way prevents the measurement of absolute time and absolute distances, but they nonetheless exist. This interpretation can be extended to gravity too, with harmonic coordinates as the straightforward candidates for the Cartesian coordinates of the background and absolute time. Nothing in quantum theory suggests that this would have to be abandoned for the quantization of gravity.

The disputes obscure an important truth: the competing approaches all say space is derived from something deeper—an idea that breaks with 2,500 years of scientific and philosophical understanding.'

And it does it without any serious justification, simply based on GR metaphysics (not physics) being fashionable.

To justify proposals to reject such old common sense notions like the existence of space and time, one needs a serious justification. Extraordinary claims require extraordinary evidence. This extraordinary evidence would have to contain something close to impossibility theorems for theories with classical space and time. At least there should be quite obvious serious problems for any theory with classical space and time, with no plausible chance to solve them. This is certainly not the actual situation. Such theories exist, have been published, they follow a straightforward path known already by Lorentz. Simply not liking them because a curved spacetime is sort of more fascinating is not enough, but nothing better has been proposed yet against them.

 

[Lynch101]

In the Bell theorem, the "free will" assumption is really the assumption that there is no correlation between the choices of which observable will be measured on different subsystems. So yes, it is an assumption of the Bell theorem, but it is not directly related to the usual psychological notion of free will.

Just another question on this point, to see if I can understand it better.

Would the choices of which observable to be measured require a common cause in order to be considered correlated? Is that the position essentially what superdeterminism implies/requires?

 

[Elias1960]

Would the choices of which observable to be measured require a common cause in order to be considered correlated? Is that the position essentially what superdeterminism implies/requires?

No, in superdeterminism correlations do not need any explanation at all. Which makes it so attractive for the tobacco industry. I would guess their lobbyists have never heard about it, else they would use the fact that "in modern physics, superdeterminism is considered and discussed as a serious possibility", with reference to this thread, to show that the correlation between smoking and lung cancer proves nothing, and that all those who require some common cause explanation are simply retrogrades, comparable to ether freaks, who are unable to grasp modern physics.

 

[PeterDonis]

These are excerpts from the paper The Strong Free Will Theorem by Kochen and Conway that refute Determinism

None of this supports your claim that the axioms hold in classical physics. The whole context of all those papers is quantum physics.

There's no evidence to support determinism.

Which is irrelevant to the point I am making, that since we know our actual universe is quantum, not classical, the fact that determinism does not appear to hold in our actual universe (assuming that is true) does not in any way mean that classical physics is not deterministic. So your response to @A. Neumaier was wrong, as I said.

 

[Lynch101]

See e.g. my http://de.arxiv.org/abs/1006.0338

Just had a quick read of that paper Demystifier. My understanding of it is probably gone awry somwhere but the following lines jumped out at me:

“free will” (FW) – the ability of experimentalists to make free choices of initial conditions – is merely an illusion. As a consequence, by entangling a part of brain (responsible for the illusion of FW)
...
one should be aware that the assumption of FW plays an important role in the derivation of the Bell theorem
...
Some implications of this assumption in QM have been discussed in [1, 2] (see also [3, 4, 5] for critiques)

I scanned the referenced papers 3 & 4 and have read read through #5. It sounds to me like all of them except #5 advocate for the common sense notion of Free Will and pretty explicitly state that it is a fundamental axiom of Bell's theorem. The only paper that appears to argue for an alternative interpretation of "Free Will" in the manner you mentioned in post #2 is paper #5 ON THE FREE-WILL POSTULATE IN QUANTUM MECHANICS by Gerard 't Hooft who is the foremost proponent of Superdeterminism.

In that paper 't Hoofty outlines the role of "Free Will" in Bell's theorem. Is this an accurate characterisation?

A class of very important questions arose when John Bell formulated his famous inequalities[1]. Indeed, when one attempts to construct models that visualize what might be going on in a quantum mechanical process, one finds that deterministic interpretations usually lead to predictions that would obey his inequalities, while it is well understood that quantum mechanical predictions violate them. In attempts to get into grips with this situation, and to derive its consequences for deterministic theories, the concept of “free will” was introduced. Basically, it assumes that any ‘observer’ has the freedom, at all times and all places, to choose, at will, what variables to observe and measure. Clashes with Bell’s inequalities arise as soon as the observer is allowed to choose between sets of observables that are mutually non commuting.

 

[Lynch101]

Again, you can only get a probability distribution. So 52 cards are deterministic. 2-12 on a dice are deterministic. We can't calculate ... what number you will roll in a dice game...

So it's inherently in-deterministic and you can never reduce the outcomes to 1.

Apologies, this will probably seem like an incredibly basic question, but would it not be possible to predict what number you will roll in a dice game if you knew nearly all of the material information. If you were watching an impossibly high definition video and slowed it right down so that you could see the force that the die was being thrown, the angle it leaves the hand, the trajectory, couples with the relevant information about the air, the firmness of the table, etc. etc. If all of this was known, wouldn't it be possible to predict the roll of a die?

Apologies if it is somewhat off-topic and basic.

 

[Lynch101]

No, in superdeterminism correlations do not need any explanation at all. Which makes it so attractive for the tobacco industry. I would guess their lobbyists have never heard about it, else they would use the fact that "in modern physics, superdeterminism is considered and discussed as a serious possibility", with reference to this thread, to show that the correlation between smoking and lung cancer proves nothing, and that all those who require some common cause explanation are simply retrogrades, comparable to ether freaks, who are unable to grasp modern physics.

If the choices of which observable to be measured had a common cause would they be correlated?

 

[PeterDonis]

would it not be possible to predict what number you will roll in a dice game if you knew nearly all of the material information

It would depend on how sensitive the result of the roll was to the exact initial conditions, and how accurately you could measure those initial conditions.

 

[PeterDonis]

you can only get a probability distribution. So 52 cards are deterministic. 2-12 on a dice are deterministic. There's 2,598,960 poker hands that can occur and that's deterministic. Knowing this, we can calculate what probabilities can occur with certainty. We can't calculate who will get dealt what hands in a poker game or what number you will roll in a dice game no more than we can calculate if you're going to measure spin up or spin down.

These claims about macroscopic processes like shuffling cards, rolling dice, etc., are not necessarily true, because it's highly likely that quantum indeterminacy does not play any role in the outcome, unlike the case of, say, a Stern-Gerlach measurement of a particle's spin. It's entirely possible that, for example, the process of die rolling is insensitive enough to its exact initial conditions that an accurate enough measurement of those initial conditions could allow us to predict the result.

 

[EPR]

This is also speculative. There is the straightforward, initial interpretation of relativity, where the ether distorts clocks and rulers and in this way prevents the measurement of absolute time and absolute distances, but they nonetheless exist. This interpretation can be extended to gravity too, with harmonic coordinates as the straightforward candidates for the Cartesian coordinates of the background and absolute time. Nothing in quantum theory suggests that this would have to be abandoned for the quantization of gravity.

And it does it without any serious justification, simply based on GR metaphysics (not physics) being fashionable.

To justify proposals to reject such old common sense notions like the existence of space and time, one needs a serious justification. Extraordinary claims require extraordinary evidence. This extraordinary evidence would have to contain something close to impossibility theorems for theories with classical space and time. At least there should be quite obvious serious problems for any theory with classical space and time, with no plausible chance to solve them. This is certainly not the actual situation. Such theories exist, have been published, they follow a straightforward path known already by Lorentz. Simply not liking them because a curved spacetime is sort of more fascinating is not enough, but nothing better has been proposed yet against them.

The aether theory was discredited decades ago by experiment. Science is not bound by pedestrian common sense. The world would appear flat, and some still contend that it is, based on common sense.

None of the mainstream approaches to quantum gravity are treating space as fundamental.

 

[Elias1960]

It was not "the ether", but a large group of particular ether theories, which have been empirically falsified by various experiments. The Lorentz ether, which is essentially nothing but a name for SR with a preferred frame, was, together with SR in the spacetime interpretation, not among them.

The Einstein equations of GR also allow for a generalization of the Lorentz ether to gravity, with harmonic coordinates defining the preferred coordinates. So, the generalization to relativistic gravity is also unproblematic, and gives a theory with some minor differences (not allowing wormholes and causal loops) but otherwise indistinguishable from GR. Feel free to provide here the evidence against this interpretation of the GR equations.

Then, I have in no way suggested that science should be bound by common sense. But if something is in conflict with common sense, this is an extraordinary claim, thus, requires extraordinary evidence. This evidence was provided against flat Earth theory.

Moreover, it is not fair against common sense to claim that flat Earth theory is required by common sense. Spherical Earth is easy enough given what we see about Sun, moon, and planets that it was sufficient for the Ancient Greeks to find it.

 

[PeterDonis]

The Einstein equations of GR also allow for a generalization of the Lorentz ether to gravity, with harmonic coordinates defining the preferred coordinates.

Can you give a reference for this theory?

 

[Elias1960]

Can you give a reference for this theory?

arxiv:gr-qc/0205035

What I reference here as the interpretation of the Einstein equations would be the limit $\Xi,\Upsilon \to 0$ of the equations of that theory.

 

[bhobba]

Is the freedom of the mind the fundamental assumption in QM then and in what sense would you say that "the mind" is free?

No its not. The entire mathematical machinery of QM is also needed and how you derive that from free will beats me. Even defining free will - well philosophers haven't solved that one. I know the history of how it entered discussions about QM and its now generally accepted it was a mistake by the great Von-Neumann - not the only one he made in QM either.

Thanks
Bill

 

[bhobba]

Can you give a reference for this theory?

It's GLET developed by Ilja Schmelzer who occasionally posts here:
https://ilja-schmelzer.de/gravity/
Its been around for a while but hasn't really taken off in any way. That doesn't make it wrong of course - but its definitely a backwater. Yes its limit is LET, but that does not change the fact the aether is superfluous in SR - SR follows from basic symmetries of inertial frames and the POR. LET was not proven wrong - simply superseded by something simpler in its assumptions, with those assumptions having direct experimental support, which the aether does not.

Thanks
Bill

 

[bhobba]

This would mean there's some mechanism that knows the Experimenter's choice

That is a logical absurdity. Determinism and choice are mutually contradictory. Determinism means initial conditions determine everything - the concept of choice does not exist. What we do know is chaos does exist so in practical terms it is impossible to predict everything even if the world is deterministic. We can never know initial conditions with exact accuracy and those inaccuracies grow to the point all we can predict is probabilities just like if it was probabilistic in the first place.

I still have zero idea how to even define free will. It looks like one of those concepts such as reality we have an intuitive idea of, but pinning down exactly has not been possible.

The free will theorem is based on assumptions of dubious validity - eg 'There is a maximal speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.' It does not rest on causality eg Newtonian gravity is a deterministic theory that is causal yet the speed of propagation is infinite. Move an object and all other objects are affected instantaneously. But even more basic is although called the free will theorem, it does not depend on any assumption of free will as generally intuitively understood, or directly support any conclusion about free will.

To be blunt in my view the theorem is simply semantics about a not generally accepted definition of what free will is proving something absurd - electrons having free will. All that shows is the concept of free will used in the theorem is not a reasonable way to look at it.

Thanks
Bill

 

[A. Neumaier]

That's the point though. In the classical case we can consider the imprint in the device as some kind of approximation of an event that occurred in the system. This is because all random variables in the classical case can be considered as functions on a space of outcomes. Thus we have some notion of the events of microsystem when no external system is present to register them.

Not really. We have measurement results (aka events) only after we specify what in the classical universe is the measurement device and how it is supposed to measure which system of interest. This is external to the Laplacian description of the universe by positions and momenta. Thus measurement theory in a classical universe needs as much externals (i.e., the Heisenberg cut) as measurement theory in a quantum universe.
The properties of the underlying probability theory are secondary to that.

So quantum theory provides a stochastic description of a system-external system interaction when supplied with a choice of external system, but it is intrinsically incapable of modelling that choice of external system. Moreover this is a feature of any non-Kolmogorovian probability theory.

This statement is interpretation dependent. For example, it does not hold in the thermal interpretation, where modeling both system and external system is done inside the quantum universe.

 

[DarMM]

Not really. We have measurement results (aka events) only after we specify what in the classical universe is the measurement device and how it is supposed to measure which system of interest. This is external to the Lapalcian description of the universe by positions and momenta. Thus measurement theory in a classical universe needs as much externals (i.e., the Heisenberg cut) as measurement theory in a quantum universe.
The properties of the underlying probability theory are secondary to that.

Do you have a reference for this?

Yes defining the measured system and measuring system split is required for a measurement theory. However since all properties of the measured system have a single Boolean algebra the device events can be seen to be approximate recordings of events occurring in the system alone. In Quantum Theory there are no events for the system alone, you can't consider the measurement result to be an approximation of some property, even a randomly driven one, in the system alone. The idea that the underlying probability theory is irrelevant seems hard to support to me in this case. It's the underlying probability theory that drives results like contextuality that utterly change the notion of measurement for most authors.

This statement is interpretation dependent. For example, it does not hold in the thermal interpretation, where modeling both system and external system is done inside the quantum universe.

Yes of course, I indicated this initially that I was speaking of QM viewed as a probability theory not the quantum state viewed as a real wave or some such representational view.

 

[A. Neumaier]

Do you have a reference for this?

No. But this needs no reference as it is obvious. Indeed classical multiparticle dynamics is chaotic but deterministic, and has no intrinsic notion of one part measuring another. So something must be added from the outside to talk about any of probability or measurement.

Yes defining the measured system and measuring system split is required for a measurement theory. However since all properties of the measured system have a single Boolean algebra the device events can be seen to be approximate recordings of events occurring in the system alone.

Not in a classical universe. Nothing about the measured system can be considered to be recorded even approximately unless you specify what recording a property of the measured system means in terms of the measuring system. You still need to specify an outcome space, but even what is an outcome - neither exists in the Laplacian universe by itself.

I was speaking of QM viewed as a probability theory not the quantum state viewed as a real wave or some such representational view.

QM is not primarily a probability theory but a dynamical theory of Nature. Reducing it to noncommutative probability theory (a mathematical discipline) means abstracting from the real content, eliminating all physics. It is analogous to reducing classical mechanics to Kolmogorov probability theory. In both cases, little is left of the substance.

 

[PeroK]

Apologies, this will probably seem like an incredibly basic question, but would it not be possible to predict what number you will roll in a dice game if you knew nearly all of the material information. If you were watching an impossibly high definition video and slowed it right down so that you could see the force that the die was being thrown, the angle it leaves the hand, the trajectory, couples with the relevant information about the air, the firmness of the table, etc. etc. If all of this was known, wouldn't it be possible to predict the roll of a die?

Apologies if it is somewhat off-topic and basic.

The difficulty is not to "predict" the role of the die after it's been thrown, but before it's been thrown!

 

[PeroK]

These claims about macroscopic processes like shuffling cards, rolling dice, etc., are not necessarily true, because it's highly likely that quantum indeterminacy does not play any role in the outcome, unlike the case of, say, a Stern-Gerlach measurement of a particle's spin. It's entirely possible that, for example, the process of die rolling is insensitive enough to its exact initial conditions that an accurate enough measurement of those initial conditions could allow us to predict the result.

It depends what you mean by initial conditions. You might claim to be able to predict whether a penalty in a soccer match is scored or not. But, if you wait to see which way the ball is kicked and which way the goalkeeper is moving, I don't consider that removes the fundamental uncertainty.

 

[PeroK]

If the choices of which observable to be measured had a common cause would they be correlated?

Not necessarily. For example, you could generate a sequence from the digits of ππ and another sequence from the digits of ee.
These two sequences of digits would be uncorrelated, even though they are completely determined in advance.

PS for further insight into the difference between indeterminacy and randomness look up the definition of "normal number".

 

[DarMM]

No. But this needs no reference as it is obvious.
...
QM is not primarily a probability theory but a dynamical theory of Nature. Reducing it to noncommutative probability theory

The point here isn't to say that QM is nothing but noncommutative probability theory, obviously there is much more to it than that. However it is the non-Boolean nature of the underlying probability that changes the notion of measurement in the theory, by introducing issues like contextuality. I do not consider it "obvious" that these seismic shifts in the ability to perform property assignment due to the non-Boolean structure cause no difference in the notion of measurement.

Nothing about the measured system can be considered to be recorded even approximately unless you specify what recording a property of the measured system means in terms of the measuring system. You still need to specify an outcome space, but even what is an outcome - neither exists in the Laplacian universe by itself.

Again this goes against most of what I've read where by in a classical theory one can consider there to be events in the absence of devices and measuring systems.

 

[Lord Jestocost]

Even defining free will - well philosophers haven't solved that one.

Exactly. Nevertheless, regarding the "freedom of choice", there is an interesting point of view.

Hans Primas in „Hidden Determinism, Probability, and Time’s Arrow“ (Section 10 Experimental Science Requires Freedom of Action):

"At present the problem of how free will relates to physics seems to be intractable since no known physical theory deals with consciousness or free will. Fortunately, the topic at issue here is a much simpler one. It is neither our experience of personal freedom, nor the question whether the idea of freedom could be an illusion, nor whether we are responsible for our actions. The topic here is that the framework of experimental science requires a freedom of action in the material world as a constitutive presupposition. In this way “freedom” refers to actions in a material domain which are not governed by deterministic first principles of physics.

To get a clearer idea of what is essential in this argument we recall that the most consequential accomplishment by Isaac Newton was his insight that the laws of nature have to be separated from initial conditions. The initial conditions are not accounted for by first principles of physics, they are assumed to be “given”. In experimental physics it is always taken for granted that the experimenter has the freedom to choose these initial condition, and to repeat his experiment at any particular instant. To deny this freedom of action is to deny the possibility of experimental science.

In other words, we assume that the physical system under investigation is governed by strictly deterministic or probabilistic laws. On the other hand, we also have to assume that the experimentalist stands out of these natural laws. The traditional assumption of theoretical physics that the basic deterministic laws are universally and globally valid for all matter thus entails a pragmatic contradiction between theory and practice. A globally deterministic physics is impossible.“

[PDF]Hidden Determinism, Probability, and Time's Arrow - Core

 

[A. Neumaier]

this goes against most of what I've read where by in a classical theory one can consider there to be events in the absence of devices and measuring systems.

This is just because, as I had already mentioned, nobody ever really addressed the classical version of the quantum measurement problem. Instead it is simply assumed that the measuring device somehow acquires the measurement value, in principle with arbitrary accuracy and without backreaction to the system measured. This is a Platonic notion of measurement, looking into God's cards so to say. In this case you may say that the events are the properties of the collection of trajectories of the particles making up the system measured. You (like everyone else in the past) are treating classical mechanics exclusively from this Platonic perspective, while you consider quantum mechanics on a different footing, e.g., by allowing for microscopic descriptions of the measuring device, or even a hierarchy of these. This gives a distorted picture of the classical vs. quantum theme.

But for a system consisting of a few interacting atoms it is impossible to measure (from within a classical universe) most of these properties as if they were unobserved, as the coupling to the measuring device distorts the trajectories as in the quantum case. This proves that classical measurement is nontrivial. Realistic measurement in a classical universe would have to consider how some observable of a classical microscopically described measuring device acquires a value correlated with some property of the observed system. The outcome space is then the range of that observable - which is not necessarily that of the property considered. Thus one needs considerable extra structure...

 

[A. Neumaier]

In experimental physics it is always taken for granted that the experimenter has the freedom to choose these initial condition, and to repeat his experiment at any particular instant. To deny this freedom of action is to deny the possibility of experimental science.

No. Part of experimental physics is to figure out which part of the initial condition can be manipulated in such a way that desired experiments are possible. Often this is the most difficult aspect of an experiment. Calibration experiments (such as various kinds of quantum tomography) are even set up to discover the initial conditions of a source through appropriate measurements.