Is Free Will a Foundational Assumption in Quantum Theory?

[A. Neumaier]

I know, but that's the way they feel, and that's what they say they believe.

That's what they say, I have had hundreds of conversations along these lines with all kinds of people that believe that they have Free Will, no matter if they are scientist or not, religious or not.

This just means that they don't care about (or are confused about) the consistency of their beliefs. Most people are inconsistent in their beliefs. Rationality is exercised only where convenient.

 

[mattt]

This just means that they don't care about (or are confused about) the consistency of their beliefs. Most people are inconsistent in their beliefs. Rationality is exercised only where convenient.

I agree completely.

 

[Morbert]

Folk intuitions about free will tend to lean compatibilist (free will is compatible with determinism), but tendencies can vary depending on the scenario being posed when discerning intuitions.

https://www.tandfonline.com/doi/abs/10.1080/09515080500264180

 

[Demystifier]

Do you really think that a child is not free in its decisions just because we can predict that it will say yes when it is asked whether it likes to have ice cream?

Loosely speaking, yes, I do think that. I think my free will is just an a posteriori interpretation of my acts, emerging from my inability to pinpoint to the exact reason why have I chosen this rather than that.

 

[A. Neumaier]

I think my free will is just an a posteriori interpretation of my acts, emerging from my inability to pinpoint to the exact reason why have I chosen this rather than that.

Ah, so according to you, the freedom of will is not in the actions (which may well be perfectly determined by Nature) but how you interpret them a posteriori. This is of course also a resolution of the problem!?

 

[Demystifier]

Ah, so according to you, the freedom of will is not in the actions (which may well be perfectly determined by Nature) but how you interpret them a posteriori. This is of course also a resolution of the problem!?

In my opinion, yes.

 

[A. Neumaier]

I think my free will is just an a posteriori interpretation of my acts, emerging from my inability to pinpoint to the exact reason why have I chosen this rather than that.

so according to you, the freedom of will is not in the actions (which may well be perfectly determined by Nature) but how you interpret them a posteriori. This is of course also a resolution of the problem!?

In my opinion, yes.

Is your a posteriori interpretation of your acts a mental activity in the Platonic worlds of ideas, independent of quantum physical laws?

 

[Demystifier]

Is your a posteriori interpretation of your acts a mental activity in the Platonic worlds of ideas, independent of quantum physical laws?

At the fundamental level it isn't, but at the emergent level it may look so.

 

[A. Neumaier]

At the fundamental level it isn't, but at the emergent level it may look so.

So at the fundamental level, there is no free will in your sense?

 

[mattt]

I think that he acknowledges that everything he does and the thoughts and the feelings that arise in Consciousness, is probably the end result of deterministic and/or stochastic processes, just that we don't have, subjectively, access to those processes, to that complete information. So subjectively, because of lack of complete information, we just don't know where it all comes from, and can attain to the illusion that maybe it is something else.

 

[Demystifier]

So at the fundamental level, there is no free will in your sense?

That's right. But of course, there is "free will" in the sense of post #2.

 

[PeterDonis]

Compatibilism is an attitude that I never understood.

One way of looking at it is that it is just recognizing what the terms "I" or "you" and "free will" actually refer to. You are not some abstract disembodied essence with magical powers. You are a physical thing, made of physical parts, that obey physical laws. So of course any interpretation of "free will" is going to have to be compatible with those facts, and any valid referent of the term "free will" is going to have to be some physical process going on in the physical system that is "you".

I think my free will is just an a posteriori interpretation of my acts, emerging from my inability to pinpoint to the exact reason why have I chosen this rather than that.

And compatibilism is simply the view that if your acts can be validly given such an interpretation, then they are acts of free will. You don't have to have magical non-physical powers to have free will.

Another way of putting it would be to say that the kind of "free will" I have just described, while it might not be what many people thought they meant by "free will", is still sufficient, because it gives us all the capability we need in practice to have the things that "free will" is supposed to give us.

 

[DarMM]

Just to say quantum theory taken as a probability theory is more than just stochastic. A quantum system constitutes a stochastic process only when provided with another system to define the space of outcomes. With no second system a given quantum system isn't even random/stochastic, there are no events in the formalism under such a scenario.

I don't know what, if anything, this means for the conventional notion of free will.

 

[Demystifier]

Just to say quantum theory taken as a probability theory is more than just stochastic. A quantum system constitutes a stochastic process only when provided with another system to define the space of outcomes. With no second system a given quantum system isn't even random, there are no events in the formalism under such a scenario.

Exactly. I would even go that far to say that Copehagen interpretation is not a stochastic interpretation. Truly stochastic interpretations are GRW interpretation and Nelson interpretation.

 

[Demystifier]

One way of looking at it is that it is just recognizing what the terms "I" or "you" and "free will" actually refer to. You are not some abstract disembodied essence with magical powers. You are a physical thing, made of physical parts, that obey physical laws. So of course any interpretation of "free will" is going to have to be compatible with those facts, and any valid referent of the term "free will" is going to have to be some physical process going on in the physical system that is "you".

And compatibilism is simply the view that if your acts can be validly given such an interpretation, then they are acts of free will. You don't have to have magical non-physical powers to have free will.

Another way of putting it would be to say that the kind of "free will" I have just described, while it might not be what many people thought they meant by "free will", is still sufficient, because it gives us all the capability we need in practice to have the things that "free will" is supposed to give us.

Could it be interpreted by saying that free will is an emergent higher level phenomenon, like e.g. a tiger? At the fundamental microscopic level there is no free will and there are no tigers, but at the higher level of organization of matter there are structures that can be interpreted as free wills or as tigers. If that's what compatibilism means, then I'm OK with it.

 

[A. Neumaier]

I would even go that far to say that Copenhagen interpretation is not a stochastic interpretation.

But Born got in 1954 the Nobel prize ''for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction''!

 

[Demystifier]

But Born got in 1954 the Nobel prize ''for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction''!

statistical $\neq$ stochastic

 

[A. Neumaier]

statistical $\neq$ stochastic

The former is based on the latter:
https://en.wikipedia.org/wiki/Statistical_model
''in a statistical model specified via mathematical equations, some of the variables do not have specific values, but instead have probability distributions; i.e. some of the variables are stochastic.''

 

[Demystifier]

The former is based on the latter:
https://en.wikipedia.org/wiki/Statistical_model
''in a statistical model specified via mathematical equations, some of the variables do not have specific values, but instead have probability distributions; i.e. some of the variables are stochastic.''

Well, it's a matter of semantics. When I say "stochastic", what I have in mind is a stochastic process, meaning something akin to Wiener process, Brownian motion, Ito calculus, etc.

 

[A. Neumaier]

Well, it's a matter of semantics. When I say "stochastic", what I have in mind is a stochastic process, meaning something akin to Wiener process, Brownian motion, Ito calculus, etc.

One has that also in a sequence of quantum measurements...

 

[Demystifier]

One has that also in a sequence of quantum measurements...

Yes, but not in the meantime between the two measurements. In the meantime the system is in an undefined state (according to Copenhagen interpretation), which cannot be said for stochastic processes in the usual sense.

 

[DarMM]

To be completely clear this is part of the formalism. Another system constitutes the POVM selected for the system under study. Only a POVM provides a well defined statistical model, the full algebra of projectors does not.

 

[A. Neumaier]

Yes, but not in the meantime between the two measurements. In the meantime the system is in an undefined state (according to Copenhagen interpretation), which cannot be said for stochastic processes in the usual sense.

There are also discrete stochastic processes. They are much used in practical time series analysis, where one only has access to a discrete series of measurements. Continuous stochastic processes arise in the quantum mechanics of continuous measurements.

 

[A. Neumaier]

To be completely clear this is part of the formalism. Another system constitutes the POVM selected for the system under study. Only a POVM provides a well defined statistical model, the full algebra of projectors does not.

Repeated application of Born's rule with collapse, as usually stated since Heisenberg and Dirac, already provides a well defined (though too idealized) statistical model involving a discrete stochastic process.

 

[DarMM]

Repeated application of Born's rule with collapse, as usually stated since Heisenberg and Dirac, already provides a well defined (though too idealized) statistical model involving a discrete stochastic process.

Of course, that's (in general) a sequence of POVMs. What distinction are you pointing out?

 

[A. Neumaier]

Of course, that's (in general) a sequence of POVMs.

Not quite. A POVM neither specifies the observed value nor the posterior state. To have a well-defined and realistic discrete stochastic process, one needs more than a POVM, namely a quantum instrument.

What distinction are you pointing out?

The main point was that no POVMs are needed to have stochastic processes in a quantum setting. Note that POVMs for quantum measurement were introduced in 1968, long after Born obtained his Nobel prize.

 

[DarMM]

Not quite. A POVM neither specifies the observed value nor the posterior state. To have a well-defined and realistic discrete stochastic process, one needs more than a POVM, namely a quantum instrument.

Of course true. I was only referring to the need for an external system to define an outcome space. That system being represented by a choice of POVM. I wasn't saying you only need a POVM, you of course need the state as well, etc. Rather it is that only after the selection of a POVM is the statistical model defined, unlike the classical case where no such selection is needed on the algebra of random variables.

The main point was that no POVMs are needed to have stochastic processes in a quantum setting. Note that POVMs for quantum measurement were introduced in 1968, long after Born obtained his Nobel prize.

Again of course. My point was more so that one needs something to select an outcome space for the system in order to have a well defined statistical model, unlike in the classical probabilistic case where events are defined without such a choice of an auxiliary system.
It's only in general that the auxiliary system is represented by a POVM, I wasn't claiming that nobody had a statistical understanding of QM prior to 1968. PVMs being a special case also represent a certain idealized such auxillary system.

 

[A. Neumaier]

My point was more so that one needs something to select an outcome space for the system in order to have a well defined statistical model, unlike in the classical probabilistic case where events are defined without such a choice of an auxiliary system.

Unlike only in simplistic classical models.

Events are also not defined in a Laplacian classical universe without such a choice of an auxiliary system.

To get a proper statistical system, one needs something to select parts of the universe to serve as observed systems and detectors, respectively, and then do some coarse-graining of the detector dynamics.

This is the Heisenberg cut! It is also necessary in classical physics if you model the detector in a microscopic way.

 

[EPR]

Smarter guys have more free will. The higher the organization, the higher the emergent new properties - lower level organisms have little or no free will(e.g. worms, mollusks, etc.). Self conscious thought must play a big role in free will. Low intelligence individuals are usually bound by their animal instincts and thus often end up in jail unable to explain why they do the stuff they do. Probably little free will to speak of. Higher consciousness is roughly equal to 'free will'.

 

[DarMM]

Unlike only in simplistic classical models.

Events are also not defined in a Laplacian classical universe without such a choice of an auxiliary system.

I don't think so. Since one simply has a Boolean algebra of propositions the events can be considered to occur independent of the device, with the device simply recording them with some small disturbance to both. All observables "mesh" correctly to be considered random variables on one sample space of outcomes.

Do you have a reference for this?

 

[Stephen Tashi]

Do you really think that a child is not free in its decisions just because we can predict that it will say yes when it is asked whether it likes to have ice cream?

We we should distinguish between "free will" as a sensation of a conscious being along the lines of "I decide to... " versus the properties of the underlying physical processes that implement this sensation. Do the physical processes that implement the sensation of free will differ in some fundamental way from the physical processes that implement the weather or the behavior of insects?

 

[mattt]

For me, it would be a huge surprise if it is ever shown that biological systems, and concretely neural systems, follow laws independent of the laws of physics.

As far as I know, there is currently not a single hint that points in that direction.

 

[A. Neumaier]

I don't think so. Since one simply has a Boolean algebra of propositions the events can be considered to occur independent of the device, with the device simply recording them with some small disturbance to both. All observables "mesh" correctly to be considered random variables on one sample space of outcomes.

Do you have a reference for this?

A classical universe has no probability - everything is deterministic. It just has particles with time-dependent positions and momenta - no observers or detectors, unless these are introduced through a Heidelberg cut.
Only the latter introduces probability - quite in the spirit of Heisenberg.

I don't know a single paper dealing with the classical measurement problem - the question how a detector subsystem of a large classical chaotic system can acquire information about a disjoint subsystem to be measured.

This would be the classical analogy of the quantum measurement situation, and has a lot of the features of the latter.

A classical event would be something happening to the measured system that is approximated by something happening in the detector. This introduces probability in an otherwise deterministic classical universe.

 

[WWGD]

For me, it would be a huge surprise if it is ever shown that biological systems, and concretely neural systems, follow laws independent of the laws of physics.

As far as I know, there is currently not a single hint that points in that direction.

The Emperor's new Mind? Not sure, read it some 10 years back -- didnt even finish it iirc.

 

[Quantum Alchemy]

A classical universe has no probability - everything is deterministic.

This can't be the case.

This would mean there's some mechanism that knows the Experimenter's choice prior to measurement and this would go against all of the evidence like the Free Will Theorem which states:

Given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments.

The Axioms are:

1. Fin: There is a maximal speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
2. Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).
3. Twin: It is possible to "entangle" two elementary particles and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of quantum entanglement, but full entanglement is not necessary for the twin axiom to hold (entanglement is sufficient but not necessary).

Free Will Theorem

There would have to be some hidden variable mechanism that would transmit information faster than light to quantum system being measured and that system would be determined by this hidden variable mechanism prior to measurement and that goes against everything that has been observed. Here's some experiments.

The Big Bell Test which closed the freedom of choice loophole.

Challenging local realism with human choices

A Bell test is a randomized trial that compares experimental observations against the philosophical worldview of local realism1, in which the properties of the physical world are independent of our observation of them and no signal travels faster than light. A Bell test requires spatially distributed entanglement, fast and high-efficiency detection and unpredictable measurement settings2,3. Although technology can satisfy the first two of these requirements4,5,6,7, the use of physical devices to choose settings in a Bell test involves making assumptions about the physics that one aims to test. Bell himself noted this weakness in using physical setting choices and argued that human ‘free will’ could be used rigorously to ensure unpredictability in Bell tests8. Here we report a set of local-realism tests using human choices, which avoids assumptions about predictability in physics. We recruited about 100,000 human participants to play an online video game that incentivizes fast, sustained input of unpredictable selections and illustrates Bell-test methodology9. The participants generated 97,347,490 binary choices, which were directed via a scalable web platform to 12 laboratories on five continents, where 13 experiments tested local realism using photons5,6, single atoms7, atomic ensembles10 and superconducting devices11. Over a 12-hour period on 30 November 2016, participants worldwide provided a sustained data flow of over 1,000 bits per second to the experiments, which used different human-generated data to choose each measurement setting. The observed correlations strongly contradict local realism and other realistic positions in bipartite and tripartite12 scenarios. Project outcomes include closing the ‘freedom-of-choice loophole’ (the possibility that the setting choices are influenced by ‘hidden variables’ to correlate with the particle properties13), the utilization of video-game methods14 for rapid collection of human-generated randomness, and the use of networking techniques for global participation in experimental science.

https://www.nature.com/articles/s41586-018-0085-3

Here's 2 more:

Experimental rejection of observer-independence in the quantum world

The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics, the objectivity of observations is not so clear, most dramatically exposed in Eugene Wigner's eponymous thought experiment where two observers can experience fundamentally different realities. While observer-independence has long remained inaccessible to empirical investigation, recent no-go-theorems construct an extended Wigner's friend scenario with four entangled observers that allows us to put it to the test. In a state-of-the-art 6-photon experiment, we here realize this extended Wigner's friend scenario, experimentally violating the associated Bell-type inequality by 5 standard deviations. This result lends considerable strength to interpretations of quantum theory already set in an observer-dependent framework and demands for revision of those which are not.

https://arxiv.org/abs/1902.05080

Wheeler's delayed-choice gedanken experiment with a single atom

The wave–particle dual nature of light and matter and the fact that the choice of measurement determines which one of these two seemingly incompatible behaviours we observe are examples of the counterintuitive features of quantum mechanics. They are illustrated by Wheeler’s famous ‘delayed-choice’ experiment1, recently demonstrated in a single-photon experiment2. Here, we use a single ultracold metastable helium atom in a Mach–Zehnder interferometer to create an atomic analogue of Wheeler’s original proposal. Our experiment confirms Bohr’s view that it does not make sense to ascribe the wave or particle behaviour to a massive particle before the measurement takes place1. This result is encouraging for current work towards entanglement and Bell’s theorem tests in macroscopic systems of massive particles.

https://arxiv.org/abs/1902.05080

So everything can't be deterministic. The freedom of choice of the Experimenter has to be totally free unless there's some faster than light hidden variable that determines the outcomes of quantum systems prior to a measurement occurring.