# Free Will in Quantum Theory

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## Summary:

Is "free will", as it is usually interpreted, a foundational assumption of QM?

## Main Question or Discussion Point

Summary: Is "free will", as it is usually interpreted, a foundational assumption of QM?

I've done a search using the term "free will" and have done a ctrl+f "free will" to go through those threads but I feel that the best way to find definitive clarification on my question is to ask specific, targeted questions in a separate thread. The specific questions I have are:

1) Is "free will" a foundational assumption in Quantum Theory?
I've read a few different things about the notion of Free Will in Bell's Theorem and have read a few articles about "closing the free will loophole". In this video the author suggests that Bell's Theorem implies that we must give up our notions of either Realism, Locality, Local and Realism, or Free Will. Is it fair to say then that [the generally understood notion of] Free Will is a foundational assumption in QT?

2) Is Free Will a foundational assumption of the scientific method?
In reading up on Free Will in Quantum Theory, I have come across the notion that Free Will is a foundational assumption in the practice of sicence itself. Is this the case?

2) If there is no "free will", does that mean that the universe must be superdeterministic?
I'm not particularly interested in the implications of superdeterminism, or what it necessitates, I'm just interested in the the necessity of it as a conclusion, if Free Will does not exist.

## Answers and Replies

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Demystifier
2018 Award
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.

PeroK
Homework Helper
Gold Member
2018 Award
Summary: Is "free will", as it is usually interpreted, a foundational assumption of QM?

Summary: Is "free will", as it is usually interpreted, a foundational assumption of QM?

I've done a search using the term "free will" and have done a ctrl+f "free will" to go through those threads but I feel that the best way to find definitive clarification on my question is to ask specific, targeted questions in a separate thread. The specific questions I have are:

1) Is "free will" a foundational assumption in Quantum Theory?
I've read a few different things about the notion of Free Will in Bell's Theorem and have read a few articles about "closing the free will loophole". In this video the author suggests that Bell's Theorem implies that we must give up our notions of either Realism, Locality, Local and Realism, or Free Will. Is it fair to say then that [the generally understood notion of] Free Will is a foundational assumption in QT?

2) Is Free Will a foundational assumption of the scientific method?
In reading up on Free Will in Quantum Theory, I have come across the notion that Free Will is a foundational assumption in the practice of sicence itself. Is this the case?

2) If there is no "free will", does that mean that the universe must be superdeterministic?
I'm not particularly interested in the implications of superdeterminism, or what it necessitates, I'm just interested in the the necessity of it as a conclusion, if Free Will does not exist.
It has always seemed to me that "free will" in the psychological sense is a red herring when it comes to science. It doesn't really matter whether

a) I am a complex system that is capable of a large number of, for all practical purposes, unpredictable actions.

b) There is some external or internal additional factor (free will, consciousness whatever) that determines what I do.

If we take a simple example. I decide to test the theory that a rubber ball bounces differently off a hard floor and a carpet. I carry out this experiment and record the results.

It doesn't really matter, IMHO, whether or not it was inevitable that I should do this. I did the experiment and recorded the results. That's all that matters.

Superdeterminism goes much further and, essentially, undermines all of science. It feels to me like clutching at philosphical straws to avoid the difficult conclusions of QM.

For example, a superdeterministic alternative to the theory that a rubber ball bounces better off a hard floor goes as follows:

1) Rubber balls bounce high or low depending on an internal parameter.
2) This parameter is correlated with all humans brains and where they decide to bounce a ball.
3) Whenever the ball is programmed to bounce high, the human is programmed to bounce the ball on a hard surface.
4) Whenever the ball is programmed to bounce low, the human is programmed to bounce the ball on a carpet.

The QM version is, no doubt, more sophisticated; but, that's the gist of it, as far as I understand it.

DarMM
Gold Member
The QM version is, no doubt, more sophisticated; but, that's the gist of it, as far as I understand it.
That's pretty much it in QM as well actually. Say in a CHSH test we are looking at the sum of correlators:
$$\left<AB\right> + \left<BC\right> + \left<CD\right> - \left<AD\right>$$
As you know this is meant to $\leq 2$ for a local classical theory. In a superdeterminisitic theory any time $AD$ is negative we are predestined to measure it. And any time the other pairs are positive we are predestined to measure one of them.

The only sophistication is that technically it need not be all of time just "enough" to tip the sum over $2$.

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.
Thanks for the reply Demystifier. I was thinking that it mustn't necessarily be the usual psychological notion of free will but I have seen various quotes from mathematicians and physicists that seem to strongly imply that it is Free Will as we usually think of it.

Would you be able to clarify what it means "that there is no correlation between the choices of which observable will be measured on different subsystems". Is this essentially saying that the choice of which observable is measured is not a deterministic process? Or that there is no common cause in the past history of the experimenters?

Just to try and understand the opposite which might help me to understand the point, what would it take for us to say that there was correlation between the choices?

It has always seemed to me that "free will" in the psychological sense is a red herring when it comes to science. It doesn't really matter whether

a) I am a complex system that is capable of a large number of, for all practical purposes, unpredictable actions.

b) There is some external or internal additional factor (free will, consciousness whatever) that determines what I do.

If we take a simple example. I decide to test the theory that a rubber ball bounces differently off a hard floor and a carpet. I carry out this experiment and record the results.

It doesn't really matter, IMHO, whether or not it was inevitable that I should do this. I did the experiment and recorded the results. That's all that matters.

Superdeterminism goes much further and, essentially, undermines all of science. It feels to me like clutching at philosphical straws to avoid the difficult conclusions of QM.

For example, a superdeterministic alternative to the theory that a rubber ball bounces better off a hard floor goes as follows:

1) Rubber balls bounce high or low depending on an internal parameter.
2) This parameter is correlated with all humans brains and where they decide to bounce a ball.
3) Whenever the ball is programmed to bounce high, the human is programmed to bounce the ball on a hard surface.
4) Whenever the ball is programmed to bounce low, the human is programmed to bounce the ball on a carpet.

The QM version is, no doubt, more sophisticated; but, that's the gist of it, as far as I understand it.
I guess it doesn't really affect how science is done bcos science is being done whichever scenario is true. But, to have a complete description of the Universe it would be a material concern (no pun in 10 did).

Demystifier
2018 Award
Just to try and understand the opposite which might help me to understand the point, what would it take for us to say that there was correlation between the choices?
Let $c_1$ and $c_2$ be the two choices and let $p(c_1,c_2)$ be the probability of the joint choice $c_1$ and $c_2$. The claim that the two choices are not correlated means that there exist probabilities $p_1(c_1)$ and $p_2(c_2)$ such that
$$p(c_1,c_2)=p_1(c_1)p_2(c_2)$$
Here all probabilities are defined in terms of relative frequencies and it does not exclude the possibility that the fundamental microscopic dynamics is deterministic (but too complex or chaotic to make deterministic predictions in practice).

Conversely, if the joint probability cannot be written in the product form above, then the choices are correlated. In other words, the choices are not statistically independent.

2) If there is no "free will", does that mean that the universe must be superdeterministic?
I'm not particularly interested in the implications of superdeterminism, or what it necessitates, I'm just interested in the the necessity of it as a conclusion, if Free Will does not exist.
No, IMHO the perfect correlation in the Bell experiment is a kind of superdeterminism. One can always try to explain the weird correlation away, for example through FTL influence (without free will).

Let $c_1$ and $c_2$ be the two choices and let $p(c_1,c_2)$ be the probability of the joint choice $c_1$ and $c_2$. The claim that the two choices are not correlated means that there exist probabilities $p_1(c_1)$ and $p_2(c_2)$ such that
$$p(c_1,c_2)=p_1(c_1)p_2(c_2)$$
Here all probabilities are defined in terms of relative frequencies and it does not exclude the possibility that the fundamental microscopic dynamics is deterministic (but too complex or chaotic to make deterministic predictions in practice).

Conversely, if the joint probability cannot be written in the product form above, then the choices are correlated. In other words, the choices are not statistically independent.
Again, thanks for the explanation. I think that I follow it - up to a point. Are there cases where the choices are correlated and cases where they are not? Or is that a subject of debate?

Is it known what would be the cause of it not being possible to write the joint probability in the product form above?

Apologies also, I keep trying to bring it back to terms that I understand better such as determinism, indeterminism, and Free Will. Am I right in saying that the if the probability function can be written in the product form above, then there is determinism. If it can't, then the Universe can't be deterministic and is possibly non-local?

Demystifier
2018 Award
Am I right in saying that the if the probability function can be written in the product form above, then there is determinism. If it can't, then the Universe can't be deterministic and is possibly non-local?
No, that's completely wrong. What made you think that?

PeroK
Homework Helper
Gold Member
2018 Award
Again, thanks for the explanation. I think that I follow it - up to a point. Are there cases where the choices are correlated and cases where they are not? Or is that a subject of debate?

Is it known what would be the cause of it not being possible to write the joint probability in the product form above?

Apologies also, I keep trying to bring it back to terms that I understand better such as determinism, indeterminism, and Free Will. Am I right in saying that the if the probability function can be written in the product form above, then there is determinism. If it can't, then the Universe can't be deterministic and is possibly non-local?
One problem is that you are trying to run before you walk. You are trying to debate the big, philosophical issues around QM without understanding the basics.

Regarding determinism in QM you should first study electron spin and the Stern-Gerlach experiment. Then you can move on to two particle entangled systems and then to the Bell theorem.

At that point you may understand the remaining philosophical wriggle room in terms of super determinism.

I think "free will" as far as it is relevant for physics is another word for the rejection of superdeterminism.

Superdeterminism is simply conspiracy theory extrapolated into complete absurdity and is reasonably rejected. But the base for the rejection of superdeterminism is not some physical theory - classical or quantum - but metatheoretical. Without a rejection of superdeterminism, there would be no longer any base for doing any statistical experiments at all. Whatever the result of such an experiment, it would be possible to explain it away with some super-conspiracy.
No, IMHO the perfect correlation in the Bell experiment is a kind of superdeterminism. One can always try to explain the weird correlation away, for example through FTL influence (without free will).
It is the other way. Superdeterminism is the ultimate way to explain away any weird correlation, without any further necessity to care about it. Explanations through FTL influence are, instead, nontrivial, they require nontrivial modifications of existing theory (introduction of a preferred frame, if one wants to preserve a notion of causality).

Science is impossible if weird correlations do not define nontrivial scientific problems. So, superdeterminism taken seriously would be the end of science.

The tobacco industry would be happy to use superdeterminism to explain away correlations between smoking and lung cancer. They would have to do nothing - the word "superdeterminism" would be already sufficient. Now they have to invent something else to explain these correlations away. But whatever they propose, it would have to be a scientific theory which makes predictions, and it would have one particular feature - that taking into account all common cause explanations, the remaining correlation would have to be zero. Which could be easily falsified by yet another statistical study.

Demystifier
2018 Award
So, superdeterminism taken seriously would be the end of science.
To paraphrase Rutherford, it would be the end of physics, but we would still have stamp collecting. In other words, we would still have useful collecting of data telling us what is correlated with what. We would just not have any theory behind it.

Demystifier
2018 Award
Regarding determinism in QM you should first study electron spin and the Stern-Gerlach experiment.
And before that I would suggest to study classical deterministic chaos and generators of pseudorandom numbers.

No, that's completely wrong. What made you think that?
Probably not the first time or the last time that will be the case :p

It might be helpful to outline where my particular interest lies. I am currently working on a piece of writing that may touch on the notion of "Free Will" and so I'd like to develop a better understanding of what it means or the role it plays in physics.

The confusion, perhaps, arises from the use of the term "Free Will". I have read a number of quotes from different sources, most notably Bell himself and John Conway [of the "Free Will" theorem]. The quotes pretty unequivocally, reference the common sense notion of "Free Will". For example:
John Bell said:
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.
I've heard arguments put forward, as above, that it isn't the common sense notion of "Free Will" that is actually meant but rather just the idea of indeterminism and the idea that the future is not predetermined. Others still, say that it - the common sense notion of "Free Will" - is a fundamental assumption of Bell's theorem. There almost seems to be some implication that "Free Will" is what gives rise to indeterminism.

I'll outline what made me think that from your post above
Here all probabilities are defined in terms of relative frequencies and it does not exclude the possibility that the fundamental microscopic dynamics is deterministic (but too complex or chaotic to make deterministic predictions in practice).
I was thinking that the probability function reflects the myriad physical elements that affect the possible outcomes. In this case determinism isn't ruled out. It might be the case, however, that it is too complex or chaotic to make deterministic predictions in practice.

Saying that this means that "there is determinism" is probably too strong, but I took it to be the case, given the alternative.

Conversely, if the joint probability cannot be written in the product form above, then the choices are correlated. In other words, the choices are not statistically independent.
With this I am inferring, possibly incorrectly, that if the joint probability cannot be written in the product form outlined, then there must be an aspect of the physical world, which is not present (or maybe accounted for) in the case where the probability can be written in that form, which leads to the choices being correlated.

I must be wrong in my conclusion that this second option represents an indeterministic universe.

I am taking the probability function to be a representation of the various elements in the physical world which can affect the possible outcomes, so if the probability is different in each case, the difference must be attributable to an element of the physical world. That is just my thinking.

When I think of determinism, I think of a long unbroken chain of causality, where every effect can be directly traced to it's preceding causes. In this case, the common understanding of the notion of "Free Will" is invalidated.

One problem is that you are trying to run before you walk. You are trying to debate the big, philosophical issues around QM without understanding the basics.

Regarding determinism in QM you should first study electron spin and the Stern-Gerlach experiment. Then you can move on to two particle entangled systems and then to the Bell theorem.

At that point you may understand the remaining philosophical wriggle room in terms of super determinism.
Thanks Perok. I have looked at all of those but I wouldn't claim to understand every aspect of them. I may have reached the limit of my understanding in that regard. I know that this is obviously a major impediment to understanding QM, which is why I try to use the things I think I understand as an inroad.

Is there any particular element of Stern-Gerlach that pertains to the "Free Will" or "Free Choice" assumption? Just to try and narrow down my search

PeroK
Homework Helper
Gold Member
2018 Award
You're missing the point. Even if the universe is completely deterministic, there is no correlation between certain data.

For example, suppose you and I in separate rooms wrote down a sequence of numbers.

Determinism might suggest that both sequences were inevitable from the big bang. But not that they are correlated.

If we find that the sequences are always the same, then that requires a different explanation. Determinism alone cannot achieve that.

Why would you and I always write the same numbers in a sequence? it doesn't matter that both sequences were determined at the big bang. Why are they the same?

Superdeterminism goes further - and further than Bell hints in what he says. In order to explain QM through superdeterminism you have the equivalent of a god who is playing tricks on us.

PeroK
Homework Helper
Gold Member
2018 Award
Thanks Perok. I have looked at all of those but I wouldn't claim to understand every aspect of them. I may have reached the limit of my understanding in that regard. I know that this is obviously a major impediment to understanding QM, which is why I try to use the things I think I understand as an inroad.

Is there any particular element of Stern-Gerlach that pertains to the "Free Will" or "Free Choice" assumption? Just to try and narrow down my search
If you don't already know that you are not in a position to debate QM! Sorry, but that's the hard truth.

Demystifier
2018 Award
I am currently working on a piece of writing that may touch on the notion of "Free Will" and so I'd like to develop a better understanding of what it means or the role it plays in physics.
Do you have any formal education in probability and statistics?

I think "free will" as far as it is relevant for physics is another word for the rejection of superdeterminism.
Thank you Elias, this is essentially one of the questions I had. If "Free Will" is the rejection of superdeterminism, what is meant by that term "Free Will"; is it the common sense notion of "Free Will"?

Would the negation of "Free Will" - whatever it's meaning - imply that the Universe is superdeterministic?

I don't want to get into the particulars of superdeterminism because I think it usually leads to threads getting closed. It is also a different idea that I will probably need to focus on, by itself to understand all the conspiratorial implications. I want to try and wrap my head around the notion of "Free Will" first, as it appears in the context of Quantum Mechanics.

Do you have any formal education in probability and statistics?
Only as far as High School unfortunately.

Demystifier
2018 Award
Only as far as High School unfortunately.
Just to test your understanding, can you give examples of two mutually correlated and two mutually uncorrelated phenomena from everyday life?

If you don't already know that you are not in a position to debate QM! Sorry, but that's the hard truth.
That's fair enough. I guess I don't see it as debating QM but trying to clarify a commonly understood term as it appears in the context of QM. I think I have a fairly decent grasp on the notion of determinism - if there isn't more to it than I understand. "Free Will" is a commonly understood, if ill defined, term and it appears to be this that is often referenced in the literature.

Indeterminism is probably a lot less intuitive but it can be spoken of in terms of the common sense idea of "Free Will" and I am familiar with the notion of indeterminism in QM.

Would you be able to direct me to the part that is relevant to "Free Will"? I often find that when I read explanations of these different experiments, I can follow generally what they describe but I require the commentary to highlight the consequences.

Just to test your understanding, can you give examples of two mutually correlated and two mutually uncorrelated phenomena from everyday life?
Thanks Demsystifier, this is very helpful.

I'm not very familair with the term mutually correlated phenomena. I would be coming from the other side hoping for examples to clarify the meaning of the term.

The examples that come to mind are those that I have encountered in the explanation of Bell's theorem, such as the case of a machine sending out 2 or 3 balls to different roulette tables.

Demystifier
I'm afraid coming from the other side (Bell theorem in this case) would not be a good idea. You have to first learn basic concepts (and the concept of correlation is very basic in this context) on less abstract examples. Trying to understand Bell theorem without understanding the concept of correlation first is like trying to understand square root (e.g. $\sqrt{427}\approx 20.66397832$) without understanding addition first (e.g. $2+3=5$). Sorry, but it simply won't work.