"Counterfactual definiteness" vs. "free will"

[greypilgrim]

Hi.

What's the exact relation between the assumptions "counterfactual definiteness" and "existence of free will"? I (think I) know their "definitions" in QM:
counterfactual definiteness: ability to speak meaningfully of the definiteness of the results of measurements that have not been performed
free will: ability to choose experimental parameters completely independently of anything (more precisely: any joint distribution of the choice of experimental parameters and any past or present event must be a product distribution)

But I'm not sure if those assumptions are equivalent or if one is stronger or if they even talk about the same matter.

My thoughts:
I think CFD must at least partly encompass free will, because in order to speak about measurements that have not been performed (because the experimental parameters have been chosen differently), one needs to assume that they could have been performed, i.e. the probability of the choice of more than one set of experimental parameters must have been nonzero.
But I think this doesn't need the full extent of the definition of free will as stated above. It needs that conditioning on any past or present event does not lead to the trivial 1-0-distribution, not that such events must not influence the choice of experimental parameters at all.

On the other hand: If free will exists and we have a useful theory of nature, we should be able to make predictions about any choice of experimental parameters, regardless of which one is actually chosen. So free will implies CFD.

So is the free will assumption stronger than CFD?

 

[Nugatory]

I think CFD must at least partly encompass free will, because in order to speak about measurements that have not been performed (because the experimental parameters have been chosen differently), one needs to assume that they could have been performed, i.e. the probability of the choice of more than one set of experimental parameters must have been nonzero.

Rejecting CFD doesn't mean that you can't speak of measurements that haven't been performed, it means that you cannot speak of the result of such a measurement. So it's consistent to say that I could have chosen to perform measurement A instead of the non-commuting measurement B that I actually did. It doesn't follow from that that A has a definite value. On the contrary, when I chose to measure B not A I also chose to make the wave function not be an eigenfunction of A, thereby ensuring that A does not have a definite value.

 

[bhobba]

A point need to be made here.

In conventional QM an assumption is made that observations appear in a completely common-sense classical world in no way dependent on conscious observers being present or not. This is a point of confusion because observer in QM is much more general than in conventional use.

See the following:
http://www.johnboccio.com/research/quantum/notes/paper.pdf

Thanks
Bill

 

[facenian]

It is interesting to note that "counterfactual definiteness (CFD)" is an invention that has nothing to do with the original derivation of the Bell inequalities. I could not find a paper by Bell where he assumed counterfactual reasoning in his derivation. Neither does the original derivation by CHSH involve counterfactual reasoning.
It is also interesting to note that the term "counterfactual definiteness" is inexistent in the formal philosophical language or at least I could not find it in a philosophical dictionary.
Counterfactual reasoning was introduced by Stapp in 1971 to prove the Bell theorem without hidden variables. However, Stapp did not drive a falsifiable inequality. GHZ also use counterfactual reasoning, but again GHZ's result is not directly falsifiable.
In my opinion, no counterfactual assertion is directly testable by an experiment. Therefore CFD is an inconsistent assumption that unfortunately produces the correct bound of the Bell inequality.
Finally, one may claim that since it produces the correct final result, then it does not matter if it is logically inconsistent. I have two reasons to reject the former assertion. One is that "shut up and calculate" is not a logically inconsistent premise. It is applied to a logically consistent calculational scheme like quantum mechanics. The other is that even when an incorrect hypothesis produces a correct result, it may lead to incorrect conclusions, as is the case with CFD

 

[stevendaryl]

There is nothing particularly mysterious about counterfactual reasoning. It is done all the time in science (and I think there is a sense in which it is at the very heart of scientific reasoning). @facenian is right that sort of by definition, counterfactual claims can't be falsified by experiment. They are predictions of a scientific theory. In science, you can ask questions such as "What would happen if we mixed chemical A with chemical B?" "What would happen if the sun had the same mass as it does now, but a radius of just 3 kilometers?" You can't empirically answer questions about "what if"s, but you can certainly ask what this or that theory of chemistry or gravity or whatever says about those what ifs.

Some "what if"s may be beyond a particular theory's ability to answer. For example, you could ask the question: "What if the sun suddenly disappeared without a trace?" Our current theories of physics can't answer that question, because they all have local conservation laws that make it impossible for an object to just disappear.

So as far as how this relates to quantum mechanics and EPR:

Suppose we have some source of anti-correlated twin pairs of particles. It's guaranteed that if you measure the spin of one particle relative to an axis, the measurement of the spin of the other particle relative to the same axis will always produce the opposite result.

Now, consider a particular case where Alice measures spin along axis ##\vec{\alpha}## and gets the result "spin-up", and Bob measures spin along axis ##\vec{\beta}## and also gets spin-up. Then you can ask the question: "What if, at the last moment, Alice changed her mind and measured her spin along axis ##\vec{\beta}##?"

You can't empirically answer such a question, but you can certainly ask what this or that theory says about it. But to make sense of the question, you have to spell out the details of the counterfactual situation. You're considering a situation that is exactly like the actual situation, except that it differs in one aspect: Alice changes her mind at the last minute about what axis to measure spin relative to. It might be that the question has no meaning for some particular theory, in the same way that "What if the sun disappeared?" has no meaning for General Relativity. Maybe there is no possible way to arrange things so that they only differ from the actual situation in Alice's last-minute choice. A superdeterministic theory, for example, would say that Alice was destined from the time of the Big Bang to choose the axis that she did, and there is no way to tweak just that one aspect of the situation.

 

[DrChinese]

It is interesting to note that "counterfactual definiteness (CFD)" is an invention that has nothing to do with the original derivation of the Bell inequalities. I could not find a paper by Bell where he assumed counterfactual reasoning in his derivation.

In my opinion, no counterfactual assertion is directly testable by an experiment.

1. Don't be fooled just because Bell didn't call it "counterfactual definiteness" (CFD). Of course that is what is being considered by Bell.

EPR asked whether the predictions of QM should be considered as correct even when more than 2 non-commuting settings are considered, even though they could not be simultaneously measured (EPR called these "elements of reality"). EPR believed (assumed) in these simultaneous elements of reality (of course EPR also assumed no FTL influences). Bell showed their assumption was logically incompatible with the statistical predictions of QM, so no experiment required if QM was correct.

Before the advent of the term CFD, the term "realism" was frequently used instead of "simultaneous elements of reality". If you choose not to consider that to be the same as CFD, then we are splitting hairs. Clearly, Bell addressed the EPR paper, and that is still the standard for the debates. I am not aware of any significant generally accepted distinction introduced by the term CFD as it relates to Bell.2. By definition, CFD is not testable by experiment. Bell tests don't test for CFD. They ONLY test QM's predictions.

 

[facenian]

@stevendaryl, @DrChinese Thank you for your feedback.
Notice that I did not say CFD is necessarily problematic. I pointed out two correct uses of CFD. One by Stapp, the other by GHZ.(Actually is counterfactual reasoning; CFD in my opinion should have not existed)
The problem is when we use it to prove the Bell inequality. There is no experiment that can falsify the inequality if we derive it using CFD. The reason is very simple, no experiment can reproduce what the derivation assumes. Experiments normally falsify indicative conditionals, not counterfactual conditionals.
@DrChinese you can interpret that Bell implied CFD, I Interpret that he did not. This is a problem because he never explicitly mentioned "not performed experiments" in a counterfactual way but neither he explicitly said the opposite, so it will forever remain a matter of personal opinion. My opinion is that Bell was a very lucid thinker and if he ever had assumed such a "big" hypothesis he would have said it explicitly.

Let me give you another example. John Clauser in a review paper complained of "Damn theorists!" because the original Bell inequality was based on the existence of perfect correlations, a thing that cannot directly be tested in experiments. That is why they contrived the CHSH inequality. I wonder what kind of blasphemy he would have uttered had Bell based his inequality on irreproducible experiments. My guess is that no experimental physicist would have ever bothered to perform a Bell inequality test.

I suppose that those researchers that find the hypothesis doubtful simply ignore it and don't use it, but nobody dares to say out loud that it is nonsense.

Before I was aware of CFD I noticed the inconsistency in some derivations that assume without justification the use of the same ##\lambda## in four different sets of experiments. I discussed this problem in the Physics forum some years ago. On that occasion, I found the discussion with you guys very useful. Especially the contribution of @stevendaryl inspired me to write a paper that I later published. Now I realize that I should have publicly recognized his contribution in the acknowledgments section but it did not occur to me at that moment.

 

[stevendaryl]

The problem is when we use it to prove the Bell inequality. There is no experiment that can falsify the inequality if we derive it using CFD. The reason is very simple, no experiment can reproduce what the derivation assumes. Experiments normally falsify indicative conditionals, not counterfactual conditionals.

I really don't understand what you mean. Bell derived an inequality, and it has been falsified by experiments. So what you're saying seems just wrong.

 

[PeroK]

A superdeterministic theory, for example, would say that Alice was destined from the time of the Big Bang to choose the axis that she did, and there is no way to tweak just that one aspect of the situation.

Here's something I've never understood. What if Alice uses the digits of pi, for example, to determine what to measure. Since the digits of pi are not dependent on the initial conditions at the big bang, and could not possibly be correlated with any physical process, then how could measurement results be correlated with the digits of pi..

As I understand superdeterminism, the initial conditions at the big bang determine how Alice and Bob decide to make their measurements and determine the state of those physical processes they use - whether simply the choice their brains make, or a computer random number generator or a seemingly unrelated physical process. Superdeterminism ensures that all these things line up to create ultimately the correct correlation to make it look as though QM is true.

But, unless superdeterminism is a actually a god, how could it ensure that physical processes are correlated with a strictly mathematical sequence?

It would, of course, determine what mathematical sequence they each use, but it cannot (as far as I can see) take the extra step of correlating physical data with mathematical data.

As is asked so often on PF, what am I missing?

 

[facenian]

I really don't understand what you mean. Bell derived an inequality, and it has been falsified by experiments. So what you're saying seems just wrong.

For an experiment to falsify a theoretical prediction it has to comply with the conditions under which the prediction was derived. Let me give you an explicit example, you predict that a rock will sink down in the water. That would be your theoretical prediction. Now in the real experiment, you throw it into liquid mercury and the rock doesn't sink. Have you falsified your prediction? The answer is no because your experiment is not according to your theoretical prediction.
@DrChinese said that the Bell inequality should not be compared with experiments, only with the quantum mechanics prediction. It happens that it can not be compared with the QM predictions for the same reasons it can't be compared with experiments.

It seems that we are not going to coincide. I can only give as a matter of fact that neither John Bell nor CHSH ever explicitly mention counterfactual experiments or explicitly talked about counterfactual reasoing. Therefore, those who interpret their derivations as containing counterfactual reasoning should recognize that it's their interpretation and there is no evidence that they meant that.

Please notice that I am not saying experiments do not falsify the Bell inequality. What I mean is that if we interpret the inequality as based on CFD, then the experiments have nothing to do with the prediction.
When the inequality is correctly derived and interpreted then experiments falsify that prediction.
The correct Bell inequality only rests on two major assumptions: Local causality and Measurement independence and if we want to derive determinism we also need Perfect Correlations. There is no need for CFD which would invalidate the derivation because it turns the result unfalsifiable.

 

[stevendaryl]

Here's something I've never understood. What if Alice uses the digits of pi, for example, to determine what to measure. Since the digits of pi are not dependent on the initial conditions at the big bang, and could not possibly be correlated with any physical process, then how could measurement results be correlated with the digits of pi..

As I understand superdeterminism, the initial conditions at the big bang determine how Alice and Bob decide to make their measurements and determine the state of those physical processes they use - whether simply the choice their brains make, or a computer random number generator or a seemingly unrelated physical process. Superdeterminism ensures that all these things line up to create ultimately the correct correlation to make it look as though QM is true.

But, unless superdeterminism is a actually a god, how could it ensure that physical processes are correlated with a strictly mathematical sequence?

It would, of course, determine what mathematical sequence they each use, but it cannot (as far as I can see) take the extra step of correlating physical data with mathematical data.

As is asked so often on PF, what am I missing?

I agree. Bell derived his inequality assuming that there were five independent factors that determined the result of Alice's and Bob's measurements:

1. Alice's choice of which measurement to perform.
2. Bob's choice of which measurement to perform.
3. Facts about the twin pair (the "hidden variable")
4. Facts about Alice's detector.
5. Facts about Bob's detector.

The superdeterministic loophole assumes, to the contrary, that 1-3 are not independent. It assumes that the choices made by Alice and Bob are correlated from the beginning with the value of the hidden variable. It's certainly logically possible to explain things this way, but in my opinion, it's wildly improbable. Alice can make her choice based on the digits of ##\pi##, as you say, or based on the number of supernovae in some distant galaxy, or baseball scores, or whatever. To make superdeterminism work, it seems that at the moment of pair production, it would be necessary to take into account a potentially unlimited amount of information about the universe.

I tried to express this uneasiness about superdeterminism to Sabine Hossenfelder, and she either didn't understand my concerns or believed that they were stupid.

 

[stevendaryl]

Weirdly, I find retrocausality more plausible than superdeterminism.

 

[facenian]

@PeroK
It is better to go to the real thing that is simple elementary mathematics. The Bell inequality needs Measurement independence ##p(\lambda|ab)=p(\lambda)##. This assumption is more accurately described by the term "no conspiracy" than "freedom" or "free will" because those last two sound very anthropomorphic.
On the other hand, I believe that all the digits of pi were determined by Euclidean Geometry even though we do not know them. But that sounds very metaphysical, let us stay with Measurement Independence.

 

[PeroK]

@PeroK
It is better to go to the real thing that is simple elementary mathematics. The Bell inequality needs Measurement independence ##p(\lambda|ab)=p(\lambda)##. This assumption is more accurately described by the term "no conspiracy" than "freedom" or "free will" because those last two sound very anthropomorphic.
On the other hand, I believe that all the digits of pi were determined by Euclidean Geometry even though we do not know them. But that sounds very metaphysical, let us stay with Measurement Independence.

The point of using mathematics is that it is unrelated to physical systems. I agree with @stevendaryl about the absurdity of, say, baseball and soccer results being correlated. But, I can see no way that the data from a physical system can be correlated with the digits of pi in base 10. Superdeterminism or not.

 

[facenian]

The point of using mathematics is that it is unrelated to physical systems. I agree with @stevendaryl about the absurdity of, say, baseball and soccer results being correlated. But, I can see no way that the data from a physical system can be correlated with the digits of pi in base 10. Superdeterminism or not.

That is too much for me I stay with Measurement independence(MI). Not everybody interprets MI as Free Will. The real thing is MI, the rest is interpretation. It is too metaphysical or philosophical.

 

[PeterDonis]

What if Alice uses the digits of pi, for example, to determine what to measure.

Superdeterminism would say that this "what if" is meaningless, since the initial conditions of the universe do not give Alice the ability to use the digits of pi to determine what to measure. In other words, superdeterminism basically rules out by fiat any scenario in which what Alice uses to determine what to measure is in fact independent of the other variables.

unless superdeterminism is a actually a god, how could it ensure that physical processes are correlated with a strictly mathematical sequence?

It doesn't. It says, instead, that the scenario you postulate is impossible.

 

[PeroK]

Superdeterminism would say that this "what if" is meaningless, since the initial conditions of the universe do not give Alice the ability to use the digits of pi to determine what to measure. In other words, superdeterminism basically rules out by fiat any scenario in which what Alice uses to determine what to measure is in fact independent of the other variables.It doesn't. It says, instead, that the scenario you postulate is impossible.

So, superdeterminism ensures that anyone (like me) who sees the flaw in superdeterminism is prevented from ever becoming an experimental physicist?

 

[PeterDonis]

superdeterminism ensures that anyone (like me) who sees the flaw in superdeterminism is prevented from ever becoming an experimental physicist?

Not at all. It just ensures that you won't be able to choose any experimental settings that would lead to results that contradict QM's predictions.

 

[PeroK]

Not at all. It just ensures that you won't be able to choose any experimental settings that would lead to results that contradict QM's predictions.

If I had the chance I would use the digits of pi and claim that for superdeterminism to work it would have to correlate physical systems with mathematical constants.

What I don't understand is why experimental physicists don't do this!

 

[PeterDonis]

If I had the chance

Superdeterminism would say the initial conditions of the universe prevent this.

What I don't understand is why experimental physicists don't do this!

Superdeterminism would say it's because the initial conditions of the universe prevent it.

 

[facenian]

Superdeterminism would say the initial conditions of the universe prevent this.Superdeterminism would say it's because the initial conditions of the universe prevent it.

I agree. In my opinion that is mere logic. Whether one likes it or not is irrelevant, it's the way the world is(or would be).

 

[PeroK]

I agree. In my opinion that is mere logic.

That's not logic, that's magic! Or, faith.

 

[Demystifier]

Here's something I've never understood. What if Alice uses the digits of pi, for example, to determine what to measure. Since the digits of pi are not dependent on the initial conditions at the big bang, and could not possibly be correlated with any physical process, then how could measurement results be correlated with the digits of pi..

To do that (that is, to use the digits of pi in measurement), Alice has to decide to do that. According to superdeterminism, it is this decision that is determined by the initial conditions at the big bang.

 

[PeroK]

To do that (that is, to use the digits of pi in measurement), Alice has to decide to do that. According to superdeterminism, it is this decision that is determined by the initial conditions at the big bang.

Absolutely, but then she is using data that is independent of the initial conditions or any deterministic physical processes. My argument is that for the results of the experiments to remain correlated, the initial conditions would need to be aligned with the mathematical constant pi. But, pi doesn't depend on the initial conditions.

The attempts I've seen to push superdeterminism involved photons from distant galaxies and other physical systems. That leaves the door open for the superdeterminist to claim that even they are correlated. But, I can see no possible physical argument that says that the cards in a shuffled deck of cards are correlated - by initial conditions at the big bang - with the digits of pi. Correlation of a pack of cards and distant quasars? Absurd, but physically possible.

 

[Demystifier]

Absolutely, but then she is using data that is independent of the initial conditions or any deterministic physical processes. My argument is that for the results of the experiments to remain correlated, the initial conditions would need to be aligned with the mathematical constant pi. But, pi doesn't depend on the initial conditions.

The attempts I've seen to push superdeterminism involved photons from distant galaxies and other physical systems. That leaves the door open for the superdeterminist to claim that even they are correlated. But, I can see no possible physical argument that says that the cards in a shuffled deck of cards are correlated - by initial conditions at the big bang - with the digits of pi. Correlation of a pack of cards and distant quasars? Absurd, but physically possible.

Well, you can say that for any decision. For instance, if I decide to use the digits 1,5,2,7, you can say that those digits do not depend on the initial condition. (And by the way, do you see a pattern in those digits, can you guess what are the next ones?) I don't see how the digits of pi are different.

 

[PeroK]

Well, you can say that for any decision. For instance, if I decide to use the digits 1,5,2,7, you can say that those digits do not depend on the initial condition. (And by the way, do you see a pattern in those digits, can you guess what are the next ones?) I don't see how the digits of pi are different.

Because those digits came from your brain - a physical system that depends on the initial conditions. The digits of pi don't depend on the initial conditions in any way.

 

[Demystifier]

Because those digits came from your brain

No they don't, they exist even without my brain. If pi exists without humans, then so does any number. It is the decision to use those digits, and not some others, that comes from my brain. Consider, for instance, the number in which every digit n of pi is replaced with n+1 (except for 9 which is replaced with 0), is it like pi or not?

 

[PeroK]

No they don't, they exist even without my brain. If pi exists without humans, then so does any number. It is the decision to use those digits, and not some others, that comes from my brain. Consider, for instance, the number in which every digit n of pi is replaced with n+1 (except for 9 which is replaced with 0), is it like pi or not?

The whole point of superdeterminism, I thought, was that all physical systems are connected and correlated superdeterministically. That keeps the theory, however contrary and absurd, in the realm of physics.

Once you accept that the digits of pi are part of this grand scheme, then we no longer have a physical theory, but essentially religion.

The decision to use the digits of pi is not sufficient to ensure correlation of the results. The specific digits of pi must also be part of the superdeterminism theory. But, they were not determined by the initial conditions of our universe.

 

[Demystifier]

Once you accept that the digits of pi are part of this grand scheme, then we no longer have a physical theory, but essentially religion.

Are you saying that pi is somehow special? What if it was not ##\pi##, but ##\pi^{3/7}-e^{1/9}##, would it still be a religion?

 

[PeroK]

Are you saying that pi is somehow special? What if it was not ##\pi##, but ##\pi^{3/7}-e^{1/9}##, would is still be religion?

Any mathematical process where the data itself cannot be determined by physical conditions would do.

 

[PeroK]

PS because then we have not superdeterminism (where determinism implies underlying deterministics laws of physics), but supercoincidence theory (where everything is just coincidentally aligned). That theory should then suddenly fail at some point!

 

[Demystifier]

Any mathematical process where the data itself cannot be determined by physical conditions would do.

How about the following process? Alice throws the dice, if it's head then she uses the digits of ##\pi##, if it's tails the she uses the digits of ##e##.

 

[PeroK]

How about the following process? Alice throws the dice, if it's head then she uses the digits of ##\pi##, if it's tails the she uses the digits of ##e##.

That doesn't add anything, because the result of the coin toss may be determined by initial conditions.

If Alice uses ##\pi## and Bob uses ##e##, then we have an interesting irony:

An intelligent human experimenter knows in advance precisely what the data will be - in one sense the data used in the experiment is completely determined.

But, the data used in the experiment is not physically connected - in the sense that the digits of ##\pi## and ##e## cannot be correlated by any physical process.

In other words, the relationship between the digits of ##\pi## and ##e## is determined by mathematics, not by the laws of physics!

 

[Demystifier]

In other words, the relationship between the digits of ##\pi## and ##e## is determined by mathematics, not by the laws of physics!

But the laws of physics that we know also have a mathematical form. So in this sense the laws of physics are laws of mathematics.

 

[Demystifier]

That doesn't add anything, because the result of the coin toss may be determined by initial conditions.

My question was this: If Alice decides by the coin to use pi or e, is it OK for superdeterminism?