"Counterfactual definiteness" vs. "free will"

[stevendaryl]

If Alice successfully tests QM by making two runs of the experiment, one based on the first digits of $\pi$ and one based on the first digits of $e$, reversing the order of the runs would have given wrong results under superdeterminism.

So what's special about superdeterminism is indeed the "supercoincidence" that Alice chose to perform the measurement using the right mathematical constant at the right time.

Yes, exactly. It wouldn't have to be a coincidence, though, as long as Alice's choice is predictable.

I guess there is a tradeoff between how much conspiracy you require in initial conditions and how much computational power you allow in the twin pair generator.

 

[A. Neumaier]

These systems are only doing what an intelligent being who understands mathematics designs them to do.

My claim is that it can't be correlated with something that doesn't have that intelligent design.

?

Every experiment in physics records things with instruments that have intelligent design. Without that no expeimetal results!

 

[A. Neumaier]

I think that the points is, whatever can be computed from the initial conditions, there is always something else. Pick that. What stops me from doing that.

Knowing what to pick!

 

[kith]

What I'm suggesting is that Alice's decision (albeit compelled by superdeterminism) to use a mathematical constant is a loophole in superdeterminism, which wrongly assumes that everything can be determined by the deterministic laws of physics and initial conditions. The loophole is that purely mathematical things are not determined this way. Hence intelligence throws a spanner in the superdeterministic works.

I don't see this.

Just to reiterate that we are on the same page: superdeterministic QM consists of two parts: the laws and the initial conditions. The laws can give answers which are wildly different from the answers of the ordinary laws of QM but if we happen to ask the right questions at the right time, we get the same answers. The initial conditions now are such that whenever QM is tested, people do happen to ask the right question at the right time.

Using my example from above again: Let's assume that Alice needs to choose 4 consecutive numbers per run. She performs the first run at time $t_1$ and the second run at time $t_2$. At $t_1$, the state of the world is such that she needs to chose the numbers $3, 1, 4, 1$ in order to reproduce the predictions of QM. At $t_2$, the state of the world is such that she needs to chose the numbers $2, 7, 1, 8$ in order to reproduce the predictions of QM. The superdeterministic initial conditions determine the coice of Alice such that she is bound to select the correct set of numbers in both runs although she feels like she could just have flipped her choice. If she had flipped it, she would have gotten answers which contradict the QM predictions. But she didn't and she couldn't.

For me, having the first $n$ digits of a mathematical constant appear here is analogous to repeatedly flipping 10 coins and coincidentally reproducing the digits of $\pi$ in the number of heads. Increasingly unprobable? Yes. Mysterious? No.

The strangeness of superdeterminism lies in the "supercoincidence" that Alice just happens to always ask the right questions at the right time.

 

[stevendaryl]

In short: we use our intelligence to use data that has not itself been superdetermined.

I really don't understand this. I would say that some fact is "superdetermined" if it is predictable in principle from the initial conditions of the universe. The digits of $\pi$ are superdetermined in this sense.

 

[kith]

I guess there is a tradeoff between how much conspiracy you require in initial conditions and how much computational power you allow in the twin pair generator.

Can you elaborate on this? What's the relationship with the twin pair generator and Alice's choices?

 

[stevendaryl]

Can you elaborate on this? What's the relationship with the twin pair generator and Alice's choices?

Bell's derivation of his inequality assumed that there is no correlation between the "hidden variable" associated with the twin-pair and the choices made by Alice and Bob. The superdeterministic loophole assumes to the contrary that they are correlated. Two extreme ways that they can be correlated are:

1. Alice's and Bob's choices are arranged ahead of time to have predetermined values. This the conspiracy approach.
2. At the moment of pair creation, Alice's and Bob's future choices are computed, and taken into account in the choice of the hidden variable.

The second option doesn't require any conspiracy, but it requires an enormous amount of computational power.

 

[DrChinese]

So what's special about superdeterminism is indeed the "supercoincidence" that Alice chose to perform the measurement using the right mathematical constant at the right time.

Admittedly, that supercoincidence is a pretty big iceberg. But it is really only the tip.

The essential idea is that QM's base prediction is wrong (for entangled pairs, as in Bell tests). Instead, the "true" coincidence rate is within local realistic bounds (as the whole point is to restore local determinism). Generally speaking:

a. QM predicts a cos^2(theta) relationship (sinusoidal)
b. LR requires a k(theta) relationship (straight line)
c. And the "superdeterminism" effect produces a statistical bias equal to the DIFFERENCE between a. and b. That restores the mistaken appearance that Bell Theorem is valid.

That requires some pretty fancy footwork. And if everything is to be local, that means there is something embedded in the local quantum system that tells that system when it needs to be measured as being this way or that. And it needs to pass that on to successor quantum systems too, so that they can operate properly within local bounds. And even that can't really explain how particles that have never interacted can know how to act when Bell tested. Again, the whole idea of superdeterminism is to restore locality.

Keep in mind that I don't believe there is an actual "theory of superdeterminism" to speak against. You may as well say it is god's handiwork, as you can't attack ideas that have no specifics and can be "hand-waved" without limit.

 

[PeroK]

I think you're still misunderstanding the point. Alice's choices don't need to be determined by anything about the universe but they need to be predictable. The digits of pi are perfectly predictable. More so than baseball results.

It's only "predictable" if you have mathematical intelligence. Baseball results arise from the evolution of a physical system, starting with the initial conditions and following the superdeterministic laws of physics. Alice's decision to use baseball results requires correlation of three sub-systems of the universe:

Alice's brain; the baseball matches; and, the quantum particles being tested.

If Alice's decision is to use the digits of, let's say, $\pi^{31}$, then there is no physical system correlated to that data. Even if SD has had since the big bang to calculate $\pi^{31}$ and get the hidden variables ready, it has no mathematical intelligence to do so. That data only exists in abstract (non physical) mathematics. $\pi^{31}$ is not a physical sub-system of the universe.

So, when Alice conducts the experiment, SD would have to correlate that sequence of data that does not exist anywhere in the physical universe with photon hidden variables. It can't be done without mathematical intelligence. No sub-system has been evolving its hidden varibles into whatever the sequence of digits of that number are.

That is the fundamental difference between using a mathematical sequence and a coin or baseball result: the mathematics has no physical existence prior to being called upon and has not been evolving under the laws of physics since the big bang.

That would require SD to be more than just the dumb deterministic laws of physics acting on physical systems.

 

[kith]

1. ...
2. At the moment of pair creation, Alice's and Bob's future choices are computed, and taken into account in the choice of the hidden variable.

Interesting, I've never looked at superdeterminism through this lens. This made a new connection between superdeterminism and retro-causality for me. Thank you!

 

[PeroK]

For me, having the first $n$ digits of a mathematical constant appear here is analogous to repeatedly flipping 10 coins and coincidentally reproducing the numbers of $\pi$ in the number of heads.

The coin is a physical sub-system of the universe, governed by SD laws. The mathematical sequence is not a physical system and independent of the laws of physics (however SD they may be).

 

[kith]

The coin is a physical sub-system of the universe, governed by SD laws. The mathematical sequence is not a physical system and independent of the laws of physics (however SD they may be).

I don't disagree but in both cases, the mathematical sequence shows up in the physics: in the first case in the numbers Alice is predetermined to choose, in the second case in the number of heads. (Sorry for the Unlike, I accidentally hit Like instead of Reply first)

 

[PeroK]

I don't disagree but in both cases, the mathematical sequence shows up in the physics: in the first case in the numbers Alice is predetermined to choose, in the second case in the number of heads. (Sorry for the Unlike, I accidentally hit Like instead of Reply first)

The mathematical predestination is not enough unless there is a physical system evolving appropriately:

1) Some quantum system under experiment: governed by initial conditions and SD laws of physics - i.e. its hidden variables

2) Alice: governed by initial conditions and SD laws of physics - hidden variables

3) Baseball matches: governed by initial conditions and SD laws of physics - hidden variables

4) $\pi^{31}$: fixed set of digits, predictable by mathematics, but not governed by initial conditions and SD laws of physics - no hidden variables in nature are associated with this precise sequence

The 4th component (the mathematical system) is different, because there are no hidden variables in nature that represent this number (in base 10). These digits (data) come out of the blue as far as nature is concerned. Nature cannot correlate that precise sequence of digits with the decision in Alice's brain - it does not have the mathematical capability to compute those digits, and understand the mathematical implication of Alice's predestined choice.

We may postulate an extravagent set of laws of physics that do fancy stuff with the hidden variables in 1), 2) and 3). But, the digits that appear in a calculation of $\pi^{31}$ are hitherto unknown to nature and not represented by hidden variables correlated (or otherwise) with natural hidden variables.

The predestined choice that Alice makes to use $\pi^{31}$ does not allow nature to correlate those digits with the hidden variables in the rest of the universe.

 

[A. Neumaier]

It's only "predictable" if you have mathematical intelligence.

like most of physics!

 

[PeterDonis]

I'm pretty sure that in the actual world, my choices are largely determined by my past and the influences of the environment.

Yes, but that is a weaker statement than the claim superdeterminism makes.

But still, if I can conceive of the idea of choosing a measurement based on the digits of pi, then I can carry out that idea.

According to our usual view of how our "making choices" works, yes. But according to superdeterminism, no, you might not be able to carry out that idea--at least not the way you are conceiving it. Your conceiving it and carrying it out, if it were possible at all, would have to be set up by the initial conditions of the universe in such a way that the measurement results you got could not prove superdeterminism to be wrong. So if you had the intuitive idea that you could somehow "test" superdeterminism in this way, your intuitive idea would be wrong if superdeterminism were true.

 

[kith]

The 4th component (the mathematical system) is different, because there are no hidden variables in nature that represent this number (in base 10). These digits (data) come out of the blue as far as nature is concerned. Nature cannot correlate that precise sequence of digits with the decision in Alice's brain [...]

Can Nature correlate any sequence of digits with the decision in Alice's brain?

 

[PeterDonis]

if Alice uses the digits of $\pi$ then we need them to be correlated with the photon polarisation

Yes.

but they are not being generated using initial conditions and the superdeterministic laws of physics.

If superdeterminism is true, then they are--the initial conditions of the universe are set up just right so that the digits of $\pi$ correlate with the photon polarizations at the times Alice makes her measurements. Of course this means that Alice is not actually free to choose the times at which she makes her measurements; the initial conditions determine those times just as they determine everything else.

The digits of $\pi$ are independent of the physcal processes that set the photon polarisation and compelled Alice to choose $\pi$.

Again, if superdeterminism is true, then no, these things are not independent. The initial conditions are set up so that these physical processes correlate in just the right way with the digits of $\pi$.

The laws of physics may control baseball scores and correlate them with photon polarisation; but, I don't see how they can correlate photon polarisation with the digits of $\pi$.

It's not the laws that make this correlation in superdeterminism, it's the initial conditions. See above.

 

[PeroK]

Yes.If superdeterminism is true, then they are--the initial conditions of the universe are set up just right so that the digits of $\pi$ correlate with the photon polarizations at the times Alice makes her measurements. Of course this means that Alice is not actually free to choose the times at which she makes her measurements; the initial conditions determine those times just as they determine everything else.Again, if superdeterminism is true, then no, these things are not independent. The initial conditions are set up so that these physical processes correlate in just the right way with the digits of $\pi$.It's not the laws that make this correlation in superdeterminism, it's the initial conditions. See above.

That's superdeterminism as god, not as a valid physical theory. In other words, nature cannot be omniscient about mathematical constants. Or, preconfigured to correlate with mathematical constants. That would require intelligent design.

 

[PeterDonis]

That's superdeterminism as god, not as a valid physical theory. In other words, nature cannot be omniscient about mathematical constants. Or, preconfigured to correlate with mathematical constants.

I'm sorry, but your objections here are simply wrong stated the way you state them, as categorical claims. There is nothing logically impossible about setting up a physical model of the universe with initial conditions tuned just right in the way I described. You might not like the idea, but that doesn't make it impossible. It might make it highly implausible (I think it is), but that's not the same thing.

That would require intelligent design.

Again, if you are making this as a categorical claim, it is simply wrong. You can give this as a reason for thinking that superdeterminism is highly implausible--that it seems extremely, astronomically unlikely that such precisely fine-tuned initial conditions could come about without intelligent design--but that's not the same thing.

 

[PeroK]

I'm sorry, but your objections here are simply wrong stated the way you state them, as categorical claims. There is nothing logically impossible about setting up a physical model of the universe with initial conditions tuned just right in the way I described. You might not like the idea, but that doesn't make it impossible. It might make it highly implausible (I think it is), but that's not the same thing.Again, if you are making this as a categorical claim, it is simply wrong. You can give this as a reason for thinking that superdeterminism is highly implausible--that it seems extremely, astronomically unlikely that such precisely fine-tuned initial conditions could come about without intelligent design--but that's not the same thing.

We'll have to disagree about that. Mathematics is not the result of the laws of physics evolving since the big bang. Mathematics has an abstract independence from the state of the universe.

I accept we can never disprove the super-coincidence theory. But, the superdetermism described as a loop-hole in QM is not a super-coincidence theory. It's supposed to be a valid set of laws of physics that is not dependent on an ever decreasing probability to hold. It's supposed to be a valid, reliable (albeit unknown) set of laws of physics that keeps everything correlated.

If it were a super-coincidence theory, then there would be no need to question free-will. We could all the free-will we want, but just by luck or coincidence make certain choices.

The removal of free-will is needed, because superdeterminism is not supposed to rest on pure luck. In fact, luck is what it's supposed to get rid of! It's supposed to remove any dependence on probabilities by having a purely deterministic theory that holds everything together. It's not supposed to rest on the pure luck or coincidence relating to the initial conditions.

 

[PeterDonis]

Mathematics is not the result of the laws of physics evolving since the big bang.

True, but irrelevant. We are not talking about pure mathematics; we are talking about a particular physical model of the universe. In that model, the initial conditions are set up (in your hypothetical) so that the photon polarizations and the particular times that Alice makes her measurements are correlated in just the right way with the digits of $\pi$. You appear to be claiming that this is logically impossible, but I have seen nothing from you to back up this claim; your only actual argument is that you find it highly implausible. I find it highly implausible too, but that's not the same thing as being logically impossible. If you only intended to claim that it was highly implausible, then you can just say so and we are in agreement.

The removal of free-will is needed, because superdeterminism is not supposed to rest on pure luck. In fact, luck is what it's supposed to get rid of! It's supposed to remove any dependence on probabilities by having a purely deterministic theory that holds everything together. It's not supposed to rest on the pure luck or coincidence relating to the initial conditions.

None of this contradicts anything I said. I agree that superdeterminism is deterministic and that our ordinary concept of "free will" is not applicable in a superdeterministic model. That doesn't mean such a model is logically impossible.

It's not supposed to rest on the pure luck or coincidence relating to the initial conditions.

This is just another way of saying that you find superdeterminism highly implausible. Which, as already noted above, I agree that it is, but that's not the same as it being logically impossible.

 

[PeterDonis]

It's supposed to be a valid set of laws of physics that is not dependent on an ever decreasing probability to hold. It's supposed to be a valid, reliable (albeit unknown) set of laws of physics that keeps everything correlated.

Where are you getting these statements about superdeterminism from? Can you give references?

 

[PeroK]

True, but irrelevant. We are not talking about pure mathematics; we are talking about a particular physical model of the universe. In that model, the initial conditions are set up (in your hypothetical) so that the photon polarizations and the particular times that Alice makes her measurements are correlated in just the right way with the digits of $\pi$. You appear to be claiming that this is logically impossible, but I have seen nothing from you to back up this claim; your only actual argument is that you find it highly implausible. I find it highly implausible too, but that's not the same thing as being logically impossible. If you only intended to claim that it was highly implausible, then you can just say so and we are in agreement.None of this contradicts anything I said. I agree that superdeterminism is deterministic and that our ordinary concept of "free will" is not applicable in a superdeterministic model. That doesn't mean such a model is logically impossible.This is just another way of saying that you find superdeterminism highly implausible. Which, as already noted above, I agree that it is, but that's not the same as it being logically impossible.

Let me just say that your objections show that you have misunderstood my point.

What I've said is that if Alice uses a mathematical sequence as a source of data, then no deterministic model can induce statistical dependence of the state of physical systems and the data from abstract, pure mathematics. I've tried to explain why that specifically is impossible.

The statistical dependence of different sub-systems of the physical universe may be highly implausible, albeit logically possible. I don't dispute that.

The main reference from an advocate of SD is:

https://arxiv.org/pdf/1912.06462.pdf

Hossenfelder makes these two key points:

1) All physical systems are statistically dependent - i.e. SD violates statistical independence. This is page 5 and appears to be the heart of the matter.

2) Attempts by physicists to ensure independence by using distant quasars etc. is refuted (I would agree quite rightly) on page 13. I agree it's pointless to look for statistical independence in physical systems to undermine a theory that insists that all systems are statistically dependent.

I can't see anything in Hossenfelder's paper that suggests that SD is just super-coincidence. It's fine-tuned, of course, but she's putting it forward as an alternative physical theory.

My point in a nutshell is that we can use human intelligence to pull data in from abstract, pure mathematics that cannot be statistically dependent on the physical system being tested. Not in the way that Hossenfelder requires. That is what I'm saying.

The key point that I believe is being overlooked is that although the choice of mathematical system is predetermined, the data that arises from that system is not statistically dependent on the physical hidden variables. Crudely:

The hidden variables determining Alice's choice of $\pi^{31}$ are not statistically dependent on the data contained in that mathematical system. That's where, I claim, the statistical dependence maintained by SD and the laws of physics breaks down. Because the laws of physics cannot determine the precise mathematical data - without intelligent mathematical computational knowledge, which nature does not possess. (*)

I would argue that this is then a test of SD. We can generate statistically independent data and then do a Bell test.

(*) To emphasise this point. There is no problem with the initial conditions determining Alice's choice and nature, in a sense, "knowing" that $\pi^{31}$ is the dependent data. But, that data is effectively independent because nature has no way of understanding the implications of that choice. The processes are dependent, but one is physical and one is mathematical and the precise data that arises from each is independent and uncorrelated.

 

[PeterDonis]

your objections show that you have misunderstood my point.

I don't think I've misunderstood your point; I just don't agree with it.

What I've said is that if Alice uses a mathematical sequence as a source of data, then no deterministic model can induce statistical dependence of the state of physical systems and the data from abstract, pure mathematics. I've tried to explain why that specifically is impossible.

I don't see that you've shown that this is impossible. Your only argument is that you find it highly implausible because you can't imagine how it could happen. That's not showing that it's impossible. You certainly have not shown mathematically that it is impossible, or given a reference that contains any such proof. I agree that it's highly implausible; I don't agree that it's impossible.

My point in a nutshell is that we can use human intelligence to pull data in from abstract, pure mathematics that cannot be statistically dependent on the physical system being tested.

And I disagree with this claim. It is perfectly possible, logically, for the initial conditions in a deterministic model to be set up such that there is a statistical dependence, within the model, between the states of some set of physical systems and the digits of pi. You have given no argument to refute that.

The hidden variables determining Alice's choice of $\pi^{31}$ are not statistically dependent on the data contained in that mathematical system.

You can't just assert this. You have to prove that it must be the case for any logically possible model. You haven't.

 

[PeterDonis]

I can't see anything in Hossenfelder's paper that suggests that SD is just super-coincidence. It's fine-tuned, of course, but she's putting it forward as an alternative physical theory.

I don't understand the distinction you are drawing here between "super-coincidence" and "fine-tuned, but alternative physical theory". What's the difference?

 

[kith]

I would argue that this is then a test of SD. We can generate statistically independent data and then do a Bell test.

I don't think Hossenfelder would agree with this.

Her idea of tests is to find indications for a fundamental superdeterministic theory underpinning QM by doing experiments until you find deviations from QM.

Your idea is to rule out superdeterminism with a single experiment. I expect her to say that results in agreement with QM simply constrain the space of possible superdeterministic theories (and I don't see an indication that she would consider your test as constraining them more than the wealth of Bell tests which have already been performed).

My question in #76 hasn't been rhetorical by the way. I genuinely don't understand this point about your view. I don't see how it makes sense to say that Nature can correlate some sequences of digits with Alice's decisions but not others.

 

[PeterDonis]

I would argue that this is then a test of SD. We can generate statistically independent data and then do a Bell test.

If superdeterminism is true, then you cannot assume you can generate statistically independent data, because the initial conditions of the universe determine what data you will generate, and if those initial conditions are such that the data you generate is not statistically independent, there's nothing you can do about it.

I think you are simply failing to consider the actual implications of superdeterminism, so you are making assumptions that are inconsistent with superdeterminism. Of course if you make such assumptions, it will seem to you that superdeterminism cannot be true; but that just means you can't make those assumptions if you want to consider models in which superdeterminism is true.

 

[EPR]

That's superdeterminism as god, not as a valid physical theory. In other words, nature cannot be omniscient about mathematical constants. Or, preconfigured to correlate with mathematical constants. That would require intelligent design.

We have no good verifiable theory why the initial conditions were what they were. You make it sound like only superdeterminism suffers from this flaw.

Even without superdeterminism it is difficult to imagine what might have happened without a god of sorts or an infinite number of universes. Or an infinite amount of time producing an infinite number of universes before the current one. The point is - you can insert this God in thousands of places that are still blank. Not just in superdeterminism.

 

[Motore]

I will ilustrate an example what superdeterminism means to me:
I go to sleep in a summer night and open the windows so the room cools overnight. The next morning a slight breeze just moves the window by a few cm so the rays from the sun bounce of the window onto my face. That wakes me up about half an hour earlier than usual and I have time to make coffee (usually I drink at work). I take the mug that has some 10 digits of Pi written on it and I decide to test QM this day using the digits I just saw. The results come back confirming QM predictions.
If I am a superdeterminist I conclude that the initial conditions from BB made it so, that the weather was hot on this particulare date, that the window moved, that I woke up earlier, drinked coffee from a mug that had digits of Pi, which made me do a QM experiment which confirmed the predictions. Everything leading to this day, on this day and all future days was predetermined from the initial conditions on BB.
I see no logical inconsistnecy, but I do believe such an interpretation is highly unlikely.
Can someone correct me if I understood superdeterminisem completely wrong?

 

[PeroK]

My question in #76 hasn't been rhetorical by the way. I genuinely don't understand this point about your view. I don't see how it makes sense to say that Nature can correlate some sequences of digits with Alice's decisions but not others.

Because nature only controls physical data, not mathematics. Nature did not determine the set of prime numbers by initial conditions at the Big Bang. The sequence of prime numbers is fundamentally different from a physically generated sequence of data.

SD does not determine which numbers are prime. That data is beyond the scope of physics. The laws of physics do not determine which numbers are prime. But, the laws of physics do determine the data from a sequebce of coin tosses.