"Counterfactual definiteness" vs. "free will"

[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.

 

[Demystifier]

Or, show how $\pi$ and $e$ depend on the initial conditions at the Big Bang.

That's a wrong question. Alice could use the digits of the constant $d=34275.2998$ (it's called Demystifier constant, by the person who first introduced it a minute ago) in her measurement setup, would you in that case ask how $d$ depends on the initial conditions at the Big Bang?

 

[PeroK]

That's a wrong question. Alice could use the digits of the constant $a=34275.2998$ in her measurement setup, would you in that case ask how $a$ depends on the initial conditions at the Big Bang?

Assuming Alice decided on all those digits, then by the hidden variables controlling her thought processes.

As long as Alice keeps making the decision about what digit to use, all the data is ultimately the result of a physical process controlled to a greater or lesser extent by the laws of physics.

If Alice decides to use prime numbers, then the initial decision is controlled by the laws of physics, but the full set of data (the set of prime numbers) is then subsequently independent of the laws of physics.

Two sets of coin tosses could be correlated (theoretically); but, one set of coin tosses cannot be correlated with the set of prime numbers.

 

[Demystifier]

Assuming Alice decided on all those digits

But she didn't. It was me who decided to give this number a name, but this number existed before I or anyone else gave it a name. Alice saw this constant here on forum and decided to use it in her experiment.

 

[PeroK]

But she didn't. It was me who decided to give this number a name, but this number existed before I or anyone else gave it a name. Alice saw this constant here on forum and decided to use it in her experiment.

We've been round this loop. I don't want to spend any more time on this thread, because obviously I'm the only one that sees mathematics as a problem for SD. Maybe it isn't a problem and maybe it is.

It can't be resolved here other than to accept the status quo that SD is impregnable. But, I simply do not understand why it is impregnable and why mathematical data (independent of the laws of physics) cannot be used by physicists in their experiments). I wish I understood, but I don't.

Sorry to have wasted everyone's time.

 

[Demystifier]

But, I simply do not understand ... why mathematical data (independent of the laws of physics) cannot be used by physicists in their experiments). I wish I understood, but I don't.

Because physicists themselves are physical objects, not mathematical objects.

But if you are interested in a deeper thinking about such questions (relations between physical objects, mathematical objects and the mind), I recommend the book R. Penrose, The Emperor's New Mind.

 

[Lynch101]

We've been round this loop. I don't want to spend any more time on this thread, because obviously I'm the only one that sees mathematics as a problem for SD. Maybe it isn't a problem and maybe it is.

It can't be resolved here other than to accept the status quo that SD is impregnable. But, I simply do not understand why it is impregnable and why mathematical data (independent of the laws of physics) cannot be used by physicists in their experiments). I wish I understood, but I don't.

Is there perhaps a hidden assumption about the nature of mathematics or with what the results are correlated?

If we think about the process by which Alice comes to know the digits of pi. It's a process which occurs entirely in her own brain. We might add in that she has learned them in school. This would be explained by SD as a deterministic process, inevitable from the big bang.

We can however, for the sake of argument, assume that Alice is the first person to discover pi. So, we need to examine the process by which she discovers it. There are an abundance of examples as to how she may have discovered it but if we imagine that Alice sees a prisoner of war tethered to a pole. The POW wants to get as much exercise as possible so he walks as far as the rope will allow him. This happens to trace out a circle around the pole with a radius the length of the rope. After a while the prisoner gets bored of this route and decides to change the path, so he walks to the centre of the circle and out to the edge of the circle on the other side.

Alice is interested to see the ratio of the two routes so she cuts a number of lengths of rope, the length of the diameter of the circle, and lays them out around the circumference. On the basis of this, she creates abstractions of similar scenarios with varying radii. She finds that the ratio of the circumference to the diameter is the same in each case. She carries out tests with varying lengths of rope and finds that this holds true.

In this case, the nature of matter [as determined at the big bang] is such that the circumference of a circle [traced out using some form of matter of a given length] will always have the ratio pi to the diameter of that circle.Even if we ascribe some transcendental qualities to pi and other mathematical constants, the process by which experimenters come to discover and know them is a physical process, which SD would say is determined from the big bang.

 

[stevendaryl]

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.

Certainly, you can never absolutely falsify superdeterminism, but we can certainly falsify the claim that it's impossible to choose EPR settings according to the digits of $\pi$.

 

[stevendaryl]

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.

As I said already, there are two ways for Alice's choices to be correlated with the hidden variables of EPR so as to reproduce the predictions of QM: (1) Alice's choices might be constrained in the appropriate way, or (2) the hidden variables might be chosen taking Alice's (future) choices into account. The second possibly doesn't require a conspiracy for Alice's choices, it only requires that they be predictable.

 

[PeterDonis]

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.

No, the laws of physics plus the initial conditions determine the data from a sequence of coin tosses. And there is nothing logically impossible about having a set of initial conditions that, combined with the applicable laws of physics, leads to the data from a sequence of coin tosses being correlated with the digits of $\pi$, or prime numbers, or any other mathematical pattern. It's highly implausible, but not logically impossible.

You have already made this argument and had this same response given to you several times now, but you have never addressed the response; you have just repeated the argument.

 

[PeterDonis]

It can't be resolved here other than to accept the status quo that SD is impregnable.

Nobody is claiming that superdeterminism is impregnable, period. All we are saying is that the arguments you have been making do not show that superdeterminism is logically impossible. They only show that it's highly implausible (and I don't think anyone disagrees about that).

 

[PeroK]

Nobody is claiming that superdeterminism is impregnable, period.

Certainly, you can never absolutely falsify superdeterminism,

 

[stevendaryl]

Well, being unfalsifiable is a strike against superdeterminism, from the point of view of science.

I'm pretty sure that it is impossible to disprove the claim that everything was fixed from the beginning of the universe, because whatever happens is consistent with the claim that that is the only possible thing that could have happened.

But that doesn't mean that you can't falsify a very specific superdeterministic theory. The theory that says that I'm destined to never utter the numbers "3", "1", "4", "1", "5", "9" is falsified by my saying them.

(I just did, so I falsified that theory.)

 

[PeterDonis]

Nobody is claiming that superdeterminism is impregnable, period.

Certainly, you can never absolutely falsify superdeterminism,

As @stevendaryl's response in post #102 shows, "unfalsifiable" is not the same as "impregnable".