I "Counterfactual definiteness" vs. "free will"

[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?

 

[martinbn]

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.

1,5,2,7,3,9,4,...

 

[PeroK]

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.

Okay, but physical data comes from the laws of physics operating on physical systems. The digits of $\pi$ and $e$ are independent of that. They are not superdetermined by the conditions at the big bang. Natural processes have no control over them.

 

[Demystifier]

1,5,2,7,3,9,4,...

Was it created by your brain, or is it a law of mathematics? I'm not asking you, I'm asking @PeroK.

 

[PeroK]

Was it created by your brain, or is it a law of mathematics? I'm not asking you, I'm asking @PeroK.

It's possible that superdeterminism fails on a more basic level - in the sense that humans already have enough knowldege of non-physical data to blow the theory out the water. Rather than undermine my argument, I think your question further undermines superdeterminism: in that a human being has enough knowldege of mathematics to produce data that is fundamentally different from data from non-intelligent physical systems.

Be that as it may, a human being can certainly decide to hand over control of data generation to a mathematically generated sequence that has no connection with physical systems and their state at a given point in time.

And that is, I claim, fundamentally different from getting data from physical systems whose data (at a point in time) may be correlated with data from any other physical system.

 

[Lynch101]

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..

There will still be a physical process involved in using the digits of pi to set the measurement settings won't there? As in, will a computer be used to return a certain digit of pi, which then determines the detector setting?

If so, would superdeterminism not say that the process which returns the digit of pi is determined at the big bang i.e. it was inevitable that that particular digit of pi would be chosen?

 

[martinbn]

It's possible that superdeterminism fails on a more basic level - in the sense that humans already have enough knowldege of non-physical data to blow the theory out the water. Rather than undermine my argument, I think your question further undermines superdeterminism: in that a human being has enough knowldege of mathematics to produce data that is fundamentally different from data from non-intelligent physical systems.

Be that as it may, a human being can certainly decide to hand over control of data generation to a mathematically generated sequence that has no connection with physical systems and their state at a given point in time.

And that is, I claim, fundamentally different from getting data from physical systems whose data (at a point in time) may be correlated with data from any other physical system.

It is probably possible to give a diagonal/Kontor type argument the superdeterminism is inconsistent. Use several different initial conditions, they give you several different universes with different Alices and Bobs with different choices. You pick anyone of them that is not the actual universe. The initial conditions of the actual universe have to be such that it leads to all these solutions by you and the choices you made. But the choice was for a different universe that ours.

 

[A. Neumaier]

But, I can see no way that the data from a physical system can be correlated with the digits of pi in base 10.

People have written computer programs printing out these digits. The computer used is obviously a physical system, whose results are even perfectly correlated with the digits of pi.

 

[facenian]

The discussion could go forever with claims of religion, science, absurdity, etc. The fact is that what the Bell theorem needs to be proved is $p(\lambda|ab)=p(\lambda)$.
It simply means that Bell assumed that the experimental "choices" are uncorrelated to the common causes determining the particles' behavior.
The discussion of what it means is rather metaphysical. I suppose we could look for those common causes until the instant the big bang occurred.

 

[PeroK]

People have written computer programs printing out these digits. The computer used is obviously a physical system, whose results are even perfectly correlated with the digits of pi.

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. Ergo superdeterminism is equivalent to a god and cannot be simply the laws of physics at work.

 

[Lynch101]

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. Ergo superdeterminism is equivalent to a god and cannot be simply the laws of physics at work.

But the process by which an intelligent being comes to understand mathematics is entirely physical, isn't it? Even if we suggest that the mathematics itself is somehow ethereal. The subsequent programming of the machines is also a physical process. Would superdeterminists not say that the process by which mathematicians discovered pi was determined at the big bang, as was their subsequent programming of the relevant systsems?

 

[stevendaryl]

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.

I sympathize with your qualms about superdeterminism, but I don't understand specifically the point about $pi$. The important issue for superdeterminism is that Alice's and Bob's choices should be computable in principle from facts about the Big Bang. The sequence of digits of $\pi$ are computable without those facts, so they are certainly computable with those facts.

I don't see the appearance of $\pi$ in a quantum experiment any more weird than the appearance of sines and cosines in the solutions of the harmonic oscillator.

 

[martinbn]

I sympathize with your qualms about superdeterminism, but I don't understand specifically the point about $pi$. The important issue for superdeterminism is that Alice's and Bob's choices should be computable in principle from facts about the Big Bang. The sequence of digits of $\pi$ are computable without those facts, so they are certainly computable with those facts.

I don't see the appearance of $\pi$ in a quantum experiment any more weird than the appearance of sines and cosines in the solutions of the harmonic oscillator.

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.

 

[stevendaryl]

Okay, but physical data comes from the laws of physics operating on physical systems. The digits of $\pi$ and $e$ are independent of that. They are not superdetermined by the conditions at the big bang. Natural processes have no control over them.

I think there might be a misunderstanding going on about how the superdeterministic loophole works. You are arguing as if it is necessary for Alice's and Bob's choices to be controllable by facts about the universe. But it's only necessary for their choices made to be predictable. If you knew what choices Alice and Bob would make, then you could choose "hidden variables" that reproduced the predictions of quantum mechanics.

 

[PeterDonis]

What stops me from doing that.

Superdeterminism says that the initial conditions of the universe do not allow you to "pick" anything that is not determined by those initial conditions.

In other words, to even think coherently about superdeterminism, you must discard your ordinary intuitions about being able to freely "pick" things like what you are going to use to determine measurement settings. According to superdeterminism, you cannot freely "pick" such things; your "pick" is determined by the initial conditions of the universe. So according to superdeterminism, you can't even coherently formulate a scenario where you "pick" something that allows you to show that superdeterminism is false.

 

[stevendaryl]

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.

I'm not sure what you mean by "something else". You mean pick something that can't be computed from the initial conditions? How would you do that? How can make a choice of what measurement to perform based on something that cannot be computed?

 

[PeterDonis]

How can make a choice of what measurement to perform based on something that cannot be computed?

According to superdeterminism, you cannot "make a choice" of what measurement to perform. What measurement is performed is determined by the initial conditions of the universe; you have no "choice" in the matter.

 

[stevendaryl]

It is probably possible to give a diagonal/Kontor type argument the superdeterminism is inconsistent.

I don't think it's inconsistent, but it would have some strange aspects.

If Alice's future actions are in principle predictable, then imagine a computer program that sets about trying to predict what choice Alice will make. Being a supercomputer, it comes up with its answer before Alice makes her choice, and tells Alice what the result is. Then Alice being a contrarian does the opposite of whatever is predicted.

That sounds like a paradox, but there are a number of loopholes that would allow us to salvage consistency.

1. Maybe in such a setup, Alice would find herself unable to choose something other than what was predicted.
2. Maybe events would conspire to prevent Alice from ever learning the results of the prediction.
3. Maybe, even though the choice is computable in principle, in practice the amount of time required to predict it would be so great that Alice will have made the choice before the prediction is completed.

For superdeterminism to work as a loophole to Bell's inequality, Alice's future choices have to be computed prior to Alice making those choices. So #3 is ruled out. 1&2 are still possible, though.

 

[PeroK]

I sympathize with your qualms about superdeterminism, but I don't understand specifically the point about $pi$. The important issue for superdeterminism is that Alice's and Bob's choices should be computable in principle from facts about the Big Bang. The sequence of digits of $\pi$ are computable without those facts, so they are certainly computable with those facts.

I don't see the appearance of $\pi$ in a quantum experiment any more weird than the appearance of sines and cosines in the solutions of the harmonic oscillator.

The idea is that mathematics itself is outside the laws of physics. There can be no physical relationship between the digits in $e$ and $\pi$ that is determined by conditions at the big bang. These digits cannot be related to initial conditions at the big bang and the laws of physics.

That we (as intelligent humans) know all about them, does not mean that nature can perfectly produce them. For example, if a message from deep space was decoded as the digits of $\pi$, then we would know that an alien intelligence had sent it.

The decision to use these mathematical constants could be determined by initial conditions and the laws of physics. But, the natural laws cannot take the next step and calculate what they are - this is my point. Superdeterminism, however interconnected it makes all physics processes, is just dumb unthinking nature processing data though the laws of physics. Unless intelligence is involved it cannot start doing mathematics, as it were. Unless there is an intelligence controlling the results of QM experiments, they experiments cannot reliably produce $\pi$, $e$ or anything mathematical - except by supercoincidence, which has a vanishingly small probability of being sustained.

So, superdeterminism cannot be a physical theory. It cannot be based on initial conditions and laws of physics. It needs either an intervening intelligence, or a increasingly large coincidence factor. It cannot be simply the laws of physics at work.

 

[PeroK]

I think there might be a misunderstanding going on about how the superdeterministic loophole works. You are arguing as if it is necessary for Alice's and Bob's choices to be controllable by facts about the universe. But it's only necessary for their choices made to be predictable. If you knew what choices Alice and Bob would make, then you could choose "hidden variables" that reproduced the predictions of quantum mechanics.

That's what I would call supercoincidence. I thought the idea of superdeterminism was that there are unknown but theorecyically plausible laws of physics at work?

 

[stevendaryl]

According to superdeterminism, you cannot "make a choice" of what measurement to perform. What measurement is performed is determined by the initial conditions of the universe; you have no "choice" in the matter.

I don't think that's a helpful way to look at it. I'm pretty sure that in the actual world, my choices are largely determined by my past and the influences of the environment. 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. Certainly, it's an illusion that it was a completely free choice. But it doesn't need to be free.

If you want to claim that our universe is such that it is impossible for Alice to base her measurement choices on the digits of pi, well, that's a falsifiable claim. And I believe it's false. We can try it out, I guess.

 

[stevendaryl]

That's what I would call supercoincidence. I thought the idea of superdeterminism was that there are unknown but theorecyically plausible laws of physics at work?

Well, I don't think that superdeterminism is plausible, but I don't see how the arguments about $\pi$ make it any less plausible.

For superdeterminism to work, the choices made by Alice and Bob must be predictable, and the choice of the hidden variable must be made taking their future choices into account.

 

[PeroK]

For superdeterminism to work, the choices made by Alice and Bob must be predictable, and the choice of the hidden variable must be made taking their future choices into account.

Even something as absurd as using baseball results open the door for superdeterminsm: the result, Alice's choice to use the baseball results and the phton polarisation are all correlated via the initial conditions and the superdeterministic laws of physics.

But, if Alice uses the digits of $\pi$ then we need them to be correlated with the photon polarisation - but they are not being generated using initial conditions and the superdeterministic laws of physics. The digits of $\pi$ are independent of the physcal processes that set the photon polarisation and compelled Alice to choose $\pi$.

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 $\pi$. Even though, to an intelligence the digits of $\pi$ are predetermined by the laws of mathematics.

 

[kith]

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.

 

[PeroK]

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.

I'm glad you think so, because that's what I set out to show. The Wikipedia entry, however, has a quotation from John Bell:

"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. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be."

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.

In short: we use our intelligence to use data that has not itself been superdetermined. The coice to use that data has, but the data itslelf is unknown to superdeterministic nature.

That leaves either supercoincidence or intelligent superdeterminism (aka god).

 

[stevendaryl]

But, if Alice uses the digits of $\pi$ then we need them to be correlated with the photon polarisation - but they are not being generated using initial conditions and the superdeterministic laws of physics. The digits of $\pi$ are independent of the physcal processes that set the photon polarisation and compelled Alice to choose $\pi$.

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.

Let me illustrate the idea behind Bell's inequality using a simulation, rather than the real laws of physics.

We have 5 computers running different programs:

1. CA: On one computer, we have a simulation of Alice.
2. CAD: On another computer, we have a simulation of Alice's detector.
3. CB: On another computer, we have a simulation of Bob.
4. CBD: On another computer, we have a simulation of Bob's detector.
5. CS: On another computer, we have a simulation of the source of twin pairs.

Their interaction is split up into a number of "rounds". Each round, the following sequence of actions takes place:

1. The computer CS produces two messages, representing the correlated twin pairs. For round number $i$, we will call the messages produced on that round $ma_i$ and $mb_i$.
2. One message $ma_i$ is sent to CAD, one message, $mb_i$ is sent to CBD.
3. The computers CA and CB each produce a detector setting (a unit vector). Let $\alpha_i$ be the setting chosen by CA on round $i$, and let $\beta_i$ be the setting chosen by CB.
4. The output of CA is sent to CAD, and the output of CB is sent to CBD.
5. Each of the computers CAD and CBD produce an output, either "spin-up" or "spin-down", based on their inputs. Let $ra_i$ be the output of CAD, and let $rb_i$ be the output of CBD.

You run this simulation for many rounds to get adequate statistics.

For any pair of unit vectors $\alpha, \beta$, let $I(\alpha, \beta)$ be the set of all rounds $i$ such that $\alpha_i = \alpha$ and $\beta_i = \beta$.

For the simulation to successfully simulate the quantum predictions for EPR, it must be the case that for every pair $\alpha, \beta$ such that there are adequate statistics (that is, the set $I(\alpha, \beta)$ should be sufficiently large), the fraction of $i$ in $I(\alpha, \beta)$ such that $ra_i = rb_i$ should be close to $sin^2(\frac{\theta}{2})$, where $\theta$ is the angle between $\alpha$ and $\beta$.

The simulation depends on 5 algorithms, for each of the 5 computers:

1. For CS: An algorithm that computes $ma_i$ and $mb_i$ based on nothing more than the round number, $i$
2. For CA: An algorithm that computes $\alpha_i$
3. For CB: An algorithm that computes $\beta_i$
4. For CAD: An algorithm that computes $ra_i$ from $\alpha_i$ and $ma_i$
5. For CBD: An algorithm that computes $rb_i$ from $\beta_i$ and $mb_i$

What you can prove (from Bell's inequality) is that there are no choice of algorithms for CS and CBD that will get the statistics of the results right, no matter what algorithms are chosen for CA and CB. To turn that around, no matter what algorithm is chosen for CS and CBD, there are algorithms CA and CB that will spoil the statistics and make them unlike the predictions of QM for the EPR experiment.

The various "loopholes" correspond to tweaks to the setup:

• The FTL loophole corresponds to allowing CBD and CAD to communicate.
• The superdeterminism loophole corresponds to allowing CS to know the algorithms CA and CB and to take those algorithms into account in computing the messages $ma_i$ and $mb_i$.
• The retrocausality loophole corresponds to allowing CS to know the settings $\alpha_i$ and $\beta_i$ before creating the messages $ma_i$ and $mb_i$.
• I suppose there is also a "mind control" loophole corresponding to CS being able to choose $\alpha_i$ and $\beta_i$, or force CA and CB to make those choices.

Anyway, to me, the plausibility or implausibility of the superdeterminism loophole is not affected by letting the choices $\alpha_i$ and $\beta_i$ depend on the digits of $\pi$. But it becomes very implausible if you allow those choices to depend on arbitrary other inputs (such as from astronomical data, baseball scores, etc.)