I Why all the rejection of superdeterminism?

[Demystifier]

Then please point out where the error is. If one assumes that the universe (including all detectors and experimentors) is described by classical physics, the initial conditions determine everything including the choices of the experimentors, and there is no freedom. This is orthodox thinking since Laplace.

Here is a more precise way to explain the difference between determinism and superdeterminism. Let $x_1(t),...,x_N(t)$ be the complete set of phase-space variables in a closed system.

Determinism is simply the property that $x_1(t),...,x_N(t)$ are functions of $x_1(0),...,x_N(0)$.

What does it mean in practice? It means that if you know $x_1(0),...,x_N(0)$, then, in principle, you can calculate $x_1(t),...,x_N(t)$ for each $t$. But if you don't know all $x_1(0),...,x_N(0)$, then you cannot calculate $x_1(t),...,x_N(t)$, despite the fact that the system is deterministic. If you don't know $x_1(0),...,x_N(0)$, then determinism is not useful. Of course, Nature always knows $x_1(0),...,x_N(0)$, but it is of no use for you if you don't know them.

Now superdeterminism. It is determinism plus one additional property. Unlike determinism, superdeterminism can be useful even if you don't know all $x_1(0),...,x_N(0)$. For instance, it may be the case that Nature was so generous that it has chosen $x_1(0),...,x_N(0)$ in a very special way, such that

$x_2(t)$ can be expressed as a function of $x_1(t)$

In practice, it means that if you know $x_1(t)$ (e.g. by measuring it) then you can also calculate $x_2(t)$. And to do the calculation, you don't need to know anything about $x_1(0),...,x_N(0)$. Of course, Nature knows all $x_1(0),...,x_N(0)$, but the point is that you don't know $x_1(0),...,x_N(0)$, and yet you still can calculate $x_2(t)$ just from $x_1(t)$. That's superdeterminism.

From this, one can see that superdeterminism is not always problematic. For instance, Nature might have chosen initial conditions such that the distance between Earth and Moon is a constant. This is an example of a non-problematic superdeterminism. A problematic example of superdeterminism would be a pseudo-random number generator at my laptop that always gives the same numbers as the ones drawn at the lottery. Why is the latter example problematic and the former is not? Because the latter example looks like a conspiracy. What is the definition of conspiracy? Unfortunately, there is no precise definition. Yet, it looks intuitively quite clear that the latter is a conspiracy and the former is not.

 

[DrChinese]

Determinism is not the issue; superdeterminism is. In order for a deterministic local variables theory to reproduce the predictions of QM, the hidden variable must be chosen taking into account the future settings of the experimenters. Yes, if everything is deterministic, this is a theoretical possibility. However, the experiment can take place arbitrarily far in the future, and the setting can be made to depend on arbitrarily large regions of the universe, including regions that were initially outside of causal contact with the source of the twin pair.

Maybe it can all be made to work, but it is certainly not obvious that it is possible in any non-ad hoc way; in a way that doesn't seem as if the universe were constructed specially to make Alice and Bob have the right statistics.

So true. Here is some of what needs to happen for superdeterminism to make sense in the context of this thread:

1. Spacelike separated Alice and Bob select their angle settings based on some algorithm related to Geiger counter clicks from independent radioactive samples. They do NOT change their settings for the course of the test run, which might be long enough to get 10-100 suitable readings. They repeat this process a sufficient number of times to accumulate a suitable total sample size.

2. The "true" rate is not the QM predicted rate, which is merely a superdeterministic illusion. For example: the observed QM predicted rate for 120 degrees is a 25% match rate, but the "true" rate is actually more like 33% match rate. Our observed result (25%) is always "off" by just the right amount relative to the "true" rate (33%) - in this case a difference of 8%. But if you measure at theta=45 degrees, the sample is an accurate reflection of the universe and the match rate is precisely 50%.

3. All samples are ALWAYS biased and NEVER represent the true population (except for 0 degrees and 45 degrees). Doesn't matter if it is a sample of 100, 1000, 10000 etc. And the mechanism driving the experimenters' angle selections permeates nature to such an extent that it does NOT matter if you shuffle cards to make an angle selection, let the people choose on their own, or if a radioactive sample is the source of angle setting choices. All possible selection methods are equally "in on the fix".

4. And the same logic could equally apply to any scientific experiment conducted anywhere at any time covering any natural phenomena. Is relativity is a superdeterministic illusion too? How could you deny this as an equally likely possibility?

 

[A. Neumaier]

The difference is there is a conspiracy taking place with superdeterminism and not with regular determinism.

I only invoked regular determinism of the kind Laplace was propagating. This is the form of superdeterminism the OP was talking about:

superdeterminism (i.e. the experimentators are not free to choose the measurement parameters)

In the article of Wikipedia on superdeterminism one can read:

in a deterministic theory, the measurements the experimenters choose at each detector are predetermined by the laws of physics. It can therefore be argued that it is erroneous to speak of what would have happened had different measurements been chosen; no other measurement choices were physically possible.

The discussion following mentions that Bell acknowledged this. According to the statement quoted in the Wikipedia article, what bell calls super-determinism is just the deterministic universe, with no additional ingredient that turns the regular determinism into super-determinism. In particular, Bohmian mechanics is by design superdeterministic in this sense.

The subsequent argument with deterministic random number generators in place of free will has no logical force because even their outcomes are determined by the initial conditions of the universe. Thus the conspiracy comes in only as a plausibility argument to camouflage the logical gap in Bell's reasoning.

 

[A. Neumaier]

superderminism. It is determinism plus one additional property.

Not according to Bell (who coined the term) or Wikipedia (whose article is based on Bell's definition).

 

[A. Neumaier]

Here is some of what needs to happen for superdeterminism to make sense in the context of this thread:

Nothing of what you list is essential in the context of this thread. You misinterpreted this context: Neither Alice nor Bob nor Bell were mentioned in the OP, which defined the context.

 

[Demystifier]

Not according to Bell (who coined the term) or Wikipedia (whose article is based on Bell's definition).

Wikipedia didn't explain it well. Can you make an exact quote of Bell?

 

[A. Neumaier]

Wikipedia didn't explain it well. Can you make an exact quote of Bell?

I am currently trusting that wikipedia quoted Bell correctly. If you think it is a misrepresentation you should provide the evidence.

 

[DrChinese]

Nothing of what you list is essential in the context of this thread. You misinterpreted this context: Neither Alice nor Bob nor Bell were mentioned in the OP, which defined the context.

I disagree, Arnold. Superdeterminism is NOT determinism, regardless of the words Bell did (or did not) use and regardless of the Wiki article. Superdeterminism is ONLY intended as an "out" for Bell's Theorem. I do not take seriously the idea that Bell considered it as an out, he was just pointing out (in a very roundabout fashion) how desperate you would have to be to reject the logic and hold onto local realism.

 

[Demystifier]

I am currently trusting that wikipedia quoted Bell correctly. If you think it is a misrepresentation you should provide the evidence.

Here is an exact quote of Bell (the bolding is mine):

"An essential element in the reasoning here is that a and b are free
variables. One can envisage then theories in which there just are no free
variables for the polarizer angles to be coupled to. In such ‘superdeter-
ministic’ theories the apparent free will of experimenters, and any other
apparent randomness, would be illusory. Perhaps such a theory could be
both locally causal and in agreement with quantum mechanical predic-
tions. However I do not expect to see a serious theory of this kind. I
would expect a serious theory to permit ‘deterministic chaos’ or
‘pseudorandomness’, for complicated subsystems (e.g. computers)
which would provide variables sufficiently free for the purpose at hand.
But I do not have a theorem about that."

 

[DrChinese]

Here is an exact quote of Bell (the bolding is mine):

"An essential element in the reasoning here is that a and b are free
variables. One can envisage then theories in which there just are no free
variables for the polarizer angles to be coupled to. In such ‘superdeter-
ministic’ theories the apparent free will of experimenters, and any other
apparent randomness, would be illusory. Perhaps such a theory could be
both locally causal and in agreement with quantum mechanical predic-
tions. However I do not expect to see a serious theory of this kind. I
would expect a serious theory to permit ‘deterministic chaos’ or
‘pseudorandomness’, for complicated subsystems (e.g. computers)
which would provide variables sufficiently free for the purpose at hand.
But I do not have a theorem about that."

Good one, Demystifier!

 

[A. Neumaier]

I disagree, Arnold. Superdeterminism is NOT determinism, regardless of the words Bell did (or did not) use and regardless of the Wiki article.

Who then has the authority to define the meaning of the word, if you reject the meaning given to it by Bell, by Wikipedia, and by the originator of the thread?
Certainly @greypilgrim meant the version discussed in Wikipedia and not yours.

Superdeterminism is ONLY intended as an "out" for Bell's Theorem. I do not take seriously the idea that Bell considered it as an out, he was just pointing out (in a very roundabout fashion) how desperate you would have to be to reject the logic

Where is the logic? I argue on pure logical grounds (the only grounds where things are indisputable). You and Bell have only plausibility arguments.

and hold onto local realism.

The question of local realism is completely irrelevant from my point of view. Nobody expects it to hold, not even the defenders of loopholes.

 

[Demystifier]

if you reject the meaning given to it by Bell

Have you read the exact quote of Bell I have given?

 

[Demystifier]

The question of local realism is completely irrelevant from my point of view. Nobody expects it to hold, not even the defenders of loopholes.

Why do you think that defenders of loopholes do not expect local realism to hold?

 

[A. Neumaier]

I
would expect a serious theory to permit ‘deterministic chaos’ or
‘pseudorandomness’, for complicated subsystems (e.g. computers)
which would provide variables sufficiently free for the purpose at hand.

Can you please enlighten me in which way deterministic chaos would provide variables sufficiently free for the purpose at hand?

Even deterministic chaos leaves no freedom for any system to choose a different setting than the one determined by the initial conditions, and hence known to Nature long before the experiment begins.

 

[A. Neumaier]

Why do you think that defenders of loopholes do not expect local realism to hold?

It is just a subjective feeling. Maybe because I am just defending the loophole without caring about the theorem.

 

[A. Neumaier]

Have you read the exact quote of Bell I have given?

I still do not doubt that the Wikipedia quote of Bell on which I relied is as exact as yours. Unlike Wikipedia you haven't even given a source.

 

[DrChinese]

Who then has the authority to define the meaning of the word, if you reject the meaning given to it by Bell, ...

First, demystifier showed you already that his (and mine) reading represents Bell and yours clearly does not.

As to who has the authority: lacking a central authority, you are well aware that usually consensus can be achieved without resorting to a Mentor to get involved. Frankly, I am surprised at your position as it doesn't seem like something worth defending.

The use of the word "superdeterminism" is clearly and unambiguously tied to an "out" for Bell's Theorem, in order to retain local realism. The "super" prefix is intended to distinguish this from ordinary determinism - La Place or whatever - in which initial conditions and laws of physics determine all subsequent events. In superdeterminism, to that definition is added the constraint that there is always a bias in the selection of samples for Bell tests such that the true results are obscured but all other scientific experiments are otherwise unaffected by such selection bias.

I cannot imagine anything I am saying as being objectionable other than any other person would use their own words to describe the same. As far as I am concerned, I am as good an authority as you or anyone on the above, given what I am saying is a generic summary and represents a composite of the viewpoints of many other physicists I have read.

 

[Demystifier]

Can you please enlighten me in which way deterministic chaos would provide variables sufficiently free for the purpose at hand?

Even deterministic chaos leaves no freedom for any system to choose a different setting than the one determined by the initial conditions, and hence known to Nature long before the experiment begins.

Deterministic chaos creates an illusion of freedom. Since one cannot measure or control the fine differences between almost identical initial conditions, it looks as if different outcomes emerge from identical initial conditions. You still have not learned the FAPP way of thinking necessary to understand Bell.

 

[Demystifier]

Unlike Wikipedia you haven't even given a source.

And if I did, would it change your conclusions?

By the way, it's J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edition, Chapter 24.

 

[DrChinese]

Maybe because I am just defending the loophole without caring about the theorem.

Your stubbornness is usually something I enjoy while reading your excellent posts. But I have no idea why you would pick this position to defend, given your usual attention to key points in Physics.

Superdeterminism deserves a flitter across the brain in the seconds before it is permanently discarded.

 

[A. Neumaier]

Can you make an exact quote of Bell?

In [1] (listed below), Bell clearly specifies his assumptions in response to critique of his original formulation (italics are his):

'It has been assumed that the settings of instruments are in some sense free variables ...' For me this means that the values of such variables have implications only in their future light cones. They are in no sense a record of, and do not give information about what has gone before.

In a deterministic universe, this assumption is obviously violated. For it means that these values are independent of the values of all observables prior to the moment the settings are made. Indeed, if they would depend on the latter, fixing one of the values provides a nontrivial relation on the prior variables in their past light cone and hence provides information about the latter. Thus they give information about what was before, in direct contradiction to Bell's assumptions.

Note that no extra ingredient allegedly distinguishing superdeterminism from determinism is necessary to arrive at this contradiction.

In addition, Bells assumption is intuitively unreasonable. Any setting created by a human experimenter is obviously determined by the latter's intentions, which precede the setting and hence violate Bell's assumptions. And any setting created by a computer-driven automatic device is obviously determined by the latter's program, which precede the setting and hence violate Bell's assumptions, too.

Thus the logic of Bell's argument requires a nondeterministic universe.

1. J. S. Bell, Free variables and local causality, Epistemological Letters, Feb. 1977. Reprinted as Chapter 12 of J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press 1987)

 

[A. Neumaier]

But I have no idea why you would pick this position to defend, given your usual attention to key points in Physics.

Because I like to distinguish between clear logic and wishful thinking.

 

[DrChinese]

... the logic of Bell's argument requires a nondeterministic universe.

It most certainly does not, and none of your reference implies as much. The fair sampling hypothesis works whether the universe is or is not deterministic. It is only by violation of the fair sampling hypothesis - and in a very specific way - that superdeterminism speculatively operates. Bell never said otherwise, as he clearly assumed that the reader would fill that point into the extent it was not stated.

Further, this entire line of reasoning is moot anyway as there are other (non-Bell) tests in which there is no statistical component and/or there is no observer choice. With GHZ, for example, a single example will produce results in contradiction to local realism. Superdeterminism does NOT rescue that.

[edited to add:] Where does your "clear logic" stand on this?

 

[DrChinese]

Because I like to distinguish between clear logic and wishful thinking.

That's the kind of comment that I was looking for!

I feel better already.

-DrC

 

[A. Neumaier]

With GHZ, for example, a single example will produce results in contradiction to local realism.

True. But this has nothing to do with the present thread, which is, according to the OP, neither about local realism nor about which things can be proved with or without superdeterminism.

 

[A. Neumaier]

It most certainly does not, and none of your reference implies as much.

I claimed that ''the logic of Bell's argument requires a nondeterministic universe'', and this is true for the argument under discussion, viewed on purely logical grounds.

On the other hand, I agree that Bell's assumptions are reasonable from a practical point of view, and in the paper I referred to he didn't want to insist on more. This is enough for me to rule out local realism in Bell's sense.

However, I still believe that Nature is deterministic and we'll discover one day a realistic description. But it will neither be one that would be local realistic in Bell's sense, nor one that is superdeterministic like Bohmian mechanics where an extraordinary fine-tuning of the actual universe is needed so that our realization of the universe behaves precisely according to the assumed quantum equilibrium hypothesis.

 

[stevendaryl]

I feel like I'm arguing a two-front war here. On the one hand, I don't think that it's impossible to have a superdeterministic explanation for QM statistics. On the other hand, I think that such a theory would be very bizarre, and nothing like any theory we've seen so far.

Let me go through a stylized description of an EPR-like experiment so that we can see where the superdeterminism loophole comes in.

We have a game with three players, Alice, Bob and Charlie. Alice and Bob are in different rooms, and can't communicate. In each room, there are three light bulbs colored Red, Yellow and Blue, which can be turned off or on.

The game consists of many many rounds, where each round has the following steps:

1. Initially, all the lights are off.
   
2. Charlie creates a pair of messages, one to be sent to Alice and one to be sent to Bob.
3. After Charlie creates his messages, but before they arrive, Alice and Bob each choose a color, Red, Yellow or Blue. They can use whatever criterion they like for choosing their respective colors.
   
4. When Alice receives her message, she follows the instructions to decide whether to turn on her chosen light, or not. Bob similarly follows his instructions.

After playing the game for many, many rounds, the statistics are:

• When Alice and Bob choose the same color, they always do the opposite: If Alice's light is turned on, Bob's is turned off, and vice-versa.
• When Alice and Bob choose different colors, they do the same thing 3/4 of the time, and do the opposite thing 1/4 of the time.

The question is: What instructions could Charlie have given to Alice and Bob to achieve these results? The answer, proved by Bell's theorem, is that there is no way to guarantee those results, regardless of how clever Charlie is, provided that

1. Charlie doesn't know ahead of time what colors Alice and Bob will choose.
2. Alice has no way of knowing what's going on in Bob's room, and vice-versa.

The superdeterministic loophole

If Charlie does know what choices Alice and Bob will make, then it's easy for him to achieve the desired statistics:

• Every round, he randomly (50/50 chance) sends either the message to Alice: "turn your light on", or "turn your light off"
• If Alice and Bob are predestined to choose the same color, then Charlie sends the opposite message to Bob.
• If Alice and Bob are predestined to choose different colors, then Charlie will send Bob the same message 3/4 of the time, and the opposite message 1/4 of the time.

Why the superdeterministic loophole is implausible

The reason that the superdeterministic loophole is not possible is because Alice and Bob can choose any mechanism they like to help them decide what color to use. Alice might look up at the sky, and choose the color based on how many shooting stars she sees. Bob might listen to the radio and make his decision based on the scores of the soccer game. For Charlie to be able to predict what Alice and Bob will choose can potentially involving everything that can possibly happen to Alice and Bob during the course of a round of the game. The amount of information that Charlie would have to take into account would be truly astronomical. The processing power would be comparable to the power required to accurately simulate the entire universe.

Why I think the superdeterministic loophole is actually impossible

What the superdeterministic loophole amounts to is that somehow Charlie has information about the initial state (before the game began) of the universe, s_0, and somehow he has a pair of algorithms, \alpha(s_0) and \beta(s_0) that predict the choice of Alice and Bob as a function of the initial state. The problem is that even if there were such algorithms, they computational time for computing the result would be greater than just waiting to see what Alice and Bob choose. So Charlie couldn't possibly know the results in time to choose his instructions to take those results into account.

Why not? Remember, we're allowing Alice and Bob to use whatever mechanism they like to decide what color to pick. So suppose Alice picks the same algorithm, \alpha, and chooses whatever color is NOT returned by \alpha(s_0)? In other words, she runs the program, and if it returns "Red", she picks "Yellow". If it returns "Yellow", she picks "Blue". If it returns "Blue", she picks "Red". She can base her choice on anything, so if there is a computer program \alpha that she can run, then she can base her choice on whatever it returns.

The only way for it to be possible that \alpha(s_0) always gives the right answer for Alice is if it takes so long to run that Alice gives up and makes her choice before the program finishes.

This is actually a fairly standard argument that even if the universe is deterministic, if you tried to construct a computer program that is guaranteed to correctly predict the future, the future would typically arrive before the computer program finished its calculations. No matter how clever the algorithm, no matter how fast the processor, there is no way to guarantee that the prediction algorithm would be faster than just waiting to see what happens.

 

[DrChinese]

1. True.

2. But this has nothing to do with the present thread, which is, according to the OP, neither about local realism nor about which things can be proved with or without superdeterminism.

1. A victory! 2. From the OP: "superdeterminism (i.e. the experimentators are not free to choose the measurement parameters) allows the formulation of a local realistic quantum theory." [PS that's the diametric opposite of what you said.]It is also true that in a deterministic universe, experimenters are not free to choose the measurement parameters. But Zeilinger (also mentioned in the OP) and others do not object to that point, as a Bohmian universe is deterministic (too) and is generally accepted as a viable interpretation of QM. The key element of a superdeterministic theory in particular is that every experimental sample is biased exactly such as to support the incorrect predictions of QM as compared to the actual local realistic laws of physics.

And further: there is no actual theory of that either because if there were, physicists would be tearing it to shreds.

 

[stevendaryl]

In a deterministic universe, this assumption is obviously violated. For it means that these values are independent of the values of all observables prior to the moment the settings are made.

In a deterministic universe, it's still the case that the initial state of the universe is undetermined. Each of us can only have knowledge of a part of the universe--that part in our backwards lightcone. We have no knowledge about other parts of the universe unless we wait long enough for information from those sections of the universe to come into our backwards lightcone.

So even in a deterministic universe, the choices made by Alice and Bob at some future time may not be determined by the part of the universe available now. So effectively, they are undetermined.

 

[DrChinese]

I feel like I'm arguing a two-front war here. On the one hand, I don't think that it's impossible to have a superdeterministic explanation for QM statistics. On the other hand, I think that such a theory would be very bizarre, and nothing like any theory we've seen so far.

I feel your pain, and recognize my own participation in it.

Yes, the theory would be bizarre, I get your point about that. But how bizarre? That is *my* point - there really is no end to the bizarre nature. As soon as you explain one thing, I would come up with another counterexample, and yet a more bizarre version will need to be put forth. We can do that all day (actually let's not and say we did).

And I think you say it nicely when you comment about the prediction algorithm and time to execute. When I considered what it would take to support a superdeterministic local realistic theory, I inevitably conclude a near-infinite amount of information would need to be stored in every particle in order to provide the local realistic instruction set for Bell test outcomes. I think you would ultimately conclude the same, and see the inevitable circular reasoning required to support that position. How would you ever be able to draw a line between which particles are to be included in some future Bell test, and which aren't? Where is the instruction set residing for photons that don't even exist now? Or observers that don't exist now (presumably it is hidden in our DNA somewhere) ? Or measurement apparati that don't exist now? Etc.