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I'm not a physicist, I have read a lot about Bell's theorem and the Einstein/Bohr debates and I have the following question:

Judging by only classical physics, it seems we live in a 100% deterministic universe. If I got that wrong, then my whole question won't make sense. But I think you would agree that we can calculate a bullet's path with 100% accuracy and we don't observe true randomness anywhere in the universe based on classical physics. When I shoot a billiard ball and all forces are known, I'm sure you will all agree that there's no uncertainty about where the ball will land. In other words, if we forget about Quantum Physics for a moment, couldn't we all agree that the universe is deterministic ?.

But Bell's theorem came along and ruled out superdeterminism , which completely contradicted all that. But when I'm looking at Bell's theorem:

  • Bell admitted there might be loopholes
  • everything that isn't on a quantum scale in the univers acts as perfectly deterministic

We assume that tiny building blocks act in non-classical physics while seeing that larger building blocks act perfectly according to classical physics and in turn determinism. So shouldn't the fact that classical physics is so well observed and tested force us to assume that there is a high probability that Bell's theorem has some sort of loophole?

At the risk of going more off topic I would like to add:

  • I don't get why Bell's Theorem is often discussed in the context of Free Will. What does the one have to do with the other? Because even if there is quantum uncertainty, how does that proof that our brains make use of this uncertainty to make decisions?
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    $\begingroup$ Frankly, it isn't clear from the question that you understand what superdeterminism means as it is used in the literature. In the interest of having a debate that isn't people speaking past each other, it would be extremely helpful if you could briefly describe what you understand the term to mean. $\endgroup$
    – Emilio Pisanty
    Nov 18, 2019 at 23:34
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    $\begingroup$ "Superdeterminism" is a technical term, which you seem to be using in the same sense as "determinism", which is much weaker. Which of the two do you actually mean? $\endgroup$
    – knzhou
    Nov 18, 2019 at 23:50
  • $\begingroup$ Due to nonlinearity, for example because billiard balls are round, uncertainties in initial values grow exponentially in time. To predict the classical future with accuracy requires that initial values are impossibly accurate. Concluding, even if the laws are deterministic, nonlinearity effects render the future uncertain. $\endgroup$
    – my2cts
    Nov 18, 2019 at 23:52
  • $\begingroup$ Thank you for the input. I was about to add as an edit that maybe the term Superdeterminism should be exchanged by whatever term you find more fitting. What I understand as "Superdeterminism" is this: Every piece of matter (within classical physics scale) that came into existence after the big bang, then bounced around in 3D space since then and obeyed classical physics law. As such, right after the big bang it was determined that those very atoms that form our moon are those very atoms and no other atoms. $\endgroup$
    – user9114945
    Nov 19, 2019 at 0:26
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    $\begingroup$ Let me add one thing that seems to have slipped the discussion. The evolution in quantum mechanics is absolutely deterministic. The non-deterministic part is only in the measurement process. $\endgroup$
    – lcv
    Nov 19, 2019 at 13:03

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I will operate under the assumption that you meant to ask about "determinism" where you wrote "superdeterminism". Superdeterminism is the notion that if you allow for every part (and in particular the measurement settings chosen by the observers) of a given measurement apparatus to be predetermined by some hidden variable, then you can describe any quantum mechanical system via local hidden variable theories. Note that any experimental outcome can be described classically if you also assume measurement choices are predetermined.

If you instead meant to ask about determinism, then I see the main problem in your argument in the following statement:

When I shoot a billiard ball and all forces are known, I'm sure you will all agree that there's no uncertainty about where the ball will land. In other words, if we forget about Quantum Physics for a moment, couldn't we all agree that the universe is deterministic?

This is like saying, if we stop looking close enough, couldn't we all agree that the universe is deterministic? Sure thing, if you don't look close enough, classical physics is a good description of physical reality, and in classical physics you can always assume that things are deterministic underneath (even though you more often than not need to still use probabilities to counter your only having partial knowledge about systems).

However, the whole point of quantum mechanics is that things get weirder when you look close enough. When you manage to measure things with high levels of accuracy, you find the usual assumptions about determinism to not be tenable anymore, at least not without some adjustments (you can maintain determinism if you give up locality, etc.).

It's important to remember that this is not about some physicist's mathematical shenanigans. We describe nature in this weird way because we have to. We observe that nature works in this unintuitive way, and are thus forced to find a fitting description of what we observe, which is what quantum mechanics is.

But Bell's theorem came along and ruled out determinism, which completely contradicted all that. But when I'm looking at Bell's theorem:

  1. Bell admitted there might be loopholes
  2. Everything that isn't on a quantum scale in the univers acts as perfectly deterministic

I think these loopholes are beside the point here. These are ways to still keep believing that local hidden variable theories are tenable despite experimental observations of Bell violations. The loopholes refer to how the violations were observed experimentally, not Bell's theorem itself. If you really want to not believe in all the evidence we have that nature violates Bell's inequalities, you can always come up with some new "loophole" to say that the experimental evidence is not enough. For example, I might like to think about the "incompetent physicists loophole", that states that experimentalists are just incompetent enough that every single experiment that has been done about this has been wrong. You cannot defend against any such criticism, it just becomes a matter of what is more likely to be true given what you know.

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  • $\begingroup$ Thank you for your input, and your assumption that I meant "determinism" is correct. I haven't read much about QM, mainly about Bell's theorem. And when just looking at Bell's theorem, I don't get it why it's so absurd to assume that there is a hidden variable somewhere after all. Which in turn would confirm relativity and everybody can be happy. $\endgroup$
    – user9114945
    Nov 19, 2019 at 9:17
  • $\begingroup$ I also read a bit about Simulation Hypothesis, where they just assume things based on probability. Can't we just assume based on probability the same way that there are hidden variables, because it would explain the reality that we face every day in our lives? $\endgroup$
    – user9114945
    Nov 19, 2019 at 9:20
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    $\begingroup$ it's not "hard" to assume that there is a hidden variable theory, it's simply in contrast with experimental observations. Things such as the "simulation hypothesis" have nothing to do with QM and are off-topic here $\endgroup$
    – glS
    Nov 19, 2019 at 9:26
  • $\begingroup$ glS, superdeterminism does not mean that "every single thing is predetermined", that's determinism. Superdeterminism implies that the physical systems used in a Bell test (the particles' source and detectors) do not have independent states, in other words, that you cannot change the state of one detector while leaving the state of the source unchanged. This is a well known behavior that arises in all theories with long-range forces (such as electromagnetism and GR). A trivial example of two distant systems that are not independent is the case of two orbiting stars. $\endgroup$
    – Andrei
    Nov 19, 2019 at 10:17
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    $\begingroup$ @Andrei it isn't as used in the context of loopholes for Bell's inequalities, because any output probability distribution $\{p(ab|xy)\}_{a,b,x,y}$ can be obtained if you allow both outcomes and measurement choices to depend on some underlying hidden variable $\endgroup$
    – glS
    Nov 19, 2019 at 11:09
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I think Bell's theorem is not at the heart of your question, so let's put it aside and concentrate on the gist of your argument.

You seem to be suggesting that since the world seems very deterministic on a macro level it ought, therefore, to be deterministic on a micro level.

Your conclusion does not necessarily follow from your premise. There is no reason for determinacy at the macroscopic level to imply determinacy at the microscopic level (or vice versa, incidentally- the weather is entirely unpredictable even though it is the result of deterministic microscopic interactions).

Strictly probabilistic events can still have well defined expectation values when large numbers are taken into account. If you roll a dice you cannot know what the result will be, but if you roll it six trillion times the outcome will be that the occurrence of each number will about a trillion- that aggregate outcome is predetermined by the relative probabilities of the individual events, even though they are individually random.

At a macro level most of the phenomena of our day-to-day experience are the aggregate results of trillions of interactions at a microscopic scale, so what we see can be the pre-determined expectation values of un-predetermined individual events at a microscopic level.

Relating Bell's theorem with free will is an error of logic made by people who have thought about neither in sufficient depth to understand their mistake.

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  • $\begingroup$ In a 100% deterministic world we can still only calculate probabilities because we don't have all data (e.g. weather data). But isn't the fact that we can calculate good probabilities evidence that there is no true randomness at play? See your dice example. If I dismiss Bell's Theorem, could you point me to other QM experiments that really proof that particles are truly random and undeterministic? $\endgroup$
    – user9114945
    Nov 19, 2019 at 14:02
  • $\begingroup$ @user9114945 "But isn't the fact that we can calculate good probabilities evidence that there is no true randomness at play?" - Isn't the fact that we can cut things into really tiny pieces evidence that there are no atoms? In both cases, the answer is no for the same reason - higher resolution is required to see the non-classical effects. $\endgroup$
    – probably_someone
    Nov 19, 2019 at 14:07
  • $\begingroup$ @user9114945 "But isn't the fact that we can calculate good probabilities evidence that there is no true randomness at play?". Why do you say that? If you take a random number generator that picks a perfectly random integer between one and a million, say, I can tell you will complete certainty that after a trillion picks the average will be close to 500,000. The truly random yields predictable outcomes when averaged out. Thus at a macroscopic level you can have truly deterministic phenomena that represent the aggregate effects of truly indeterminate microscopic events. $\endgroup$
    – Marco Ocram
    Nov 19, 2019 at 14:41
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    $\begingroup$ I am not arguing that reality is indeterminate at a microscopic level, I am simply saying that determinacy at the macroscopic level does not require determinacy at a microscopic level. $\endgroup$
    – Marco Ocram
    Nov 19, 2019 at 14:49
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Judging by only classical physics, it seems we live in a 100% deterministic universe.

They could do the math simpler with that assumption. Classical physics was perfectly compatible with the idea that mass is infinitely divisible -- they didn't know about atoms until they found out. You could just as easily say "Judging by classical physics, gold is infinitely divisible" but it isn't that classical physics makes that claim. They just had no reason to complicate their math when they didn't know.

Modern physics uses statistics to deal with many situations where we can't measure individual details. This is appropriate, but it might not be correct to assume that the details can't be deterministic.

It's like -- if you are in a helicopter high above a city traffic jam, you can't tell much about individual cars. As the cars on the freeway approach a major turn-off, you might be able to predict that 2/3 of the cars will stay on the freeway and 1/3 will turn off. You can make predictions from that.

Is it true that each individual car has a 2/3 chance to stay on the freeway and a 1/3 chance to turn off? Probably not. Probably each physicist in the traffic jam is heading home to his own wife, and not to a random destination. But how would you know from the helicopter?

If you could keep all but one car off the freeway and observe that one from your helicopter, you might predict that it has a 2/3 chance to take one path and a 1/3 chance to take the other. The driver might know exactly where he's going, but how could you know? What's going on in his mind is hidden from you.

I have seen claims that there are proofs that in physics there are no hidden variables. That would be just like knowing for sure that each car on the freeway is being driven by statistical rules and none of them actually have a plan. That would be very very interesting if true, and someday I want to study it carefully and see what it would mean to physics if it was in fact true. In the meantime I will treat it as another convenient simplification that makes our theories easier to use, and I will not assume that the statistical theories are more true than the classical physics calculus which calculated the effects of tiny amounts of mass or charge smeared uniformly across volumes of space. It's theory which gets the correct statistical results given statistical measurements.

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On the quantum scale the “particles” either are or are associated with “wave packets” of finite size. The magnitude of the wave disturbance at any point determines the probability that is will interact with something else at that point, and this interaction may or may not occur anywhere with the body of the wave. Your determinism is reduced to a matter of probabilities.

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user9114945,

"Judging by only classical physics, it seems we live in a 100% deterministic universe."

True, both classical electromagnetism and general relativity (modern classical theories) are deterministic.

"Bell's theorem came along and ruled out determinism"

No, it did not. In order to understand Bell's theorem you need to look for the EPR argument because Bell intended to refine that argument. In a nutshell EPR proves that QM is either non-local (instantaneous action at a distance, like in the case of Newtonian gravity) or incomplete (the quantum state is not a complete description of the system). I want to stress here that the only way to preserve locality is to assume that QM is a statistical description of a deterministic hidden variable theory. Without determinism there is simply no way to explain the EPR correlations locally.

Bell devised an experiment to check which of the above options is true. Do we live in a non-local world (which can be either deterministic or non-deterministic) or in a local and deterministic one?

Now, there are two assumptions in Bell's theorem. One is locality, the other is independence (the hidden variables do not depend on the measurements' settings).

The theorem says:

No physical theory that fulfills the above assumptions can reproduce QM's predictions.

Many experimental tests have been performed and each time the QM's prediction was confirmed, so we either can accept that physics is non-local, or that the independence assumption is false. Both options are still open, and both of them allow for determinism.

"I don't get why Bell's Theorem is often discussed in the context of Free Will. What does the one have to do with the other?"

Free will is a way to impose the independence assumption. If we accept that humans' decisions cannot be the result of a deterministic process and we use such decisions in a Bell test, there is no way the hidden variables could depend on them. But, as far as I know, there is no evidence in favor of this strong type of free will.

In conclusion, there is no evidence from QM that determinism is false, on the contrary, we have reasonable evidence that it is true as it remains the only way locality can be preserved and locality is a very well established physical principle.

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  • $\begingroup$ Bell's theorem assumes (and experimental tests refute) local realism. I'm not sure if your concept of "independence" is equivalent to realism, but I wouldn't assume that it is without some justification on your part. $\endgroup$
    – probably_someone
    Nov 19, 2019 at 13:46
  • $\begingroup$ This is false claim, even if widespread. Independence has nothing to do with realism. Did you actually read my answer above? I've explained there what independence means and I presented the logical arguments behind EPR and Bell. If you think there are errors please point them out. Take a look at Bell's paper and see if and where the "realism" assumption is used! $\endgroup$
    – Andrei
    Nov 19, 2019 at 14:45
  • $\begingroup$ Sorry, but if you're advancing your own interpretation of Bell's work, you're going to have to back that up with at least some justification from Bell's actual work. $\endgroup$
    – probably_someone
    Nov 19, 2019 at 14:57
  • $\begingroup$ Sure, let's take a look at Bell's paper, "ON THE EINSTEIN PODOLSKY ROSEN PARADOX" (cds.cern.ch/record/111654/files/vol1p195-200_001.pdf). The abstract reads: "THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. $\endgroup$
    – Andrei
    Nov 20, 2019 at 5:00
  • $\begingroup$ Cont: "It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty." So, Bell is saying here that EPR allows you to choose between non-locality and local hidden variables (local realism). It is this place where most physicists go wrong because they assume that rejecting realism can save locality. This is wrong, local realism is the only type of locality that survives EPR. $\endgroup$
    – Andrei
    Nov 20, 2019 at 5:05

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