Warning: This “free will” post is for those interested in quantum mechanics, and who have a general understanding of the field and terms used within it.
If there was one theorem that has driven physicists to accept an indeterministic model of quantum mechanics the most, Bell’s theorem would be on the top pedestal. With the acceptance of such a theorem, certain quantum events simply cannot have a local “hidden variable”. This means that if one is to suggest a cause that we cannot “observe” for the event (a “hidden” variable), the cause has to be “non-local”. This idea of a non-local cause means that there is instantaneous action at a distance, something Einstein labeled as “spooky action at a distance”. And though quantum entanglement has been “demonstrated” (but with the loophole I’ll be discussing below), many physicists prefer different quantum interpretations that do not rely on non-local hidden variables, and tend to lean toward indeterministic models which says that there actually is nothing that determines the event. A less common leaning is toward a deterministic model that postulates an almost infinity of invisible worlds. The least common, though still accepted by many, are non-local hidden variable “deterministic” models such as pilot-wave theory (Bohmian Mechanics) – a model I have great appreciation for.
In the physics world, however, local hidden variable interpretations are seen as less than science, even though they would explain the “probabilistic nature” of events without the metaphysical problems of ontic probability, acausality, non-locality, or invisible worlds decohered from each other. These local accounts are looked down upon, spit on, kicked, and grounded into the dirt. The large bulk of the reasoning behind this rests on this important theorem by John Stewart Bell. This is because, per Bell’s theorem: “No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics”. It shows that any physical theory would require information to travel faster than the speed of light, a limitation put on speed in physics that is for the most part undeniable.
But is Bell’s theorem really this powerful, undefeated theorem that should be accepted no questions asked? Well, it is difficult to say if it should be accepted, but one thing is for sure, there are questions that need to be asked before it is!
Hey Bell’s Theorem, you got some ‘splainin’ to do!!!
Part of Bell’s theorem is Bell’s inequality, which addresses the relationship that needs to hold for measurements of particles given different setups. For Bell’s inequality to hold, however, an assumption needs to be made. In physics the assumption here is called “counterfactual definiteness”. This is one of those terms that are often confusing, but the key part of the term for this article is that it means “it is necessary to be able to speak meaningfully of what the result of the experiment would have been, had different choices been made”.
To put this in clear terms, it means that when we look at the results of an experiment, we need to also look at what results “would have been” had the experimenter “set up the experiment differently” in order for Bell’s inequality to fly.
You see, Bell’s theorem depends on an assumption of the type of free will that would not exist given causal determinism. It seems to be a little “cart before the horse”.
The problem with this sort of counter-factual is that it doesn’t really exist given most deterministic theory. In an entirely causally deterministic universe, the experiment that will be run is the experiment that causality dictates will be run. The other experimental setups were not a real possibility. The measurement that would be chosen by the experimenter is one that is dictated by the laws of physics (given determinism), therefore it is a mistake to speak about what the results “would have been” in any meaningful way
Bell himself discussed this loophole in the 1980’s:
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 Bell calls “super-determinism” here is just the philosophical notion that all things are causally deterministic, including conscious thoughts and actions, and therefore there is no free will (in the sense of “could have done otherwise”). It’s also important to denote that “knows” is in quotes. It isn’t really that the universe “knows” but rather that the universe is in a state that follows to the very specific measurement that will entirely dictate an exact outcome of the experiment that could not be a different one.
So once determinism is assumed, it does seem that faster than light speed is not required, at least according to Bell. At the same time, however, Bell claims that this is implausible. According to him, even if the measurements performed are chosen by deterministic random number generators, the choices can be assumed to be “effectively free for the purpose at hand.” His rationale for this, something I find less than compelling, can be found in his book “Speakable and Unspeakable in Quantum Mechanics”. Here is an excerpt:
To me this explanation is insufficient. Why would he say that the millionth decimal place being odd or even would “unlikely be a vital piece for any distinctively different purpose” when in fact the output of either a or a’ relies entirely on it? It seems to me that there is absolutely no “forgetfulness” that can be equated here – not even an imaginary forgetfulness. It seems to me that the above excerpt just says “complexity therefore free enough” without any sufficient explanation. Perhaps there is more hidden here, but if so it is very elusive, and I have yet to find a good answer. I’m still searching though, so if there are any physicists out there that have answers I’m all ears.
Also, the fact that this sort of thing is used in the Clauser-Horne analysis doesn’t mean it is appropriate in that context either if causal determinism is the case.
To give more context to Bell’s position on his use of “free will” for the theorem, he says this:
In other words, for the very theorem, he is “entertaining the hypothesis that experimenters have free will”. According to him, he is simply pursuing his profession of theoretical physics.
But it is important to understand that when hypothesizing X we should not, in science or philosophy, just accept the Y that follows. Rather, the contingent “if” is a key factor that the conclusion should make every attempt to denote: “if X is the case, Y follows”. If “free will” is the case, then Bell’s theorem follows and local variables have been ruled out. Bell has done this to some degree, but I don’t think in a strong enough way.
When it’s just posited as an unlikely “loophole” by Bell, that is the very idea I would like questioned. Is it really “unlikely”? Can a deterministic pseudo-random number generator really accomplish the “freedom” required? Or is it really the case that it is unlikely that such pseudo-random number generator could accomplish the freedom involved? If so, isn’t the “free will” or even “true randomness” assumptions just begging the question in the first place?
Theoretical physicist Sabine Hossenfelder, in her blog, suggests that with the removal of free will comes the removal of Bell’s theorem:
“Free will of the experimentalist is a relevant ingredient in the interpretation of quantum mechanics. Without free will, Bell’s theorem doesn’t hold, and all we have learned from it goes out the window.”
Sabine’s post: Free will is dead, let’s bury it.
When ideas such as the freedom of the experimenter is just taken as a granted and the opposition to this is taken as “unlikely”, other scientists have a tendency to cease to look at X and just assume Y as a static given to base the rest of their work on. And though there are some who are working on a potential local story of causality in quantum mechanics, they are considered an almost obsolete fringe who are stuck in their “Newtonian mindset”, all due to metaphysical baggage laden assumptions in scientific theory. The irony, however, is that a true scientist doesn’t look at a theorem such as Bell’s as a scriptural fact, but rather as something to be challenged, especially if it assumes non-empirical baggage.
Luckily there are some who have proposed ways to test these ideas about “free will” in Bell’s theorem in order to “close the loophole”: Researchers propose using distant quasars to test Bell’s theorem. Basically the test will be to use two distant quasars that wouldn’t have causal contact since the big bang, meaning one has no causal influence over the other for the particle detector settings. Per the article:
“The researchers reason that since each detector’s setting is determined by sources that have had no communication or shared history since the beginning of the universe, it would be virtually impossible for these detectors to “conspire” with anything in their shared past to give a biased measurement; the experimental setup could therefore close the “free will” loophole.”
We will we have to wait and see on this as these are long term and complicated initiatives. Physicists led by Dr. Kaiser and Alan H. Guth (M.I.T.), financed by the National Science Foundation, will attempt to accomplish an experiment that will insure greater independence of distant “objects” in 2016, and then attempt to capture the light from quasars “near the edge of the universe” in 2017 and 2018. It’ll be interesting to see if the results “close the loophole”. I do hope that these tests can be done in an entirely impartial light and replicated by others.
Until then, the conclusion that many scientists accept as almost written in stone, in particular regarding the “impossibility” of local hidden variables to account for the probability distributions we see in quantum mechanics, currently relies on an “if”. And it’s a big, scary “if” of “if free will exists” that just assumes that “super-determinism” (as suggested by Bell) isn’t the case, or assumes that a random generator can grant “enough freedom” without really explaining how pseudo-random but entirely deterministic complexity is really “more free” for the experiments than the most simple of causally deterministic mechanisms. If the loophole becomes closed through experimentation like the above quasar experiment, and that closer is sufficiently explained, then free will will not be required for Bell’s theorem to hold. If it doesn’t get closed, I think we should be a little more skeptical on accepting the theorem on it’s face, and open the door to more local variable possibilities.
This article in no way has the answers , but I do hope it at least gets people to question if Bell’s theorem is truly reliant on a notion of a “free will” of the experimenter. If it is, then that is just one more reason to explain why such free will is logically incoherent. If it isn’t really reliant on this free will and can be explained even given a “super-deterministic” universe using pseudo-random number generators, I’d like to see more information on that. And if it get’s sufficiently closed by using distant quasars that are causally disconnected since the big bang, I’d still suggest that a deterministic non-local hidden variable account of quantum mechanics is just as likely as any other interpretation (if not more likely than some), even if local accounts have been sufficiently ruled out.
Are you a quantum physicist or autodidact who has answers here about Bell’s theorem requiring “free will”? If so, comment below or shoot me an email! I’d love to make a new article on this subject in the future as I obtain further information.