The Quantum Rescue: How quantum mechanics saved free will from Albert Einstein
Albert Einstein was a fierce critic of uncertainty in quantum mechanics famously saying “God does not play dice!”, but why? Uncertainty in…
Albert Einstein was a fierce critic of uncertainty in quantum mechanics famously saying “God does not play dice!”, but why? Uncertainty in the quantum mechanics of photons and electrons is different than uncertainty in what physicists call the “classical” world of ordinary life. It all has to do with the curious case of Bertlmann’s socks.
Professor Bertlmann never wore matching socks, you see. If you saw one sock was green, the other would be red or pink or yellow. It was inevitable. It was as if the good professor has a drawer full of singleton socks, having lost all the matches.
The uncertainty in the color of one sock given the other is an example of classical uncertainty. We assume, based on our Bayesian model, that if one sock is green the other will not be green. Therefore, it reduces our uncertainty of the other color by one. If we know all the possible colors of socks in his drawer, we can give an exact probability for it. For example, if there are six colors and we see that one of his socks is green, then the probability that the other sock will be red is 1/5.
Having seen one sock we can also assume that the other sock has a definite color. Before we look at it, it is an example of a “hidden variable”, something with a definite value that we just don’t know yet. All classical uncertainty involves hidden variables. Some of them we can never know because they are impossible to measure like the position of every air molecule on the planet at one time. Nevertheless, every air molecule on the planet has a definite position, and we can create models that make that assumption and tell us something useful about the weather.
In 1934, having fled Nazi Germany the prior year, Albert Einstein was fed up with quantum mechanics. The theories of Niels Bohr and Werner Heisenberg about bizarre concepts like quantum wavefunction collapse and uncertainty principles had taken the physics world by storm. As far as Einstein was concerned quantum mechanics had a long way to go before it could be a “complete” theory of the universe.
The problem was that quantum mechanics, as it was formulated mathematically, did not agree with the notion of hidden variables that we used to talk about Bertlmann’s socks. Instead, it suggested that, in a quantum universe, if we saw that one sock was green, the other did not have to have a definite color. There was no hidden variable at all, but all possibilities were in “superposition” with one another, meaning that they all existed as realities at the same time until one was observed and then all the other realities vanished. This was called, at the time, wavefunction collapse but is now more generally known as loss of superposition or quantum decoherence.
Worse still, it suggested that, for a quantum Bertlmann, if I saw one of his socks were green in Switzerland, it could affect the color of socks that his mismatched colleague Professor Smith was seen to be wearing in California without any communication between the two, raising the probability that Smith’s socks will not be green. This second idea is called nonlocality or “spooky action at a distance” which allows for kinds of uncertainty where observations are “correlated”, meaning that the probability of one depends on the other and vice versa, but don’t require people or things being able to communicate, even unintentionally. Instead, it is as if everything in the universe is in direct contact with everything else until it is observed.
In 1935, Einstein collaborated with Podolsky and Rosen at the Institute for Advanced Study in Princeton to publish a paper that has now become famous among physicists for laying out the Einstein-Podolsky-Rosen or EPR Paradox. In it, the scientists suggested an experiment where you have two particles, A and B, that interact and then move apart. You can then measure one particle and infer something about the state of the other particle without measuring it. The authors didn’t agree on what this actually meant, only that it was a problem with quantum mechanics. Podolsky suggested it violated Heisenberg’s uncertainty principle which says you can’t measure position and momentum at the same time. Niels Bohr said in a response that this was a sketchy argument. Einstein agreed. Einstein argued instead that the problem is that, depending on how you choose to measure particle A, the actual state of particle B is affected. Einstein’s is a far deeper insight, and it gets worse than that because, not only does the way you measure A affect the state of B, but the way you measure B affects your measurement of B as well.
The first problem, that how you measure A affects B, is called nonlocality because your measurement of A at the location of A causes a change in what happens at the location of B. So, unlike Vegas, what happens at A does not stay at A. The second problem is a violation of what Einstein liked to call “realism” meaning that particles have definite hidden variables. If how you measure B changes what you will measure at B, then B can’t have a hidden state. Instead, reality itself is responding to the way you do your measurements.
The lack of objective reality that quantum physics implied offended Einstein’s deeply held philosophy. Einstein had developed his theory of General Relativity, which explains the force of gravity, as not only a theory of how stars and planets behave but as a description of space and time. In his theory, time was no different than space, and, therefore, the past and the future were as set in stone as the cement in a building. Einstein was what philosophers call an Eternalist. His philosophy did not allow free will of any kind. In exchange, it promised that the past and future were always “out there” somewhere. Kurt Vonnegut wrote a novel based on this Eternalist perspective called Slaughterhouse Five in which a man becomes “unstuck” in time and travels back and forth through his life, able to witness everything in it but unable to change anything that happens. If you are an Eternalist, you believe that human beings are simply witnesses of reality, not true participants, and that our ability to affect events for good or bad is an illusion.
If quantum mechanics allowed for the kind “dice playing” God that Einstein accused, then it might mean that the future was not really “there” but only came into being when He rolled the dice. If that were so, then bye-bye to Einstein’s crystalline spacetime. Instead, the universe would be randomly unfolding with no predetermined future.
Many physicists such as Bohr did not accept Einstein’s viewpoint. In fact, they preferred a universe where time was more than a spatial dimension, one where a universe actually changed and evolved, even if it were random. Nevertheless, physicists also did not fully accept that quantum uncertainty worked differently than classical. In the 1950s, David Bohm created a successful theory that could explain some quantum spookiness with hidden variables (but not without nonlocality), but his theory only worked when detectors were placed at right angles to one another.
Einstein’s universe finally came tumbling down in 1964 when John Bell considered the more general cases that Bohm did not. He noticed a difference between the probabilities you get when doing a quantum measurement and what you would expect if they worked like Bertlmann’s socks. He wrote it up as a mathematical theorem, one that experimenters could use to determine if quantum mechanics really was as “spooky” as it seemed to be. In 1981, he published a paper called “Bertlmann’s Socks and the Nature of Reality” to explain his theorem. It opens:
The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by the [Einstein-Podolsky-Rosen] correlations. He can point to many examples of similar correlations in everyday life. The case of Bertlmann’s socks is often cited. Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience with Bertlmann, gives the immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is this [Einstein-Podolsky-Rosen] business just the same?
It was not. What John Bell invented is now called Bell’s inequality or Bell’s theorem, which shows that quantum measurements do work differently than classical ones. There is, in fact, no way to show that before you measure particle A, particle B has a definite state except under some very contrived circumstances, and, likewise, how you measure A does affect the state of B even when light has no time to traverse the distance between them before you do the measurements.
This may not mean a lot for the “philosopher in the street” except to say that we now know, through countless demonstrations in real experiments of Bell’s inequality, that there is no definite, objective reality. When we characterize classical uncertainty, we are describing what we don’t know, but, when we characterize quantum uncertainty, we are describing what doesn’t exist yet (at least for us). I go into the implications in more detail in Chapter 8 of my book.
Philosophically, I think quantum uncertainty shows us that reality is vastly more mysterious that it appears to be. In a universe where all states exist and are predetermined, it is hard to argue for a concept of free will, which is why Einstein did not believe in it. He even believed his own discoveries were inevitable. That is not our universe. Instead, we live in a universe where the very act of observation determines reality itself. While that doesn’t prove free will exists for certain, it does open the door to the possibility that our choices do impact the future. So far, thanks to John Bell, free will is safe from Albert Einstein, but who can say what the future holds? Not I.
Bell, John S. “Bertlmann’s socks and the nature of reality.” Le Journal de Physique Colloques 42.C2 (1981): C2–41.
Note: If you are wondering where “Rock, Paper, Scissors and the Curious Case of Bertlemann’s Socks Part II” is, this article is it.