"God doesn't play dice."
I'm sure the reader has heard this famous saying from Einstein in a 1926 letter to fellow physicist Max Born. Perhaps not so clear to most people is what God and what dice Einstein was referring to. His worries reflect a deep concern about how far our explanations of Nature can go. They speak to the heart of what science is, an issue that remains contentious to this day.
Einstein was referring to quantum physics, the physics that describes the behavior of molecules, atoms and subatomic particles — like electrons and the Higgs boson. The "dice" relate to probabilities, the fact that in the quantum world the cozy determinism of our classical worldview goes down the drain.
In our everyday life objects follow well-behaved histories from point A to point B. In the realm of the very small this determinism fails completely. We can, at most, compute probabilities that a particle will be at this or that point in space (within the accuracy of the measuring device). Even more bizarre, before we detect a particle we can't even tell if it exists. All we have is potentiality.
In an extreme interpretation, we can say that the act of detection "creates" the particle. But if that's the case, what about bigger objects? Aren't they made of atoms, which are quantum objects? Does a mountain only exist when we look at it? Surely, that's kind of ridiculous. Mount Everest is there whether we look at it or not. But how can you tell? Do we know that Mount Everest is out there when we are not looking, or do we infer that from common sense?
To Einstein, this loss of predictive determinism couldn't be the last word in our description of Nature. Another theory, deeper and broader, should be able to explain the paradoxes of the quantum world. Was he right?
A lot has happened in eight decades. Experiments have tried again and again to find flaws in traditional quantum mechanics, perhaps opening a window into an alternative theory. All to no avail: it really looks as if quantum mechanics is here to stay. Nature is inherently uncertain and we have to come to terms with it.
Heisenberg's uncertainty principle, stating that we can't know both position and velocity of a particle with arbitrary accuracy, is more than an obstacle to knowledge; it's the way Nature operates. God does seem to play dice, and the tremendous successes of quantum physics are a testament to our ability to make sense of a very bizarre state of affairs.
Einstein's sentence in his letter to Born is actually different from the snippet above:
Quantum mechanics demands serious attention. But an inner voice tells me that this is not the true Jacob. The theory accomplishes a lot, but it does not bring us closer to the secrets of the Old One. In any case, I am convinced that He does not play dice.
The "Old One" here is a metaphorical figure representing not the Jewish-Christian God but Nature's inner spirit, the essence of reality. To Einstein, the goal of science is to unveil this essence, to reveal how the world works.
On the other hand, he was quite aware that our scientific theories were necessarily incomplete approximations to what truly goes on:
What I see in Nature is a magnificent structure that we can comprehend only very imperfectly, and that must fill a thinking person with a feeling of humility.
What bothered Einstein was how the interpretation of quantum mechanics went head-on against his way of seeing the world. To him, stating that something exists only when we interact with it didn't make sense; he and Schrödinger and Planck and de Broglie were scientific realists. They believed in an underlying reality of things independent of the observer.
Heisenberg, Bohr, Pauli, Jordan, and Dirac went the other way, taking the weirdness of quantum mechanics at face value. Detection creates reality. It bridges the world of the very small with the world of the very large, where the detectors exist.
Schrödinger "wave mechanics," an equation describing how the electron orbited the nucleus of atoms, made things worse. Initially it was celebrated as a return to sanity, given that waves are things that we see everyday. You throw a rock on a pond and water waves propagate outwards from the point of impact. An equation describes what goes on. But in Schrödinger's wave equation, the waves were not real things. After some trial and error by Schrödinger, Born came up with the strange idea that the wave was a wave of potentialities which, once squared properly (for the experts, by taking the absolute value as the wave function is a complex quantity) would produce the probability that the electron be found at this or that orbit around the nucleus. The same for other situations where the equation is applied: the result is always some kind of probability.
In other words, the fundamental equation of matter didn't describe matter!
The essence of Nature was not some concrete material realm but a mathematical abstraction. The theory worked beautifully, producing efficient descriptions of countless experiments. Quantum physics revolutionized the world. But its interpretation, if you so choose to think about it, remains mysterious.
This was the problem Einstein had with the dice-playing God. Even today, when pushed hard to think about what quantum mechanics is telling us, most physicists will show at least a hint of anxiety. "Better to leave such issues behind," is the usual comment. Or, if it's an annoying graduate student, "Just shut up and calculate."
But surely, as the French polymath Bernard de Fontenelle wrote in 1686, "we want to know more than we can see." And here's the rub: there is only so much we can see.