It has not been a good century for deterministic views of the universe.
He proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency.
His incompleteness theorems meant there can be no mathematical theory of everything, no unification of what’s provable and what’s true. What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring.
Since Gödel’s discovery, mathematicians have stumbled upon just the kinds of unanswerable questions his theorems foretold. For example, Gödel himself helped establish that the continuum hypothesis, which concerns the sizes of infinity, is undecidable, as is the halting problem, which asks whether a computer program fed with a random input will run forever or eventually halt. Undecidable questions have even arisen in physics, suggesting that incompleteness afflicts not just math, but—in some ill-understood way—reality.
Well, the 2022 Nobel Prize in Physics may just be another nail in the coffin for determinists.
2022 Nobel Prize in Physics
The 2022 Nobel Prize in Physics was just awarded to scientists that just proved one of the more unsettling discoveries in the past half a century: the universe is not locally real. In this context, “real” means that objects have definite properties independent of observation—i.e. an apple can be red even when no one is looking. “Local” means that objects can be influenced only by their surroundings and that any influence cannot travel faster than light. This means that the influence of a particle can’t move faster than the speed of light. Investigations of quantum physics have found that these things cannot both be true. Instead the evidence shows that objects are not influenced solely by their surroundings, and they may also lack definite properties prior to measurement.
Many determinists held out the idea there were ‘hidden variables’ – or a lower level of reality we haven’t found yet – that would somehow be communicating between the particles and keeping the idea of realism (locally real) alive. However, in 1964 Bell released a paper showing that quantum mechanical behaviors do violate the idea that there could be ‘hidden variables’ – and even described the ways those violations would show up mathematically. What remained to be done was to develop an experiment to prove or disprove his assertions.
To disprove this idea of ‘hidden variables’ and prove Bell’s assumptions, they did this by using experiments on entangled particles that keep their state linked. Particles that are entangled (in this case photons with a certain polarization) and sent in two different directions yet still remain entangled in state.
They devised a clever experiment in the dungeons under Vienna’s Hofburg palace over the space of kilometers. They analyzed the results of passing these entangled photons through different filters and found that they do indeed adhere to Bell’s equations – and hence disprove particles adhere to the properties of being locally real (both at the same time).
The work does not prove which of those two principles (local or real) are false. Just that at least one (or both) is false.
Confused? Here’s a video that also describes the conundrum and what is going one really well:
Side note: Reading the state of one entangled photon determines the state of the other – but this state is always completely random (which is why faster than light quantum communication is not possible – you still need to compare the two results independently of the system to know if the random result was the ‘correct’ bit in the original message or the ‘wrong’ bit. Otherwise you just get a string of bits each random set to being correct or incorrect – which as it turns out is the only truly safe and unbreakable cipher).