Superdeterminism

The more I think about quantum mechanics the more I find it disturbing. 

I'm part of a minority who thinks quantum mechanics is not a fundamental description of reality but merely a statistical approximation of an underlying deterministic dynamics, and all of the quantum weirdness people keep talking about is merely the result of our own ignorance on how the world works at the most basic level. 

It's not a popular view.

The defenders of quantum mechanics as a fundamental description of physical reality usually bring up Bell's Theorem as the final nail in the coffin of such vain hopes, and with reason. Bell's Theorem is a brilliant and extremely powerful result which greatly constrains any theory that wishes to replace quantum mechanics.

Technically, Bell's Theorem derives an upper bound on the amount of correlation between the outcomes of two statistically independent measurements in deterministic theories that obey local realism. This bound is experimentally violated, which means that one of three things has to be true about our universe:

1. The universe violates locality, realism, or both (vanilla quantum mechanics).
2. All possible measurements are physically realized in disconnected universes of which the experimenter has access to only one (many-worlds interpretation).
3. No two parts of the universe are ever truly statistically independent (superdeterminism).

All deeply unsettling conclusions.

Quantum mechanics falls within the class of theories in 1. and specifically violates both locality and realism. Let's pause a second and think about what that means. 

Realism
In quantum mechanics particles do not have definite properties until measured. Particles can be in superspositions of states until they are measured, whereby they collapse to a single state with a well-defined value for a given property. 

Take a qubit as the simplest example. The qubit can be in two states, UP and DOWN. Classically the qubit would have to be in either the state UP or DOWN, but in quantum mechanics it can also be in a superposition state of UP and DOWN (there are an infinite number of those states by the way). So in a sense the qubit is both UP and DOWN at the same time.

"But wait a minute", you say, "you can have those states in classical mechanics as well! It doesn't mean the qubit is literally in both states at the same time, it just means that we don't know whether it is UP or DOWN because we lack information. Kinda like with a classical random process, which we describe with a probability distribution of possible events, but we don't literally mean that the system is in all events at once until we measure which one occured. We just mean that we can't track the dynamics of the system exactly so we model our ignorance with probability theory."

How nice that would be. Unfortunately, that is exactly what quantum mechanics is not. We model quantum states in superposition not because we are missing information on the underlying dynamics: the quantum wave function gives a complete description of a physical system. A superposition state in quantum mechanics doesn't mean we don't know which state the system is in, it literally means the system has no definite state, and it's in all of them at once. 

Bonkers!! This also means that when we make an observation and the system collapses to a definite state with a definite value of some property like position, momentum, or what have you, we are in a sense bringing that value into being by the mere act of measuring. The question "Which value did that property have before we measured it?" is technically meaningless. There was no value. There was no well-defined property even. 

This violates philosophical realism, the doctrine that things exist independently of the observer. With no observer (or no measurement, as perhaps measurement doesn't require an observer) particles don't have definite properties. They exist in the fuzzy realm of quantum indeterminacy. In a sense, existence in quantum mechanics is relational: things exist if and when they interact. 

Locality
Let's now take two qubits! The qubits can be prepared in an entangled state, like this:
|UP>1|DOWN>2 + |DOWN>1|UP>2,
where 1 and 2 refer to the two qubits. 

Now if someone measures the first qubit to be UP, the collective wave function of the system collapses and the second qubit will be measured to be DOWN, and viceversa if the first qubit is DOWN, the second one will necessarily be found to be UP. This is not because the two qubits were prepared in advance and we just don't happen to know whether they were prepared in the state |UP>1|DOWN>2 or |DOWN>1|UP>2. They really are in a superposition state of UP and DOWN, and were prepared in such a way that they are always anti-correlated, no matter which way we measure them. 

Now for the weird(er) part: the collapse of the wave function happens instantaneously. This means that if Alice finds qubit 1 to be UP, Bob's qubit will collapse to the state DOWN immediately. If superposition was a matter of lack of information, this would not bother us: it's merely an update of my knowledge about the system, and that can propagate instantaneously. But this is not what's happening here. Superposition is real, not just a formalization of my ignorance, therefore the two-particle state ontologically exists in superposition, and when one qubit is measured, the physically real state of the other particles changes instantly, even if the two qubits are in different galaxies. 

Bonkers!! This violates locality, i.e. the idea that particles can only be influenced by other particles in the local vicinity of them, which is defined by the cosmic speed limit (speed of light). The information about the state of the first qubit after it's measured seems to propagate to the second qubit with infinite speed. This doesn't make sense. 

Superdeterminism
What does make sense instead is that we lack information on the precise dynamics of the quantum system, and that's what leads to indeterminacy: superposition just models our ignorance about the real state of the system, and the collapse of the wavefunction happens instantaneously because again it's just a formalization of the knowledge of the experimenter. This was Enstein's dream, and I still think it's valid.

But Bell's Theorem!! I'll gloss over implication number 2. for now, and go to 3. A tacit assumption of Bell's Theorem is that the experiments are statistically independent, or can be performed in a way that is statistically independent. But if that's not true, if the experiment settings are somehow correlated, that correlation can cascade to the experiment outcomes and strengthen their correlation, thereby violating Bell's inequality. 

This is what is usually called superdeterminism. It's the idea that the universe at the bottom is deterministic, but also highly correlated in all its parts, and that's the reason why we have been fooled in believing it random. 

I'm not 100% sold on superdeterminism, but I somehow find it preferable to hypothesis 1. and 2. above. I feel like a highly correlated deterministic universe is preferable to a non-local non-real mess, or even worse a multiverse that branches every time someone makes an observation (what does that even mean??).

Cosmology also kinda points in that direction already. We know that there once was a Big Bang, so every single particle in the universe shares a common origin. The correlations might conceivably have been created at the Big Bang by some local process. It's actually hard to believe the contrary: that in a universe with a common origin point there would be absolutely no correlations between even distant regions of spacetime. I guess the devil is in the details in matters like these, and it will be a matter of finding out exactly how much correlation we expect to see. 

The good thing about any superdeterministic theory is that it is empirically testable, as it makes different predictions than QM in certain regimes (depending exactly on the microscopic details of the theory). For once, the indeterminacy in the dynamics of a microscopic system should disappear when viewed at very small (space-time) scales, i.e. out of the chaotic regime where QM resides.