The universe just is.

1. Simultaneity is frame dependent. Events in one observer’s past are in another observer’s future. Distances in space and intervals of time are frame dependent. They are not good physical quantities, a property of the world independent of your frame of reference. However, spacetime intervals between events (in technical terms, proper times) are.

There is no way to uniquely divide up spacetime into present, past and future. There’s no physical reason to consider future events any less real than past events, as somehow conditional while the past is immutable.

2. Experiment has shown that the quantum world can not be simultaneously deterministic, causal, and local. One often uses “deterministic” and “causal” interchangeably. Here, deterministic means law abiding; non-random, while “causal” means that future events depend on past events, and not the other way around.

Quantum entanglement is always described in a non-local fashion. You can probably guess which of the three properties I prefer to toss out: causal. I believe we can demonstrate that quantum information can propagate either way in time, but classical information is thermodynamically constrained to propagate forward in time.

The biggest outstanding problem then becomes the measurement problem. There is, presently, no deterministic model of the projective measurement. But I believe I know the form of the solution.

The problem with quantum mechanics is that it’s linear. If you represent the state as a superposition in the basis of some Hermitian operator, it will always (well, generically anyway) remain in a superposition state. Until you apply the non-deterministic, non-linear projective measurement rule.

The key being non-linear. We already have a non-linear field theory: general relativity. I get the feeling that a non-linear, deterministic field theory, say one that can incorporate gravity, will yield the projective measurement in a decoherence-like process.

Decoherence is a problem because it depends on our description of the system. But this is true of all thermodynamic variables; that doesn’t make them less useful or accurate. It is basically just classical statistical mechanics on quantum systems. And it’s still, technically, non-deterministic. It demonstrates why we don’t observe superpositions, but it still has no mechanism of projection.

Must the world be deterministic? The fact that I can’t imagine otherwise doesn’t necessarily make it so. I can’t put my head around what it would mean for it to be non-deterministic. If spacetime just is, then determinism is merely a statement that it is smooth. It’s much like the problem of stretching an elastic membrane over a hoop. The membrane finds a configuration where it has no unnecessary bumps and dips. We can find an equation that describes the shape, given the boundary condition (the shape of the hoop)*. You wouldn’t say the membrane is governed by the equation. It doesn’t give a damn about the equation, it just does its thing, as it has to do. That’s physics.

For the ancient Greeks, Necessity was the ultimate deity. Even the gods were subject to fate. We’ve simply learned to cope without the concept of a weaver.

Inspired by a Sean Caroll post. I take it for granted that “prove” means, in any context other than the confines of a formal language, what Sean explains.

*Most people could learn enough in about two years of college to handle the membrane-and-hoop problem. The problem of how physical fields are stretched over spacetime is proving a bit more difficult.