Atheism and the existence of peanut butter

[R00tKiT]

 In point of fact, I don't think there is asuch a thing as synthetic a priori knowledge. 

I suspect that you have a self-refuting sentence here (I might be wrong). The assertion : "there is no synthetic a priori knowledge" is either synthetic a priori or not. If it is, it refutes your own claim. If it isn't, we can dismiss your claim as a baseless a posteriori assertion.

And the fact that QM is a supreme example of a scientific theory AND is acausal is enough to show that causality isn't required to do science. Just repeatability and testability.

I don't think it's fair to say that QM is acausal. It surely changes our commonsense picture of causality, but there is always a kernel of causal order that underlies any physical theory.
And if we define a cause as an explanation of an effect, then it's wrong to say QM is acausal, since its main goal is to explain the behavior of atoms/ subatomic particles.

Exactly. Special relativity is a non-quantum theory. It is a classical theory. When quantum mechanics is added on, we get quantum field theories. So, in the classical theory, all influences remain in the light cone. In the quantum version, the correlations outside of the light cone are zero.

A good reference is Peskin and Schroeder, 'An Introduction to Quantum Field Theory'. The relevant section is even labeled 'Causality', pp 27-29. Here' the description of causality is that no measurement can affect any other measurement outside of the light cone. How is this achieved? By having the commutator of the fields be zero (no correlation) for events outside of each others light cones.  In order for this to happen, anti-particles must have the same mass as the ordinary particles. this discussion of causality comes up in the determination of the propagator.

Or, if you prefer Nachtman's book 'Elementary Particle Physics', the relevant equations are 3.50, once again describing the commutator of events outside of each others light cones and requiring the commutator be zero. Once again, this means no correlation.

Or, if you prefer Kaku's book, 'Quantum Field Theory', the description of microcausality in section 3.4 once again hinges on the nature of the commutators and thereby the correlations between events separated in a way that light could not travel between them.

Or, if you prefer Weinberg's book, The Quantum Theory of Fields (Vol 1), you can find the same discussion in section 3.5.

In ALL of these, the term 'causality' is used precisely when the events outside of each others light cones have vanishing commutators. In other words, they are uncorrelated.

Are those valid enough sources for you? All are standard texts for graduate physics in this subject (although Kaku's book is pretty poor, frankly).

Now, I don't believe for a second you have actually read/understood anything about quantum field theories that goes beyond the popular treatments. I have. And the notion of causality used in quantum mechanics isn't the type of causality you require for your program. It is a matter of probabilities and correlations and NOT of what is 'necessary' for other events to happen. And yes, it has to do with vanishing commutators outside of light cones, just as I said.

Physics isn't my field of expertise, my studies in physics stopped a while ago at some basic applications in QM of Schrödinger's equation, in addition to other undergraduate level courses in newtonian mechanics, electromagnetism, thermodynamics, etc. Is there some accessible interpretation of the "vanishing commutators outside of light cones" ? And does it allow for violating causal order? 

After doing a bit of research I again found what seems to contradict your assertions above:

Quote: "For a quantum field theory the equal time commutation relations are the equivalent of the initial conditions on classical field equations. It is a requirement on the dynamical equations that the property of commutation between two local observables is extended to all pairs of points with spacelike separation. This is the equivalent of the requirement of causal propagation in a (well-behaved) classical field theory."

Source: https://www.researchgate.net/post/What_i...eld_theory

In other words, there is still a requirement of causality even in quantum field theory.