Atheism and the existence of peanut butter

[polymath257]

 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.

On the contrary, it is an example of extrapolation from known cases and is thereby an example of analytic knowledge. All claims I have found for a statement being synthetic a priori have been easily seen to be wrong.

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.

Nope. It *describes* the behavior. it does NOT explain specific instances of the behavior. For example, there is no explanation of why any particular nucleus decays at one time as opposed to another. it does describe the probability of decay, though.

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? 

Since you have not defined what 'causal order' means aside from temporal order and since nothing other than temporal order is ever used in physics, the question itself is irrelevant.

As for your education, you are at least above many people. I have done the PhD qualifying exams in physics, as well as having a PhD in mathematics.

I doubt that there is an 'accessible' interpretation of what vanishing commutators implies that actually deals with the substance of the concept. That is because it is a technical property involving the operators that describe the quantum fields at any point. If you don't know what the commutator of two operators is and how it affects the quantum mechanics (through an uncertainty principle), then you can't grasp the impact.

But I'll try. A non-zero commutator means the quantities involved show an uncertainty principle, like position and momentum, or time duration and energy uncertainty. Measurements of one cannot be done without affecting the probabilities of the other. For events outside of the light cones, the opposite happens: the measurements are guaranteed not to affect the other. In other words, the results are independent.

But, the essence is that events outside of the light cones have zero correlation.

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.

Yes, it is the 'equivalent' in the same way that Schrodinger's equation is the equivalent of F=ma in the classical setting.

In this context, the *meaning* of causality is that the non-zero commutators are limited to the forward light cone. it does NOT mean what philosophers would like it to mean.