You need to distinguish different notions of local causality. SR implies in most forms a very strong form of local causality that you seem to be using here. But it is important to note that very well behaved systems can not obey this, and it isn’t just weird systems. For example, a purely Newtonian universe won’t obey this sort of strong local causality. A particle from far away can have arbitrarily high velocity and smack into the region we care about. The fact that such well behaved systems are ok with weaker forms of local causality suggests that we shouldn’t assign such importance to local causality.
What I can’t make out is whether Lorentz violation throws away locality; employs a more complicated definition of c which is different in some directions than others; makes the effect of the constant different on neutrinos and photons; or, well, what exactly
This isn’t a well-defined question. It depends very much on what sort of Lorentz violation you are talking about. Imagine that you are working in a Newtonian framework and someone asks “well, if gravity doesn’t always decrease at a 1/r^2 rate, will the three body problem still be hard?” The problem is that the set of systems which violate Lorentz is so large that saying this isn’t that helpful.
The trouble is that physicists don’t read books like Causality and don’t understand local causality as part of the apparent character of physical law,
The vast majority of physicists aren’t thinking about how to do things that replace the fundamental laws with other fundamental more unifying laws. The everday work of physicists is stuff like trying to measure the rest mass of elementary particles more precisely, or being better able to predict the properties of pure water near a transition state, or trying to better model the behavior of high temperature superconductors. They don’t have reason to think about these issues. But even if they did, they probably wouldn’t take these sorts of ideas as seriously as you do. Among other problems, strong local causality is something which appeals to a set of intuitions. And humans are notoriously bad at intuiting how the universe behaves. We evolved to get mates and avoid tigers, not to be able to intuit the details of the causal structure of reality.
You need to distinguish different notions of local causality. SR implies in most forms a very strong form of local causality that you seem to be using here. But it is important to note that very well behaved systems can not obey this, and it isn’t just weird systems. For example, a purely Newtonian universe won’t obey this sort of strong local causality. A particle from far away can have arbitrarily high velocity and smack into the region we care about. The fact that such well behaved systems are ok with weaker forms of local causality suggests that we shouldn’t assign such importance to local causality.
This isn’t a well-defined question. It depends very much on what sort of Lorentz violation you are talking about. Imagine that you are working in a Newtonian framework and someone asks “well, if gravity doesn’t always decrease at a 1/r^2 rate, will the three body problem still be hard?” The problem is that the set of systems which violate Lorentz is so large that saying this isn’t that helpful.
The vast majority of physicists aren’t thinking about how to do things that replace the fundamental laws with other fundamental more unifying laws. The everday work of physicists is stuff like trying to measure the rest mass of elementary particles more precisely, or being better able to predict the properties of pure water near a transition state, or trying to better model the behavior of high temperature superconductors. They don’t have reason to think about these issues. But even if they did, they probably wouldn’t take these sorts of ideas as seriously as you do. Among other problems, strong local causality is something which appeals to a set of intuitions. And humans are notoriously bad at intuiting how the universe behaves. We evolved to get mates and avoid tigers, not to be able to intuit the details of the causal structure of reality.