It's not about transmitting information into the past - it's about the locality of causality. Consider Judea Pearl's classic graph with SEASONS at the top, SEASONS affecting RAIN and SPRINKLER, and RAIN and SPRINKLER both affecting the WETness of the sidewalk, which can then become SLIPPERY. The fundamental idea and definition of "causality" is that once you know RAIN and SPRINKLER, you can evaluate the probability that the sidewalk is WET without knowing anything about SEASONS - the universe of causal ancestors of WET is entirely screened off by knowing the immediate parents of WET, namely RAIN and SPRINKLER.

Right now, we have a physics where (if you don't believe in magical collapses) the amplitude at any point in quantum configuration space is causally determined by its immediate neighborhood of parental points, both spatially and in the quantum configuration space.

In other words, so long as I know the exact (quantum) state of the universe for 300 meters around a point, I can predict the exact (quantum) future of that point 1 microsecond into the future without knowing anything whatsoever about the rest of the universe. If I know the exact state for 3 meters around, I can predict the future of that point one nanosecond later. And so on to the continuous limit: the causal factors determining a point's infinitesimal future are screened off by knowing an infinitesimal spatial neighborhood of its ancestors.

This is the obvious analogue of Judea Pearl's Causality for continuous time; instead of discrete causal graphs, you have a continuous metric of relatedness (space) which shrinks to an infinitesimal neighborhood as you consider infinitesimal causal succession (time).

This, in turn, implies the existence of a fundamental constant describing how the neighborhood of causally related space shrinks as time diminishes, to preserve the locality of causal relatedness in a continuous physics.

This constant is, obviously, c.

I've never read this anywhere else, by the way. It clearly isn't universally understood, because if all physicists understood the universe in these terms, none of them would believe in a "collapse of the wavefunction", which is not locally related in the configuration space. I would be surprised neither to find that the above statement is original, nor that it has been said before.

I am attempting to bet that physics still looks like this after the dust settles. It's a stronger condition than global noncircularity of time - not all models with globally noncircular time have local causality.

If violating Lorentz invariance means that physics no longer looks like this, then I will bet at 99-to-1 odds against violations of Lorentz invariance. But I can't make out from the Wikipedia pages whether Lorentz violations mean the end of local causality (which I'll bet against) or if they're random weird physics (which I won't bet against).

I am also willing to bet that the fundamental constant c as it appears in multiple physical equations is the constant of time/space locality, i.e., the constant we know as c is fundamentally the shrinking constant by which an infinitesimal neighborhood in space causally determines an infinitesimal future in time. I am willing to lose the bet if there's still locality but the real size of the infinitesimal spatial neighborhood goes as 2c rather than c (though I'm not actually sure whether that statement is even meaningful in a Lorentz-invariant universe) and therefore you can use neutrinos to transmit information at up to twice the speed of light, but no faster. The clues saying that c is the fundamental constant that we should expect to see in any continuous analogue of a locally causal universe, are strong enough that I'll bet on them at 99-to-1 odds.

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.

I would happily amend the bet to be annulled in the case that any more complicated definition of c is adopted by which there is still a constant of time/space locality in causal propagation, but it makes photons and neutrinos move at different speeds.

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, which is why some of them still believe in the "collapse of the wavefunction" - it would be an exceptional physicist whom we could simply ask whether the Standard Model Extension preserves locally continuous causality with c as the neighborhood-size constant.