One of the research paradigms that I consider insanely overrated is the idea that the fundamental theory of Nature may break the Lorentz symmetry – the symmetry underlying the special theory of relativity – and that the theorist may pretty much ignore the requirement that the symmetry should be preserved.
The Super-Kamiokande collaboration has published a new test of the Lorentz violation that used over a decade of observations of atmospheric neutrinos:
They haven't found any evidence that these coefficients are nonzero which allowed them to impose new upper bounds. Some of them, in some parameterization, are 10 million times more constraining than the previous best upper bounds!
I don't want to annoy you with some technical details of this good piece of work because I am not terribly interested in it myself, being more sure about the result than about any other experiment by a wealthy enough particle-physics-like collaboration. But I can't resist to reiterate a general point.
The people who are playing with would-be fundamental theories that don't preserve the Lorentz invariance exactly (like most of the "alternatives" of string theory meant to describe quantum gravity) must hope that "the bad things almost exactly cancel" so that the resulting effective theory is almost exactly Lorentz-preserving which is needed for the agreement with the Super-Kamiokande search – as well as a century of less accurate experiments in different sectors of physics.
But in the absence of an argument why the resulting effective theory should be almost exactly Lorentz-preserving, one must assume that it's not and that the Lorentz-violating coefficients are pretty much uniformly distributed in a certain interval.
Before this new paper, they were allowed to be between \(0\) and a small number \(\epsilon\) and if one assumes that they were nonzero, there was no theoretical reason to think that the value was much smaller than \(\epsilon\). But a new observation shows that the new value of \(\epsilon\) is 10 million times smaller than the previous one. The Lorentz-breaking theories just don't have any explanation for this strikingly accurate observation, so they should be disfavored.
The simplest estimate what happens with the "Lorentz symmetry is slightly broken" theories is, of course, that their probability has decreased 10 million times when this paper was published! Needless to say, it's not the first time when the plausibility of such theories has dramatically decreased. But even if this were the first observation, it should mean that one lines up 10,000,001 likes of Lee Smolins who are promoting similar theories and kills 10,000,000 of them.
(OK, their names don't have to be "Lee Smolin". Using millions of his fans would be pretty much OK with me. The point is that the research into these possibilities should substantially decrease.)
Because nothing remotely similar to this sensible procedure is taking place, it seems to me that too many people just don't care about the empirical data at all. They don't care about the mathematical cohesiveness of the theories, either. Both the data and the mathematics seem to unambiguously imply that the Lorentz symmetry of the fundamental laws of Nature is exact and a theory that isn't shown to exactly preserve this symmetry – or to be a super-tiny deformation of an exactly Lorentz-preserving theory – is just ruled out.
Most of the time, they hide their complete denial of this kind of experiment behind would-be fancy words. General relativity always breaks the Lorentz symmetry because the spacetime is curved, and so on. But this breaking is spontaneous and there are still several extremely important ways how the Lorentz symmetry underlying the original laws of physics constrains all phenomena in the spacetime whether it is curved or not. The Lorentz symmetry still has to hold "locally", in small regions that always resemble regions of a flat Minkowski space, it it must also hold in "large regions" that resemble the flat space if the objects inside (which may be even black holes, highly curved objects) may be represented as local disturbances inside a flat spacetime.
One may misunderstand the previous sentences – or pretend that he misunderstands the previous sentences – but it is still a fact that a fundamentally Lorentz-violating theory makes a prediction (at least a rough, qualitative prediction) about experiments such as the experiment in this paper and this prediction clearly disagrees with the observations.
By the way, few days ago, Super-Kamiokande published another paper with limits, those for the proton lifetime (in PRD). Here the improvement is small, if any, and theories naturally giving these long lifetimes obviously exist and still seem "most natural". But yes, I also think that the theories with a totally stable proton may also exist and should be considered.