The Standard Model, which models everything else, is continuous. A specific part of it, QED, is the most accurate theory known, agreeing with experiment to better than 10 parts in a billion.
There is no known violation of these two theories, which explain all of the observable universe. There is an issue on how to glue them together, and one of the leading methods, string theory, is also continuous. I am unaware of any theory that can replace these that has no continuous parts, such as symmetries.
> it is not known that anything is continuous either
Every physics theory that we use to explain the universe is continuous, and not a single one is not, so I'm betting that there are continuous things in reality.
> Every physics theory that we use to explain the universe is continuous
Are you suggesting thete are no discrete models?
Any discrete model may be similar to leading continuous models, so the explanatory power of both isn't relevant unless it can only be produced by continuous models.
Which theories discretize all variables? I'm well aware people make models all the time, but they usually fail to explain all we observe or are toy models, like 2D TQFT models, not designed to mirror reality, but to fiddle with to see if they extend.
LQG, for example, treats space as quantized at the Plank length, but this has already been disproven experimentally [1,2], forcing LQG to reassess. LQG still has continuous parameters, such as symmetry, and is based on the same continuous math as GR and TQFTs. It's simply trying to discretize (somewhat) spacetime, but it certainly has not yet succeeded at that.
Hogan's holometer experiment [3] also has shown that the scales LQG wanted to discretize spacetime at are incorrect.
So there is at least 2 different experiments invalidating a central piece of LQG. Of course LQG can simply retrench and claim scales are smaller than the Plank length.
There is no experimental evidence pointing to LGQ as reality. It has not even been shown to reproduce GR in the semi-classical limit, so it may end up simply being mathematical fantasy. LQG also has lots of other technical problems that may in the end throw it on the heap of failed theories, of which there have been many. It makes no prediction not already covered under GR.
So, yes, I realize there are people trying to discretize the universe, but so far none of these theories have reproduced what we observe in experiment, and the only theories that have reproduced all we observe in experiment are continuous.
>Any discrete model may be similar to leading continuous models, so the explanatory power of both isn't relevant unless it can only be produced by continuous models.
Which model using only discrete variables can make the same predictions of GR or SM? I cannot think of one, I cannot find one, so it may be that so far the only models that work are continuous.
Heck, even going simpler - what discrete model can reproduce only GR? LQG so far cannot, despite significant effort trying to make it do so. So that surely puts the burden of proof on showing discrete models as equivalent to continuous ones.
So I'm game for something to break current models, because that would be cool. However, nothing has, and no theories is really even close to replacing SM and/or GR.
[1] https://arxiv.org/abs/1102.2784
