But there are such experiments. String theory says that the result of such experiment is: Lorentz invariance not violated.

> but our other theories

This is not how scientific research is done. The way you do it is you a theory, the theory makes predictions, you make experiments, and the predictions fail, you reject that theory. The fact that you might have other theories saying other things doens't matter for that theory.

So string theories said "Lorentz invariance not violated", we've made the experiments, and the prediction wasn't wrong, so you don't reject the theory. The logic is not unlike that of p-testing. You don't prove a theory correct is the experiments agree with it. Instead you prove it false if the experiments disagree with it.

There are no such experimental results satisfying the criteria I laid out. You may be right in objecting to the criteria I laid out, but, the fact remains that it does not satisfy these (perhaps misguided) criteria.

In particular, predicting something different from our best other theories in good standing, was one of the criteria I listed.

And, I think it’s pretty clear that the criteria I described, whether good or not, were basically what the other person meant, and should have been what you interpreted them as saying, not as them complaining that it hadn’t been falsified.

Now, when we gain more evidence that Lorentz invariance is not violated, should the probability we assign to string theory being correct, increase? Yes, somewhat. But, the ratio that is the probability it is correct divided by the probability of another theory we have which also predicts Lorentz invariance, does not increase. It does not gain relative favor.

Now, you’ve mentioned a few times, youtubers giving bad arguments against string theory, and people copying those arguments. If you’re talking about Sabine, then yeah, I don’t care for her either.

However, while the “a theory is tested on its own, not in comparison to other theories” approach may be principled, I’m not sure it is really a totally accurate description of how people have evaluated theories historically.

And, I think, not entirely for bad reasons?

> But there are such experiments. String theory says that the result of such experiment is: Lorentz invariance not violated.

This is not a new prediction... String theory makes no new predictions, I hear. I don't understand why you need to be told this.

To your point, there exist various reformulations of physics theories, like Lagrangian mechanics and Hamiltonian mechanics, which are both reformulations of Newtonian mechanics. But these don't make new predictions. They're just better for calculating or understanding certain things. That's quite different from proposing special relativity for the first time, or thermodynamics for the first time, which do make novel predictions compared to Newton.