In other words as we probe lower scales, string theory predicts thtat Lorenz invariance will never break,

as long we have to do with a consistent string like theory.

Is my understanding correct?

> If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? Nay, more, has this right way any existence outside our illusions? Can we hope to be guided safely by experience at all when there exist theories (such as classical mechanics) which to a large extent do justice to experience, without getting to the root of the matter? I answer without hesitation that there is, in my opinion, a right way, and that we are capable of finding it. Our experience hitherto justifies us in believing that nature is the realisation of the simplest conceivable mathematical ideas. I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena. Experience may suggest the appropriate mathematical concepts, but they most certainly cannot be deduced from it. Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.

- Albert Einstein

This is his argument that mental experiments are a good basis to construct a theory. If relativity had 0 experimental evidence to this day it would be held in considerably lower regard.

There is no a priori reason why a bunch of meatbags would have the ability to test all laws of physics of this universe. I think we may have gotten lucky for a while there. String theory is so far out there that a new methodology has been developed, namely using beauty or symmetry or Occam's Razor to choose between competing theories. None of these have the pedigree of empiricism, but they may also not be wrong. I hope some aesthetic could be applied to the laws of the universe, but that is also not at all guaranteed.

Occam's razor is perfectly empirical: "entities must not be multiplied beyond necessity". It's what people repeatedly accuse string theory of violating in low-rent popsci criticism.

The other things you refer to are still Occam's razor: symmetry is handy because it eliminates symmetry-breaking entities even though we know they can happen in the standard model (Higgs) and "beauty" is really just another way of saying Occam's razor - you'd prefer your theory to not be full of dozens of free parameters because it starts to fit any possible outputs and be less predictive.

At all points the issue is that unless you've fully explored a simpler space with less entities, don't start adding them because you can always keep adding them to solve any problem but predict nothing (ala epicycles keeping geocentric solar models alive. You could probably run a space program assuming the Earth is the center of the universe, but it would be fiendishly difficult to model).

You seem to be intuiting some kind of chi squared minimization. It is true that fewer free parameters constrain models, but there is nothing in nature that prefers simplicity. That is probably the most annoying thing to us physicists. Even thermodynamics is always shoving us toward disorder. Just look at plasma physics some time for deterministically intractable problems stemming from four little equations (one if you like tensors).

I think it's better to think of most real world models as being low dimensional-ish, where there is a decaying power law of eigenvalues, and most are quite small, though not zero. You can get quite far by looking at the largest modes and ignoring small ones, but you're not exact, so you're not seeing The Truth, or whatever. Forcing your self to use fewer parameters is a way of denoising, however, that is quite effective.

> I hope some aesthetic

Certainly internal self-consistency will take you a long way if you don't have experiments. Some people find beauty in this :-)

This is good and all but then it is not really physics as it is generally intended

It might be worth considering what you think research in a field like mathematics actually entails when asking such questions.

Because you can write a lot of mathematics with no practical applications for generations (then whoops: number theory and cryptography!)

Mathematics often does apply to the real world, but that isn't the goal. Physics is about the study of the real universe. If you want to call string theory a branch of mathematics I'd be fine with it, but they keep trying to claim they are physicists and that puts a higher bar on what we expect from them.

Of course physicists sometimes do make wrong predictions and it can take some time to figure out the hypothesis is wrong. However the goal is always to make something they can test to prove the hypothesis holds, which string theory has so far failed to do.

Good question, I touch on this on the same comment, in the paragraph starting with "I keep repeating these things on HNs".

The TLDR is that you can never expect the same level of certainty when you don't have direct experiments, but you can still rule out _some_ hypothesis, and see how far other hypothesis take you. This is called theoretical physics. Just because you can't make an experiment doesn't mean you can't do anything.