Hey Will!
You've given this claim a lot of thought which is fantastic. I have a few points though, and I hope they can offer some guidance:
- Has length contraction been disproved through circular particle accelerators?
- Have particle accelerators been able to prove the ‘ladder in the barn’ paradox through the concept of length contraction?
These are good questions, but I would be careful with your language. In science, we can't "prove" anything. We can find evidence that supports a given conjecture, but we can never prove anything. The best we can do is provisionally accept hypotheses until they are refuted by anomalous or competing findings.
I think these questions are good, however it may be more difficult to find evidence for it than it would be if you were looking into time dilation.
- The constant of light has been proved through particle accelerators?
This one lacks a clear connection to the special relativity component of the claim. So I probably wouldn't choose this one.
- Have particle accelerators been able to prove the twins paradox through the concept of time dilation?
This is a good question, just refrain from using the word "prove".
Aside from that, this is a great candidate for your research question.
Here is a really interesting article (you may have seen while doing your research) that explores this topic. If you do decide to go with this one I'm sure you'd be able to find some graphs and quantitative evidence in research papers and stuff
- Have particle accelerators been able to prove the existence of dark matter within the universe?
This one lacks a clear connection to the special relativity component of the claim. So I probably wouldn't choose this one.
- Are particle accelerators able to find correlations between…
I would probably try to refrain from looking into correlations. What's of interest to scientists are causations (because correlations don't really mean much in the grand scheme of things).
- Have particle accelerators used similtaintity to show how length contraction…
- Does simultaneity need to be taken into consideration when trying to prove length contraction in particle accelerators?
I feel that the first one would be difficult to work with.
- Why can particle accelerators not speed up electrons and other lgutb weight particle faster than the speed of light?
- Can current particle accelerators speed up particles faster than the speed of light?
These would be hard to write about given that we know the speed of light is the cosmic speed limit and that nothing can go faster than that. I don't feel that this would be worth investigating. You can essentially explain this speed limit in just a few sentences using the relationship between momentum and velocity.
- Want to try write a question about ‘internal frames of reference’ as if it is in a circular PA it is turning and thus not in an internal frame
- LINACs…
Do you mean inertial? If not, I'm not quite sure what you mean by internal frames of reference.
As for LINACs you could definitely look into those for evidence if you are able to find a way to connect it to length contraction or time dilation in a meaningful manner (this could also be a good way of providing evidence for the practical application of these physics concepts).