eli5 Why does length contraction matter in the LHC?


Why does length contraction matter in the LHC?

We’re doing an assignment on special relativity and it’s uses. For one of my investigation points I was looking at the Higgs Boson in the LHC and tine dilation. I was of the understanding that the main problem after creating the Higgs Boson was that it had such a short lifespan so we couldn’t observe it. After doing the tine dilation calculations I found that going at 99.9999% the speed of light it still had a short lifespan but much more observable. However while it’s lifespan does increase the way its discovered isn’t just by looking at it but what happens after it decays. I was told by my teacher that length contraction is much more important in the desogn of the LHC but I can’t find data or understand why. Doing the calculations from the protons point of view it is travelling three and a bit metres in a circle when it is actually moving around a 26.6 km circle. My best guess is that this matters because of the forces on the proton from its point of view but I can’t find any data on why it’s important.
Any help’s greatly appreciated.

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