eli5 Why does length contraction matter in the LHC?

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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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