Using the formula... er... l0 = l/(root of 1-v^2/c^2)
l0 is the proper distance, i.e. in the protons frame, l in our frame... should be larger in the protons frame?
Proper means in the frame of the thingy doing the distance/two events
The protons are the ones passing the two points at whatever speed, not us
Hence the distance they record is l0, ours is l
I really need to **** right now, sorry for lack of help ;-;
Okay. Had my business, so...
When we derived our formula, l0 was the proper distance.
The meaning of proper in this case is that the distance represented will be that of the frame of reference which was moving at whatever velocity, visiting these two locations.
Our distance watching the protons isn't proper, i.e. we're not in the protons frame, at that velocity, moving between those two locations at that particular time.
Thus, we are L, the protons are L0, and we use that in the equation.
Hope I gave a better explanation!
The way I think of it is just that objects are fastest in their own reference frame, lightest in their own reference same and longest in their own reference frame. A stationary observer perceives the object as slower, heavier and shorter. So I always just rearrange the equation while keeping in mind the bolded statement.
Bit brainless but x)