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AFAIK when particles accelerate, their mass increase.
Do you know how many times proton mass is increased at the LHC at 3.5 TeV?
Do only the mass increase or also the size of the proton increase as well?
If yes, does it means that at higher energies (7 TeV) collision ratio should increase by the size increase?

Thanks very much.

see http://lhc-machine-outreach.web.cern.ch ... ch-faq.htm

Thanks very much Zaim. But regarding the last questions, do the size (diameter) increase with the relativistic mass increase?
Thanks!

It it not quite correct to say the proton mass has increased... Special relativity modifies Newton's law F=ma, and in this particular case it is as if the proton mass had increased by the relativistic factor gamma. But the proton itself has not become "bigger"...

The way I am imagining it (I may be wrong) the mass of the proton does not really increase, what continues increasing proportionally to added energy is the proton "inertia". It's just the classic view on inertia being proportional to speed rather than energy that we need to say it's mass that increases.
The truth however is, the proton scattering radius does change with energy, too. That's what the TOTEM experiment was measuring but the change sure isn't proportional to the increased mass.

Mass in relativistic physics can mean one of two things: the rest mass (the mass of the particle when it is not moving) and the relativistic mass (inertial mass). The relativistic mass grows as the speed of the particle increases, and is the mass you would measure for the particle as it zips past. It's only the rest mass that is an intrinsic property of the particle, as the relativistic mass depends on the speed of the observer relative to the particle. When the particle is at rest, the two kinds of mass coincide - and this remains a pretty good approximation unless you are moving at some significant fraction of the speed of light.

While protons don't get "bigger" as they get heavier, they do deform due to Lorentz contraction. At the LHC, they will basically look like pancakes from the point of view of the experiments. (Of course "look like" has to be taken with a large pinch of salt as we are talking about subatomic particles, but the effect is noticeable...) This is not a consequence of the increased relativistic mass, rather both the Lorentz contraction and the relativistic mass are a consequence of the fact that you are looking at an object moving very close to the speed of light.

Photino is correct. I'll just add that the Lorentz contraction affects only the length in the direction of movement. So the photons get shorter (in the direction of travel) but keep the same diamater (in the perpendicular directions). Thus they do indeed end up looking like pancakes. But since their cross-sectional area hasn't changed, the collision rate remains the same.

Thanks very much for the detailed answer. Really appreciate it, it is a very interesting (and sometimes confusing) topic for me (no physics beyond high school). It is much clear now.