# Mass Observed to Increase as Velocity Increases?

#### crybllrd

With CERN's Large Hadron Collider being in the news recently, I began to think of a question that bothered me for years about particle accelerators.
It is well known in physics that mass increases as velocity does (Special Relativity if I'm not mistaken), so if these particles in the LHC are being accelerated to 99.9% of the speed of light, then would their mass be increasing to infinity?
Or, would his only happen when it is even CLOSER to approaching c, say, 99.999999%?

Just curious..

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#### Bill_K

crybllrd, Mass does not increase with velocity. This is an old-fashioned idea.

There's a quantity γ we use to describe relativistic effects, γ = (1 - v2/c2)-1/2.

The so-called "relativistic mass" is what increases. It's an artificial quantity defined because the momentum for a relativistic particle is p = γmv. Thus by defining M = γm we can make it look like the nonrelativistic form, p = Mv. But the only mass with actual physical significance is the rest mass m, which does not increase.

You can easily calculate these quantities for the LHC. The relativistic formula for the energy is E = γ mc2. For a proton the rest energy mc2 is about 1 GeV, so for a 3.5 TeV beam of protons, γ = 3500. A little algebra will tell you what v/c is - about a ten-millionth less than 1.

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