In the LHC, protons are accelerated to 99.9999991% of lightspeed. So gamma ~7500. At gamma of 7500, the energy content of proton is 7 TeV. So two colliding protons together should have a(adsbygoogle = window.adsbygoogle || []).push({}); totalmass-energy equivalentof 14 TeV.

Now, I want to calculate the total energy differently. The relative speed between the two protons is (using v = (u+v)/(1+uv/c^2)) 0.99999999999999995949.... Now, I assume one proton is at rest and the other is approching it at a speed of 0.99999999999999995949c. So the total energy is:

mp*c^2 + gamma(0.99999999999999995949)*mp*c^2

which turns out to be 104235 TeV, much greater than the 14TeV that was in the closed system of 2 protons.

Thetotalenergy content of the closed system was calculated to be 14TeV by an observer seeing two protons approaching each other at speeds of 0.999999991c. So it should have matched the calculation from the viewpoint of one of the protons (ie it is not moving and the other is coming towards it at 0.99999999999999995949c).

What am I doing wrong?

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# Energy calculation in STR

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