Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Energies in the LHC

  1. Sep 1, 2014 #1
    Due to the blogs being removed, I thought it might be worthwhile posting a few in the forums-

    The Large Hadron Collider has produced collisions at 7 TeV. For collisions at 7 TeV, protons need to be ‘ramped’ to 3.5 TeV, the proton has a mass of 1.6726e−27 kg which, according to mass–energy equivalence (E=mc2), is 938.272 MeV where 1 eV= 1.6022e−19 Joules. The proton will be accelerated to 0.999999964c (11,103.4 revolutions of the LHC per second) which means the following relativistic equation can be used-

    ET= γmc2

    where ET is energy total and γ=1/√(1-(v2/c2)). γ is the Lorentz factor and tells us how much the energy of an object increases due to kinetic energy.

    which produces a total of ET=3.4967 TeV

    This is also supported by Einstein’s more complete mass-energy equation-


    where p is momentum and is expressed p=γmv (or p=h/λ in the case of light where h is Planck’s constant and λ is wavelength).

    which produces a total of ET=3.4959 TeV

    CERN hope to conduct collisions at 14 TeV which would require speeds of up to 0.999999991c (1-8.98e−9c)

    Another interesting aspect is the effect on time for the proton. The relativistic equation for time dilation is-


    where τ is proper time relative to the proton and t is coordinate time, or time according to a (relatively) static frame. In this case, at energys of 3.5 Tev, the time dilation for the proton is 2.6833e−4 which means for every hour that passes outside the accelerator, only 1 second passes for the proton (0.966 seconds), at 7 TeV, only ½ a second would pass (0.483 seconds). The application of the Lorentz factor to time dilation can be supported by looking at a basic spacetime metric derived from Minkowski space time, accordingly-


    again, where τ is the proper time of the moving object, t is coordinate time and x is the distance covered. x can be rewritten as-


    where v=dx/dt (i.e. velocity is m/s), v2=dx2/dt2 which can be rewritten as above. The spacetime metric can now be written as-





    = dt√(1-v2/c2)

    which is equivalent to τ=t/γ.

    Time dilation for relativistic sub-atomic particles is also supported by muons (high energy leptons) which enter the atmosphere from space, according to our clocks, the muon should decay at 660 m into the atmosphere based on a life span of 2.2e−6 seconds and a velocity of 0.9996678c but due to time dilation (τ=0.02577), muons survive the flight to earth's surface and can penetrate tens of meters of rock before decaying.
    Last edited: Sep 1, 2014
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted