What energy density expected at LHC point of collision?

[Martin]

Can anyone provide an estimate of the energy density, expressed say in GeV per cubic fermi, where two particles collide at LHC energies?

[Severian]

To say an energy density is a little difficult, since it is a little bit ill defined. For example, would you consider particles which don't collide as part of the collision? probably not. If you just consider the particles which do collide (the gluons usually), then they are point particles.

 

However, gluons do sort of have a spacial extent due to their wave like properties. If you work it out, their wavelength at the LHC comes to about 10^-16m, into which radius we are squeezing 1TeV.

 

If you want to compare to with the big bang though (which I suspect is your motivation), it is best to compare the LHC's 1TeV energy with the Planck scale at 10¹⁹ GeV. So we would need an extra 16 orders of magnitude in energy.

 

Here are some extra statistics for the LHC:

 

Nominal energy, protons: 7 TeV

 

Minimum distance between bunches: ~7 m

 

Design luminosity: 10³⁴ cm^-2s^-1

 

Number of bunches per proton beam: 2808

 

Number of protons per bunch (at start): 1.1x10¹¹

 

Number of turns per second: 11 245

 

Number of collisions per second: 600 million

[Martin]

To say an energy density is a little difficult, since it is a little bit ill defined. For example, would you consider particles which don't collide as part of the collision? probably not. If you just consider the particles which do collide (the gluons usually), then they are point particles.

 

However, gluons do sort of have a spacial extent due to their wave like properties. If you work it out, their wavelength at the LHC comes to about 10^-16m, into which radius we are squeezing 1TeV.

 

thanks, and for the extra specs!

it looks like a nominal energy density of

10⁵ to 10⁶ GeV/fermi³

 

I have in mind that the Planck energy density is

2.9 x 10⁷⁸ GeV/fermi³

 

that would say that the energy densities around meaningful collision reactions (vague as the idea is) fall short of "big bang" conditions by more than 72 orders of magnitude.

 

This really makes me wonder about that BBC movie. Shouldn't LHC publicity and outreach people be warned not to risk a "hype backlash" by giving the impression that expected energy densities are near Big Bang when they are actually so far away?

I really enjoyed the movie visually, and it wouldn't take too much editing to clear up some of the language so it doesnt seem to give the public an exaggerated impression.

 

I also take your point that a solider comparison would be the 16 orders of magnitude in kinetic energy----comparing 1000 GeV with 10¹⁹ GeV.

Simply comparing kinetic energies of particles---LHC versus Planck---makes good sense, but recently I have been hearing talk comparing energy densities.