# Question on Lorentz contraction and size of pancakes

1. May 5, 2012

### zincshow

Question on Lorentz contraction and size of "pancakes"

I have read that nucleons (protons in particular) appear to look like flattened "pancakes" hitting each other due to the lorentz contraction when crashed together at high speeds. Do any of the colliders give a hint at the "size" of the pancakes? Ie. At say 99.99% of the speed of light, protons must be within ??? picometers of each other to react with each other and create a "crash". This number is confussing as I understand the pancakes can also pass through each other without a collision.

2. May 5, 2012

### Bob S

Re: Question on Lorentz contraction and size of "pancakes"

An excellent simulation of the Lorentz contraction (up to β = 0.95) can be seen in the Cal Tech simulation of a moving charge. See http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Use the slider to change β and hit GO. Watch in particular the center (of 7) field lines in the simulation. It always remains perpendicular to the velocity, and the other field lines are beginning to flatten (pancake) against it as β increases.

At high energies, the total proton-proton croass section is about 40 x 10-27 cm2. See top plot on page 12 of http://pdg.lbl.gov/2011/reviews/rpp2011-rev-cross-section-plots.pdf. This means that if you have 1 proton in a 1 cm2 area, and you shoot another proton at it, the probability of hitting it is 40 x 10-27.. But if you put 1012 protons in each of the two colliding bunches, the probability of a collision is 1024 x 40 x 10-27., or 4%..