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Re: the energy



We didn't, in our wildest imaginations, dream that the proton had
structure in those days. (I arrived at Berkeley in the fall of '56). The
kinematics of the Bevatron had nothing to do with quarks, gluons or QCD.
The kinematics is identical to that for car-car collision where one of the
cars was parked before the collision. A lot of the energy in the final
state just comes from center-of-mass motion.
To see this (this is where John's gamma's can be helpful), first
do the calculation for a collider, where the net spatial momentum is zero
before and after the collision. The final energy (3 protons and a p-bar,
all at rest in the center of momentum system) must equal the the original
energy. The square of the total energy in the center-of-momentum system
is an invariant, S=(E^{2}-p^{{2})=16, since p=0. Now calculate the same
quantity in the lab system where one of the two initial protons is at
rest, to get the canonical result.
Regards,
Jack


On Mon, 25 Oct 2004, John Denker wrote:

David Bowman wrote:

I believe you left out the effects of a very important
fact here. Protons are *not* elementary particles.

When a proton interacts deeply with another proton asymptotic freedom
becomes relevant. In the collision what may appear to us to be a
proton interacting with another proton is in fact a single quark from
one proton interacting with a single quark of the other proton. The
remaining 4 quarks are oblivious bystanders to what is going on with
the 2 colliding/interacting quarks. This means that all the KE in
these by-standing quarks is essentially *unavailable* for creating
particle-antiparticle pairs.

OK, I'll bite. Why then does the proton-smacking-proton calculation
give the empirically-correct answer?!

I'm told this calculation was used in the early 1950s as the
basis for the design of the Bevatron ... which worked!
http://livefromcern.web.cern.ch/livefromcern/antimatter/history/AM-history01-b.html

This was a decade or more before quarks were conceived of.

In any event, the problem has a high cuteness coefficient anyway.

Oh yeah.



--
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just before leading them into the Little Big Horn Valley