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MARKUS KLUTE: Welcome back
to 8.20 Special Relativity.

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In this section, we're going
to talk about particles

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and accelerators.

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And we use the Large
Electron-Positron Collider

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at CERN as an example.

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LEP, the Large
Electron-Positron Collider,

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was a collider which was
operated in the late 1980s

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up to the year 2000 at
center-of-mass energies

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from 91 GeV up to 209 GeV.

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These energies
were used to probe

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the Z boson to produce
pairs of W boson

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and also to look for the Higgs
boson, which didn't quite

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work because its energy
wasn't quite sufficient.

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The 27-kilometer over
a 16-mile circumference

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collider is now the home of the
Large Hadron Collider at CERN.

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And it's being used there to
collide protons with protons.

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LEP had four experiments,
ALEPH, DELPHI, L3, and OPAL.

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And I was happy to study data
from the particle as part

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of my undergraduate thesis.

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So this was very
good memories there.

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But that's not the topic today.

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So the topic today is
to find out how quickly,

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how fast the particles
in the collider

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are moving when we know
the center-of-mass energy.

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So we know the center-of-mass
energy to be 209 GeV.

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We know that the
energy in the beam

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is half of that, 104.5 GeV.

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So now to figure out how fast
the electrons are moving--

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the electrons and
the positrons--

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we can use our relativistic
total energy for the electron

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or for the positron, which
is the kinetic energy

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plus the rest mass of the
electron or positron, which

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is M0 gamma times c square.

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So with a mass of 511
KeV over c square,

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and this energy
of 104.5 GeV, this

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results in a gamma
factor of 200,000.

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And if you do the
math, you'll find

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that electrons and
positrons are almost

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moving with the speed of light.

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They're moving with the
speed of light [INAUDIBLE]..

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A fun additional fact is
we are working right now

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on proposing a even
larger collider, which

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will then allow us
to efficiently go up

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to energies of 350 GeV.

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And that collider then will be
able to study the Higgs boson

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with precision but also look
at [INAUDIBLE] production--

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[INAUDIBLE] production in
these kind of colliders.

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Another fun fact is
that CERN, the collider,

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which is about 100
meters under the surface,

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is spanning two countries,
Switzerland and France.

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And so each particle,
lep, when we make the lep,

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makes about 11,200
leps per second.

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That means that there is
about 44,800 border crossings

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for an electron and positron.

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So they always constantly have
to show their passport when

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they're moving around in LEP.

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To look at a second example
here with a small accelerator,

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we can accelerate
electrons through

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an electrostatic potential
of 511 kilovolts or 0.511

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megavolts.

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The total energy then is,
again, the kinetic energy

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plus the rest energy,
which is, in this example,

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4.511 MeV plus 0.511 MeV.

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And so here we find
the gamma factor of 2

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and a velocity of 0.866.

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So even in this smaller
electrostatic potential

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of 500 kilovolts, we
find that electrons

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are moving with
very high velocities

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with velocities very close
to the speed of light.