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MARKUS KLUTE: Welcome
back to 8.701.

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So in the last two videos, we
looked at the Dirac equation

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and we looked at
solutions Dirac equations.

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And in the last
lecture we found that,

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along with positive
energy states,

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we had those negative
energy states.

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Since we cannot simply drop
them or disregard them,

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we do have to find physical
interpretation for these

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negative energy solutions.

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The first one which
was put forward,

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is the one where you think
about negative energy

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states all being populated--

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and that is the vacuum.

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The vacuum is basically a sea
full of negative energy states

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which are all populated.

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So if you have a
positive energy state,

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and there are electrons sitting
in this energy state here,

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the electron, because of the
Pauli exclusion principle

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cannot fall down into the
negative energy state.

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But you are able to kick
them out, for example,

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to excite them with a photon.

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Very excited.

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The negative energy state,
you get an electron out.

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This process is then
will lend to the creation

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of a positron and an
electron pair with a photon.

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[INAUDIBLE] pair production.

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It can also explain
undulation where

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there's an empty and
a negative energy

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stage where the electron just
folds into creating a photon.

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So while the
interpretation is useful

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and it explains pair production
and undulation processes,

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they fail to explain
what this vacuum,

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the sea of negative
energy state even is.

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So a more useful interpretation
is one part forward that

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Feynman and Stückelberg, which
came out of the discussion

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of quantum field theory.

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And we already discussed
this interpretation

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when we looked at
Feynman [INAUDIBLE]..

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So have a look at
this Feynman diagram

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here where you have an
electron with a positive energy

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and an electron with
a negative energy,

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building a photon,
which is twice

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the energy in the symmetric
configuration of the electrons

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before.

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And you're interpreting the
negative energy solution

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here of the electron as the
electron moving backward

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in time.

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This is an equivalent to a
positron with a positive energy

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and an electron with
a positive energy

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where the positron and the
electron move forward in time.

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Again, in both cases, you
see the energy of the photon

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is two times the energy
of those two particles.

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All right.

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So this is a very
short discussion.

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And we will see later on
how we use the spinodes

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for antiparticles together with
spinodes for particles order

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to make relations that
could have matrix element.

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And so we move forward with our
discussion of Feynman rules,

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this time now, with
spin-1/2 particles included.