Re: On explanation of negative energy states and electron pair creation

Oh No wrote:

Thus spake zak <b.zarychta@xxxxxxxxxxxxxx>
Dirac's theory of the electron predicted that there were identical
particles of equal mass but of negative energy.

What I think you are actually talking about here is Dirac's
relativistic wave equation for the electron, which is sort of like
Schrodinger's wave equation, except fully relativistic. It is thus not
really Dirac's 'theory of the electron', but Dirac's application of
Einstein's theory of relativity to the pre-relativistic wave mechanics
of early 20th century quantum theory.

Dirac was astute enough as a physicist, and competent enough as a
mathematician to recognise that this relativistic wave equation
predicted negative as well as positive energy states.

He appealed to the Pauli exclusion principle and proposed that there
was a negative energy 'sea' of electrons that was full up to -2mc^2 in
order to answer critics that positive energy electrons described by the
Dirac electron theory would simply decay down to -infinity.
With this description pair creation is described by absortion of a
photon (where the energy of the photon E_p > 2mc^2) by a negative
energy electron that scatters up to a poitive energy state leaving
behind a hole.

This hole is the negative energy 'sea' has equal but opposite charge to
the electron and is commonly known as a positron.

I belive that this description is somewhat old hat and not used anymore
in modern QFT circles. Can anybody give me a not too technical
explanation to why the 'old hat' qualitative explanation is
unsatisfactory ?

Good question. It certainly seems to be true that Dirac has fallen out
of favour in the mainstream physics community, of late. When I was
still an undergrad, I asked my personal tutor if we could do Dirac
then, and he responded that Dirac was "too difficult". However, I
personally found Dirac beautifully simple conceptually, at the same
time as being advanced for its era (which I think was the 1920's). I
thus found Dirac's negative energy solution of his own relativistic
wave equation to be a good conceptual "stepping stone".

I find the Stuckelburg-Feynman interpretation better, that negative
energy particles are particles for which proper time is reversed.

I am inclined to agree.

They are literally particles going backwards in time.

Fine. This ties in with the Feynmann diagram.

Then the creation of a
negative energy particle appears from the point of view of macroscopic
time as the annihilation of a positive energy one.

I am not sure what you mean by this.

Consider a point in spacetime that is identified in arbitrary Gaussian
coordinates as the point of interaction between a photon, a positron,
and an electron.

We have 2 distinct situations to consider here.

A) Creation of a particle/antiparticle pair from the destruction of a
photon.
B) Creation of a photon from the interaction between (hence anihilation
of) a particle/antiparticle pair

Consider (A) first. Within the context of the Stuckelburg-Feynman
interpretation, the simlest way to look at this is probably as a
collision between a positron and a photon, where the photon's energy
and momentum are 'just right' to reflect that positron in the dimension
of time, thus turning that positron into an electron, with the
resultant annihilation of the photon.
I see no difficulties with that iviewpoint.

Now, the really neat thing about the Feynmann diagram is you can just
rotate your coordinate system by 180 degrees, to obtain situation (B).

John (Liberty) Bell
http://global.accelerators.co.uk
(Change John to Liberty to respond by email)

.

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