From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Feynman 41 zero-point atomic Lamb shift
Organization: Whole Earth 'Lectronic Link
Date: Tue, 22 Dec 1992 19:21:57 GMT


Remember, the purpose of these "lectures" is to review the essentials of
Feynman's pictures of the world so that we can more intelligently evaluate
Hal Puthoff's proposals for zero-point energy engines and my proposals for
quantum connection communication devices - recall there are two possible
classes of ftl communication devices
1. those requiring a new kind of quantum mechanics that relaxes the full
unitarity constraint to "diagonal" unitarity which is sufficient to
conserve the sum of probabilities for local measurements. Such a new
quantum mechanics (like non-Euclidean geometry compared to Euclidean
geometry) does not require tapping zero point energy to get quantum
connection communication - however, Lyle Fuller has shown that quantum
connection communication, if it exists, will induce extraction of energy
from the vacuum in order to obey the Kip Thorne-Igor Novikov "global self-
consistency" conditions on traversable wormhole time machines to the past.
The question is will a simple polarization sensitive interferometer with a
half-wave plate in one path implement the non-unitary extension of
conventional quantum mechanics - or is some new phenonomenon -perhaps vital
to living matter far from thermal equilibrium involved - a kind of PK
effect?

2. those that retain full unitarity but use something like the Puthoff
Casimir pinch effect in which the apparent violation of unitarity required
in quantum connection communication is the result of opening new channels
from the induced vacuum phase transition.

Feynman 41 QED & renormalization Part III Lamb Shift
"... in a closed system all quanta can be considered as virtual (i.e. they
have a known source and are eventually absorbed) ...

K1(3,4;1,2)=-ie^2S^2[K+a(3,5)K+b(4,6)GauGbuD+(s56^2)K+a(5,1)K+b(6,2)d5d6]
(4)

(4) can be rewritten as describing the action on a,

K1(3,1) = iS[K+(3,5)A(5)K+(5,1)d5

of the potential

A(5) = e^2S[K+(4,6)D+(s56^2)GK+(6,2)d6] arising from Maxwell's equations

-WAVE A = 4pij from a current

j(6) = (e^2)K+(4,6)GK+(6,2)"

I note that the local current j(6) is actually nonlocal in that it depends
also on events 4 and 3 which are in future and past of it!

"This is in virtue of the fact that

-WAVE D+(s21^2) - 4piDirac(2,1) (5)

.. our primary concern here will be for processes in which the quanta are
virtual ...

... the amplitude that an electron in going from 1 to 2 absorbs a quantum
whose vector potential .. is ce^-ikx = C(x) is

K1+(2,1) = -iS[K0+(2,3)C(3)K0+(3,1)d3]

(Like the exclusion principle) The Bose statistics of the quanta can , in
all cases, be disregarded in intermediate states. The only effect of the
statistics is to change the weight of initial or final states. If there are
among quanta, in the initial state, some n which are identical then the
weight of the state is 1/n! of what it would be if these quanta were
considered as different (similarly for the final state).

3. The self-energy problem
... the interaction of the charge with itself ... to first order in e^2"

*I will be loosely paraphrasing from now on - important details in original
papers in Schwinger's reprint collection (Dover books).*

                          / 2
                        /
                      / K0+(2,4)
                    /
                  /
                 |\ 4
                 | \
                 |   \
K0+(4,3)         |     \ D+(s43^2)
                 |    /
                 |  /
                 |/
                / 3
              /
            / K0+(3,1)
          /
        / 1

this self-energy Feynman diagram in space-time has the intuitively obvious
formula

K1(2,1) = (-ie^2)S^2[K0+(2,4)GK0+(4,3)GK0+(3,1)d3d4D+(s43^2)]

     / 2
                        / 2
                      / p
                    /
                  /
                 |\ 4
                 | \
                 |   \
         p-k     |     \ k^-2
                 |    /
                 |  /
                 |/
                / 3
              /
            / p
          /
        / 1

the same diagram Fourier transformed to momentum-energy space which comes
from assuming that initially we have electron in state f(1) a free-particle
plane wave and similarly for final state g(2)  "a change in energy dE1 ll
the amplitude for arrival in f (spinor part u) at t2 is altered by a factor
e^-idE1(t2-t1) ...

dE1 = (e^2)S[(uGK0+(4,3)Gu)e^ipx43D+(s43^2)d4]

note there is no d3 integral - the reason is tricky and is artifact of
normalization scheme  (u*u) = 1 * is ordinary c.c. not adjoint) described
by Feynman in detail in original .. (u*u) = (E/m)(uadju)) the # integration
gives a VT factor in the normalization,

"One can likewise obtain an expresion for the energy (Lamb) shift for an
electron in a hydrogen atom. Simply replace K0+ by K+V the exact kernel for
electron in V =e^2/r and f by " a bound state...

For the first order correction to the electron Lamb shift in hydrogen due
to a single virtual "zero point vacuum" photon self-energy diagram "the de1
that results is not real. The imaginary part is negative and in e^-idE1T
produces an exponentially decreasing amplitude with time. This is because
we are asking for the amplitude that an atom initially with no photon in
the field, will still appear after time T with no photon. If the atom is in
a state that can radiate, this amplitude must decay with time. The
imaginary part of dE1 when calculated does indeed give the correct rate of
radiation from atomic states. It is zero for the ground state and for a
free electron. ....