160
R. Barrett and P. P. Delsanto
The first improvement on Dirac’s theoretical value (which was 2) for the
electron magnetic moment was made by Julian Schwinger, who obtained
α e = 0.001 161 4 in 1948. This result effectively made use of only the
most important Feynman diagram. As more complex Feynman diagrams were
added, this theoretical prediction became more and more refined. Remember:
in principle all of the infinite number of Feynman diagrams should be
included. However, the contributions from Feynman diagrams become less
and less important as the diagrams become more complex, which makes it
possible to terminate the summation at some stage. Currently the best analytical result for α e is 0.001 159 652 181 643 (764). The number in parentheses
is the possible error attributed to neglected Feynman diagrams.
The agreement between theory and experiment here is astonishing.
However, in all honesty it must be admitted that a skilled piece of legerdemain has taken place. The theoretical values depend on a fundamental
physical constant known as the Fine Structure Constant (see Chap. 3), which,
to add to the confusion, is represented by the symbol α. Physicists have not
found a way to compute the value of α from first principles , and must rely on
obtaining it from experimental observations, by adjusting it until the QED
predictions agree with experimental measurements.
Clearly such a procedure (adjusting a constant to obtain the desired result)
would not normally be acceptable, but fortunately, the anomalous magnetic
moment is not the only physical quantity that depends on the fine structure
constant. For instance, atom-recoil measurements give a value of α such that:
−1
α = 137.03599878(91),
which is to be compared with the value
−1
α = 137.035999070 (98)
obtained from the magnetic moment experiments. (As we mentioned
already in Chap. 3, the fine structure constant is usually expressed as a reciprocal.) The consistency of these two results is a demonstration of the internal
consistency of QED. In addition, there are other physical quantities that can
also be used to determine α, but the above two provide the most accurate
values.
The low value of α (approximately 1/137) is the reason that higher order
Feynman diagrams can be neglected in the summation process described
above. Each Feynman diagram contains the factor α multiple times, equal to
the order of the diagram. As a consequence third order diagrams have three α
R. Barrett and P. P. Delsanto
The first improvement on Dirac’s theoretical value (which was 2) for the
electron magnetic moment was made by Julian Schwinger, who obtained
α e = 0.001 161 4 in 1948. This result effectively made use of only the
most important Feynman diagram. As more complex Feynman diagrams were
added, this theoretical prediction became more and more refined. Remember:
in principle all of the infinite number of Feynman diagrams should be
included. However, the contributions from Feynman diagrams become less
and less important as the diagrams become more complex, which makes it
possible to terminate the summation at some stage. Currently the best analytical result for α e is 0.001 159 652 181 643 (764). The number in parentheses
is the possible error attributed to neglected Feynman diagrams.
The agreement between theory and experiment here is astonishing.
However, in all honesty it must be admitted that a skilled piece of legerdemain has taken place. The theoretical values depend on a fundamental
physical constant known as the Fine Structure Constant (see Chap. 3), which,
to add to the confusion, is represented by the symbol α. Physicists have not
found a way to compute the value of α from first principles , and must rely on
obtaining it from experimental observations, by adjusting it until the QED
predictions agree with experimental measurements.
Clearly such a procedure (adjusting a constant to obtain the desired result)
would not normally be acceptable, but fortunately, the anomalous magnetic
moment is not the only physical quantity that depends on the fine structure
constant. For instance, atom-recoil measurements give a value of α such that:
−1
α = 137.03599878(91),
which is to be compared with the value
−1
α = 137.035999070 (98)
obtained from the magnetic moment experiments. (As we mentioned
already in Chap. 3, the fine structure constant is usually expressed as a reciprocal.) The consistency of these two results is a demonstration of the internal
consistency of QED. In addition, there are other physical quantities that can
also be used to determine α, but the above two provide the most accurate
values.
The low value of α (approximately 1/137) is the reason that higher order
Feynman diagrams can be neglected in the summation process described
above. Each Feynman diagram contains the factor α multiple times, equal to
the order of the diagram. As a consequence third order diagrams have three α