6.3 Maxwell’s Theory of Electromagnetism
185
behavior of electric and magnetic phenomena, James Clerk Maxwell, in 1865,
succeeded in formulating a logically complete and unified description of electricity,
magnetism, and light. The idea behind Maxwell’s Theory of Electromagnetism is
that certain kinds of particles have a long-range interaction which depends on an
intrinsic and additively conserved local property that they carry called their charge.
Maxwell’s electromagnetism theory was allied with Dirac’s relativistic quantum
theory in 1948. The resulting description, called quantum electrodynamics, has been
tested more extensively than any other devised by humans, with no deviations as
yet found in comparison to observation. 6 In principle, quantum electrodynamics
is capable of predicting all of chemistry, starting with nuclei and electrons. This
includes biochemistry and, therefore, the mechanisms of life. Of course, in practice,
we use higher-level models and descriptions in biochemistry which already assume
atoms and molecules as their basic structures.
New relationships can evolve in the behavior of large-scale systems in chemistry
and biology because there is a natural ordering that occurs in these open systems.
We will discuss this tendency in Sect. 9.25 and Chap. 15. The basis of biochemistry
is essentially the quantum electrodynamics of a large number of interacting atoms
and molecules acting near statistically likely states, or states that are quasi-stable,
building on dynamical pathways ‘discovered’ by nature during evolution.
6.3 Maxwell’s Theory of Electromagnetism
Maxwell’s theory is most often applied in two-steps. First, one determines the
location and speed v of the “source charges”, described by their density in space,
ρ, and their motion, described by their current density, J = ρv. We say that these
charges create a disturbance in the surrounding space, named the electromagnetic
field. This field is expressed in terms of the electric field, E, and the magnetic
field, B, produced by the charges. Second, the electromagnetic field acts on other
charges q moving with velocities v . All dynamics of how charges behave in
electromagnetic fields are predicted by Maxwell’s equations 7 :
∇ · E = 4πρ
(6.1)
6 The most accurate tests of quantum electrodynamics measure atomic transition frequencies and
the electron magnetic moment, and show agreement to at least one part in 10 11 . In contrast, because
gravity around here is relatively weak, most tests of general relativity are not so precise. An
exception is the period of a neutron star in a binary system measured by the Hulse-Taylor for
the pulsar PSR 1913+16, giving an agreement with Einstein’s theory including gravitational waves
to at least one part in 10 14 !
7 Here, we have used the cgs system of units, and abbreviated c ≡ 1/
√ 0 μ 0 , where 0 is the
electric permittivity and μ 0 the magnetic permeability of a vacuum. The first Maxwell equation
is the differential form of Gauss’ law. The fourth contains Faraday’s law but adds the effect of a
time-changing electric field.
185
behavior of electric and magnetic phenomena, James Clerk Maxwell, in 1865,
succeeded in formulating a logically complete and unified description of electricity,
magnetism, and light. The idea behind Maxwell’s Theory of Electromagnetism is
that certain kinds of particles have a long-range interaction which depends on an
intrinsic and additively conserved local property that they carry called their charge.
Maxwell’s electromagnetism theory was allied with Dirac’s relativistic quantum
theory in 1948. The resulting description, called quantum electrodynamics, has been
tested more extensively than any other devised by humans, with no deviations as
yet found in comparison to observation. 6 In principle, quantum electrodynamics
is capable of predicting all of chemistry, starting with nuclei and electrons. This
includes biochemistry and, therefore, the mechanisms of life. Of course, in practice,
we use higher-level models and descriptions in biochemistry which already assume
atoms and molecules as their basic structures.
New relationships can evolve in the behavior of large-scale systems in chemistry
and biology because there is a natural ordering that occurs in these open systems.
We will discuss this tendency in Sect. 9.25 and Chap. 15. The basis of biochemistry
is essentially the quantum electrodynamics of a large number of interacting atoms
and molecules acting near statistically likely states, or states that are quasi-stable,
building on dynamical pathways ‘discovered’ by nature during evolution.
6.3 Maxwell’s Theory of Electromagnetism
Maxwell’s theory is most often applied in two-steps. First, one determines the
location and speed v of the “source charges”, described by their density in space,
ρ, and their motion, described by their current density, J = ρv. We say that these
charges create a disturbance in the surrounding space, named the electromagnetic
field. This field is expressed in terms of the electric field, E, and the magnetic
field, B, produced by the charges. Second, the electromagnetic field acts on other
charges q moving with velocities v . All dynamics of how charges behave in
electromagnetic fields are predicted by Maxwell’s equations 7 :
∇ · E = 4πρ
(6.1)
6 The most accurate tests of quantum electrodynamics measure atomic transition frequencies and
the electron magnetic moment, and show agreement to at least one part in 10 11 . In contrast, because
gravity around here is relatively weak, most tests of general relativity are not so precise. An
exception is the period of a neutron star in a binary system measured by the Hulse-Taylor for
the pulsar PSR 1913+16, giving an agreement with Einstein’s theory including gravitational waves
to at least one part in 10 14 !
7 Here, we have used the cgs system of units, and abbreviated c ≡ 1/
√ 0 μ 0 , where 0 is the
electric permittivity and μ 0 the magnetic permeability of a vacuum. The first Maxwell equation
is the differential form of Gauss’ law. The fourth contains Faraday’s law but adds the effect of a
time-changing electric field.