MOTION MOUNTAIN

230 6 classical electrodynamics
Page 216
Page 26
Page 35
Challenge 231 s
Vol. II, page 103
Challenge 232 ny
Ref. 201
Vol. I, page 372
Vol. I, page 373
LikeforanymotiondescribedbyaLagrangian,themotionofthefieldisreversible, continuous,
conserved and deterministic. However, there is quite some fun in the offing;
even though this description is correct in everyday life, during the rest of our mountain
ascent we will find that the last basic statement must be wrong: fields do not always follow
Maxwell’s equations. A simple example shows this.
At a temperature of zero kelvin, when matter does not radiate thermally, we have the
paradoxical situation that the charges inside matter cannot be moving, since no emitted
radiation is observed, but they cannot be at rest either, due to Earnshaw’s theorem. In
short, the simple existence of matter – with its charged constituents – shows that classical
electrodynamics is wrong.
In fact, the overview of the numerous material properties and electromagnetic effects
given in Table 17 makes the same point even more strongly; classical electrodynamics can
describe many of the effects listed, but it cannot explainthe origin and numerical values
of anyof them. Even though few of the effects will be studied in our walk – they are not
essential for our adventure – the general concepts necessary for their description will be
the topic of the upcoming part of this mountain ascent, that on quantum physics.
In fact, classical electrodynamics fails intwo domains.
Strong fields and gravitation
First of all, classical electrodynamics fails in regions with extremely strong fields. When
electromagnetic fields are extremely strong, their energy density will curve space-time.
Classicalelectrodynamics,whichassumesflatspace-time,isnot valid in such situations.
The failure of classical electrodynamics is most evident in the most extreme case of all:
when the fields are extremely strong, they will lead to the formation of black holes.The
existence of black holes, together with the discreteness of charge, imply maximum electricandmagneticfield
values. These upper limits were mentioned in Table 3, which lists
various electric field values found in nature, and in Table 8, which lists possible magnetic
field values. Can you deduce the values of these so-calledPlanckfields?
Theinterplaybetweencurvature of space and electrodynamics has many aspects. For
example, the maximum force in nature limits the maximum charge that a black hole
can carry. Can you find the relation? As another example, it seems that magnetic fields
effectively increase the stiffness of empty space, i.e., they increase the difficulty to bend
empty space. Not all interactions between gravity and electrodynamics have been studied
up to now; more examples should appear in the future.
In summary, classical electrodynamics does not work for extremely high field values,
when gravitation plays a role.
Charges are discrete
Classical electrodynamics fails to describe nature correctly also for extremely weak field
values. This happens also in flat space-time and is due to a reasonalready mentioned a
number oftimes:electriccharges are discrete. Electricchargesdo not vary continuously,
but change in fixed steps. Not only does nature show a smallest value of entropy – as we
found in our exploration of heat, – and smallest amounts of matter; nature also shows a
smallest charge.Electric chargevaluesare quantized.
In metals, the quantization of charge is noticeable in the flow of electrons. In electro-
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net