MOTION MOUNTAIN

86 2 the description of electromagnetic field evolution
Challenge 89 e
Challenge 90 s
Vol. II, page 86
Challenge 91 s
Vol. V, page 251
Vol. V, page 26
describes a conserved quantity.
We can sum up by stating that in nature, energy and momentum are conserved, if
we take into account the momentum and energy of the electromagnetic field. And the
energy–momentum tensor shows again that electrodynamics is a gauge invariant description:theenergyandmomentum
values do not depend on gauge choices.
The energy–momentum tensor, like the Lagrangian, shows that electrodynamics is
invariant undermotioninversion. If all charges change direction of motion – a situation
often confusingly called ‘time inversion’ – they move backwards along the same paths
they took when moving forward. Every example of motion due to electric or magnetic
causes can also take place backwards.
On the other hand, everyday life shows many electric and magnetic effects which are
not time invariant, such as the breaking of bodies or the burning of electric light bulbs.
Can you explain how this fits together?
We also note that charges and mass destroy a symmetry of the vacuum that wementioned
in special relativity: only the vacuum is invariant under conformal transformations.
In particular, only the vacuum is invariant under the spatial inversionr→1/r.
Any other physical system does not obey conformal symmetry.
To sum up, electrodynamic motion, like all other examples of motion that we have
encountered so far, is deterministic, slower thanc, reversible and conserved. This is no
big surprise. Nevertheless, two other symmetries of electromagnetism deserve special
mention.
What is a mirror? Is nature parity-invariant?
We will study thestrange propertiesof mirrors several times during our walk. We start
with the simplest one first. Everybody can observe, by painting each of their hands in a
different colour, that a mirror does not exchange right and left, as little as it exchanges
up and down; however, a mirror does exchange right and lefthandedness. In fact, it does
so by exchanging front and back.
Electrodynamics give a second answer: a mirror is a device that switches magnetic
north and south poles. Can you confirm this with a diagram?
But is it always possible to distinguish left from right? This seems easy: this text is
quite different from a version, as are many other objects in our surroundings.
But take a simple landscape. Are you able to say which of the two pictures of Figure 47
is the original?
Astonishingly, it is actually impossible to distinguish an original picture of nature
from its mirror image if it does not contain any human traces. In other words, everyday
nature is somehow left–right symmetric. This observation is so common that all
candidate exceptions have been extensively studied. Examples are the jaw movement of
ruminating cows, the helical growth of plants, such as hops, the spiral direction of snail
shells or the left turn taken by all bats when exiting their cave.The most famous example
is the position of the heart.The mechanisms leading to this disposition are still beinginvestigated.
Recent research discovered that the oriented motion of the cilia on embryos,
in the region called thenode, determines the right–left asymmetry.
Most human bodies have more muscles on the right side for right-handers, such as
AlbertEinsteinandPabloPicasso,andcorrespondinglyontheleftsideforleft-handers,
mirrored
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net