MOTION MOUNTAIN

the description of electromagnetic field evolution 79
current
current
magnet
vector
potential
vector
potential
N
S
Challenge 77 s
Ref. 1, Ref. 24
F I G U R E 45 Vector potentials for selected situations.
We conclude that any sort of field leading to particle interactions must carry bothenergy
and momentum, as the argument applies to all such cases. In particular, it applies
to nuclear interactions. Indeed, in thequantum part of our adventure we will even find
an additional result: all fields are themselves composed of particles.The energy andmomentumoffieldsthenbecomeanobvious
state of affairs. In short, it makes sense to say
that electromagnetic fields move, because they carry energy and momentum.
The gauge field – the electromagnetic vector potential
The study of moving fields is called field theory and electrodynamics is the prime example.(Theotherclassicalexampleisfluiddynamics;moving
electromagnetic fields and
moving fluids are very similar mathematically.) Field theory is a beautiful topic; field
lines, equipotential lines and vortex lines are some of the concepts introduced in this
domain.They fascinate many.* However, in this mountain ascent we keep the discussion
focused on motion.
We have seen that fields force us to extend our concept of motion. Motion is not only
the change in state of objects and ofspace-time,butalsothechangeinstateof fields.We
thereforeneed,alsoforfields,acompleteandprecisedescriptionoftheirstate.
Theobservations using amber and magnets have shown us thatelectromagneticfields
possess energy and momentum. Fields can impart energy and momentum to particles.
The experiments with motors have shown us that objects can add energy and momentum
to fields. We therefore need to define a state function which allows us to define energy
and momentum for electric and magnetic fields. And since electric and magnetic fields
transport energy, their motion must follow the speed limit in nature.
Hertz and Heaviside defined the state function of fields in two standard steps.The first
* What is the relation, for static fields, between field lines and (equi-) potential surfaces? Can a field line
crossapotentialsurfacetwice?Formoredetailsontopicssuchasthese,seethefreetextbookbyBo Thidé,
ElectromagneticFieldTheory,onhiswww.plasma.uu.se/CED/Bookwebsite.Andofcourse,inEnglish,have
alook atthetexts bySchwinger andbyJackson.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net