MOTION MOUNTAIN

classical physics in a nutshell 321
are called transformation relations, and for different gauges they are called gauge transformations.
Motion of each everyday objects is fully described by the principle of least
action: motion minimizes action.
Radiation also moves. Everyday types of radiation, such as light, radio waves and their
related forms, are travelling electromagnetic waves. They are described by same equationsthatdescribetheinteractionofchargedormagneticobjects.Thespeedofmassless
fieldsisthemaximumpossibleenergyspeedinnatureandisthesameforallobservers.
The motion of radiation describes the motion of images.Theintrinsicproperties ofradiationareitsdispersionrelationanditsenergy–angularmomentumrelation.Thestateof
radiationisdescribedbyitselectromagneticfieldstrength,itsphase,itspolarizationand
itscoupling to matter. Themotionoftheelectromagneticfieldandofradiation minimizesactionandchange.
Space-time is also able to move, by changing its curvature. The state of space-time is
given by the metric, which describes distances and curvature, and thus the local warpedness.
The warpedness can oscillate and propagate, so that empty space can move like a
wave. Also the motion of space-time minimizes change. The principle of least action is
valid. The intrinsic properties of space-time are the number of dimensions, its metric
signatureanditstopology.Experimentsshowthatthelargescaletopologyofspace-time
issimple.
Horizonscanbeseenaslimitcasesofeitherspace-timeormatter-radiation.Theshare
thesameintrinsicandstateproperties.Thedarknightsky,theboundaryoftheuniverse,
is the most important example of a horizon. Other examples are the boundaries of black
holes. The universe, both its space-time and its matter content, shows maximum age
anddistance values. The history of the universe is long, about three times as long as the
history of the Earth. On large scales, all matter in the universe moves away from all other
matter: the universe, and its horizon, is expanding.
Properties of classical motion
Around us, we observe motion for objects, radiation, space-time and horizons. In our
exploration of classical physics, we distilled six specific properties of all classical – or
everyday – motion.
1. Everyday motion is continuous. Continuous motion allows defining space and time.
All energy moves in the way space-timedictatesit,andspacemoves the way energy
dictates it. This relation describes the motion of the stars, of thrown stones, of light
beams and of the tides. Rest and free fall are the same, and gravity is curved spacetime.Massbreaksconformalsymmetryandthusdistinguishesspacefromtime.
The continuity of motion is somewhatlimited: The (local) speed of energy, mass
andchargeisboundfromabove by a universal constantc, and (local) energy change
per time is bound from above by a universal constantc 5 /4G. The speed valuecis
realized for the motion of massless particles. It also relates space to time. The power
valuec 5 /4G is realized by horizons. Horizons are found around black holes and at the
border of the universe. The maximum power value also relatesspace-timecurvature
to energy flow and thus describes the elasticity ofspace-time.
Thecontinuity ofmotionislimitedinasecondway:Notwoobjectscanbeatthe
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net