16.2. THEFREEELECTRONGAS 263
theequationalsopredictednegativeenergystates
E=−√
p^2 c^2 +m^2 c^4 (16.51)Thishadtheuncomfortableconsequencethatanelectroncouldradiateenergyindef-
initely,asitdroppedintoeverlowernegativeenergystates. Toavoidthisproblem,
Diracpostulatedthateverynegativeenergystatewasfilled;thelowestenergystatein
naturebeinganinfinitecollectionofnegativeenergyelectronsknownasthe”Dirac
sea.”theoryalsoallowedforthepossibilitythananegative energyelectroncould
absorbaphotonandjumptoapositive energylevel,leavingan unoccupiedposi-
tioninthenegativeenergylevels. Itturnedoutthatthisunoccupiedpositionwould
behaveineverywayasthoughitwereitselfaparticlewiththeelectronmassand
spin,butwiththeoppositecharge:a”positron.”Theseparticleswerediscoveredby
Anderson,incosmicraystudies,justafewyearsaftertheirexistencewaspredicted
byDirac.
Itsclearthatelectronspin,andthespin-statisticstheorem,explainsalot.Iten-
ablesustounderstandthequalitativefeaturesoftheperiodictableandtheexistence
ofconductionbandsincrystals. Itallowsustoestimatethebulkmodulusofsolids,
andtheradiiofdeadstars. Andthisisnotevenhalfthestory! Inadditiontode-
generatefermiongases,therearealsodegeneratebosongases,inwhicheveryparticle
occupiesthelowestenergylevel. Aggregatesofthatkindareofcrucialimportance
inunderstandingsuchstartlingphenomenaas superconductivity andsuperfluidity.
Itwouldbenicetodiscussthosethingsalso,buttherearelimitstothenumberof
thingsonecandoinayear.