Kaluza-Klein theory

Kaluza-Klein theory ismodel which unifies classical gravity electromagnetism. It was discovered bymathematician Theodor Kaluza that if general relativityextended tofive-dimensional spacetime,equations can be separated out into ordinary four-dimensional gravitation plus an extra set, whichequivalentMaxwell's equations forelectromagnetic field, plus an extra scalar field known as"dilaton". Oskar Klein proposed thatfourth spatial dimensioncurled up withvery small radius, i.e. thatparticle movingshort distance along that axis would returnwherebegan. The distanceparticle can travel before reaching its initial positionsaidbesize ofdimension. This,fact, also gives risequantizationcharge, as waves directed alongfinite axis can only occupy discrete frequencies.

Kaluza-Klein theory can be extendedcoverother fundamental forces - namely,weakstrong nuclear forces - butstraightforward approach, if done using an odd dimensional manifold runs into difficulties involving chirality. The problemthat all neutrinos appearbe left-handed, meaning that theyspinning indirection offingers ofleft hand when theymoving indirection ofthumb. All anti-neutrinos appearbe right-handed. Somehow particle reactionsasymmetric whencomesspinitnot straightforwardbuild this intoKaluza-Klein theory sinceextra dimensionsphysical spacesymmetricrespectleft-hand spinningr-hand spinning particles.

But see Orbifoldone possible solution.

Some physicists have speculated that inearly universe, cosmic inflation causes three ofspace dimensionsexpandcosmological size whileremaining dimensionsspace remained microscopic.

Moreovertheory asstands does not dealquantum effects. However,same approachunificationforcestaken by some more modern theories, notably string theory andrelated M-theory.

Kaluza-Klein theory

Further reading