Article for Novices: Kaluza-Klein Theory

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<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Kaluza-Klein theory is a model which unifies classical gravity and\nelectromagnetism. It was discovered by the mathematician Theodor\nKaluza that if general relativity is extended to a five-dimensional\nspacetime, the equations can be separated out into ordinary\nfour-dimensional gravitation plus an extra set, which is equivalent to\nMaxwell\'s equations for the electromagnetic field, plus an extra\nscalar field known as the "dilaton". Oskar Klein proposed that the\nfourth spatial dimension is curled up with a very small radius, i.e.\nthat a particle moving a short distance along that axis would return\nto where it began. The distance a particle can travel before reaching\nits initial position is said to be the size of the dimension. This, in\nfact, also gives rise to quantization of charge, as waves directed\nalong a finite axis can only occupy discrete frequencies.\n\nKaluza-Klein theory can be extended to cover the other fundamental\nforces - namely, the weak and strong nuclear forces - but a\nstraightforward approach, if done using an odd dimensional manifold\nruns into difficulties involving chirality. The problem is that all\nneutrinos appear to be left-handed, meaning that they are spinning in\nthe direction of the fingers of the left hand when they are moving in\nthe direction of the thumb. All anti-neutrinos appear to be\nright-handed. Somehow particle reactions are asymmetric when it comes\nto spin and it is not straightforward to build this into a\nKaluza-Klein theory since the extra dimensions of physical space are\nsymmetric with respect to left-hand spinning and r-hand spinning\nparticles."\n\nKaluza-Klein theory From Wikipedia, the free encyclopedia.\n\nIs this still at the basis of string/Mtheory today?\n\n[Moderator\'s note: Yes, Kaluza-Klein theory remains one of the essential\nparadigms underlying string/M-theory, although its concepts have been\nextended enormously. By the way, string theory is able\nto obtain the left-right asymmetric (chiral) spectrum of particles very\nnaturally, and some of the comments above about the impossibility to\nget chirality are obsolete even in field theory. LM]\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Kaluza-Klein theory is a model which unifies classical gravity and
electromagnetism. It was discovered by the mathematician Theodor
Kaluza that if general relativity is extended to a five-dimensional
spacetime, the equations can be separated out into ordinary
four-dimensional gravitation plus an extra set, which is equivalent to
Maxwell's equations for the electromagnetic field, plus an extra
scalar field known as the "dilaton". Oskar Klein proposed that the
fourth spatial dimension is curled up with a very small radius, i.e.
that a particle moving a short distance along that axis would return
to where it began. The distance a particle can travel before reaching
its initial position is said to be the size of the dimension. This, in
fact, also gives rise to quantization of charge, as waves directed
along a finite axis can only occupy discrete frequencies.

Kaluza-Klein theory can be extended to cover the other fundamental
forces - namely, the weak and strong nuclear forces - but a
straightforward approach, if done using an odd dimensional manifold
runs into difficulties involving chirality. The problem is that all
neutrinos appear to be left-handed, meaning that they are spinning in
the direction of the fingers of the left hand when they are moving in
the direction of the thumb. All anti-neutrinos appear to be
right-handed. Somehow particle reactions are asymmetric when it comes
to spin and it is not straightforward to build this into a
Kaluza-Klein theory since the extra dimensions of physical space are
symmetric with respect to left-hand spinning and r-hand spinning
particles."

Kaluza-Klein theory From Wikipedia, the free encyclopedia.

Is this still at the basis of string/Mtheory today?

[Moderator's note: Yes, Kaluza-Klein theory remains one of the essential
paradigms underlying string/M-theory, although its concepts have been
extended enormously. By the way, string theory is able
to obtain the left-right asymmetric (chiral) spectrum of particles very
naturally, and some of the comments above about the impossibility to
get chirality are obsolete even in field theory. LM]

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