David Union
Apr14-04, 05:49 PM
<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>Hi\n\nThe Wienberg/Shallom/Glashow theorum of around \'80\'s was,\nIMO, basically this idea. Find a set of dimensions so that you can\nwrite \'equations of motion\' in n-space (in that case it was\nan SU 3x4, or in general terms 12 dimensions) that when projected\nonto our \'3+1\' dimensions yielded more than just Mechanics & EM\nbut also the electroweak forces. The assumption then is that to do\nthe same with gravity would take probably \'more\' dimensions.\n\nThis has been a long time. I remember reading the original paper\nwhen it came out but not since. I sort of recall a bunch of folks\ntrying to add gravity with a 24 dimensional model but nothing\nthat worked out completely - SGUTS theories, etc. Does\nmemory correctly serve or has age taken too much of a toll?\n\nDMU\n\n\n"Alex Hunter" <aw015c0834@blueyonder.co.uk> wrote in message\nnews:u41s5051dkqpe0kmce7vdaem4ilcvt01ot@4 ax.com...\n>\n> In Kaluza-Klein theory, the gauge symmetries for all the fundamental\n> forces are mapped onto the higher spatial dimensions.\n> So the internal symmetries are now externalised.\n>\n> Does this imply that you can extend the analogy with gravity further:\n> so for example, if the 5th dimension contains the guage symmetry of\n> EM, do electromagnetic charges produce distortions in the 5th\n> dimension, in the same way that mass produces distortions in 4D\n> space-time?\n>\n> If so then presumably you can rewrite Maxwell\'s equations in a 1D 5th\n> dimensional sub-space, as the sum of a curvature scalar and a metric\n> scalar field equals the charge density scalar field, just as the\n> gravitational field equation is written as a sum of a curvature tensor\n> and a metric tensor field equals the energy-momentum tensor field?\n>\n> The relative field strength of electromagnetism, compared with the\n> much weaker gravitational field, could then explain why the 5th\n> dimension is compactified; whereas space-time is not.\n>\n> Also, because of symmetry breaking, the gravitational field equation\n> is presumably no longer invariant in the higher spatial dimensions.\n> So if you wanted to write an equation of motion for a mass under\n> gravity in 5 dimensions, how would you construct it?\n\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>Hi
The Wienberg/Shallom/Glashow theorum of around '80's was,
IMO, basically this idea. Find a set of dimensions so that you can
write 'equations of motion' in n-space (in that case it was
an SU 3x4, or in general terms 12 dimensions) that when projected
onto our '3+1' dimensions yielded more than just Mechanics & EM
but also the electroweak forces. The assumption then is that to do
the same with gravity would take probably 'more' dimensions.
This has been a long time. I remember reading the original paper
when it came out but not since. I sort of recall a bunch of folks
trying to add gravity with a 24 dimensional model but nothing
that worked out completely - SGUTS theories, etc. Does
memory correctly serve or has age taken too much of a toll?
DMU
"Alex Hunter" <aw015c0834@blueyonder.co.uk> wrote in message
news:u41s5051dkqpe0kmce7vdaem4ilcvt01ot@4ax.com...
>
> In Kaluza-Klein theory, the gauge symmetries for all the fundamental
> forces are mapped onto the higher spatial dimensions.
> So the internal symmetries are now externalised.
>
> Does this imply that you can extend the analogy with gravity further:
> so for example, if the 5th dimension contains the guage symmetry of
> EM, do electromagnetic charges produce distortions in the 5th
> dimension, in the same way that mass produces distortions in 4D
> space-time?
>
> If so then presumably you can rewrite Maxwell's equations in a 1D 5th
> dimensional sub-space, as the sum of a curvature scalar and a metric
> scalar field equals the charge density scalar field, just as the
> gravitational field equation is written as a sum of a curvature tensor
> and a metric tensor field equals the energy-momentum tensor field?
>
> The relative field strength of electromagnetism, compared with the
> much weaker gravitational field, could then explain why the 5th
> dimension is compactified; whereas space-time is not.
>
> Also, because of symmetry breaking, the gravitational field equation
> is presumably no longer invariant in the higher spatial dimensions.
> So if you wanted to write an equation of motion for a mass under
> gravity in 5 dimensions, how would you construct it?
The Wienberg/Shallom/Glashow theorum of around '80's was,
IMO, basically this idea. Find a set of dimensions so that you can
write 'equations of motion' in n-space (in that case it was
an SU 3x4, or in general terms 12 dimensions) that when projected
onto our '3+1' dimensions yielded more than just Mechanics & EM
but also the electroweak forces. The assumption then is that to do
the same with gravity would take probably 'more' dimensions.
This has been a long time. I remember reading the original paper
when it came out but not since. I sort of recall a bunch of folks
trying to add gravity with a 24 dimensional model but nothing
that worked out completely - SGUTS theories, etc. Does
memory correctly serve or has age taken too much of a toll?
DMU
"Alex Hunter" <aw015c0834@blueyonder.co.uk> wrote in message
news:u41s5051dkqpe0kmce7vdaem4ilcvt01ot@4ax.com...
>
> In Kaluza-Klein theory, the gauge symmetries for all the fundamental
> forces are mapped onto the higher spatial dimensions.
> So the internal symmetries are now externalised.
>
> Does this imply that you can extend the analogy with gravity further:
> so for example, if the 5th dimension contains the guage symmetry of
> EM, do electromagnetic charges produce distortions in the 5th
> dimension, in the same way that mass produces distortions in 4D
> space-time?
>
> If so then presumably you can rewrite Maxwell's equations in a 1D 5th
> dimensional sub-space, as the sum of a curvature scalar and a metric
> scalar field equals the charge density scalar field, just as the
> gravitational field equation is written as a sum of a curvature tensor
> and a metric tensor field equals the energy-momentum tensor field?
>
> The relative field strength of electromagnetism, compared with the
> much weaker gravitational field, could then explain why the 5th
> dimension is compactified; whereas space-time is not.
>
> Also, because of symmetry breaking, the gravitational field equation
> is presumably no longer invariant in the higher spatial dimensions.
> So if you wanted to write an equation of motion for a mass under
> gravity in 5 dimensions, how would you construct it?