<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>\nDear Alejandro,\n\n"arivero" <arivero@posta.unizar.es> wrote in\nnews:arivero.1c8a8h@physicsforums.com...\n> A particle in a gravitational circular orbit around a mass M fullfills,\n> for generical space time dimension D:\n>\n> c^2 R^(5-D) Lp^(D-2) = LM I^2\n>\n> being I= 1/2 R x V, V the speed of the particle,\n> Lp the Planck Length, and LM the Comptom Length of M.\n>\n> I wonder if someone has been this very easy (Newtonian!) relationship\n> in any textbook or article, and/or exploited\n> it to single out sort of critical or special dimensions.\n>\n> D=2 is simply the fact that in a line the density of force lines keeps\n> constant, so forces do not depend of distance.\n>\n> D>5 or D<5 can be used to register different regimes for constant\n> angular momenta. But there one should break the balance of D=5 by\n> introducing general relativity or variants.\n>\n> The most interesting trick comes if one quantises "I" in units of\n> Planck Length. So we have, if I=n Lp (note now the natural units,\n> c=h=1):\n>\n> R^(5-D) Lp^(D-4) = LM n^2\n>\n\nhave you noticed that this equation is absolutely independent of setting\nc=h=1 ?\nJust insert\n\nI=n cLp\n\ninto your first equation.\n\nI would say, that a choice c=h=1 could prevent you from going further.\nWith\n\nLp = h/Mpc\n\nwhere Mp is the Planck mass, we have\nIMp = n h\n\nIn this quantum relation the purely geometric part I contains the same SI\nspace/time units (meter, second) like h, so I/h does not dependent on the\nchoice of SI geometric units and means that Mp is proportional to n. If the\nmass Mp can be divided by n, Mp/n could be more fundamental than Mp.\n\nWhere could n come from? Generally, with Mp = h/Lpc and the choice M0 = Mp\nn^(D-3)\n\nR0^(5-D) Lp^(D-4) = n^2 h/M0c = n^(5-D) h/Mpc\n\nwe have a fundamental length\n\nR0= n Lp\n\nassuming that I = cR0 is fundamental quantum. Consequently, M0 could be more\nfundamental than Mp. With\n\nIM0 = n^(D-2) h\n\nin a compactified D=2 geometry, both, M0 = Mp/n and I would be as\nfundamental as h.\n\nCould there be a special n with a physical meaning?\nTransforming\n\nn^2 = hc/(GM0^2)\n\ninto a Newton type relation\n\nn^2 G M0^2/R = hc/R\n\nwe could find a clear interpretation:\nn^2 M0-masses interacting gravitationally would reach the electromagnetic\ncoupling of about 137 charges at any distance R.\n\nWith the Planck mass\nhttp://scienceworld.wolfram.com/physics/PlanckMass.html\nand taking M0 as the proton mass we get i.e.\n\nn ~ 3*10^19\nn^2 ~ 9*10^38\n\nI expect, that c^2 R^(5-D) Lp^(D-2) = LM I^2 is correct, that I is a\nquantum, and that n can be found from a pure geometrical (Gaussian)\napproach relating different kind of topologies.\n\nRegards,\nBernd\n\n\n\n> I am specially interested on bibliographical references to this family\n> of arguments because I did a very short note in this line\n> http://dftuz.unizar.es/~rivero/research/simple.pdf\n> and I would like to be able to see if I should upload something similar\n> in gr-qc.\n>\n>\n>\n> Univ Zaragoza, PhD\nScience---------------------------------------------------------------------\n---\n> This post submitted through the LaTeX-enabled physicsforums.com\n> To view this post with LaTeX images:\n> http://www.physicsforums.com/showthread.php?t=41844#post304135\n>\n\n\n\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>Dear Alejandro,
"arivero" <arivero@posta.unizar.es> wrote in
news:arivero.1c8a8h@physicsforums.com...
> A particle in a gravitational circular orbit around a mass M fullfills,
> for generical space time dimension D:
>
> c^2 R^(5-D) Lp^(D-2) = LM I^2
>
> being I= 1/2 R x V, V the speed of the particle,
> Lp the Planck Length, and LM the Comptom Length of M.
>
> I wonder if someone has been this very easy (Newtonian!) relationship
> in any textbook or article, and/or exploited
> it to single out sort of critical or special dimensions.
>
> D=2 is simply the fact that in a line the density of force lines keeps
> constant, so forces do not depend of distance.
>
> D>5 or D<5 can be used to register different regimes for constant
> angular momenta. But there one should break the balance of D=5 by
> introducing general relativity or variants.
>
> The most interesting trick comes if one quantises "I" in units of
> Planck Length. So we have, if I=n Lp (note now the natural units,
> c=h=1):
>
> R^(5-D) Lp^(D-4) = LM n^2
>
have you noticed that this equation is absolutely independent of setting
c=h=1 ?
Just insert
I=n cLp
into your first equation.
I would say, that a choice c=h=1 could prevent you from going further.
With
Lp = h/Mpc
where Mp is the Planck mass, we have
IMp = n h
In this quantum relation the purely geometric part I contains the same SI
space/time units (meter, second) like h, so I/h does not dependent on the
choice of SI geometric units and means that Mp is proportional to n. If the
mass Mp can be divided by n, Mp/n could be more fundamental than Mp.
Where could n come from? Generally, with Mp = h/Lpc and the choice M0 = Mpn^(D-3)R0^(5-D) Lp^(D-4) = n^2 h/M0c = n^(5-D) h/Mpc
we have a fundamental length
R0= n Lp
assuming that I = cR0 is fundamental quantum. Consequently, M0 could be more
fundamental than Mp. With
IM0 = n^(D-2) h
in a compactified D=2 geometry, both, M0 = Mp/n and I would be as
fundamental as h.
Could there be a special n with a physical meaning?
Transforming
n^2 = hc/(GM0^2)
into a Newton type relation
n^2 G M0^2/R = hc/R
we could find a clear interpretation:
n^2 M0-masses interacting gravitationally would reach the electromagnetic
coupling of about 137 charges at any distance R.
With the Planck mass
http://scienceworld.wolfram.com/physics/PlanckMass.html
and taking M0 as the proton mass we get i.e.n ~ 3*10^19n^2 ~ 9*10^38
I expect, that c^2 R^(5-D) Lp^(D-2) = LM I^2 is correct, that I is a
quantum, and that n can be found from a pure geometrical (Gaussian)
approach relating different kind of topologies.
Regards,
Bernd
> I am specially interested on bibliographical references to this family
> of arguments because I did a very short note in this line
> http://dftuz.unizar.es/~rivero/research/simple.pdf
> and I would like to be able to see if I should upload something similar
> in gr-qc.
>
>
>
> Univ Zaragoza, PhD
Science---------------------------------------------------------------------
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> To view this post with LaTeX images:
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>