View Full Version : [SOLVED] MOND-like effect of not assuming flatness at infinity
jonathan_scott@vnet.ibm.com
Sep13-05, 03:56 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>In local GR calculations, one normally assumes that space\nis flat at a sufficient distance from the local mass or\nmasses which are being studied. However, if the local\nmass m constitutes a fraction m/M of the total mass of\nthe universe, then this assumption might be questionable.\nIf the universe is spatially finite at a given moment in\ntime, then a more plausible assumption would be that\nthe region containing a fraction m/M of the total mass\nwould also loosely speaking contain a related fraction\nof the 3D "angle" needed to close the universe, so the\nlimit would be "conical" rather than "flat".\n\nMore specifically, a starting hypothesis might be that a\nsphere enclosing a fraction m/M of the total mass of the\nuniverse would effectively be slightly "conical", missing\na constant proportion of its surface area at a given radius.\nThe effect of this would be to curve space-time by some\namount which is a function f of (m/M) and is proportional\nto 1/r. This would then give rise to an extra\ngravitational acceleration c^2/r f(m/M).\n\nIn MOND, the extra acceleration is sqrt(G m a0)/r where\na0 is an arbitrary constant set to be approximately\n1.2e-10 ms^-2 to fit the experimental results. For\nour hypothesis to match MOND, we require that the\nfunction f is the square root, and that M is equal to\n(c^4 / G a0), which is around 10^54 kg. Although trivial\nmethods of estimating the mass of the universe give a\nresult a little lower, around 3 * 10^52 kg, this seems to\nme to be an interestingly close fit. This would suggest\nthat the existing MOND acceleration term could perhaps\nbe written instead as c^2/r sqrt(m/M), where M is around\n10^54 kg and may well correspond in some sense to the\ntotal mass of the universe, and that it might be possible\nto find a way to relate this physically to a "conical"\nlimit instead of a "flat" limit in gravitational\ncalculations.\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>In local GR calculations, one normally assumes that space
is flat at a sufficient distance from the local mass or
masses which are being studied. However, if the local
mass m constitutes a fraction m/M of the total mass of
the universe, then this assumption might be questionable.
If the universe is spatially finite at a given moment in
time, then a more plausible assumption would be that
the region containing a fraction m/M of the total mass
would also loosely speaking contain a related fraction
of the 3D "angle" needed to close the universe, so the
limit would be "conical" rather than "flat".
More specifically, a starting hypothesis might be that a
sphere enclosing a fraction m/M of the total mass of the
universe would effectively be slightly "conical", missing
a constant proportion of its surface area at a given radius.
The effect of this would be to curve space-time by some
amount which is a function f of (m/M) and is proportional
to 1/r. This would then give rise to an extra
gravitational acceleration c^2/r f(m/M).
In MOND, the extra acceleration is \sqrt(G m a0)/r where
a0 is an arbitrary constant set to be approximately
1.2e-10 ms^-2 to fit the experimental results. For
our hypothesis to match MOND, we require that the
function f is the square root, and that M is equal to
(c^4 / G a0), which is around 10^54 kg. Although trivial
methods of estimating the mass of the universe give a
result a little lower, around 3 * 10^52 kg, this seems to
me to be an interestingly close fit. This would suggest
that the existing MOND acceleration term could perhaps
be written instead as c^2/r \sqrt(m/M), where M is around
10^54 kg and may well correspond in some sense to the
total mass of the universe, and that it might be possible
to find a way to relate this physically to a "conical"
limit instead of a "flat" limit in gravitational
calculations.
jonathan_scott@vnet.ibm.com
Sep17-05, 11:16 AM
<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>In my previous posting, I assumed the function f(m/M) to\nbe the square root simply in order to match MOND.\n\nHowever, if the surface area of a sphere surrounding the\nmass is assumed to have exactly a fraction m/M missing,\nthen the effective radius of the sphere has been contracted\nby a factor sqrt(1-m/M). This forms the cosine of the\nangle by which the cone deviates from flatness, so the\nsine of the same angle (and the angle itself in radians)\nis equal to sqrt(m/M).\n\nThis therefore provides a model which gives the\nsame predictions as MOND but with a single physically\nmeaningful parameter (the mass M of the universe)\nrather than an arbitrary acceleration parameter.\nAt the same time, the geometric model in terms of\ncones might help to make it easier to analyze situations\ninvolving multiple sources, such as clusters of galaxies.\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>In my previous posting, I assumed the function f(m/M) to
be the square root simply in order to match MOND.
However, if the surface area of a sphere surrounding the
mass is assumed to have exactly a fraction m/M missing,
then the effective radius of the sphere has been contracted
by a factor \sqrt(1-m/M). This forms the cosine of the
angle by which the cone deviates from flatness, so the
sine of the same angle (and the angle itself in radians)
is equal to \sqrt(m/M).
This therefore provides a model which gives the
same predictions as MOND but with a single physically
meaningful parameter (the mass M of the universe)
rather than an arbitrary acceleration parameter.
At the same time, the geometric model in terms of
cones might help to make it easier to analyze situations
involving multiple sources, such as clusters of galaxies.
<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><jonathan_scott@vnet.ibm.com> wrote in message\nnews:1126626085.132327.296670@o13g2000cwo .googlegroups.com...\n> In local GR calculations, one normally assumes that space\n> is flat at a sufficient distance from the local mass or\n> masses which are being studied. However, if the local\n> mass m constitutes a fraction m/M of the total mass of\n> the universe, then this assumption might be questionable.\n> If the universe is spatially finite at a given moment in\n> time, then a more plausible assumption would be that\n> the region containing a fraction m/M of the total mass\n> would also loosely speaking contain a related fraction\n> of the 3D "angle" needed to close the universe, so the\n> limit would be "conical" rather than "flat".\n>\n> More specifically, a starting hypothesis might be that a\n> sphere enclosing a fraction m/M of the total mass of the\n> universe would effectively be slightly "conical", missing\n> a constant proportion of its surface area at a given radius.\n> The effect of this would be to curve space-time by some\n> amount which is a function f of (m/M) and is proportional\n> to 1/r. This would then give rise to an extra\n> gravitational acceleration c^2/r f(m/M).\n>\n> In MOND, the extra acceleration is sqrt(G m a0)/r where\n> a0 is an arbitrary constant set to be approximately\n> 1.2e-10 ms^-2 to fit the experimental results. For\n> our hypothesis to match MOND, we require that the\n> function f is the square root, and that M is equal to\n> (c^4 / G a0), which is around 10^54 kg. Although trivial\n> methods of estimating the mass of the universe give a\n> result a little lower, around 3 * 10^52 kg, this seems to\n> me to be an interestingly close fit. This would suggest\n> that the existing MOND acceleration term could perhaps\n> be written instead as c^2/r sqrt(m/M), where M is around\n> 10^54 kg and may well correspond in some sense to the\n> total mass of the universe, and that it might be possible\n> to find a way to relate this physically to a "conical"\n> limit instead of a "flat" limit in gravitational\n> calculations.\n>\nThe problem with the Milgom-Beckenstein MOdification\nhas been to take it form an ad hoc thing to an approach\nwith consistent theoretical backing. To this end the scale\nexpanding cosmology of Johan Masreliez might help.\nYou can find an updated version with supporting evidence\nin his recent paper in Astrophysics and Space Science\nvolume 299, issue 1, pp. 83-108.\n\n/Kurtan\n\ncosmological theory\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><jonathan_scott@vnet.ibm.com> wrote in message
news:1126626085.132327.296670@o13g2000cwo.googlegr oups.com...
> In local GR calculations, one normally assumes that space
> is flat at a sufficient distance from the local mass or
> masses which are being studied. However, if the local
> mass m constitutes a fraction m/M of the total mass of
> the universe, then this assumption might be questionable.
> If the universe is spatially finite at a given moment in
> time, then a more plausible assumption would be that
> the region containing a fraction m/M of the total mass
> would also loosely speaking contain a related fraction
> of the 3D "angle" needed to close the universe, so the
> limit would be "conical" rather than "flat".
>
> More specifically, a starting hypothesis might be that a
> sphere enclosing a fraction m/M of the total mass of the
> universe would effectively be slightly "conical", missing
> a constant proportion of its surface area at a given radius.
> The effect of this would be to curve space-time by some
> amount which is a function f of (m/M) and is proportional
> to 1/r. This would then give rise to an extra
> gravitational acceleration c^2/r f(m/M).
>
> In MOND, the extra acceleration is \sqrt(G m a0)/r where
> a0 is an arbitrary constant set to be approximately
> 1.2e-10 ms^-2 to fit the experimental results. For
> our hypothesis to match MOND, we require that the
> function f is the square root, and that M is equal to
> (c^4 / G a0), which is around 10^54 kg. Although trivial
> methods of estimating the mass of the universe give a
> result a little lower, around 3 * 10^52 kg, this seems to
> me to be an interestingly close fit. This would suggest
> that the existing MOND acceleration term could perhaps
> be written instead as c^2/r \sqrt(m/M), where M is around
> 10^54 kg and may well correspond in some sense to the
> total mass of the universe, and that it might be possible
> to find a way to relate this physically to a "conical"
> limit instead of a "flat" limit in gravitational
> calculations.
>
The problem with the Milgom-Beckenstein MOdification
has been to take it form an ad hoc thing to an approach
with consistent theoretical backing. To this end the scale
expanding cosmology of Johan Masreliez might help.
You can find an updated version with supporting evidence
in his recent paper in Astrophysics and Space Science
volume 299, issue 1, pp. 83-108.
/Kurtan
cosmological theory
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