View Full Version : Blue limit
Norbert Gasch
May6-04, 10:50 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>I today´s universe there is an expansion of the space and therefore a\nredshift. These forces objets far away to an appareantly fast motion and in\na special distance, theit velocity seem to exceed this of light. The\nintensity of their radiation drops with this effect to zero. Further than\nthis distance we cannot see: the red limit.\n\nBut what may happen, if our universe would be shrinking instead? Then, the\neffect should give a large mass of galaxies getting nearer with\nsuperluminous velocity (!?!) and their radiation should increase to infinity\nbeyond a "blue limit".\n\nBut: here should be an error or shrinking universes are impossible?\n\nThanks a lot in advance!\n\nBest wishes: Norbert Gasch\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>I today´s universe there is an expansion of the space and therefore a
redshift. These forces objets far away to an appareantly fast motion and in
a special distance, theit velocity seem to exceed this of light. The
intensity of their radiation drops with this effect to zero. Further than
this distance we cannot see: the red limit.
But what may happen, if our universe would be shrinking instead? Then, the
effect should give a large mass of galaxies getting nearer with
superluminous velocity (!?!) and their radiation should increase to infinity
beyond a "blue limit".
But: here should be an error or shrinking universes are impossible?
Thanks a lot in advance!
Best wishes: Norbert Gasch
chronon
May12-04, 05:05 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>\n\n"Norbert Gasch" <NGC@gmx.com> wrote in message news:<20296.1083661576@www19.gmx.net>...\n> I today´s universe there is an expansion of the space and therefore a\n> redshift. These forces objets far away to an appareantly fast motion and in\n> a special distance, theit velocity seem to exceed this of light. The\n> intensity of their radiation drops with this effect to zero. Further than\n> this distance we cannot see: the red limit.\n>\n> But what may happen, if our universe would be shrinking instead? Then, the\n> effect should give a large mass of galaxies getting nearer with\n> superluminous velocity (!?!) and their radiation should increase to infinity\n> beyond a "blue limit".\n\nIf you think in terms of special relativity then it is impossible for\nanything to travel faster than light. If you think of an object\ntravelling at 0.9 of the speed of light then an object twice as far\naway will NOT be travelling at 1.8 times the speed of light as that\nisn\'t the way velocities add in SR. Thus the idea of a horizon beyond\nwhich we can have no contact is wrong. There will be no limit in the\nshrinking case either. The only way to get a horizon is to introduce\nsome form of acceleration.\n\nStephen Lee\nwww.chronon.org\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>"Norbert Gasch" <NGC@gmx.com> wrote in message news:<20296.1083661576@www19.gmx.net>...
> I today´s universe there is an expansion of the space and therefore a
> redshift. These forces objets far away to an appareantly fast motion and in
> a special distance, theit velocity seem to exceed this of light. The
> intensity of their radiation drops with this effect to zero. Further than
> this distance we cannot see: the red limit.
>
> But what may happen, if our universe would be shrinking instead? Then, the
> effect should give a large mass of galaxies getting nearer with
> superluminous velocity (!?!) and their radiation should increase to infinity
> beyond a "blue limit".
If you think in terms of special relativity then it is impossible for
anything to travel faster than light. If you think of an object
travelling at .9 of the speed of light then an object twice as far
away will NOT be travelling at 1.8 times the speed of light as that
isn't the way velocities add in SR. Thus the idea of a horizon beyond
which we can have no contact is wrong. There will be no limit in the
shrinking case either. The only way to get a horizon is to introduce
some form of acceleration.
Stephen Lee
www.chronon.org
ebunn@lfa221051.richmond.edu
May14-04, 09:33 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>\nIn article <60b2eda6.0405112213.1bb9d985@posting.google.com>, \nchronon <stephen@chronon.org> wrote:\n\n>"Norbert Gasch" <NGC@gmx.com> wrote in message news:<20296.1083661576@www19.gmx.net>...\n\n>> I today´s universe there is an expansion of the space and therefore a\n>> redshift. These forces objets far away to an appareantly fast motion and in\n>> a special distance, theit velocity seem to exceed this of light. The\n>> intensity of their radiation drops with this effect to zero. Further than\n>> this distance we cannot see: the red limit.\n>>\n>> But what may happen, if our universe would be shrinking instead? Then, the\n>> effect should give a large mass of galaxies getting nearer with\n>> superluminous velocity (!?!) and their radiation should increase to infinity\n>> beyond a "blue limit".\n>\n>If you think in terms of special relativity then it is impossible for\n>anything to travel faster than light.\n\nThat\'s true, but our Universe is not governed by special relativity;\nit\'s governed (we think) by general relativity. In general\nrelativity, there\'s not one unique, natural way to define the velocity\n(relative to us) of a very distant object. Different choices of\ncoordinates give different velocities. In some coordinate systems\n(including the ones cosmologists actually use to chart our Universe),\ndistant galaxies *are* receding from us with coordinate velocities in\nexcess of c.\n\nIn any case, I think that Norbert Gasch\'s main question is largely\nindependent of this point. As I understand it (please correct\nme if I\'m wrong!) the big question is this:\n\nIn an expanding Universe, there are galaxies with infinite redshift.\nSo in a contracting Universe, are there galaxies with infinite\nblueshift?\n\nThe answer turns out to be no.\n\nIn either an expanding or a contracting Universe [fine print: that\'s\nhomogeneous and isotropic], the redshift / blueshift of a distant\nlight source is given by the rule\n\n1 + z = a(t_0) / a(t_e).\n\nHere a(t) is the scale factor of the Universe at time t, and t_0 and\nt_e are the present age of the Universe and the age of the Universe at\nthe age at the time the light we\'re now seeing from the source was\nomitted. z is the redshift: defined by\n\n1+z = observed wavelength / emitted wavelength\n\nor\n\nz = (observed wavelength - omitted wavelength) / emitted wavelength.\n\nIn an expanding Universe, the ratio a(t_0)/a(t_e) is always bigger\nthan 1, so z is positive. As you look at more and more distant\nobjects, t_e gets smaller and smaller. (You\'re looking back further\nand further in time.) At some finite distance, a(t_e) = 0. (The\nlight we see from those sources was emitted right at the moment of\nthe big bang.) Objects at that distance have infinite redshift.\nObjects at greater distances are outside our horizon; we can\'t see\nthem.\n\nIn a contracting Universe, z is always negative (i.e., we have\nblueshifts rather than redshifts). An "infinite blueshift" would\ncorrespond the observed wavelength going to zero, so it would mean\n1+z = 0. That could only happen if a(t_e) = infinity. So in\na contracting Universe, you\'d only have infinite blueshifts\nif there are points such that light now reaching us was emitted\nwhen the Universe was infinitely large! In realistic cosmological\nmodels that doesn\'t happen. As you look at more and more distant\ngalaxies, the blueshift gets larger and larger, but you don\'t\nget to infinite blueshift for any finite distance.\n\n>If you think of an object\n>travelling at 0.9 of the speed of light then an object twice as far\n>away will NOT be travelling at 1.8 times the speed of light as that\n>isn\'t the way velocities add in SR.\n\nTrue in special relativity. Not true in cosmology.\n\n>Thus the idea of a horizon beyond\n>which we can have no contact is wrong.\n\nDitto. There are horizons in realistic cosmological models.\n\n>There will be no limit in the\n>shrinking case either. The only way to get a horizon is to introduce\n>some form of acceleration.\n\nIt\'d be better to replace the word "acceleration" here with "spacetime\ncurvature" or something. Universes with spacetime curvature\n(that is, Universes in which you can\'t apply special relativity)\ndon\'t correspond precisely with Universes exhibiting accelerated\nexpansion. For instance, a spatially flat (Omega_total = 1)\nUniverse with non-accelerated expansion (a(t) a linear function of t)\nhas spatial curvature and has a horizon.\n\n-Ted\n\n--\n[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]\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>In article <60b2eda6.0405112213.1bb9d985@posting.google.com>,
chronon <stephen@chronon.org> wrote:
>"Norbert Gasch" <NGC@gmx.com> wrote in message news:<20296.1083661576@www19.gmx.net>...
>> I today´s universe there is an expansion of the space and therefore a
>> redshift. These forces objets far away to an appareantly fast motion and in
>> a special distance, theit velocity seem to exceed this of light. The
>> intensity of their radiation drops with this effect to zero. Further than
>> this distance we cannot see: the red limit.
>>
>> But what may happen, if our universe would be shrinking instead? Then, the
>> effect should give a large mass of galaxies getting nearer with
>> superluminous velocity (!?!) and their radiation should increase to infinity
>> beyond a "blue limit".
>
>If you think in terms of special relativity then it is impossible for
>anything to travel faster than light.
That's true, but our Universe is not governed by special relativity;
it's governed (we think) by general relativity. In general
relativity, there's not one unique, natural way to define the velocity
(relative to us) of a very distant object. Different choices of
coordinates give different velocities. In some coordinate systems
(including the ones cosmologists actually use to chart our Universe),
distant galaxies *are* receding from us with coordinate velocities in
excess of c.
In any case, I think that Norbert Gasch's main question is largely
independent of this point. As I understand it (please correct
me if I'm wrong!) the big question is this:
In an expanding Universe, there are galaxies with infinite redshift.
So in a contracting Universe, are there galaxies with infinite
blueshift?
The answer turns out to be no.
In either an expanding or a contracting Universe [fine print: that's
homogeneous and isotropic], the redshift / blueshift of a distant
light source is given by the rule
1 + z = a(t_0) / a(t_e)[/itex].
Here a(t) is the scale factor of the Universe at time t, and t_0 and
t_e are the present age of the Universe and the age of the Universe at
the age at the time the light we're now seeing from the source was
omitted. z is the redshift: defined by
1+z = observed wavelength / emitted wavelength
or
z = (observed wavelength - omitted wavelength) / emitted wavelength.
In an expanding Universe, the ratio a(t_0)/a(t_e) is always bigger
than 1, so z is positive. As you look at more and more distant
objects, t_e gets smaller and smaller. (You're looking back further
and further in time.) At some finite distance, a(t_e) = . (The
light we see from those sources was emitted right at the moment of
the big bang.) Objects at that distance have infinite redshift.
Objects at greater distances are outside our horizon; we can't see
them.
In a contracting Universe, z is always negative (i.e., we have
blueshifts rather than redshifts). An "infinite blueshift" would
correspond the observed wavelength going to zero, so it would mean
1+z = . That could only happen if a(t_e) = infinity. So in
a contracting Universe, you'd only have infinite blueshifts
if there are points such that light now reaching us was emitted
when the Universe was infinitely large! In realistic cosmological
models that doesn't happen. As you look at more and more distant
galaxies, the blueshift gets larger and larger, but you don't
get to infinite blueshift for any finite distance.
>If you think of an object
>travelling at .9 of the speed of light then an object twice as far
>away will NOT be travelling at 1.8 times the speed of light as that
>isn't the way velocities add in SR.
True in special relativity. Not true in cosmology.
>Thus the idea of a horizon beyond
>which we can have no contact is wrong.
Ditto. There are horizons in realistic cosmological models.
>There will be no limit in the
>shrinking case either. The only way to get a horizon is to introduce
>some form of acceleration.
It'd be better to replace the word "acceleration" here with "spacetime
curvature" or something. Universes with spacetime curvature
(that is, Universes in which you can't apply special relativity)
don't correspond precisely with Universes exhibiting accelerated
expansion. For instance, a spatially flat (\Omega_total = 1)
Universe with non-accelerated expansion (a(t) a linear function of t)
has spatial curvature and has a horizon.
[itex]-Ted
--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]
chronon
May17-04, 07:51 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>ebunn@lfa221051.richmond.edu wrote in message news:<c82j8c\\$557\\$1@lfa222122.richmond.edu>...\ n> In article <60b2eda6.0405112213.1bb9d985@posting.google.com>, \n> chronon <stephen@chronon.org> wrote:\n>\n> >"Norbert Gasch" <NGC@gmx.com> wrote in message news:<20296.1083661576@www19.gmx.net>...\n>\n> >> I today´s universe there is an expansion of the space and therefore a\n> >> redshift. These forces objets far away to an appareantly fast motion and in\n> >> a special distance, theit velocity seem to exceed this of light. The\n> >> intensity of their radiation drops with this effect to zero. Further than\n> >> this distance we cannot see: the red limit.\n> >\n> >If you think in terms of special relativity then it is impossible for\n> >anything to travel faster than light.\n>\n> That\'s true, but our Universe is not governed by special relativity;\n> it\'s governed (we think) by general relativity. In general\n> relativity, there\'s not one unique, natural way to define the velocity\n> (relative to us) of a very distant object. Different choices of\n> coordinates give different velocities. In some coordinate systems\n> (including the ones cosmologists actually use to chart our Universe),\n> distant galaxies *are* receding from us with coordinate velocities in\n> excess of c.\n\nMy argument is that it is a fallacy to think things further than a\ncertain distance are travelling away from us faster than light and so\ncannot be seen. The Special Relativity viewpoint provides the best\nway of seeing this.\n\nImagine a universe which is expanding like our own, but without\ngravity or spacetime curvature (but in which galaxies and the like\nstill exist). We can choose to coordinatize this in different ways.\n\nFirstly we can choose an SR point of view. However this doesn\'t fully\nspecify the coordinates, we also have to choose a preferred frame of\nreference - which will be based on where we are. If we are asked when\nsomething happened in a distant galaxy, the answer is based on our\nproper time, not that of the distant galaxy. (Note that when thinking\nin SR terms we generally try to think in coordinate-free way.)\n\nAlternatively we could choose a coordinate system for which the time\ncoordinate of each galaxy is based on its proper time, and the space\ncoordinates agree with those local to each galaxy. This does not\nrequire us to choose a preferred frame of reference, and corresponds\nto the way cosmologists look at the universe.\n\nIn the first coordinate system we see that the addition rule for\nvelocities in SR means that nothing is actually travelling away from\nus faster than light. In the second system some galaxies may have\nvelocities greater than c but this doesn\'t mean that we can\'t see them\n– in fact these will be the galaxies with a redshift greater than one,\nnot with an infinite redshift.\n\nIn our universe the existence of spacetime curvature doesn\'t\nsubstantially change this argument.\n\nStephen Lee\nwww.chronon.org\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>ebunn@lfa221051.richmond.edu wrote in message news:<c82j8c$557$1@lfa222122.richmond.edu>...
> In article <60b2eda6.0405112213.1bb9d985@posting.google.com>,
> chronon <stephen@chronon.org> wrote:
>
> >"Norbert Gasch" <NGC@gmx.com> wrote in message news:<20296.1083661576@www19.gmx.net>...
>
> >> I today´s universe there is an expansion of the space and therefore a
> >> redshift. These forces objets far away to an appareantly fast motion and in
> >> a special distance, theit velocity seem to exceed this of light. The
> >> intensity of their radiation drops with this effect to zero. Further than
> >> this distance we cannot see: the red limit.
> >
> >If you think in terms of special relativity then it is impossible for
> >anything to travel faster than light.
>
> That's true, but our Universe is not governed by special relativity;
> it's governed (we think) by general relativity. In general
> relativity, there's not one unique, natural way to define the velocity
> (relative to us) of a very distant object. Different choices of
> coordinates give different velocities. In some coordinate systems
> (including the ones cosmologists actually use to chart our Universe),
> distant galaxies *are* receding from us with coordinate velocities in
> excess of c.
My argument is that it is a fallacy to think things further than a
certain distance are travelling away from us faster than light and so
cannot be seen. The Special Relativity viewpoint provides the best
way of seeing this.
Imagine a universe which is expanding like our own, but without
gravity or spacetime curvature (but in which galaxies and the like
still exist). We can choose to coordinatize this in different ways.
Firstly we can choose an SR point of view. However this doesn't fully
specify the coordinates, we also have to choose a preferred frame of
reference - which will be based on where we are. If we are asked when
something happened in a distant galaxy, the answer is based on our
proper time, not that of the distant galaxy. (Note that when thinking
in SR terms we generally try to think in coordinate-free way.)
Alternatively we could choose a coordinate system for which the time
coordinate of each galaxy is based on its proper time, and the space
coordinates agree with those local to each galaxy. This does not
require us to choose a preferred frame of reference, and corresponds
to the way cosmologists look at the universe.
In the first coordinate system we see that the addition rule for
velocities in SR means that nothing is actually travelling away from
us faster than light. In the second system some galaxies may have
velocities greater than c but this doesn't mean that we can't see them
– in fact these will be the galaxies with a redshift greater than one,
not with an infinite redshift.
In our universe the existence of spacetime curvature doesn't
substantially change this argument.
Stephen Lee
www.chronon.org
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