Paradox about age of universe. [Archive]

Edgar A Pearlstein

May22-04, 04:48 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>Astronomers tell us that light from the farthest galaxies so far\ndetected took about 13 billion years to reach us, that those galaxies\nare about 13 billion light years distant from us, and that the universe is\nabout 13 billion years old.\nThis seems to be inconsistent. For 13 billion years ago, when the light\nleft those galaxies, they were a lot closer to us; so how could the light\nhave taken that long to get here?\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>Astronomers tell us that light from the farthest galaxies so far
detected took about 13 billion years to reach us, that those galaxies
are about 13 billion light years distant from us, and that the universe is
about 13 billion years old.
This seems to be inconsistent. For 13 billion years ago, when the light
left those galaxies, they were a lot closer to us; so how could the light
have taken that long to get here?

Gordon D. Pusch

May24-04, 04:31 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\nepearlst@unlserve.unl.edu (Edgar A Pearlstein) writes:\n\n> Astronomers tell us that light from the farthest galaxies so far\n> detected took about 13 billion years to reach us, that those galaxies\n> are about 13 billion light years distant from us, and that the universe is\n> about 13 billion years old.\n> This seems to be inconsistent. For 13 billion years ago, when the light\n> left those galaxies, they were a lot closer to us; so how could the light\n> have taken that long to get here?\n\nShort, crude, and somewhat oversimplified answer: The space between\nthe emitting galaxy and our own galaxy has _also_ been expanding,\nwhich invalidates the naive "flat, static spacetime" intuition you are\nincorrectly attempting to apply above to estimate how long it woild take\nfor the light to get here. See Ned Wright\'s Cosmology FAQ and Tutorial:\n\n<http://www.astro.ucla.edu/~wright/cosmology_faq.html>,\n<http://www.astro.ucla.edu/~wright/cosmo_01.htm>, etc.\n\n-- Gordon D. Pusch\n\nperl -e \'\\$_ = "gdpusch\\@NO.xnet.SPAM.com\\n"; s/NO\\.//; s/SPAM\\.//; print;\'\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>epearlst@unlserve.unl.edu (Edgar A Pearlstein) writes:

> Astronomers tell us that light from the farthest galaxies so far
> detected took about 13 billion years to reach us, that those galaxies
> are about 13 billion light years distant from us, and that the universe is
> about 13 billion years old.
> This seems to be inconsistent. For 13 billion years ago, when the light
> left those galaxies, they were a lot closer to us; so how could the light
> have taken that long to get here?

Short, crude, and somewhat oversimplified answer: The space between
the emitting galaxy and our own galaxy has _also_ been expanding,
which invalidates the naive "flat, static spacetime" intuition you are
incorrectly attempting to apply above to estimate how long it woild take
for the light to get here. See Ned Wright's Cosmology FAQ and Tutorial:

<http://www.astro.ucla.edu/~wright/cosmology_faq.html>,
<http://www.astro.ucla.edu/~wright/cosmo_01.htm>, etc.

-- Gordon D. Pusch

perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'

Thomas Cuny

May24-04, 11:58 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>\ng_d_pusch_remove_underscores@xnet.com (Gordon D. Pusch) wrote in message news:<gi65amwdml.fsf@pusch.xnet.com>...\n> epearlst@unlserve.unl.edu (Edgar A Pearlstein) writes:\n>\n> > Astronomers tell us that light from the farthest galaxies so far\n> > detected took about 13 billion years to reach us, that those galaxies\n> > are about 13 billion light years distant from us, and that the universe is\n> > about 13 billion years old.\n\n> Short, crude, and somewhat oversimplified answer: The space between\n> the emitting galaxy and our own galaxy has _also_ been expanding,\n> which invalidates the naive "flat, static spacetime" intuition you are\n> incorrectly attempting to apply above to estimate how long it woild take\n> for the light to get here. See Ned Wright\'s Cosmology FAQ and Tutorial:\n>\n> <http://www.astro.ucla.edu/~wright/cosmology_faq.html>,\n> <http://www.astro.ucla.edu/~wright/cosmo_01.htm>, etc.\n>\n> -- Gordon D. Pusch\nDoes the redshift depend on the current speed differential between our\ngalaxy and the\nemitting galaxy? How would a photon know how much space expanded\nbetween it and\nthe emitting galaxy?\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>g_{d_pusch_remove_underscores}@xnet.com (Gordon D. Pusch) wrote in message news:<gi65amwdml.fsf@pusch.xnet.com>...
> epearlst@unlserve.unl.edu (Edgar A Pearlstein) writes:
>
> > Astronomers tell us that light from the farthest galaxies so far
> > detected took about 13 billion years to reach us, that those galaxies
> > are about 13 billion light years distant from us, and that the universe is
> > about 13 billion years old.

> Short, crude, and somewhat oversimplified answer: The space between
> the emitting galaxy and our own galaxy has _also_ been expanding,
> which invalidates the naive "flat, static spacetime" intuition you are
> incorrectly attempting to apply above to estimate how long it woild take
> for the light to get here. See Ned Wright's Cosmology FAQ and Tutorial:
>
> <http://www.astro.ucla.edu/~wright/cosmology_faq.html>,
> <http://www.astro.ucla.edu/~wright/cosmo_01.htm>, etc.
>
> -- Gordon D. Pusch
Does the redshift depend on the current speed differential between our
galaxy and the
emitting galaxy? How would a photon know how much space expanded
between it and
the emitting galaxy?

ebunn@lfa221051.richmond.edu

May25-04, 01:32 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 article <c8jir5\\$il7\\$1@unlnews.unl.edu>,\nEdgar A Pearlstein <epearlst@unlserve.unl.edu> wrote:\n> Astronomers tell us that light from the farthest galaxies so far\n>detected took about 13 billion years to reach us, that those galaxies\n>are about 13 billion light years distant from us, and that the universe is\n>about 13 billion years old.\n> This seems to be inconsistent. For 13 billion years ago, when the light\n>left those galaxies, they were a lot closer to us; so how could the light\n>have taken that long to get here?\n\nOne surprising but important fact about cosmology is that there are\nmultiple different ways to quantify the distance to a faraway object.\nThese don\'t always agree with each other, and there\'s generally not a\nsingle clearly "right" one. This is actually a key part of general\nrelativity: if spacetime is curved, then distances become problematic.\n\nFor this reason, when cosmologists talk to each other (as opposed to\ntalking to reporters or the general public), they don\'t generally talk\ntoo much about distances to faraway galaxies. They\'re more likely to\ntalk about redshifts, which are what\'s actually measured.\n\nIt\'s perfectly OK to talk about distances; you just have to throw in a\nlot of fine print about what distance you actually mean. Probably the\nmost common way to quantify distance to a faraway object in cosmology\nis the number you get when you calculate the distance from us to the\nlocation of the galaxy *at the present time*. Once you add that last\nclause, and assuming you agree to measure distances along geodesics\n("straight lines"), this is a well-defined prescription for assigning\na distance to any object.\n\nThat prescription is different from the distance from the object to us\n*at the time the light was emitted*, simply because the Universe has\nexpanded between then and now.\n\nHere are a couple of other common prescriptions people use to quantify\ndistances:\n\n-"Luminosity distance," which is what you get when you naively apply\nthe inverse-square law of light to infer a distance from the apparent\nbrightness and absolute luminosity of an object\n\n-"Angular diameter distance," which is what you get when you naively\napply geometry to get a distance from the angle subtended by an\nobject and its actual diameter.\n\n-Distance inferred by naively assuming that the cosmic time (in\nyears) the light has been traveling equals the distance (in\nlight-years) it has gone.\n\n(In all cases, "naively" means "pretending we live in good old\nnon-expanding flat spacetime." In the last one, the word "cosmic"\nbefore "time" is an explicit statement which set of coordinates we\'re\nusing to describe time. This is often implied without being\nexplicitly stated.)\n\nApparently you\'ve read sources that use the last one as their\ndefinition of distance. Personally, I think that that\'s a poor\nchoice, because it leads to precisely the problem that you pointed\nout. But the main thing to realize is not that this notion of\ndistance is "wrong"; it\'s that there are multiple notions of distance,\nnone of which has a terribly strong claim to be "right." Ideally,\npeople who write about cosmology for non-specialists would\npoint this out, but they generally don\'t.\n\n-Ted\n\n--\n[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]\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 <c8jir5$il7$1@unlnews.unl.edu>,
Edgar A Pearlstein <epearlst@unlserve.unl.edu> wrote:
> Astronomers tell us that light from the farthest galaxies so far
>detected took about 13 billion years to reach us, that those galaxies
>are about 13 billion light years distant from us, and that the universe is
>about 13 billion years old.
> This seems to be inconsistent. For 13 billion years ago, when the light
>left those galaxies, they were a lot closer to us; so how could the light
>have taken that long to get here?

One surprising but important fact about cosmology is that there are
multiple different ways to quantify the distance to a faraway object.
These don't always agree with each other, and there's generally not a
single clearly "right" one. This is actually a key part of general
relativity: if spacetime is curved, then distances become problematic.

For this reason, when cosmologists talk to each other (as opposed to
talking to reporters or the general public), they don't generally talk
too much about distances to faraway galaxies. They're more likely to
talk about redshifts, which are what's actually measured.

It's perfectly OK to talk about distances; you just have to throw in a
lot of fine print about what distance you actually mean. Probably the
most common way to quantify distance to a faraway object in cosmology
is the number you get when you calculate the distance from us to the
location of the galaxy *at the present time*. Once you add that last
clause, and assuming you agree to measure distances along geodesics
("straight lines"), this is a well-defined prescription for assigning
a distance to any object.

That prescription is different from the distance from the object to us
*at the time the light was emitted*, simply because the Universe has
expanded between then and now.

Here are a couple of other common prescriptions people use to quantify
distances:

-"Luminosity distance," which is what you get when you naively apply
the inverse-square law of light to infer a distance from the apparent
brightness and absolute luminosity of an object

-"Angular diameter distance," which is what you get when you naively
apply geometry to get a distance from the angle subtended by an
object and its actual diameter.

-Distance inferred by naively assuming that the cosmic time (in
years) the light has been traveling equals the distance (in
light-years) it has gone.

(In all cases, "naively" means "pretending we live in good old
non-expanding flat spacetime." In the last one, the word "cosmic"
before "time" is an explicit statement which set of coordinates we're
using to describe time. This is often implied without being
explicitly stated.)

Apparently you've read sources that use the last one as their
definition of distance. Personally, I think that that's a poor
choice, because it leads to precisely the problem that you pointed
out. But the main thing to realize is not that this notion of
distance is "wrong"; it's that there are multiple notions of distance,
none of which has a terribly strong claim to be "right." Ideally,
people who write about cosmology for non-specialists would
point this out, but they generally don't.

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

chronon

Jun1-04, 04:43 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>\nepearlst@unlserve.unl.edu (Edgar A Pearlstein) wrote in message news:<c8jir5\\$il7\\$1@unlnews.unl.edu>...\n> Astronomers tell us that light from the farthest galaxies so far\n> detected took about 13 billion years to reach us, that those galaxies\n> are about 13 billion light years distant from us, and that the universe is\n> about 13 billion years old.\n> This seems to be inconsistent. For 13 billion years ago, when the light\n> left those galaxies, they were a lot closer to us; so how could the light\n> have taken that long to get here?\n\nYou can think of this in two ways. Firstly, the cosmological, general\nrelativistic way, in which case the idea of distance is chosen to have\nno preferred frame, but doesn\'t necessarily correspond to our idea of\ndistance and velocity locally (i.e. you need to imagine space\nstretching).\n\nSecondly you can think in terms of special relativity based on our\nlocal frame of reference (which most people don\'t). This means that\nthe galaxies are moving away from us at close to the speed of light,\nand although the light was emitted from them when they were fairly\nyoung (less than 1 billion years from the big bang, for the sake of\nexample - I don\'t know when galaxies actually formed), time dilation\nmeans that in our frame it was emitted billions of years after the big\nbang, meaning that (travelling close to the speed of light) they were\nbillions of light years away.\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>epearlst@unlserve.unl.edu (Edgar A Pearlstein) wrote in message news:<c8jir5$il7$1@unlnews.unl.edu>...
> Astronomers tell us that light from the farthest galaxies so far
> detected took about 13 billion years to reach us, that those galaxies
> are about 13 billion light years distant from us, and that the universe is
> about 13 billion years old.
> This seems to be inconsistent. For 13 billion years ago, when the light
> left those galaxies, they were a lot closer to us; so how could the light
> have taken that long to get here?

You can think of this in two ways. Firstly, the cosmological, general
relativistic way, in which case the idea of distance is chosen to have
no preferred frame, but doesn't necessarily correspond to our idea of
distance and velocity locally (i.e. you need to imagine space
stretching).

Secondly you can think in terms of special relativity based on our
local frame of reference (which most people don't). This means that
the galaxies are moving away from us at close to the speed of light,
and although the light was emitted from them when they were fairly
young (less than 1 billion years from the big bang, for the sake of
example - I don't know when galaxies actually formed), time dilation
means that in our frame it was emitted billions of years after the big
bang, meaning that (travelling close to the speed of light) they were
billions of light years away.

Stephen Lee
www.chronon.org