Center of Universe?
Hannu Poropudas
By the way do you know where in our Universe is the center of
the space (I mean the mass center of all galaxies).?
---
Best Regards,
Hannu Poropudas.
"It's Not What You Know That Matters
... It's Knowing What You Don't."
Emory F. Bunn
Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:
>Hannu Poropudas (hannu.P...@ericsson.fi) wrote:
>
>: By the way do you know where in our Universe is the center of
>
>masses of the continents in the surface of the Earth.
That's right. As far as we can tell, the Universe is roughly
homogeneous on large scales. There doesn't seem to be any special
point that you'd want to call "the center." The analogy with the
surface of the Earth is a good one. Let me expand on it just a little
bit, in case anyone missed the point.
The Universe may be spatially finite and yet have no boundary. This
initially may sound impossible, but it's not. The surface of sphere
is a two-dimensional surface that has finite area and yet has no
boundary, and one can imagine analogous three-dimensional "surfaces"
(although such objects are hard to visualize).
If the Universe is of this form, then we can get some intuition about
what's going on by considering the analogy with the spherical
surface. It's crucial to remember that in this analogy the entire
three-dimensional volume of space is being compared to the
two-dimensional surface of the sphere. It may help to imagine a
species of little two-dimensional creatures crawling around on the
surface of the sphere. Since they live in only two dimensions, they
have no idea that their world is actually "curved" into "the third
dimension." As far as they're concerned, that two-dimensional surface
is all there is.
Now, these creatures could do experiments and discover that their
world is shaped like a sphere. They might find this result surprising
at first, but they'd get used to it eventually, and they'd realize
that although their world has finite area, it has no boundary. Nor
does it have a center, at least not one that they can point to. There
is no point on the surface of the sphere that you'd call the center:
all points on the surface look exactly the same. Similarly, if our
three-dimensional Universe is curved like a sphere, it could be finite
and yet have no center.
On the other hand, our Universe might be infinite. We have no way to
tell. If it's infinite, it still might not have a center. It might
just stretch on forever, with each point looking more or less like
every other point.
In fact, if you take our observations of the distribution of stuff in
the Universe, and extrapolate them in the simplest possible way, you
find that these two possibilities (curved like a sphere or extending
forever homogeneously) are the two simplest, most natural hypotheses.
That doesn't necessarily mean that either is right, of course. The
big problem is that we can only see a finite amount of the Universe:
since the Universe is only about 15 billion years old, we can't see
anything further away than about 15 billion light-years. That
distance is known as our "horizon." The Universe seems to be pretty
much homogeneous throughout the volume enclosed by our horizon, so
it's natural to guess that maybe things continue that way outside of
the horizon, but since we can't see out there, that's just a guess.
>You can try to define it as (1/M) SUM r_i m_i, where M is
>the total mass of the universe, m_i is the mass of the i-th
>particle of the universe, r_i is a position vector of that
>particle, and the sum goes throght all the particles in the
>universe (perhaps about 10^80, I am ignoring quantum efects).
>But in a curved space there is no such a thing as "position
>vector". If you substitute it by, say, the lenght of the
>geodesic from some "fix" point taken as origin, the result
>is going to depend on the point chosen.
Absolutely right. But things are even worse than that, because that
number 10^80 is the number of particles in the *observable* Universe
(i.e., within our horizon), not the number in the whole Universe. The
observable Universe is a sphere centered on us, since it's the set of
all points close enough to us for us to see them. So even if you
could get around the problems of spatial curvature, you wouldn't get
reliable results by computing the center of mass of all of the
observable particles. If you did compute such a thing, you'd find
that the center of the Universe was right here (or pretty close to
it), simply because you've artificially restricted your attention to a
sphere centered on us, instead of considering the whole Universe.
An alien in a distant galaxy could perform the same computation
using his own observable Universe, and he'd find that *he*
was at the center instead.
-Ted
mikko....@vtt.fi
>By the way do you know where in our Universe is the center of
>the space (I mean the mass center of all galaxies).?
No, we don't even know whether there is any centre. The Universe
looks the same in every direction, which suggests that no
point is more central than any other. If there is a centre,
it can be anywhere -- right here or far from anything we can see.
The usual definition of the mass centre does not work in curved
space; and, as far as I know, there is no definition that works.
-----------------------------------------------------------------
Mikko J. Levanto Tel. +358 81 551 2448
VTT Electronics Fax +358 81 551 2320
P.O.Box 1100 Internet: Mikko....@vtt.fi
FIN-90571 Oulu, Finland
--------------- VTT - Technical Research Centre of Finland ------
Miguel Lerma
: By the way do you know where in our Universe is the center of
: the space (I mean the mass center of all galaxies).?
Probably it is indefined. It is like asking about a center of
masses of the continents in the surface of the Earth.
You can try to define it as (1/M) SUM r_i m_i, where M is
the total mass of the universe, m_i is the mass of the i-th
particle of the universe, r_i is a position vector of that
particle, and the sum goes throght all the particles in the
universe (perhaps about 10^80, I am ignoring quantum efects).
But in a curved space there is no such a thing as "position
vector". If you substitute it by, say, the lenght of the
geodesic from some "fix" point taken as origin, the result
is going to depend on the point chosen.
Miguel A. Lerma
Andrew Cooke
Edward Green <egr...@nyc.pipeline.com> wrote:
>'t...@physics2.berkeley.edu (Emory F. Bunn)' wrote:
>
>>The
>>big problem is that we can only see a finite amount of the Universe:
>>since the Universe is only about 15 billion years old, we can't see
>>anything further away than about 15 billion light-years.
>
>big bang.
just after the `big bang' everything was so hot that photons were
continually scattering off particles (mainly electrons).
as things expanded and cooled this became less important, and
the effective change was actually quite sudden - so we can see
back to a certain point, but then no further because it is
`misty' due to all the scattering.
this `misty' early universe is what people are looking at when
they look at fluctuations in the microwave background. since
the universe was still expanding very rapidly at that time it
is at a very high redshift (about 1000 if i remember correctly).
that's why people were so interested in the fluctuations - they
were the very beginnings of the structures that are now galaxies.
and they are only just big enough (if they hadn't been seen people
would have had big problems because it would have been too smooth
to form the universe we have today).
andrew
--
work phone/fax: 0131 668 8356, office: 0131 668 8357
institute for astronomy, royal observatory, blackford hill, edinburgh
http://www.roe.ac.uk/ajcwww
Richard A. Schumacher
>Earth have a center, but it is outside of Earth's surface.
Correct! The center of Earth's surface is not on the surface.
And the same is true of the universe: the center of the universe
is not in the universe. It lies outside the universe, 15 billion
or so years in the past. The center is not "near the center of
Virgo Super Cluster" or anywhere else accessible to us.
Paul J. Kossick
of the universe in 3-dimensional space? To answer this would require
knowledge of the actual 'shape' of the universe in that space, and I
don't believe anyone actually agrees on that.
--
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
Paul J. Kossick Standing on a hill in my mountain of dreams
kos...@crl.com Telling myself it's not as hard, hard, hard as it seems
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
Hannu Poropudas
In article <4chedk$i...@geraldo.cc.utexas.edu>
which is dated 4 Jan 1996 20:47:48 GMT
mle...@arthur.ma.utexas.edu (Miguel Lerma) wrote:
>Hannu Poropudas (hannu.P...@ericsson.fi) wrote:
>
>: By the way do you know where in our Universe is the center of
>: the space (I mean the mass center of all galaxies).?
>
>Probably it is indefined. It is like asking about a center of
>masses of the continents in the surface of the Earth.
>
Earth have a center, but it is outside of Earth's surface.
Perhaps center of the space (center of all galaxies) is
outside of visible Universe, perhaps in the side of
contracting part of it (please take a look of README-articles
in my directory mentioned below).?
Perhaps it could be somewhere near center of Virgo Super Cluster.
Perhaps in invisible center of M87.?
>You can try to define it as (1/M) SUM r_i m_i, where M is
>the total mass of the universe, m_i is the mass of the i-th
>particle of the universe, r_i is a position vector of that
>particle, and the sum goes throght all the particles in the
>universe (perhaps about 10^80, I am ignoring quantum efects).
>But in a curved space there is no such a thing as "position
>vector". If you substitute it by, say, the lenght of the
>geodesic from some "fix" point taken as origin, the result
>is going to depend on the point chosen.
>
>
>Miguel A. Lerma
Sure there is no such a thing as "position vector" in a curved
space. You have to generalize vector concept to be as "directed
geodesic line" in a curved space. You have to define also how
to add, subtract and multiply by scalar these "directed geodesic
lines". For example on two dimensional sphere surface you can
define multiplication and division of these "directed geodesic
lines". One problem remain and that is how to define these
four operations for these objects which starts from different
points on the sphere. Also this "algebra" has two characteristic
features, namely non-associativity and non-distributivity.
Please take a look at my trial in WWW.FUNET.FI (or FTP.FUNET.FI)
and directory pub/doc/misc/HannuPoropudas article is PostScript
file called surface_algebras.Z.
David Jacob
On 4 Jan 1996, Hannu Poropudas wrote:
>
> By the way do you know where in our Universe is the center of
> the space (I mean the mass center of all galaxies).?
>
>
> ---
>
>
> Best Regards,
>
> Hannu Poropudas.
In the beginning, the Universe issued from a single point, and was
composed of a at least 11 dimensions. Then the universe became unstable,
and all but 3 of the dimensions collapsed, releasing tremendous energies,
and causing the center of the universe to actualy detach and become a
free wandering anomolie. The Center of the Universe has been wandering
around ever since, and has been sought after by the various civilizations
and species of the galaxy since the dawn of life. It is said that
whomsoever possesses the true center of the universe possesses infinite
power to reshape reality and bend others to his will...
Dave
ps--if any hollywood types wish to use the above for the
plot of a movie or something, dont forget my check...
Miguel Lerma
[...]
: Earth have a center, but it is outside of Earth's surface.
I guess the closest to this idea is what Richard A. Schumacher says
in his post: the center is 15 million years in the past (Big Bang).
But I think this assumes that only the 3-space is curved, and that
the whole 4-dimensional manifold made up with the whole past, present
and future history of the universe is Euclidean. It is still possible
that the universe is even more complicated than that. I think Hawking
suggested that the whole 4-dimensional manifold is curved, and that
the Big Bang and the Big Cruch are just points like any other
else except for the fact that in a certain system of cordinates
all coordinates except one (i.e.: the three spacial coordinates
but not time) converge there (something similar to what happens
in the surface of the Earth with meridians and paralels). If that
is so, then the "center" of the universe can be conceived only
with help of a fith dimension, so than the universe is a 4-sphere
inmersed in a 5-dimencional Euclidean space.
Miguel A Lerma
Emory F. Bunn
>I think the question might be better stated as: Where would be the center
>of the universe in 3-dimensional space? To answer this would require
>knowledge of the actual 'shape' of the universe in that space, and I
>don't believe anyone actually agrees on that.
I'm not sure I understand what you mean here. Space, as far as we can
tell, looks like a three-dimensional manifold. It fills all of
three-dimensional space, more or less by definition, and so it doesn't
have a "shape in 3-dimensional space." It seems to me that one only
talks about the "shape" of something if the something is embedded in
some larger volume. For example, we might talk about the shape of a
spherical volume that's embedded in a larger three-dimensional space.
But since the Universe doesn't seem to be embedded in a larger
three-dimensional space, I don't know what meaning one would attach to
a phrase like "the shape of the Universe in three-dimensional space."
If you like, you can choose to imagine that the Universe is embedded
in some space of a larger number of dimensions. This is a useful
thing to do when trying to get some intuition about curved spacetime,
although we have no particular reason to believe that space really is
embedded in such a way. In this context, it would make sense to talk
about the shape of the Universe within this larger (four or more
dimensional) space.
-Ted
Edward Green
>big problem is that we can only see a finite amount of the Universe:
>since the Universe is only about 15 billion years old, we can't see
>anything further away than about 15 billion light-years.
big bang.
Ed Green
egr...@nyc.pipeline.com
MARSHALL DUDLEY
-> By the way do you know where in our Universe is the center of
-> the space (I mean the mass center of all galaxies).?
This is an interesting question. I believe some of the hyperspace equations
show that if the universe is closed then there is no center, or alternative
every point can be viewed as the center. Of course to see this requires
viewing in more than 3 dimensions, but an analogy is to view the earth's 2
dimensions from 3 dimensions, and then it is obvious that no point on the
surface of the earth is the center, and that every point can also be viewed as
the center, since all other points on the surface are symetrically surrounding
it.
Marshall
Victor Grauer
red shifted photons which are relics of a time very close to the time of
the big bang, then, to me, this clearly means that the center of the
universe is at the periphery.
Bruce Scott TOK
: If, at the farthest reaches of space in all directions we see extremely
: the big bang, then, to me, this clearly means that the center of the
: universe is at the periphery.
Don't forget you are looking back in time. As someone else said, this
means the center of the universe is its beginning.
[At t=0 in the standard model, the curvature is infinite for all values
of the other three coordinates.]
--
Mach's gut!
Bruce Scott The deadliest bullshit is
Max-Planck-Institut fuer Plasmaphysik odorless and transparent
b...@ipp-garching.mpg.de -- W Gibson
Emory F. Bunn
Victor Grauer <gra...@oberon.pps.pgh.pa.us> wrote:
>If, at the farthest reaches of space in all directions we see extremely
>red shifted photons which are relics of a time very close to the time of
>the big bang, then, to me, this clearly means that the center of the
>universe is at the periphery.
That conclusion doesn't follow. When we look at the farthest reaches
of space, we are looking far into the past, since light from those
points has taken a long time to reach us. In fact, the limit on the
furthest points we can see is set by the age of the Universe: we can't
see objects further than about 15 billion light-years, since light
from more distant objects hasn't had time to reach us.
So when we look at the furthest objects we can see, we're necessarily
going to be seeing them as they were when the Universe was very
young. That's why points near the edge of the observable Universe
look like they're "close to the big bang". They're not *spatially*
any closer to the center than we are. The light we see from those
points did originate from *times* close to the big bang, but that's
just because we happen to be looking at those points from very far
away; it's not anything special about that region of space.
Here's another way to put it. At this very moment there could be a
race of creatures in a galaxy at the edge of our observable Universe.
If they look our way, they will see radiation that left our patch of
space shortly after the moment of the big bang. They might conclude
that our patch of space is "close to the big bang", just as we might
conclude the same thing from our observations of their patch of
space. But we'd both be wrong.
-Ted
Miguel Lerma
> In article <4ck30f$b...@geraldo.cc.utexas.edu>,
> Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:
> >I guess the closest to this idea is what Richard A. Schumacher says
> >in his post: the center is 15 million years in the past (Big Bang).
> You mean "billion" rather than "million." Specifically, I should
> point out for the benefit of non-U.S. readers that I mean a
> U.S. billion, 1000000000, not a U.K. billion, which is 1000 times
> bigger. (I think even Nature uses "billion" in the U.S. sense
> now, by the way.)
Right, I meant (US) "billion". Sorry.
> >But I think this assumes that only the 3-space is curved, and that
> >the whole 4-dimensional manifold made up with the whole past, present
> >and future history of the universe is Euclidean.
> I can't speak for Richard Shumacher, but I can tell you that this isn't
> how I interpreted what he wrote. Standard theories of cosmology
> are based on the theory of general relativity. In general relativity,
> spacetime is modeled as a four-dimensional manifold, but definitely
> not a Euclidean one. Spacetime has curvature in all of these models.
[...]
Your remarks are perfectly sound. I was just playing around with
"naive" models of the universe, just to see in what extent they
could provide some meaning to the original question. In particular,
the idea that places the "center" of the universe in the Big Bang
comes from a model in which the universe is like a balloon growing
from an initial point, and the radial coordinate would be the time.
The center would correspond to t=0. Of course, if we want to
deal with "state of the art" models of the universe, we need to
look at relativistic cosmology.
By the way, I have always found intriguing the relation between
the local structure of the universe (as a differenciable manifold)
and its global topology. I think most of the time cosmologists make
implicit assumptions about how they are related. In particular they
estimate the size of the universe from its local curvature. However,
it seems to me that they are different problems. I can imagine, for
instance, manifolds of zero curvature and finite size, e.g. a plane
torus. Also I can conceive, say, infinite 2-manifolds with constant
positive curvature. A sofisticated but interesting example is the
following: let H be the the open upper half complex plane, Q the set of
rational numbers, H-hat = H union Q union {infinity}, j: H-hat -> P^1(C)
the j-invariant (P^1(C) is the Riemann sphere, j appears in the theory
of modular forms), and s: P^1(C) -> S^2 a stereographic projection. S^2
(2-sphere) is assumed to have its usual constant curvature differential
structure. Recall that j is invariant by the modular group, and that H-hat
can be partitioned into infinitely many fundamental domains. The interesting
thing is that the H-hat can be endowed with a contant positive curvature
differential structure via the map z -> s(j(z)), and each fundamental
domain maps bijectively to S^2. It is like having infinitely 2-spheres
glued together in a single 2-manifold.
In short, I do not think that the local structure of the universe
allows us to get conclusions about its global structure without
additional assumptions.
Miguel A. Lerma
Emory F. Bunn
Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:
>By the way, I have always found intriguing the relation between
>the local structure of the universe (as a differenciable manifold)
>and its global topology. I think most of the time cosmologists make
>implicit assumptions about how they are related. In particular they
>estimate the size of the universe from its local curvature. However,
>it seems to me that they are different problems. I can imagine, for
>instance, manifolds of zero curvature and finite size, e.g. a plane
>torus.
You're absolutely right. The "standard model" of cosmology
involves a couple of assumptions that people sometimes don't bother
to state explicitly:
1. The density is roughly uniform over very large scales
2. The Universe is simply connected.
There's pretty good evidence for 1, at least over the scales that we
can observe. On the other hand, if the Universe is much larger than
our horizon, it's quite plausible that the density might vary
dramatically over scales of, say, a trillion light-years, and we'd
never know it. So even if someone found an incredibly clever way to
measure the density within our horizon and thereby established that
space was negatively curved around here, that wouldn't prove that the
Universe was truly open, since openness is a global property that
depends on what things look like at arbitrarily large distances.
The second assumption (the one about topology) is the one you were
talking about. Cosmologists usually say that if the Universe has zero
or negative curvature, then it goes on forever. That conclusion
depends on assumption 2. For both flat and negatively curved models,
the only simply connected topology is the one that goes on forever,
but in both cases you can change the topology to get a compact space.
(In the flat case, the simplest way is to make space a 3-torus, as you
say. If there's uniform negative curvature then you have to go to
more complicated topologies.)
There is a relatively small literature of attempts to place
constraints on these alternative topologies. As far as I know, only
the flat toroidal case has been considered, since the open case is
much more complicated. As you'd expect, if the size of the torus is
much larger than our horizon, there's no way you can tell you're in a
torus rather than an infinite space. If the size is comparable to the
horizon or smaller, then there are observational tests you can
perform. If anyone is really interested, I can look up the limits
that have been placed on the torus size in these models. (I think the
length of the torus is constrained to be larger than something like
0.2 to 0.5 horizon sizes.)
>Also I can conceive, say, infinite 2-manifolds with constant
>positive curvature.
That's interesting. I didn't know that such things existed. I'm
afraid I didn't really understand your construction of such a thing on
first reading; I'll try to look at it more carefully later.
I have the impression that you can't make a noncompact 3-manifold with
constant positive curvature. Do you know if that's true or not? (I'm
a couple of miles from my book on Riemannian geometry at the moment;
I'll try to look it up later if I remember.) If that's true, then the
conventional wisdom that locally positive curvature implies a finite
Universe depends only on assumption 1 above, not on assumption 2.
(Note that we cosmologists think we're doing pretty well if our
conclusions depend on only *one* wholly unverifiable assumption! :-)
>In short, I do not think that the local structure of the universe
>allows us to get conclusions about its global structure without
>additional assumptions.
Agreed. For what it's worth, most working cosmologists know
this, although we're frequently to careless to say so.
-Ted
Miguel Lerma
> >Also I can conceive, say, infinite 2-manifolds with constant
> >positive curvature.
> That's interesting. I didn't know that such things existed. I'm
> afraid I didn't really understand your construction of such a thing on
> first reading; I'll try to look at it more carefully later.
I mentioned that example because it is related to a problem I have
been studying recently, but there are simpler examples. However
one should be cautious, because that kind of surface is not
completely homogeneous, it contains some exceptional points
(perhaps I abused the language by calling it "manifold"). For instance,
consider the Riemann surface for f(z) = sqrt(z). It can be seen as two
Riemann spheres glued along the negative real axis. If you identify each
of those Riemann spheres with S^2 and look at its differential structure,
you see an object of constant positive curvature with the size of two
spheres of the same curvature. But it contains two branching points:
0 and infinity. Almost everywhere that manifold looks like a sphere,
but at z=0 (and at z=infinity) little circles surounding that point
have length close to 4*pi*r instead of 2*pi*r.
In my example, the surface can be seen as infinitely many
spheres glued in a certain way along the negative real axis
and the interval [0,1728]. At almost every point that manifold
looks like a piece of sphere, but the point 0 is exceptional.
If you are close to z=0 in one of the spheres and go around it
in a small circle, you will go through six diferent spheres
making an arc of 180 degrees in each one, so you need to turn
180*6 = 1080 degrees arround that point to return to the
starting point. At the point z=1728, a path arround it goes
through two different spheres 360 degrees each, 720 in total.
At z=infinity the circles go through infinitely many spheres
and have infite length.
> I have the impression that you can't make a noncompact 3-manifold with
> constant positive curvature. Do you know if that's true or not? (I'm
[...]
I guess that can also be done in a similar way as above, but if
exceptional branching points are not allowed, you might be right.
Miguel A. Lerma
Ben Weiner
>By the way, I have always found intriguing the relation between
>the local structure of the universe (as a differenciable manifold)
>and its global topology. I think most of the time cosmologists make
>implicit assumptions about how they are related. In particular they
>estimate the size of the universe from its local curvature. However,
>it seems to me that they are different problems. I can imagine, for
>instance, manifolds of zero curvature and finite size, e.g. a plane
>torus.
Interestingly, universes with torus-like geometry (that is, periodic
in one or more spatial dimensions, often called "small universes")
can be ruled out by observations. The spatial periodicity introduces
a long-wavelength cutoff and this distorts the spectrum of the cosmic
microwave background radiation. I believe the limits from observations
are actually good enough now to rule out these small-universe models.
>Also I can conceive, say, infinite 2-manifolds with constant
>positive curvature. A sofisticated but interesting example ... [deleted]
>In short, I do not think that the local structure of the universe
>allows us to get conclusions about its global structure without
>additional assumptions.
Well, quite probably, but the limits on alternative (non-Friedmann)
universes may be quite strict. If one can cook up a model which
fits all the observations and makes no predictions differently from
a Friedmann model, that is of theoretical interest but may not be
of any practical interest to astronomers, especially observers.
Them's the breaks.
--
NO STEP
Robert Israel
Ben Weiner <bwe...@electron.rutgers.edu> wrote:
> Outside the horizon, the universe could do just
>about anything it wants and we'd have no way of knowing. There could
>be a domain wall sweeping everything into oblivion heading for us at
>the speed of light, ready to come through the horizon tomorrow, and we
>wouldn't know - nor should we care much. It wouldn't get here for
>approximately a bazillion years anyway.
??? If it's heading directly for us at the speed of light, we wouldn't
know about it until it was already here.
--
Robert Israel isr...@math.ubc.ca
Department of Mathematics (604) 822-3629
University of British Columbia fax 822-6074
Vancouver, BC, Canada V6T 1Y4
Ben Weiner
>Interestingly, universes with torus-like geometry (that is, periodic
>in one or more spatial dimensions, often called "small universes")
>can be ruled out by observations. The spatial periodicity introduces
>a long-wavelength cutoff and this distorts the spectrum of the cosmic
>microwave background radiation. I believe the limits from observations
>are actually good enough now to rule out these small-universe models.
That is, to rule out models in which the periodicity is significantly
smaller than the horizon size (the size of the observable universe),
as Ted Bunn said. Outside the horizon, the universe could do just
about anything it wants and we'd have no way of knowing. There could
be a domain wall sweeping everything into oblivion heading for us at
the speed of light, ready to come through the horizon tomorrow, and we
wouldn't know - nor should we care much. It wouldn't get here for
approximately a bazillion years anyway.
This is what I alluded to when I said that nonstandard topologies
may be theoretically amusing but not of much practical interest.
I believe de Oliveira-Costa & Smoot (1995, Ap.J. 448, 477 - "Constraints
on the Topology of the Universe from the 2 Year COBE Data") discusses
the present limits. Oh, I found another abstract:
Stevens, Scott & Silk, 1993, Phys Rev Lett 71, 20 -
"Microwave background anisotropy in a toroidal universe."
Abstract: Large-scale cosmic microwave background temperature
fluctuations are calculated for a universe with the topology of a
3-torus. In such a universe only perturbations which are harmonics of
the fundamental mode are permitted. By comparison with data from the
Cosmic Background Explorer satellite, we find that the minimum
(comoving) scale of a cubic toroidal universe is 2400/h Mpc for an n =
1 inflationary model. This is approximately an order of magnitude
greater than previous limits and 80 percent of the horizon scale,
implying that a topologically 'small' universe is no longer an
interesting cosmological model.
--
"If current World Wide Web usage trends continue, as with prior Internet growth,
we project that the US economy will collapse on June 10, 1998, as the rate of
white collar workers going pointy-clicky pointy-clicky all day goes asymptotic."
--- President's Council of Economic Advisors report, 12/1/95 (classified)
Arsenio Novo
Re: Center of Universe? (05 Jan 96 06:09:00)
ko> @MSGID: 99:99/100 62D7758A
ko> I think the question might be better stated as: Where would be the
ko> center of the universe in 3-dimensional space? To answer this would
ko> require knowledge of the actual 'shape' of the universe in that
space,
ko> and I don't believe anyone actually agrees on that.
ko> Paul J. Kossick
ko> kos...@crl.com
Worse yet the universe may be much larger than what we can detect
locally. Our notion of the BB may as an analogy be like a flash bulb
illuminating but a small part of a big ship. We can only detect a part
about 15 billion LY or so in size because our horizon is limited by C.
Looking at the furthest detectable objects is a trip back in time
towards the "center". Since everywhere you look is the "center" then
aren't we perhaps still inside the center but only much later in time?
Wouldn't it be stanger yet if we are at the event horizon of the BB?
Arsenio
Ilja Schmelzer
>I think Hawking
>suggested that the whole 4-dimensional manifold is curved, and that
>the Big Bang and the Big Cruch are just points like any other
>else except for the fact that in a certain system of cordinates
>all coordinates except one (i.e.: the three spacial coordinates
>but not time) converge there (something similar to what happens
>in the surface of the Earth with meridians and paralels).
1. It is not a suggestion of Hawking, but a solution of the Einstein
equations found by Friedman (~1922), which is now the "standard model"
of the evolution.
2. The "big bang" is not a point like the other, but a singularity,
that means in this point it is not a solution of the Einstein
equations.
>If that
>is so, then the "center" of the universe can be conceived only
>with help of a fith dimension, so than the universe is a 4-sphere
>inmersed in a 5-dimencional Euclidean space.
3. There is no center of the universe in these solutions.
4. "Curvature" is a purely mathematical notion. Mathematicians have a
strange habit to use the same name for completely different things, if
only they may be described with the same formulas. Nice and simple for
mathematicians, but often confusing for laymen.
If you measure the distances in a room using a ruler, without
considering any relativistic effects, the "geometry" you obtain is
also "curved" in the mathematical sense. Simply because the
temperature has an influence on the length of your ruler.
"Curved space-time" does not mean that the space-time is really a
curved surface in something higher-dimensional. It also simply
describes the fact that our "rulers" are influenced by the
gravitational field. Nothing more.
Ilja
--
My concept for the quantization of gravity: ~/PG/
--------------------------------------------------------------------------
Ilja Schmelzer, D-10178 Berlin, Keibelstr. 38, <schm...@wias-berlin.de>
my WWW ~ page: http://www.wias-berlin.de/~schmelze
--------------------------------------------------------------------------
Hannu Poropudas
which is dated 5 jan 1996 20:51:27 GMT
mle...@arthur.ma.utexas.edu (Miguel Lerma) wrote:
(I copied article by hand below)
>I guess the closest to this idea is what Richard A. Schumacher says
>in his post: the center is 15 million years in the past (Big Bang).
>But I think this assumes that only the 3-space is curved, and that
>the whole 4-dimensional manifold made up with the whole past, present
>and future history of the universe is Euclidean. It is still possible
>that the universe is even more complicated than that. I think Hawking
>suggested that the whole 4-dimensional manifold is curved, and that
>the Big bang and Big Crunch are just points like any other
>else except for the fact that in a certain system of cordinates
>all coordinates except one (i.e.: the three spacial coordinates
>but not time) converge there (something similar what happens
>in the surface of the earth with meridians and paralels). If that
>is so, then the "center" of the universe can be conceived only
>with help of a fifth dimension, so than the universe is a 4-sphere
>inmersed in a 5-dimensional Euclidean space.
I don't know if above is correct but when I asked Hanna-Maria question
about center of space in due time she answered that the Highest could
not live without the 'big ball in center of the space'. And I
understood that the Universe could not exist if that 'big ball
in center of the space' (= 'big strange crystal', which mass is
about +10^50 kg, and which resists contraction of the space around
it inside 'event horizon', in center of the space) would not exist.
Then I asked her that is center of space in center of Virgo Super
Cluster in center of M87 and she answered yes it is there.
If there does not exist center of the space, then the Universe
could not exist.?
Perhaps it is so that expansion of Universe needs those 'strange
crystals' as a 'springboard' for its expansion.?
Please take a look those README-articles in my directory in anonymous
WWW.FUNET.FI (or FTP.FUNET.FI) pub/doc/misc/HannuPoropudas.
Edward Green
>"Curved space-time" does not mean that the space-time is really a
>curved surface in something higher-dimensional. It also simply
>describes the fact that our "rulers" are influenced by the
>gravitational field. Nothing more.
--
Ed Green
egr...@nyc.pipeline.com
Miguel Lerma
> >I think Hawking
> >suggested that the whole 4-dimensional manifold is curved, and that
> >the Big Bang and the Big Cruch are just points like any other
> >else except for the fact that in a certain system of cordinates
> >all coordinates except one (i.e.: the three spacial coordinates
> >but not time) converge there (something similar to what happens
> >in the surface of the Earth with meridians and paralels).
> 1. It is not a suggestion of Hawking, but a solution of the Einstein
> equations found by Friedman (~1922), which is now the "standard model"
> of the evolution.
>
> 2. The "big bang" is not a point like the other, but a singularity,
> that means in this point it is not a solution of the Einstein
> equations.
Here is where Hawking's claim comes. It seems that quantum
considerations allows to conclude that t=0 it is not really a
singularity, but a "normal" point. I mention it because it
makes more natural the comparison with the surface of Earth.
[...]
> "Curved space-time" does not mean that the space-time is really a
> curved surface in something higher-dimensional. It also simply
> describes the fact that our "rulers" are influenced by the
> gravitational field. Nothing more.
I know that. I was just trying to imagine an scenary in which
the original question could make some sense, and a possibility
is to think of space-time as a submanifold of a higher dimensional
Euclidean space, since only in an Euclidean space the computation
of a "center" makes sense. But physical experience does not allow us
to go beyond intrinsic geometry.
Miguel A. Lerma
Holger Bruns
>In the beginning, the Universe issued from a single point, and was
>composed of a at least 11 dimensions. Then the universe became unstable,
>and all but 3 of the dimensions collapsed, releasing tremendous energies,
>and causing the center of the universe to actualy detach and become a
>free wandering anomolie. The Center of the Universe has been wandering
>around ever since, and has been sought after by the various civilizations
>and species of the galaxy since the dawn of life. It is said that
>whomsoever possesses the true center of the universe possesses infinite
>power to reshape reality and bend others to his will...
Thank you for pointing that out. It sounds like Star Trek....
Holger
Holger Bruns
>In article <4chedk$i...@geraldo.cc.utexas.edu>
>which is dated 4 Jan 1996 20:47:48 GMT
>mle...@arthur.ma.utexas.edu (Miguel Lerma) wrote:
>>Hannu Poropudas (hannu.P...@ericsson.fi) wrote:
>>
>>: By the way do you know where in our Universe is the center of
>>: the space (I mean the mass center of all galaxies).?
>>
>>Probably it is indefined. It is like asking about a center of
>>masses of the continents in the surface of the Earth.
>>
>Earth have a center, but it is outside of Earth's surface.
As far as I know, a center of the universe does not exist. The universe has no
beginning and no end in time and space.
Holger
john baez
>Here is where Hawking's claim comes. It seems that quantum
>considerations allows to conclude that t=0 it is not really a
>singularity, but a "normal" point.
Well, sort of, but it's rather subtler than you might expect.
Ilja Schmelzer
>> 2. The "big bang" is not a point like the other, but a singularity,
>> that means in this point it is not a solution of the Einstein
>> equations.
>Here is where Hawking's claim comes. It seems that quantum
>considerations allows to conclude that t=0 it is not really a
>singularity, but a "normal" point. I mention it because it
>makes more natural the comparison with the surface of Earth.
It is clear that quantum theory has to say something about this
point. It may be that this point becomes a normal point. Everything
may be :-). But it is not a "conclusion" at the current moment. Many
other things may happen with this point.
In my concept of quantum gravity, this point is simply not part of the
complete solution (see ~/PG/bibBang.html).
Ilja Schmelzer
>>"Curved space-time" does not mean that the space-time is really a
>>curved surface in something higher-dimensional. It also simply
>>describes the fact that our "rulers" are influenced by the
>>gravitational field. Nothing more.
>You speak with great confidence about the unknowable.
The reverse is true.
That the rulers are influenced by the gravitational field is the only
thing we _know_. We can measure it and speak with great confidence
about this effect.
The other things which people usually associate with the notion of
"curved space-time" are the "unknowable". Nonetheless many (other)
people speak with great confidence about them.
mikko....@vtt.fi
>The universe has no beginning and no end in time and space.
For space, that seems to be true; if there is an edge of any
kind, it is so far that we can't see it. But for time, the
world looks different: it looks like it had existed only a finite
time.
-----------------------------------------------------------------
Mikko J. Levanto Tel. +358 81 551 2448
VTT Electronics Fax +358 81 551 2320
P.O.Box 1100 Internet: Mikko....@vtt.fi
FIN-90571 Oulu, Finland
--------------- VTT - Technical Research Centre of Finland ------
Richard A. Schumacher
>You big thinkers aren't listening to the question. Forget the math for a
>minute and listen. I want to know where the center of the universe is
>located. When I stand outside at night and look at the Southern Cross,
>or Ursa Major, or Polaris or whatever. I want to point to one of them
>and say, "So the Center of the Universe is that way." Can't one of you
>answer that question?
No, at least not with the kind of answer you want, because the question
is ill-formed. There is no point in the universe which could be called
the center any more than any other point. Now, do you want to know _why_
that is so?
Maybe we should go back to the old terminology used in popular
descriptions of cosmology before 1965 or so. Then the two possibilities
for the global structure or "shape" of the universe were described as
"infinite" and "finite but boundless". These may seem a bit mysterious,
but at least they don't encourage the reader to think erroneously of a
"center".
Henry Warwick
>Wouldn't it be stanger yet if we are at the event horizon of the BB?
Being a mere novice in such matters, I am not certain- but I do
believe that our fair galaxy IS at the event horizon of the BB from
the perspective of those fine and lovely sentient critturs who are
located in the distant galaxies that evolved from the QSOs and red
shifted blobs that we percieve to be at OUR Event Horizon.
Mr Warwick
====================================================================
"In the beginning there was this turtle....
====================================================================
john baez
>That the rulers are influenced by the gravitational field is the only
>thing we _know_. We can measure it and speak with great confidence
>about this effect.
>
>The other things which people usually associate with the notion of
>"curved space-time" are the "unknowable". Nonetheless many (other)
>people speak with great confidence about them.
There's nothing wrong with speaking about the unknowable. You can say
whatever you want about it, since we'll never know if you're right. The
thing to keep in mind, though, when speaking about the unknowable, is
that you shouldn't get upset if someone else says the opposite of what
you do! It's perfectly fine for them to say whatever they want, too.
That's why it's perfectly acceptable to speak of "curved spacetime" and
so on as is usually done in general relativity, and it's also perfectly
acceptable to say that spacetime is not curved and that it's just the
rulers that get stretched.
Bob Baker
>In article <4csjnr$r...@geraldo.cc.utexas.edu> mle...@arthur.ma.utexas.edu (Miguel Lerma) writes:
>
>>> 2. The "big bang" is not a point like the other, but a singularity,
>>> that means in this point it is not a solution of the Einstein
>>> equations.
>
>>Here is where Hawking's claim comes. It seems that quantum
>>considerations allows to conclude that t=0 it is not really a
>>singularity, but a "normal" point. I mention it because it
>>makes more natural the comparison with the surface of Earth.
>
>It is clear that quantum theory has to say something about this
>point. It may be that this point becomes a normal point. Everything
>may be :-). But it is not a "conclusion" at the current moment. Many
>other things may happen with this point.
>
>In my concept of quantum gravity, this point is simply not part of the
>complete solution (see ~/PG/bibBang.html).
>
>
>--
>My concept for the quantization of gravity: ~/PG/
>--------------------------------------------------------------------------
>Ilja Schmelzer, D-10178 Berlin, Keibelstr. 38, <schm...@wias-berlin.de>
>my WWW ~ page: http://www.wias-berlin.de/~schmelze
>--------------------------------------------------------------------------
You big thinkers aren't listening to the question. Forget the math for a
Kevin Johnson
> In article <4d24ih$7...@agate.berkeley.edu>,
> t...@physics12.Berkeley.EDU (Emory F. Bunn) wrote:
> >
> >Or maybe you aren't listening to the answers. The answer, as several
> >of us have said, is that as far as we know there is no such place.
> >
> In other words, it isn't that there is no such place. Its just that they
> can't answer your question. The original question is a fair one, however.
Is this a fair question? WRT the location of our solar system right now,
what is a good estimation of the location of the origin of the Universe
when it first formed? No answer?
--
_____ _____ _____ | "The problem of the | Kevin Johnson
\ \/ /\/ /\ (R) | outsider is that he sees | kevin....@waii.com
\ / / / / \ | too deeply and too much, |_______________________
\ / / / / \ | and what he sees is |
\____/\/____/\_____\ | essentially chaos." | My company doesn't
| -- The Outsider, | agree with me about
WESTERN GEOPHYSICAL | Colin Wilson | anything.
Tom Gossman
t...@physics12.Berkeley.EDU (Emory F. Bunn) wrote:
>
>Or maybe you aren't listening to the answers. The answer, as several
>of us have said, is that as far as we know there is no such place.
>
In other words, it isn't that there is no such place. Its just that they
can't answer your question. The original question is a fair one, however.
Thomas L Gossman (Tom) thomas....@wmich.edu
FCL/Haworth College of Business Phone: 616-387-5524
Western Michigan University FAX: 616-387-5710
Kalamazoo MI 49008-3811
"Outside of a dog, a book is man's best friend. Inside of a dog,
its too dark to read." --Groucho Marx
Richard A. Schumacher
>An assertion that "it is currently believed (by most cosmologists)" and
>another assertion that the question is just plain nonsense make me very
>suspicious.
And yet this is the case. One should always be prepared to suspect that
one does not know the whole story :->
>It seems logical that when we had the Big Bang, and space was
>created forming out in all directions, it all began at some point which is
>still there in that created space. Of course science can be contrary to
>common logic, but so far I have seen noting to indicate that there is any
>accpted theory (beyond assertions) that such is the case here.
Accepted theories are mostly similar to the Robertson-Walker metric.
The universe is either infinite and will expand forever, or is
finite _but with no boundary_ and will one day collapse on itself
again. You can read much more about the current state of affairs
in "In Search of the Big Bang" by John Gribben, and "The First
Three Minutes" by Steven Weinberg. They explain what we think we
know about the universe, and why we think we know it.
>As to the questions being nonsense, I disagree. It is a perfectly rational
>question, unlike a question about the color of time, etc.
They're both valid in the sense that asking them allows one
to clear up some evident misconceptions in the questioner
(time has no color, the universe need not have a center).
Ville Sinkko
: By the way do you know where in our Universe is the center of
: the space (I mean the mass center of all galaxies).?
Just listen for the sound of the flutes... ;)
--
65
Zn
30
Miguel Lerma
[...]
> So far you've been offered three answers:
> 1. There is no center (dominant answer)
> 2. The question is ill-posed (We're not sure what to say)
> 3. Each point anywhere at all is the "center"
Let me pose the subject in another way. Let's try the following
definition of "center" of the universe:
The mass center of the universe is the point of position
vector R such that:
(1/M) SUM (r_i - R) m_i = 0
where M is the total mass of the universe, m_i is the mass
of the i-th particle of the universe, r_i is a position vector
of that particle, and the sum goes throght all the particles in
the universe.
Posed that way, the problem looks like just solving an equation
with an unknown R, right? If the universe has a center, the equation
should have a unique solution. No center (answer "1" above) could mean
that the equation has no solution (although I think that many people
answering "1" actualy mean "2"). "Any point is the center"
(answer "3") means that the equation is indeterminate. But the
fact is that in the currently accepted models of the universe,
there are no such a thing as vectors "r_i", so the equation
cannot be even posed. The right answer is "2" (at least according
to current models), but we do know what to say: the question rests
on wrong assumptions. The universe lacks a center not because the
equation has no solutions, but because there is not even equation.
Miguel A. Lerma
Mahipal Singh Virdy
Bob Baker <rba...@foothill.net> wrote:
>
>You big thinkers aren't listening to the question. Forget the math for a
>minute and listen. I want to know where the center of the universe is
>located. When I stand outside at night and look at the Southern Cross,
>or Ursa Major, or Polaris or whatever. I want to point to one of them
>and say, "So the Center of the Universe is that way." Can't one of you
>answer that question?
I'm a mechanical engineering by the "training". Let me try answer.
So far you've been offered three answers:
1. There is no center (dominant answer)
2. The question is ill-posed (We're not sure what to say)
3. Each point anywhere at all is the "center"
The question of center is complicated because one has to define what
integer dimension (1,2,3,4, ..., Multi, ..., Inf) our Universe is.
That's a hotly debated issue and thus there can be no concensus among
the holders of the varying perspectives. You want to bypass all that
gibberish. I'm with you! ;-)
At any frozen time instant, the Universe is 3 spatial dimensions. Don't
wake up any of the string theorists because no one knows what plane
they're on at any given moment. 10, 26? Let's say space is just 3D and
time is frozen dead still. A Kodak Moment. Where's the center in this
sense?
You want the geometric center, the mass weighted center, the temperature
weighted center, the money weighted center, or ...? There are many
useful centers to define. Let's assume you mean the geometric center. In
this sense, think of a Cartesian Grid. Where's point (0,0,0) becomes
your question.
Space extends for infinty in all direction. At least, observably we here
on Earth can see equally far in all directions. According to many
models, this would be true no matter where you translate yourself in the
Universe. Of course, this is untestable and unprovable for all intents
and practical purposes.
To me, this means that the center is where ever you want it to be! It's
undefinable yet everywhere. The expanding surface of the baloon analogy
is used to make this point that all points are equivalent centers. I'm
sure this is *not* what you wanted to hear, read I mean.
Let me ask you, where's the center of one's "mind"? Does it bother you
in any significant way that a human can't exactly locate a center even
within the spatial confines of one's own self?
The Universe is a 4D object as a minimum. ... How about this, the center
of the Universe is precisely every place where you instanteously happen
not to be? ;-) That is if you can't *handle* the idea of a Universe
centered around you. Enjo(y).
[I could go on but I tire...]
Mahipal |meforce>
http://www.princeton.edu/~msvirdy/index.html
Miguel Lerma
> An assertion that "it is currently believed (by most cosmologists)" and
> another assertion that the question is just plain nonsense make me very
> still there in that created space. Of course science can be contrary to
> common logic, but so far I have seen noting to indicate that there is any
> accpted theory (beyond assertions) that such is the case here.
Well, sometimes science is contrary to a naive extrapolation of
common experience. For instance, the most natural extrapolation
of what we see arround us is to believe that the surface of the
Earth is flat, and perhaps either extended infinitely in all
directions, or ending somewhere. So it could seem natural to
ask where the border of the surface of the Earth is. However
it is currently believed (by most geographers) that the Earth
is not flat, but round like a sphere, so the question, even if
perfectly acceptable, actually does not make sense, because
it rests on a wrong assumption (i.e.: that the Earth is flat).
The idea of the space forming out in all directions from a
starting is another kind of missconception. The points of
the space have no individual indentity, so the question of
if some point is the one where the Big Bang started does
not make any sense either. When we talk of some place on
Earth, such as Paris, or the dinner room in my house, we
are not talking about space, but about material objects.
What remains is the object (Paris, a room, or whatever),
not the "space". Anyway, it reminds me of an old joke about
a man who had a stick that was too long, so he decided to
cut out its golden handle. When someone asked why he didn't
cut the stick at the other end, he answered: "at the other
end the stick was ok, it is at the handle end where it was
too long".
> As to the questions being nonsense, I disagree. It is a perfectly rational
> question, unlike a question about the color of time, etc.
I think it is a perfectly understable question, but if the
universe is as cosmologists currently believe, then that
question rests on wrong assumptions.
So you are claiming that the "color of time" is a nonsense?
How do you know? What do we know about the nature of time?
Miguel A. Lerma
P.S.: By the way, the members of the Flat Earth Society
claim that the Earth is flat, so the "theory"
that the Earth is round is not universally accepted.
Emory F. Bunn
Bob Baker <rba...@foothill.net> wrote:
:You big thinkers aren't listening to the question. Forget the math for a
:minute and listen. I want to know where the center of the universe is
:located. When I stand outside at night and look at the Southern Cross,
:or Ursa Major, or Polaris or whatever. I want to point to one of them
:and say, "So the Center of the Universe is that way." Can't one of you
:answer that question?
Or maybe you aren't listening to the answers. The answer, as several
of us have said, is that as far as we know there is no such place.
-Ted
john baez
>john baez (ba...@guitar.ucr.edu) wrote:
>: There's nothing wrong with speaking about the unknowable. You can say
>: whatever you want about it, since we'll never know if you're right.
>The funny thing about the unknowable is that it has a nasty habit of
>becoming known.
The unknown becomes known quite often, the unknowable less so. But
when it does, it wasn't really the unknowable after all, so you should
have been more careful about what you say about it.
Jeff Candy
>In article <4d24ih$7...@agate.berkeley.edu>,
> t...@physics12.Berkeley.EDU (Emory F. Bunn) wrote:
>>
>>of us have said, is that as far as we know there is no such place.
>>
>can't answer your question. The original question is a fair one, however.
Before you can ask, "what is the centre of the universe?",
you have to define the "centre of the universe". The geometry
of space-time is more complicated than the flat 3-D space which
forms the basis of most people's intuition, and an analogue to
the concept "centre" not immediately obvious. Define the concept
of centre and we'll tell you the answer, or point out how it can be
estimated. By one definition, the "centre" is at t=0+, for reasons
which have already been discussed.
This thread reminded me of the impossible-to-explain (sometimes)
question "what happened before the big bang?". Since the space-time
manifold is concieved to be a set open at t=0 (i.e., the universe
exists only for t>0), the question is ill-posed. This answer
typically illicits the response, "yeah, but what happened before
that???".
Jeff Candy ... man -- every man -- is an end
Analytic Theory Group in himself, not the means to the
JET Joint Undertaking ends of others ...
--- Ayn Rand
===============================================================================
The above article is the personal view of the poster and should not be
considered as an official comment from the JET Joint Undertaking
===============================================================================
Miguel Lerma
> In article <4d24ih$7...@agate.berkeley.edu>,
> t...@physics12.Berkeley.EDU (Emory F. Bunn) wrote:
> >
> >Or maybe you aren't listening to the answers. The answer, as several
> >of us have said, is that as far as we know there is no such place.
> >
> In other words, it isn't that there is no such place. Its just that they
> can't answer your question. The original question is a fair one, however.
Not at all. If the universe is as it is currently believed to be
(by most cosmologists), then there is _no_ point that can be called
"the center of the universe" for any reasonable definition of the
term (some of us have been making a big effort of imagination trying
to make some sense of the question). It is like asking about the border
of a borderless surface (such as the surface of the Earth), or about the
"last" natural number, about the colour of time, or about the sex of the
last angel that can be put in the head of a pin. It is not that the answer
is unkonwn, or even that the question has no answer... in some way the
"question" is not even a question, but plain nonsense.
Note that I am not saying that such a question should not be asked.
It is perfectly right to honestly ask nonsense questions, but then
the right answers are going to deal rather with the nature of the
question and the hidden assumptions behind it.
Miguel A. Lerma
BEN
> Is this a fair question? WRT the location of our solar system right now,
> what is a good estimation of the location of the origin of the Universe
> when it first formed?
Right here. Out there. Everywhere.
Ben
Richard A. Schumacher
>>Or maybe you aren't listening to the answers. The answer, as several
>>of us have said, is that as far as we know there is no such place.
>>
>In other words, it isn't that there is no such place. Its just that they
>can't answer your question. The original question is a fair one, however.
No, it ain't. The only answer a cosmologist can give to the original
question is: to the best of human knowledge there is _no such place_.
The universe is either infinite, or finite but unbounded. Neither of
those possiblities has a center.
Clear enough?
john baez
>You big thinkers aren't listening to the question. Forget the math for a
>minute and listen. I want to know where the center of the universe is
>located. When I stand outside at night and look at the Southern Cross,
>or Ursa Major, or Polaris or whatever. I want to point to one of them
>and say, "So the Center of the Universe is that way." Can't one of you
>answer that question?
Sure, the center is in the direction of Antares.
Of course, this answer is complete bullshit, because the question is
meaningless. But if you want an answer anyway, this is as good as any.
Richard E. Carney
>:located. When I stand outside at night and look at the Southern Cross,
>:or Ursa Major, or Polaris or whatever. I want to point to one of them
>:and say, "So the Center of the Universe is that way." Can't one of you
>:answer that question?
>
>of us have said, is that as far as we know there is no such place.
>
The problem is that you have to stop thinking of the universe as a 'regular'
3-d object. If you take a sphere or a cube, you can explicitly say where the
centre is - in the case of the cube where the diagonals intersect. However,
thinking of the universe or space in such a way is wrong. Well not so much
incorrect as misleading, in the same way that considering atoms via the
billiard
ball model can be misleading. (c.f. QM)
I imagine that you consider yourself to be inside a large spherical
shell (the universe) and want to know which way to the centre of the shell.
Well look at it this way: If you are on a surface, the surface of the earth
say,
which direction will take you to the centre of the surface. Whichever direction
you choose will be the same and just move you to a different point. After you
have moved you are still no nearer or further away from your desired central
point. In this case if you keep going in the chosen direction for long enough
you will come back to where you started from.
This is how the earths surface can be finite in area but have no boundary. An
analogous version can be applied to the universe (although it is in a higher
order than a 2-d surface).
Hopefully this will have clarified things a little.
john baez
>I would tend to avoid saying that the question of where the center of
>the Universe is is "nonsense," since that's such a pejorative term,
>and you have to have studied the subject some before you understand
>why it's not a good question to ask. It turns out, however, that it's
>not a good question to ask. Specifically, it appears to be a question
>without an answer.
Ted Bunn is being levelheaded, evenhanded and fair here, as usual. In
more peevish responses, various people (including me) have been saying
that the question is "meaningless", "nonsense", or various other nasty
things.
The point is this: there are lots of questions in physics that start out
sounding like very interesting, important questions. Sometimes,
however, it turns out that --- as far as we can tell! --- they have no
answer. The reason is that the universe just isn't built in the way
that the question implicitly presupposed. For example, the question
of how many angels can fit on the head of a pin turns out to be
unanswerable when we find out there aren't any angels, or that angels
aren't the sort of thing that you can stack on a pinhead.
Now, when this happens, it doesn't mean the question wasn't worth asking
in the first place. Often the only way you can learn that the
presuppositions of your question were wrong is by asking the question
and doing your best to answer it! Gradually you realize you have hit a
dead end... and then you turn around, back out, and go somewhere new and
interesting.
One must always be open to the possibility that a given question will turn
out to have no answer... or at least, no answer *as far as we can tell*.
One shouldn't pigheadedly demand an answer after someone gently informs
one that the question has no answer. Instead, one should try ones best
to understand how the question could have no answer... and to see if it
does or not.
One learns amazing things when one learns that an interesting question has no
answer. It's an experience to be relished!
BEN
(Matthew Jones) writes:
> If all the galaxies have flying apart ever since the big bang then
> shouldn't it be possible to work out the direction they are travelling in
> and therefore the direction that they came from? If this was done for all
> the galaxies then shouldn't these lines all cross at some point which
> would make that the center of the universe?
Indeed, you can do that, and you will find that they are all moving
directly away from us.
Any observer anywhere else will see the same thing.
So, can you now answer the question?
Ben
Bob Silverman
Matthew Jones <mat...@mcb.net> wrote:
>If all the galaxies have flying apart ever since the big bang then
>shouldn't it be possible to work out the direction they are travelling in
>and therefore the direction that they came from? If this was done for all
>the galaxies then shouldn't these lines all cross at some point which
>would make that the center of the universe?
>
>why this is wrong but I am just curious as to why this wouldn't work.
Put some black dots on a deflated balloon. Now blow up the balloon.
The back dots all move away from each other, don't they?
The "universe" is represented by the surface of the balloon. Where
is the center? The center of the balloon is well-defined, but that
center is not part of the universe. The universe is given by only
the surface of the balloon.
--
Bob Silverman
The MathWorks Inc.
24 Prime Park Way
Natick, MA
Matthew Jones
shouldn't it be possible to work out the direction they are travelling in
and therefore the direction that they came from? If this was done for all
the galaxies then shouldn't these lines all cross at some point which
would make that the center of the universe?
Notice that I have posed this as a question as I'm sure there is a reason
why this is wrong but I am just curious as to why this wouldn't work.
Thanks in advance.
/-------------------------+------------+--------------\
| Matthew Jones | Dex on | The Truth Is |
| mat...@mcb.net | IRC | Out There |
\-------------------------+------------+--------------/
Paul Budnik
: The unknown becomes known quite often, the unknowable less so. But
: when it does, it wasn't really the unknowable after all, so you should
: have been more careful about what you say about it.
For example you should be careful about claiming that probabilities
are irreducible. Someday someone may reduce them.
--
Paul Budnik
pa...@mtnmath.com, http://www.mtnmath.com
allan padgham
from where you are.
Sebastien Lepine
>If all the galaxies have flying apart ever since the big bang then
>shouldn't it be possible to work out the direction they are travelling in
>and therefore the direction that they came from? If this was done for all
>the galaxies then shouldn't these lines all cross at some point which
>would make that the center of the universe?
Astronomers observe all distant galaxies to be redshifted, wherever they are
looking in the sky. If you extrapolate their "movement" backwards, you reach
the conclusion that YOU ARE the center of the universe, because all their
"travelling lines" cross just where we are (apart from some small deviations
that are due to the local movement of our galaxy); every distant galaxy is
exactly going away from us.
However, you should reach the same conclusion wherever you are in the universe!
Why? Because the galaxies are not travelling away from some definite point
(like shrapnels from an exploding grenade), but rather going AWAY
FROM EACH OTHER (like raisins in a rising cake).
That's why the question "Where is the center of the universe?" is so subtle,
because the "center" is (if we refer to the recession of galaxies) everywhere
at the same time.
--
Sebastien Lepine
Hannu Poropudas
v...@clinet.fi (Ville Sinkko) wrote:
>Just listen for the sound of the flutes...;)
Anisotropy of cosmic background radiation could also
indicate very slow rotational angular frequency of
the Universe.?
How this kind rotation is possible if it does
not happen as rotation about the center of space.?
The topology of the Universe may be weird and complicated,
it is possible also question about 10 dimensional curved
space, where 6 dimensions could be curled up into very
small scale and we know nothing about them (and possible
we will never know much about them as I have understood),
so it could be safe always not to say anything certain
about structure of the Universe.?
I would also to remind that I'am only an amateur physicist
and that is why my understanding about these matters is far
from complete and my writings could contain my own errors.
--
Best Regards,
Hannu Poropudas.
"It's Not What You Know That Matters
... It's Knowing What You Don't."
Emory F. Bunn
Tom Gossman <gos...@hcob.wmich.edu> wrote:
>An assertion that "it is currently believed (by most cosmologists)" and
>another assertion that the question is just plain nonsense make me very
>suspicious.
I would tend to avoid saying that the question of where the center of
the Universe is is "nonsense," since that's such a pejorative term,
and you have to have studied the subject some before you understand
why it's not a good question to ask. It turns out, however, that it's
not a good question to ask. Specifically, it appears to be a question
without an answer.
>It seems logical that when we had the Big Bang, and space was
>created forming out in all directions, it all began at some point which is
>still there in that created space.
I don't know what you mean by "logical" here. That certainly is a
logical possibility; it's also a logical possibility that there is no
such point. I think what we're talking about here is not logical
possibility but intuitive plausibility. To many people the notion of
expansion without a center is intuitively hard to grasp or
implausible. That's perfectly natural, but it's important to remember
that the Universe is not required to behave in ways that please our
intuition.
>Of course science can be contrary to
>common logic, but so far I have seen noting to indicate that there is any
>accpted theory (beyond assertions) that such is the case here.
Again, I think you mean something more like "intuition" than "logic"
here. I'm unaware of any scientific theories that are intrinsically
illogical, but many are counterintuitive to the uninitiated. Quantum
mechanics and relativity are the classic examples; the big bang
seems to be another.
>As to the questions being nonsense, I disagree. It is a perfectly rational
>question, unlike a question about the color of time, etc.
I agree. It's a rational question that happens to have no answer, as
far as we know.
-Ted
Wilbert Dijkhof
>>>
>>>Or maybe you aren't listening to the answers. The answer, as several
>>>of us have said, is that as far as we know there is no such place.
>>>
>>can't answer your question. The original question is a fair one, however.
>
>you have to define the "centre of the universe". The geometry
>of space-time is more complicated than the flat 3-D space which
>forms the basis of most people's intuition, and an analogue to
>the concept "centre" not immediately obvious. Define the concept
>of centre and we'll tell you the answer, or point out how it can be
>estimated. By one definition, the "centre" is at t=0+, for reasons
>which have already been discussed.
>
>This thread reminded me of the impossible-to-explain (sometimes)
>question "what happened before the big bang?". Since the space-time
>manifold is concieved to be a set open at t=0 (i.e., the universe
>exists only for t>0), the question is ill-posed. This answer
>typically illicits the response, "yeah, but what happened before
>that???".
>
>
>
>Jeff Candy ... man -- every man -- is an end
>Analytic Theory Group in himself, not the means to the
>JET Joint Undertaking ends of others ...
> --- Ayn Rand
>
>
>===============================================================================
> The above article is the personal view of the poster and should not be
> considered as an official comment from the JET Joint Undertaking
>===============================================================================
Ever heard of:
- Superstringtheory : The Big-Bang (didn't start at t=0 but at t=10^(-43)) is
by-product of the collapsing of the 10 dimensional universe
in a 4 and 6 dimensional one.
- The oscillating universe: There happened indeed something (= Big-Crunch of the former
universe) at/before t=0.
* The 4-dimesional universe didn't exist only for t>0, but since 10^(-43) since
time is quantizited. The 10-dimensional universe hovever did exist between t=0 and
t=10^(-43).
WDijkhof
Edward Green
>>As to the questions being nonsense, I disagree. It is a perfectly
rational
>>question, unlike a question about the color of time, etc.
>
>I agree. It's a rational question that happens to have no answer, as
>far as we know.
the color of time". If the universe conforms to certain models, than it
no more has the property "center" than time has the property "color". The
difference is, no theory of time appears to map time to color space,
while some models of the universe would place it in the category "things
that have a center". But the question whether the universe is in this
category is itself open, though consensus is tending to "no".
Now watch, somebody will say "time is red".
--
Ed Green
egr...@nyc.pipeline.com
Emory F. Bunn
Hannu Poropudas <Hannu.P...@ericsson.fi> wrote:
>Anisotropy of cosmic background radiation could also
>indicate very slow rotational angular frequency of
>the Universe.?
Actually it can't. Although rotation of the Universe would indeed
produce anisotropy in the microwave background radiation, it would
produce a pattern of anisotropy that's quite different from what
we actually see.
>How this kind rotation is possible if it does
>not happen as rotation about the center of space.?
It turns out, somewhat surprisingly perhaps, that it's possible for
the Universe to rotate and yet to have no center. That is, it can
have "angular momentum" about any point you choose to regard as the
center, even if all points look exactly the same. People seem to
regard this fact as even more surprising than the fact that the
Universe can expand without a center, but maybe that's just because
they're less used to thinking about rotating Universes.
-Ted
Edward Green
>
>It turns out, somewhat surprisingly perhaps, that it's possible for
>the Universe to rotate and yet to have no center. That is, it can
>have "angular momentum" about any point you choose to regard as the
>center, even if all points look exactly the same. People seem to
>regard this fact as even more surprising than the fact that the
>Universe can expand without a center, but maybe that's just because
>they're less used to thinking about rotating Universes.
like the universe has a "curl"; not what we would consider a rigid body
rotation, but a kind of an extended intensity of rotation. Is that about
right?
I assume the language of this observation is GR, and hinges on
identification of certain terms with angular momentum, and the existence
of solutions in closed universes in which these terms are non-zero. Still
close?
--
Ed Green
egr...@nyc.pipeline.com
Ilja Schmelzer
>Now watch, somebody will say "time is red".
Reasonable. Looking back in time we see things redshifted. As more
time has been left, as more redshifted.
Obviously time is red :-)
Ilja
--
My concept for the quantization of gravity: ~/PG/
--------------------------------------------------------------------------
Ilja Schmelzer, D-10178 Berlin, Keibelstr. 38, <schm...@wias-berlin.de>
my WWW ~ page: http://www.wias-berlin.de/~schmelze
--------------------------------------------------------------------------
Hannu Poropudas
t...@physics12.Berkley.EDU (Emory F. Bunn) wrote:
>In article <4d55r2$1...@lmfpub.lmf.ericsson.se>,
>Hannu Poropudas <Hannu.P...@ericsson.fi> wrote:
>>Anisotropy of cosmic background radiation could also
>>indicate very slow rotational angular frequency of
>>the Universe.?
>
>Actually it can't. Although rotation of the Universe would indeed
>produce anisotropy in the microwave background radiation, it would
>produce a pattern of anisotropy that's quite different from what
>we actually see.
Could it then be possible that our Milky Way galaxy would be situated
in one of 'event horizons' of the Universe (='radiation peripheries')
which 'event horizon' (='radiation preiphery') would rotate very slowly
about 'center of space'.?
(This kind of rotation was indicated by arrows very clearly
in one H-M's drawing.)
What kind of anisotropy pattern this would cause in the cosmic
background radiation.?
Victor Grauer
<4d46o5$4...@geraldo.cc.utexas.edu>
<matthew-1201...@mattsmac.mcb.net>
<4d6jhb$k...@epervier.CC.UMontreal.CA>: Distribution: world
Finally after studying for a week all the many interesting responses to
the question about the center of the universe, I find that I finally have
the answer to the question _I_ originally posed: If the farther out into
the depths of the universe we go, the closer we get in time to the Big
Bang, doesn't that mean that the center of the universe (the place where
the Big bang originated) is at the periphery?
No one really provided a completely satisfactory answer, so I had
to figure it out myself (you all helped).
Here it is --
The center of the universe is indeed "everywhere", but not quite.
It is everywhere only at a point in time billions of years in the past.
The periphery of the universe seems privileged (closer to the center)
because the fact that it is so far away means that we are seeing it at a
_time_ when it was close to the time of the big bang. We are so close to
the space we are in that we cannot see what it was like in the distant
past in and around where we are now. Thus we have the illusion that the
distant past took place in an area that is _spatially_ distant. If we
could see the distant past of the space we are now in, we would also see
remnants of the Big Bang. Thus the center of the universe is not at the
periphery and we do not need Hawking to save us. We have me. But really,
I couldn't have done it without the help of all the wonderful people on
this thread.
Hannu Poropudas
of the same subject, I wrote:
>Could it then be possible that our Milky Way galaxy would be situated
>in one of 'event horizons' of the Universe (='radiation peripheries')
>which 'event horizon' (='radiation preiphery') would rotate very slowly
>about 'center of space'.?
I would like to correct this text as (please take a look
those H-M's drawings in anonymous computer www.funet.fi which
I have mentioned perhaps I'am not able to explain everything correctly):
Our Milky Way galaxy would be situated in the side of one 'event horizon'
of the Universe (='radiation periphery') where neutrinos can move freely
(this is essentially expanding side of the Universe in the largest scale).?
Universe may consist hundreds of thousands of such 'radiation peripheries'
around 'big color strange crystal in center of space' each of which
'radiation periphery' could have time difference 100000-300000 years.?
The other part of the Universe is that where those 'neutrino cages'
(areas which absorb neutrinos) are (this is essentially contracting
side of the Universe in the largest scale).?
The repeating structure in the Universe would be expanding and contracting
part and between them 'radiating periphery' (multidimensional 'mirror'
was in it).?
'Event horizon (='radiating periphery') is not expanding and it
not also contracting (it is perhaps multidimensional 'mirror'
in H-M's drawings, see that drawing which was detail structure
of it, it was consisted of different types of neutrinos from
both sides of the Universe).?
Question:
--------
Q. If these 'radiation peripheries' would rotate very slowly
about 'the center of space' (as this kind of rotation was indicated
by arrows very clearly in one H-M's drawing) and if it would be
like I tried to describe above then what kind of anisotropy pattern
Jeppe Stig Nielsen
I think what has been found out about the universe is derived using the
following assumptions:
1: Cosmos is homgenous, i.e. invariant under translations, at large scale.
This means the universe behaves the same in any point.
2: Cosmos is isotrope, i.e. invariant under rotations, at large scale.
So, it is the same in any direction.
Introducing in any way a centre of the universe would contradict (1).
Therefore, all known theories of the universe become meaningless, if one
assumes a centre.
The current theories are capable of explaining a lot of observations.
No-one has ever observed anything indicating the existence of a universal
centre.
There is nothing illogical about a space without centre.
Consider for example these two-dimensional cases:
A: An (infinite) plane. No point is more `centre' than another.
B: A sphere, i.e. the surface (and only the surface) of a three-dim. ball.
This space is two-dimensional (use as coordinates longitude and lattitude),
and of finite area. No point of the sphere is different from the others.
C: The surface of an infintely long cylinder. This space is bounded in one
direction and unbounded in the other.
Of course, the universe isn't two-dimensional (its spatial part is 3D and
according to the theory of relativity it can be described by a 4D space-time)
but the spaces like A, B and C generalizes to higher dimensions easily.
It is still unknown what the geometry of the universe really is and we don't
know if its volume ("3D area") is finite.
/Jeppe
Daniel Victor Tausk
view than in fact any set of particles must have a center of mass.
But, if you consider general relativity instead, I know of no definition
of center of mass. In general relativity theory the universe is
considered to be a pseudo-Riemannian 4-dimensional manifold, and there is
probably no definition of center of mass for a general pseudo-Riemannian
manifold. In fact, the most popular model of the universe is (as an
aproximation) the homogeneus model. In that case, it's obviously
impossible to define center of mass, since in an homogeneus space no
point is better than any other point.
So, since there is no meaning to consider this kind of cosmology question
from the Newtonian viewpoint, the answer is just that center of mass can
not be defined.
Keith Ramsay
mle...@arthur.ma.utexas.edu (Miguel Lerma) writes:
|Let me pose the subject in another way. Let's try the following
|definition of "center" of the universe:
|
|The mass center of the universe is the point of position
|vector R such that:
|
| (1/M) SUM (r_i - R) m_i = 0
|
|where M is the total mass of the universe, m_i is the mass
|of the i-th particle of the universe, r_i is a position vector
|of that particle, and the sum goes throght all the particles in
|the universe.
|
|Posed that way, the problem looks like just solving an equation
|with an unknown R, right?
It looks like it, but there is a catch. The vector algebra you
are using only works in the usual way for vectors in space when
space is not curved.
For example, given three points R, r1 and r2, you need to be able
to find the sum of the vectors from R to r1 and from R to r2. One
typical way of defining this sum is to construct a parallelogram
with vertices R, r1, r2, r3, and consider the vector from R to r3.
In Euclidean geometry, you can make parallelograms, but the real
world seems not to work quite like that. Euclidean geometry is
only a good approximation for local areas. Try drawing a parallelogram
on the surface of a sphere and you'll probably see what sort of problem
arises.
It also assumes a finite-mass universe.
In article <matthew-1201...@mattsmac.mcb.net>,
mat...@mcb.net (Matthew Jones) wrote:
|If all the galaxies have flying apart ever since the big bang then
|shouldn't it be possible to work out the direction they are travelling in
|and therefore the direction that they came from? If this was done for all
|the galaxies then shouldn't these lines all cross at some point which
|would make that the center of the universe?
Direction of motion as usually defined is defined only relative to
a frame of reference. There seems not to be any "natural" choice of
frame of reference which would make this quest for a center pan out.
You can make a frame of reference in which the galaxies near here are
generally moving away from here, but that's artificial-- one could
do the same thing for someplace else as well.
Of course there have been theories which if true would imply that one
place was a natural "center", but I've never seen any evidence of such
a theory being correct.
Keith Ramsay
DAMMIT ALL
: gra...@oberon.pps.pgh.pa.us (Victor Grauer) wrote:
: > The center of the universe is indeed "everywhere", but not quite.
[. . .]
: 1: Cosmos is homgenous, i.e. invariant under translations, at large scale.
: This means the universe behaves the same in any point.
Y'all are arguing some theology it'd take centuries of centuries
of irrelevant ecumenical councils to settle into orthodoxy while
all around you stars to-and-fro in the dance of oblivion. This is
where "Science" took a wrong turn: who cares where it came from if
you don't know what it is or what to do with it, and how can you
argue about whether it has a center if you don't what it is?
David
--
i practice philosophy only in self-defense
I PRACTICE PHILOSOPHY ONLY IN SELF-DEFENSE
(--Gordon Fitch, 11 Jan. 1996)
Emory F. Bunn
>>It turns out, somewhat surprisingly perhaps, that it's possible for
>>the Universe to rotate and yet to have no center. That is, it can
>>have "angular momentum" about any point you choose to regard as the
>>center, even if all points look exactly the same. People seem to
>>regard this fact as even more surprising than the fact that the
>>Universe can expand without a center, but maybe that's just because
>>they're less used to thinking about rotating Universes.
>
>Well, pursuing the analogy with expansion, I assume this means something
>like the universe has a "curl"; not what we would consider a rigid body
>rotation, but a kind of an extended intensity of rotation. Is that about
>right?
Yes. Specifically, you can fill the Universe with matter and give that
matter a velocity field that has a curl at every point. If you do
then the Universe looks like it's rotating about whatever point you
choose to regard as its center.
>I assume the language of this observation is GR,
Yes.
>and hinges on
>identification of certain terms with angular momentum, and the existence
>of solutions in closed universes in which these terms are non-zero. Still
>close?
Yes. As it turns out, the identification of angular momentum is not
particularly tricky or controversial in this case. Specifically, you
can just lay down a locally inertial coordinate system at any
particular pont in spacetim and ask whether the stuff near the origin
of that coordinate system has any angular momentum or not.
-Ted
Emory F. Bunn
Edward Green <egr...@nyc.pipeline.com> wrote:
>'t...@physics2.berkeley.edu (Emory F. Bunn)' wrote:
>>I agree. It's a rational question that happens to have no answer, as
>>far as we know.
>
>That is diplomatic, but in another sense, it is precisely like "What is
>the color of time".
Well, I have a certain weakness for pedantic disputes about semantics,
so let me try to clarify what I was getting at.
I think that you and I fundamentally agree about these matters,
although we may disagree about the best words to use to express
ourselves. I just think that it's inaccurate (as well as
undiplomatic) to characterize the question about where the center of
the Universe is as fundamentally irrational. Ultimately it's a bad
question, because it's based on assumptions about the nature of the
Universe that turn out not to be correct, but one has no way of
knowing that until one has studied for quite a while. In this sense,
it's different from the question about the color of time: one question
is manifestly meaningless at first glance, while the other can only be
recognized as meaningless after one has gone to a lot of trouble. I
think it's best to reserve harsh words like "nonsense" or "irrational"
for questions in the former category.
-Ted
Martin Hardcastle
Emory F. Bunn <t...@physics.berkeley.edu> wrote:
>In article <4dai4c$o...@pipe9.nyc.pipeline.com>,
>Edward Green <egr...@nyc.pipeline.com> wrote:
>>'t...@physics12.Berkeley.EDU (Emory F. Bunn)' wrote:
>
>>>It turns out, somewhat surprisingly perhaps, that it's possible for
>>>the Universe to rotate and yet to have no center. That is, it can
>>>have "angular momentum" about any point you choose to regard as the
>>>center, even if all points look exactly the same. People seem to
>>>regard this fact as even more surprising than the fact that the
>>>Universe can expand without a center, but maybe that's just because
>>>they're less used to thinking about rotating Universes.
>>
>>Well, pursuing the analogy with expansion, I assume this means something
>>like the universe has a "curl"; not what we would consider a rigid body
>>rotation, but a kind of an extended intensity of rotation. Is that about
>>right?
>
>Yes. Specifically, you can fill the Universe with matter and give that
>matter a velocity field that has a curl at every point. If you do
>then the Universe looks like it's rotating about whatever point you
>choose to regard as its center.
>
>>I assume the language of this observation is GR,
>
>Yes.
But it doesn't have to be. Just as it's easily shown that the universe
can expand with no centre from simple vector algebra if it follows
Hubble's law
(let an observer on earth observe n galaxies at vector distances r_1,
r_2 ... r_n, with vector velocities v_1, v_2 ... v_n given by v_i = H
r_i; then on the j'th galaxy the distance to galaxy i is r_i - r_j,
the velocity is v_i - v_j = H (r_i - r _j) and so the observer on
galaxy j sees the same Hubble law and the same universal recession)
it can also be shown that a universal rotation transforms in the same way
(let us observe all bodies rotation about us with an angular velocity w.
Galaxies have distances r_1, r_2 ... r_n as before. v_i = w_i x r_i, where
x denotes the vector cross product and w_i is a vector having the property
that it is always perpendicular to r_i and of magnitude w. Then on the j'th
galaxy the distance to galaxy i is r_i - r_j, the velocity is v_i - v_j
= (w_i x r_i) - (w_j x r_j) = w_ij x (r_i - r_j) where w_ij has magnitude
w as before and is perpendicular to r_i - r_j; so the observer on galaxy j
sees the same universal rotation).
The idea that there's no centre in either case isn't difficult at all...
Martin
--
Martin Hardcastle Mullard Radio Astronomy Observatory, Cambridge
... she'll offer her charms to the darkness and danger of
something that she's never known / And open her arms at
the smile of a stranger who'll love her and leave her alone.
Emory F. Bunn
Victor Grauer <gra...@oberon.pps.pgh.pa.us> wrote:
> The center of the universe is indeed "everywhere", but not quite.
>The periphery of the universe seems privileged (closer to the center)
>because the fact that it is so far away means that we are seeing it at a
>_time_ when it was close to the time of the big bang.
You've got it exactly right. Lest anyone get confused, though, I just
want to point out that the word "seems" is critical in the above
sentence. If Hamlet knew anything about the big bang, he would
refrain in this particular context from saying, "Seems, Madam? Nay,
it is. I know not 'seems.'" In this case, "seems" and "is" are very
different things.
From our particular vantage point, there are certain locations in the
Universe that are "on the periphery" of what we can observe.
Specifically, these are the points on our horizon, or the points that
are located about 15 billion light-years away from us. From our
particular vantage point, those locations *seem* special, but that's
not because they really *are* special -- rather, it's just that we're
looking at them from just the right distance to make them *look*
special. Imagine that there was someone exactly like you right now
living in a galaxy at "the periphery of the Universe" as seen by us.
To that person, we would be "on the periphery." Our patch of the
Universe would look to him exactly the way his looks to us. Our
location and his are identical in all fundamental respects.
>We are so close to
>the space we are in that we cannot see what it was like in the distant
>past in and around where we are now. Thus we have the illusion that the
>distant past took place in an area that is _spatially_ distant. If we
>could see the distant past of the space we are now in, we would also see
>remnants of the Big Bang.
Exactly right.
Boris Mohar
>On 15 Jan 1996 13:54:17 GMT Jeppe Stig Nielsen (jeppesn) wrote:
>: gra...@oberon.pps.pgh.pa.us (Victor Grauer) wrote:
>
>: > The center of the universe is indeed "everywhere", but not quite.
>[. . .]
>
>: 1: Cosmos is homgenous, i.e. invariant under translations, at large scale.
>: This means the universe behaves the same in any point.
>
>Y'all are arguing some theology it'd take centuries of centuries
>of irrelevant ecumenical councils to settle into orthodoxy while
>all around you stars to-and-fro in the dance of oblivion. This is
>where "Science" took a wrong turn: who cares where it came from if
>you don't know what it is or what to do with it, and how can you
>argue about whether it has a center if you don't what it is?
>
>
>David
>
>--
>i practice philosophy only in self-defense
>I PRACTICE PHILOSOPHY ONLY IN SELF-DEFENSE
> (--Gordon Fitch, 11 Jan. 1996)
>
Because by looking for it one might find center of something else,
such as oneself.
Boris