Palmer Conjecture

Seeing a picture of an Einstein Ring got me wondering. Do you suppose
that a light beam that departs something going one direction would
eventually pass a light beam that departs the same source in very
different direction? Both beams being effectively bent into a rough
circle by the mass of the entire universe. I'm thinking yes. If this
is true, and there was no dark matter in space, then the sky would have
to appear totally lighted if the time for a round trip by a light beam
were much smaller than the age of the universe itself because an object
would have to be visible everywhere. Since we don't see a completely
lighted sky at night there must either be lots of dark matter stopping
much of the starlight or the round trip time for a beam of light is
very long compared to the age of the universe itself.

If the universe was the right size and does not have too much dark
matter, we are potentially seeing the same objects many times each
today but don't know it. And if it is not true today, as Hubble extends
the distance of visible objects, the odds that this could happen are
growing. We might see an object that we think is 150 light years away
in one direction and the same object looking 8 billion light years away
in another. Of course, if this was true, our view of each image would
be from such a different direction that we could not recognize the
position of objects around it. And since the image we are seeing is
from such a different time, the characteristics of the object might be
quite different as well (an evolving star cluster in one and something
quite different in another).

So I'm a little perplexed with the question of how we might know that
this is what we're seeing, if it is. It would be a real shame if we
could theoretically see the same object many times but that the amount
of dark matter is so great that no light beam can actually make a round
trip.

In message .com,
Bruce writes
Seeing a picture of an Einstein Ring got me wondering. Do you suppose
that a light beam that departs something going one direction would
eventually pass a light beam that departs the same source in very
different direction?


So I'm a little perplexed with the question of how we might know that
this is what we're seeing, if it is. It would be a real shame if we
could theoretically see the same object many times but that the amount
of dark matter is so great that no light beam can actually make a round
trip.


You might look up the idea that the universe is a dodecahedron, which
will apparently have an effect on the spectrum of the CMB. Look at
http://physicsweb.org/article/news/7/10/5 for instance.
Another way this is being examined is to see if there are actual
repeating patterns in the background. Here's an example
http://www.etsu.edu/math/gardner/aas/empir.htm
I don't know if anyone's looked for repeating patterns in the 3D
structure of the universe. I'd think it would be impossible to tell,
given the billions of years that have passed since the light set out.
There are lots of other possibilities if the universe isn't a simple
"flat" structure. Try "horn universe", for instance
http://www.newscientist.com/article.ns?id=dn4879
Of course, going even further out there's the idea that the CMB might
have an artificial pattern, in which case there's possibly no way to
tell the real shape :-)

Bruce wrote:
Seeing a picture of an Einstein Ring got me wondering. Do you suppose
that a light beam that departs something going one direction would
eventually pass a light beam that departs the same source in very
different direction? Both beams being effectively bent into a rough
circle by the mass of the entire universe. I'm thinking yes.

In general, this depends on the topology -- roughly, the large-scale
connectivity -- of the Universe. If space is infinite, and matter
is roughly evenly distributed ("homogeneous"), you're very unlikely
to get such an effect; a light beam will be bent as it passes matter,
but over long distances the bending will average out, and the beam
will just keep going. If, on the other hand, space is spherical, or
has some more complicated topology, then we could conceivably see
multiple images of the same object.

[...]
If the universe was the right size and does not have too much dark
matter, we are potentially seeing the same objects many times each
today but don't know it. And if it is not true today, as Hubble extends
the distance of visible objects, the odds that this could happen are
growing. We might see an object that we think is 150 light years away
in one direction and the same object looking 8 billion light years away
in another. Of course, if this was true, our view of each image would
be from such a different direction that we could not recognize the
position of objects around it. And since the image we are seeing is
from such a different time, the characteristics of the object might be
quite different as well (an evolving star cluster in one and something
quite different in another).

So I'm a little perplexed with the question of how we might know that
this is what we're seeing, if it is.

There's been a good deal of work on this. Probably the best limits
come from looking at the cosmic microwave background and searching for
identical patterns in different directions. You might want to look at
a nontechnical summary at http://arxiv.org/abs/physics/0509171, and at
the references in that paper, for a start. (The best limits I know
appear in a more technical paper, http://arxiv.org/abs/astro-ph/0310233,
though there are some recent arguments that the data may be too noisy
to see the effect; see http://arxiv.org/abs/astro-ph/0511726.)

Steve Carlip

Steve Carlip






It would be a real shame if we
could theoretically see the same object many times but that the amount
of dark matter is so great that no light beam can actually make a round
trip.

Steve, thanks a million for the pointers to the papers. Outstanding.
It looks like my conjecture has been conjectured already by lots of
folks. Without being explicit about it, I had assumed that the big
bang included the universe itself and not just a bunch of material in
an already existing infinite universe.