
The Question
(Submitted December 17, 1996)
I'm not a rocket scientist, but I play one on TV. Here are
a couple of questions I've been pondering.
 Is the Universe rotating? With reference to what?
 Is dark matter necessarily within the bounds of the Universe?
In other words, could something spatially disconnected from
the Universe be having a gravitational effect on it?
 If you drew a circle of radius 1 billion light years,
what would be the value of its circumference divided by its diameter
(taking into consideration the curvature of space)?
Same question but the largest circle that could be drawn in the Universe?
 If the speed of light had been slowing since the big bang,
would there be any way of knowing it? (Assuming that everything else
would have been slowing with it.)
I think these fall into the category, "there's no such thing
as a stupid question, just stupid people who don't ask questions."
Thanks in advance for any light you can shed.
The Answer
Thank you again for your interesting questions. In addition to
our Ask an Astrophysicist
staff at Imagine the Universe!, Demos Kazanas in the Astrophysics Science Division also contributed to these answers to your questions.
 As far as we know, the Universe is not rotating. The presence of
rotation would induce a type of change in the Cosmic Microwave Background
temperature which has not been observed. In addition, the presence
of rotation would imply that locations along the axis of the rotation
were somehow "special", which violates our understanding of relativity
that the Universe appears the same regardless of the location of the
observer.
 Yes, dark matter as we normally discuss it lies within the bounds
of the Universe. The effect of gravity is propagated by spacetime, which
is the fabric of the Universe itself. "Outside" the Universe there is
no spacetime, hence gravity has no effect. Remember that the best
analogy for the "shape" of the Universe is that of a balloon being
blown up. There is no "edge" to it. What lies "outside" it is
undefined.
 It depends on the value of the spatial curvature, which in turn
depends on the density of the Universe compared to the critical density
to just halt the expansion of the Universe. If the Universe has any
curvature (which results from the density being anything other than the
critical density), then the circumference is larger than what it would
be on a flat plane. The size of the effect does depend on the radius
of the circle.
To get a sense of scale, the farthest object that we can see to is
~ 20 billion light years away.
(Sorry we're not giving you a specific numerical answer on this one !)
 This one caused us the most thought and reflection. I found
a book entitled "Gravitation and Spacetime" by Hans C. Ohanian
(1976, Norton & Co.) to be helpful in settling some issues.
We'll first tackle the question you asked  whether a change in
the speed of light could be detected. The answer is, in principle,
yes. One way is that the values for atomic transitions depend on
the speed of light. We observe these transitions as lines in a
spectrum. Hence, if the speed of light has changed, then the values
for these transitions from sources far away (and hence which emitted
their light long ago) would be different from present day values.
The difficulty is that there are many other factors which cause the
observed values of these transitions to change. These factors
include the Doppler shift due to the expansion of the Universe,
local motions of the object, gravitational redshifts, etc. In
practice, it would be difficult to disentangle the effect of a
changing speed of light from these.
Another way is to rely on a technique which utilizes the decay rates
of various radioactive isotopes. These decay rates are very sensitive to
the physical constants  the speed of light among them. If the values
of these constants change with time, then nuclear "clocks" based on
different isotopes would disagree. (A practical problem is figuring
out which of the "constants" changed.) Nonetheless, evidence shows that
the ages of rocks measured by these different clocks agree quite well and
hence puts tight constraints on the time variations of the physical constants.
So in principle it can be done, and there is evidence that the
physical constants are quite "constant". However, we should take this
further and ask whether we should expect the speed of light to change
with time.
The speed of light is not just something we measure about light,
but rather (as I've already implied) is a fundamental physical constant
itself. Indeed, the constancy of the speed of light in space and time
is an essential feature of special relativity. Time enters in because
relativity treats time on an equal footing with space (hence the term,
spacetime). Consistent equations cannot be written if it is taken
to be variable. In addition, general relativity and our understanding
of the evolution of the Universe is built upon the same premise.
So my conclusion is that the speed of light is truly constant.
You've given us a good workout. We hope our answers are helpful.
Jim Lochner
for Imagine the Universe!
