Regarding Dick Fischer's question:
>Okay, so how can two material objects - that quasar and this earth - in a
>14 billion year old universe (give or take two) get 26 billion light years
>apart? Neither of us can travel at anything like light speed! Am I
>missing something?
Dick, your question is a common one. The answer lies in the realization
of the nature of the cosmic expansion of the universe as understood by
general relativity. *If* spacetime was the nondynamical static flat
spacetime of special relativity and the matter (and radiation) in the
universe expanded from some fixed spatial center by exploding outwards
into the preexisting empty space (as happens in a conventional explosion)
then your observation would be correct that the distance between any two
particles carried by the explosion cannot increase with time any faster
than c.
*But* this is *not* how the Hubble expansion of the universe is
envisioned. The various galaxies (quasars and other large-scale
structures) are *not* moving very fast through a static space. In fact,
to a reasonable approximation their own local motions (w.r.t. a local
frame of reference in which the expansion proceeds isotropically) can be
*ignored altogether* on the larger length scales of the universe, and
they can be thought of as being *at rest*. The picture is that there is
no outer domain of empty space for the matter to expand into. Rather
*all* the space of the universe is (and always has been since the Big
Bang) more or less uniformly filled (on sufficiently large length scales
much larger than typical intergalactic distances) with matter which is
locally at rest. The universe expands because the space between the
particles (i.e. galaxies and galactic clusters) is *stretching*. The
distance between the galaxies is growing because more space is
continuously being created between them as the space between them
stretches.
General relativity places no prior speed limit on how fast the cumulative
effect of this stretching may occur.
The Hubble law is that the rate of increase of separation between any two
distant galaxies (i.e. rate of increase in the proper geodesic distance
between these galaxies w.r.t. cosmic standard time) is directly
proportional to the (proper) distance between them, v = H_0*d (where v is
the rate of increase in the separating distance between the galaxies, H_0
is the Hubble 'constant' and d is their current separation distance).
The separation distance between two very mutually distant galaxies
increases with time faster than it does for two galaxies that happen to
be close together. Thus, for any two galaxies that happen to be farther
apart than c/H_0 (i.e. d > c/H_0) the distance between them increases
faster than c (i.e. v > c).
So the reason that when light left the quasar 10 billion years ago when
it was only 4 billion light years from Earth (or, more properly, from
the part of the universe from which the Earth would later be formed) and
it is just arriving here now with the current distance to the Quasar (or,
more properly, to the remnant left behind by the quasar that it has since
become) being 26 billion light years is simply that the quasar and Earth
*have* been separating from each other *faster* than c. The average
'speed' of this increasing separation during the light travel time has
apparently been 2.2*c.
Like special relativity, general relativity *does* put a restriction on
how fast one object can move with respect to another one at *the same
place* (or nearly the same place). IOW, when object A emits object B,
when object A absorbs or is struck by object B, and/or when object B
passes by object A in a 'near miss' the magnitude of the velocity of
object B relative to object A must never exceed c, and it is *only*
exactly c when object B is massless (such as a photon of light).
Otherwise this relative velocity has a speed which is less than c. Here
we have implicitly assumed that object A had a positive mass so we could
consider the velocity of B respect to it, i.e. w.r.t. a frame in which
object A is at rest. The main restriction imposed by relativity
regarding speeds is that no *causally informative influence* can travel
*locally* any faster than c. To the extent that the dynamical nature
of the geometry of spacetime itself can be ignored (such as in
special relativity or in general relativity on a length/time scale
much shorter than billions of (light)years), then this speed restriction
also extends to relative velocities between objects that are not at the
same place. But if the space/time separations between the objects
are comparable to that of the horizon size and age of the universe itself
then the v < c speed restriction does not apply for motions between such
widely separated objects. But even in this case the Hubble expansion
cannot be used to propagate causally significant influences between
different objects any faster than c. If the cosmic expansion carries two
objects apart faster than c then these objects can't exert any causal
influence on each other unless the expansion either slows down enough
in the future or if it was slow enough in the past for a light ray
from one object to eventually make it to the other one.
I hope this explanation helps.
David Bowman
David_Bowman@georgetowncollege.edu
This archive was generated by hypermail 2b29 : Sat Apr 15 2000 - 08:44:45 EDT