I'm grateful for your info but:
Yes, (a) we can dispense with the balloon analogy, of which I was aware, (b) I am happy with the universe expanding (c ) from the Wiki article: “The horizon is the boundary beyond which objects are moving away too fast to be visible from Earth.”
Yes. Right now, our cosmological horizon is about 46 billion light years from Earth. This is the location of objects that emitted light at the time of (or shortly after) the Big Bang RIGHT NOW. Things beyond that horizon essentially don't exist as far as we're concerned. Note that the age of the universe is 13.7 billion years, which is much smaller than the horizon. The actual travel distance for photons reaching us from the horizon is 13.7 billion years, i.e., they've been traveling at exactly the speed of light the whole time. Although the objects that emitted those photons were (and still are) moving away from us far faster than the speed of light, the photons have been traveling through regions of space that are moving away more and more slowly, and they have finally "caught up" with us. Note that the reason that the horizon (46 GLY) is larger than the age of the universe (13.7 GY) is because the rate of expansion is slowing.http://en.wikipedia.org/wiki/Observable_universe#Size
So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.
My question, inelegantly expressed earlier, remains – what would cause an object at a greater distance to exceed the speed of light? Points on an horizon cannot increase at greater speed than the speed of the objects which give rise to those points. The speed of objects is limited by their initial motive power unless an exterior force influences them. To exceed a speed of light, the impetus would have to be greater than the speed of light.
Reference the bolded part, you've got it backwards. The objects don't give rise to the points in space. The points in space are the fabric of space-time. The objects are just along for the ride. We could have a completely empty universe that was uniformly expanding, although it would obviously be extremely difficult, probably completely impossible, to gauge the relative speed of expansion in such a universe.
The thing to keep in mind is that we're not saying that Object X is moving at the speed of light. We're saying that relative to us
, Object X is moving away at faster than the speed of light. Relative to something closer, it's going to be moving away more slowly.Here is a pretty good article that explains the difference.
Notice that, according to Hubble's law, the universe does not expand at a single speed. Some galaxies recede from us
at 1,000 kilometers per second, others (those twice as distant) at 2,000 km/s, and so on. In fact, Hubble's law predicts
that galaxies beyond a certain distance, known as the Hubble distance, recede faster than the speed of light. For the
measured value of the Hubble constant, this distance is about 14 billion light-years.
Does this prediction of faster-than-light galaxies mean that Hubble's law is wrong? Doesn't Einstein's special theory of
relativity say that nothing can have a velocity exceeding that of light? This question has confused generations of
students. The solution is that special relativity applies only to "normal" velocities--motion through space. The velocity in
Hubble's law is a recession velocity caused by the expansion of space, not a motion through space. It is a general
relativistic effect and is not bound by the special relativistic limit. Having a recession velocity greater than the speed of
light does not violate special relativity. It is still true that nothing ever overtakes a light beam.
The only answer is that the singularity did exceed the speed of light in it’s initial expansion and the inverse square law has reduced any common gravitational effect between distant particles – however, (1) as we do not know the original size of the singularity and the expansion is expressed as a percentage of the original size, then, regardless of how many powers of 10 it is expressed by, is this not mere speculation? And (2) when in the form of the singularity, the strong at weak forces must have been at their maximum, so any expansion would have lessened, rather than increased, their mutual attraction, thus, increasing their velocity as the forces waned and everything everywhere would be travelling faster than light.
1) The actual size of the singularity is unknown. There are some theories that say that the entire universe is actually smaller
that the observable universe, there are theories that say the whole thing could actually be infinite, and everything in between. For all practical purposes though, things outside of our cosmological horizon simply don't exist since light hasn't had time to reach us from there yet.http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf
This ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size.
Cosmologists sometimes state that the universe used to be the size of a grapefruit, but what they mean is that the part
of the universe we can now see--our observable universe--used to be the size of a grapefruit.
Observers living in the Andromeda galaxy and beyond have their own observable universes that are different from but
overlap with ours. Andromedans can see galaxies we cannot, simply by virtue of being slightly closer to them, and vice
versa. Their observable universe also used to be the size of a grapefruit. Thus, we can conceive of the early universe as
a pile of overlapping grapefruits that stretches infinitely in all directions. Correspondingly, the idea that the big bang was
"small" is misleading. The totality of space could be infinite. Shrink an infinite space by an arbitrary amount, and it is still
What we can
do is take the observations of distances and relative expansion that we see now and rewind the film to try to figure out what the parts of the universe that we can
see looked like shortly after the Big Bang. Obviously, we can't actually measure the events in the early universe directly, but we can make predictions about them based on what we know about particle physics. http://www.lifesci.sussex.ac.uk/home/John_Gribbin/cosmo.htm
This might all seem like a philosophical debate as futile as the argument about how many angels can dance on the head of a pin, except for the fact that observations of the background radiation by COBE showed exactly the pattern of tiny irregularities that the inflationary scenario predicts. One of the first worries about the idea of inflation (long ago in 1981) was that it might be too good to be true. In particular, if the process was so efficient at smoothing out the Universe, how could irregularities as large as galaxies, clusters of galaxies and so on ever have arisen? But when the researchers looked more closely at the equations they realised that quantum fluctuations should still have been producing tiny ripples in the structure of the Universe even when our Universe was only something like 10(exp-25) of a centimetre across -- a hundred million times bigger than the Planck length.
In short, they took predictions about the state of the early Universe based on the inflationary model, applied quantum mechanics to predict what we should
see if they were true, and eventually found those effects. That obviously doesn't prove
that the inflationary model of the early universe is correct, but it's pretty strong evidence that we're on the right track.
As for 2) the inflaton field that is predicted would have been far more powerful than any standard force that we know of today. It would have been an exponentially accelerating force that got stronger and stronger as time went by - we simply have no classic analogue to this. You are right though, from the point of view of a single point in space, the rest of the universe would have been ripped away and disappeared from view, leaving only a very, very tiny cosmological horizon behind. The thing is that the inflaton field was extremely short-lived. Once it turned off the universe was coasting and then ordinary forces did
begin to pull the universe back together and slow the expansion. Gravity has been slowing things down ever since.
It may well be the case that “While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such constraint in general relativity.” but this speaks more of a lack of a ToE than certainty. I can’t see that it much matters than there may be more dimensions. If they do exist and a particle has another dimension that allows it to “reappear” somewhere else, it has not actually defied the limit of the speed of light: a line of length 20cm will never fit in a sphere of diameter 10cm.
It's not really a lack of a ToE at all. The relevant piece that's missing from that is how gravity affects things on an extremely small distance scale.
So we don't know, for example, how gravity works between two hydrogen atoms, but we're about as sure as we can be on any theory that we understand how it works on massive objects over large distances. General relativity tells us that, in an expanding universe, objects that are far enough away should
be moving away at faster than the speed of light, and, indeed, our measurements seem to confirm that that is exactly what is happening. The only alternative is that our present understanding of the universe is wrong at a much
greater level than what we had in the classical physics days before we developed the theories of quantum mechanics and relativity.
And to reiterate, nobody
is saying that a beam of light ever has or ever will
travel through space faster than the speed of light. It's just that the region of space through which they're traveling through might be moving away, relative to another observer such as us, faster than the light can travel.http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf
The idea of seeing faster-than-light galaxies may sound mystical, but it is made possible by changes in the expansion
rate. Imagine a light beam that is farther than the Hubble distance of 14 billion light-years and trying to travel in our
direction. It is moving toward us at the speed of light with respect to its local space, but its local space is receding from
us faster than the speed of light. Although the light beam is traveling toward us at the maximum speed possible, it
cannot keep up with the stretching of space. It is a bit like a child trying to run the wrong way on a moving sidewalk.
Photons at the Hubble distance are like the Red Queen and Alice, running as fast as they can just to stay in the same