How is it that the universe is expanding faster than the speed of light?

What you understand of relativistic physics appears to only be special relativity. Indeed, the speed of light is constant in all inertial frames of reference.

But there is no inertial frame of reference that contains both you (the observer) and very distant stars. That is what general relativity means by "curvature."

Also, you don't understand the Lorentz transformations if you think that they tell you about what light "witnesses," because you will not find a Lorentz transformation that describes the rest frame of a light ray.

Yes, that indeed possible and in fact space expanding much faster than light is the only way for the Big Bang theory to make sense. There is an echo from the Big Bang, red shifted all the way down to the microwave region of the electromagnetic spectrum that shows the universe was fearsomely hot in it's infancy. However, this radiation background is almost perfectly uniform in every direction. There is no way for the universe to reach a vast size and have time to equalize it's temperature if it expanded slower than light with large variations in temperature throughout at the beginning. But if it expanded slowly at first while still very small, it would have had a chance to reach near perfect uniformity in temperature, then when runaway inflation took hold the universe would remain nearly uniform in temperature. I don't know if it's still expanding faster than light today, but there's no laws of physics I've heard of that prohibit this from happening.

I say a very good question. For those of us who find it unrealistic to stay abreast of advanced theories in physics and astronomy, it is sometimes convenient to review the Speed of Light first. Light was faster than anything else which could be measured on Earth. It's speed is relative to Earth; later mass averages of stars and so on.

Yet light is like sound, a vibration which travels thru (what?) at a certain speed. If an object like a star and planets moves away from here at the speed of light, the Doppler means we see nothing and over there the clocks maybe moving the other way. If you can catch up with a certain planet, you could find out how your ex-wife used to be doing a few years back.

In the meantime, I say that light has a finite speed, but mass does not. We just thought that C was the biggest number imaginable. Apparently, not true.

lorentz transformations and the other stuff you're talking about are defined in the context of special relativity. in that theory, spacetime is flat (i.e. not curved). a 'meter stick' here is the same as a meter stick a billion years ago, or a billion light years away. but as you say, the universe is expanding... space is expanding with time. this is a form of spacetime curvature, so special relativity is insufficient. to handle curvature you need general relativity. in general relativity, the speed of light is only locally constant... that is, if you are close enough to an event or process that spacetime isn't noticeably curved, light moves at the speed of light, special relativity and lorentz contractions apply, and so on. objects that are further away are quite a different story though. the expansion is proportional to distance: more distant objects are receding faster. so there will always be a distance for which the recession velocity is faster than light, it's only a matter of whether that distance is far away (as it is now) or close by (as it was during the inflationary era in the early universe). another way to think of it is that distant objects are receding not by moving *through* space faster than light (which would be forbidden) but because *space itself* is expanding. locally, objects are still limited by the speed of light. it is perhaps hard to understand from a description how these principles can be consistent, but mathematically there is no problem.

"how would the expansion of spacetime appear to such an observer."

it's not 'expansion of spacetime'. it is either 'expansion of space with time' or more generally, 'curvature of spacetime'. there is a notion of distance in spacetime:

ds^2 = dt^2 - dx^2

where dt is the time interval between two events, dx is the space interval, and ds is the spacetime interval. this is more fundamental than the lorentz transformations. observers in different reference frames can disagree on the values of duration (dt) and distance (dx), but not on the spacetime interval (ds). for light, dx = dt (assuming you're using units of seconds and light-seconds, or equivalent), so that ds = 0. all points on a light ray are the same spacetime interval apart: zero. that applies whether or not spacetime is curved. in a flat space, light rays are straight lines. in a curved space, light rays are curves (called 'null geodesics'). I think it isn't really correct to refer to the spacetime interval as either space or time when it's zero. the notion of space and time being separable has no meaning in that case. this is equivalent to Lola's comment that "you will not find a Lorentz transformation that describes the rest frame of a light ray."

The universe is a singularity - an infinitesimally small dimensionless point. Within our singularity universe there are really only two things, static matter and continuously expanding time and space.

Also within the singularity is energy (E), which is the static matter (m) directly conflicting with the continuously expanding time and space (c) at the subatomic level and this interaction is expressed as E=mc^2.

Every point in our singularity universe observes itself to be the oldest and most centralized point in the entire universe.

New time and space is continuously being created within the singularity throughout the universe. This is why the point of our origin is about 46.5 billion light years away in every direction in our 13.7 billion year-old universe.

To use the quaint balloon analogy: When you inflate a balloon, you blow the air in at a single point; in our singularity balloon universe the air is being created around every point at the same time - it has inflated beyond the boundary that its mere age can account for and every point in the universe observes itself to be in the center of the singularity balloon.

The universe is incomprehensibly simple!

In general relativity, no object can pass another object faster than the speed of light. However, if you accelerate the reference frame, the distance to objects to the front and rear changes in proportion to the distance. The rate of change of distance to the front and rear due to acceleration of the reference frame is not considered to be a real velocity in general relativity.

Example: You accelerate your reference frame from zero to c/2 toward the core of our galaxy, in 300 million seconds. That's about one g acceleration for 10 years. In those 10 years, the far side of the galaxy (60,000 light years away now) will appear to move about 8,000 light years closer. And that's just the far side of our own galaxy. Imagine how fast the most distant galaxies would appear to move toward us.

In effect, you have warped space in order to arrive at your destination faster than light but without exceeding the speed of light. That's an almost plausible explanation of warp drive. Only trouble is you would need to use matter and antimatter fuel with many times the mass of your ship to accelerate to that speed, and then you would have to have enough fuel left over to decelerate at your destination.

Back to the expansion of space: The rate of expansion H0 appears to be about 2.5 x 10^-18/s. Objects farther than c/H0 (about 13 billion light years) are expanding away from us at the speed of light. More distant objects may exist, but their light can never reach us.

This concept is easy to get hung up on. Think of the speed of light as being the "universal speed limit" for motion THROUGH space. Expansion of space, however, is not motion through space; it's expansion of space itself. If you subtract the expansion of space when determining the speed at which galaxies are moving, they are moving THROUGH space well under the speed of light.

The "universal speed limit" only applies to a particle moving through the curvatures of space-time. The fabric of space-time, however, can exceed this speed limit and does.