You're quite right about the time dilation effects, Dave. Nevertheless, according to Relativity, neither the occupants of a continually accelerating spaceship nor outside observers can ever see the ship reaching the speed of light, although it can in theory get arbitrarily close. I like your explanation about the relation between time and space, BTW.
Skeptic, the true nature of photons, matter and energy are unknown. So is the relation between inertial mass and gravitational mass, and rotational inertia and what we perceive as the physical universe. We have a great deal yet to learn.
Photons are said to have zero mass, even though they have energy. I don't know enough about quantum physics and relativity to say much more than that, except that I don't think it's valid to calculate a mass for a photon using E=mc^2. Photons have properties of both classical particles and waves. No one knows what they "really" are. All we can do is perform experiments on them and try to describe and understand the results.
One of the most profoundly disturbing properties of photons, and for that matter, small particles like electrons that have mass, is that they seem to behave both like particles and waves. One way to see this is to perform the famous "double slit" experiment. In this, monochromatic, coherent light such as from a sodium lamp is shined through two slits that are fairly closely space, about a millimeter apart if I remember right. The light is projected onto a special detection screen consisting of a material that glows when light hits it, or just a regular photographic film. The close-spaced slits produce a "diffraction pattern" consisting of alternating dark and light lines. This is normally thought of as being produced by "interference", where the high and low points of the light waves going through each slit reinforce or cancel each other when they hit the screen.
Normal photographic film can replace the fluorescent screen and you can then record the result. This phenomenon of diffraction is a classic result of the mathematics of wave propagation and interference, so this experiment indicates that light is a wave phenomenon. However, what happens when the intensity of the light is decreased to the point where a photo film takes many weeks to become exposed? The diffraction pattern still appears, which is not particularly surprising at first glance. However, if you observe what happens using the fluorescent screen instead, using a microscope to observe it, you find tiny flashes of light occurring from time to time all over the screen. What happens is that a single molecule absorbs the energy of the light, which then re-radiates the energy in the form of a light flash that you can see. This indicates that light consists of particles, since it is not evident how a single molecule could instantly absorb the energy of a spread-out light wave. If you use a camera focused on the fluorescent screen to photograph it over a period of weeks, or if you expose the film to these individual flash-events for weeks, lo and behold! You find the same diffraction pattern! This is extremely surprising if you try to look at light from the particle viewpoint. The particle of light must have traveled through either one slit or the other, right? And since the intensity is so low, only a single light particle at a time could be present in one slit or the other. The question then is: if only a single particle of light is present in one slit or the other, then what is interfering with what in order to produce the diffraction pattern? The answer is: no one knows. This experiment shows how light behaves as both a wave and a stream of particles.
Some physicists have written that anyone who is not profoundly disturbed by the result of the double-slit experiement does not understand physics.
Another disturbing thought is just how a rotating body "knows" that it is rotating. In the 19th century, I believe, it was proposed that rotation is defined in relation to the distant stars. However, according to relativity, matter and energy are limited by the speed of light in how they can project their effects on other bits of matter and energy. Thus, nothing that happens locally can possibly be affected by the distant stars. Think of it this way: suppose you managed to travel to a place out in intergalactic space where the density of matter is so low as to be completely neglible, perhaps one molecule per cubic meter, and the intensity of light from the distant stars is extremely low as well. We have little doubt that if you spun your little spaceship around, you'd feel the normal forces associated with rotational motion. But how would the matter in your body and your ship "know" that it was rotating? There could be no instantaneous communication with the distant stars, and the density of matter and energy outside your ship would be neglible, right? Yet you'd still be able to measure your rotation. The same goes for linear acceleration. How would you know you were accelerating? Accelerating with respect to what?
These are all profound questions that show that we have no understanding of what matter and energy are on a deep level, or what the "true" structure of our universe is. We can measure things, and manipulate matter and energy to a certain extent, and describe how they act, but we don't really know anything fundamental.
AlanF