Clarifying the relativity theory

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Hi!

I have been studying the relativity theory a few times in different popular media, and I have come to find if not logical errors, at least lacking information to make this theory complete. The problem is that there is a mixup between light as we see it and light as photons.

Taking the example of time dilation, as this video describes it:
http://www.youtube.com/watch?v=KHjpBjgIMVk&feature=related

There are two spaceships which send light in between them, both traveling at the same very high speed, in the same direction. A stationary observer is also seeing this light. Now, if the observer is watching the light going between the ships, the distance the light is traveling is longer than the distance seems to be from one of the spaceships.

Now I would like to STOP here. Before going further and making the standard relativity conclusions, I would like to question the reasoning here. The question is how the observer is actually seeing the light, and if really is possible to see light from "the side".

Looking at a source of light on a car for example, we can of course see the light both if we are traveling inside the car and as a stationary observer outside the car. However, do we perceive the same light? The way I see it, we see different photons from a light source. The light source spurts out gazillions of photons in every direction, and because of that both the car driver and the stationary observer see a light source summed up of these gazillions of photons. However, the light source the car driver sees is made up from different photons than the light source the stationary observer is watching.

Of course we could see light traveling from one spaceship to another if it were like a laser, which is light that can be seen from the side, at least it looks like that to the observer. However, the light we are seeing from the side, is it really light observed from the side, scientifically speaking? Isn't the light seen from the side of a laser actually photons bouncing off other particles? In other words, the light we actually see is coming directly from the source (the photon bouncing off a particle)?

If this is true, the normal reasoning of the relativity theory seems to be wrong. Any photon traveling from somewhere to meet our eye can indeed travel at the speed of light, but this observation is made when the photon is traveling directly to the eye, and can in no way be observed from the side (which would cause time and space dilation).

Taking into account that the spaceship observers and the stationary observer, from the example above, perceive different photons, the stationary observer cannot observe the light traveling between the two spaceships described above. The light traveling between the spaceships can very well be at the speed of light, but how could the stationary observer perceive this at all? He only perceives the photons coming to his eye directly, and the movement in between the ships would be "illustrated" depending on how the flow of photons happen to bounce off particles in between the ships. The "speed of the light" observed by the stationary observer would then not be the speed of light, but the "illustration" of light at the speed of which different photons together "illustrate" a ray of light.
 
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The animations from the observer's perspective are idealized schematic ones, they are meant to show the actual coordinates the light beam passes through in the observer's coordinate system (as might be measured by a set of light detectors at rest at different positions relative to the observer, with synchronized clocks attached to each detector to measure the time the passing light sets off that detector), not what the observer "sees" visually (in space you can't see lasers at all unless you're directly in their path, since there's no air for photons to scatter off of and reach your eyes if you're not on their path).
 
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