Right, which is one of my fundamental disconnects (read: problems) with how objects at speed are discussed.
How it appears to an outside observer is completely inconsequential. The object itself is still the same size/shape it was at rest because the entirety of the object is moving at the given speed.
Which leads to another part of the discussion - the question over whether turning on a flash light at light speed would project light forward onto something likewise moving at the speed of light. Again without being one of the aforementioned mathematicians I say “yes, it does” because I can’t see why the flash light/filament/photons care that they’re already moving at the speed of light. The source and target are comparatively stationary.
If the target were moving away from the source at the “speed of light”, sure, the light never makes it to the target because “that’s how fast light goes”.
The real question should be - “why is the speed of light...the speed of light?” There is so much we don’t know about this universe, and likely never will.
“How it appears to an outside observer is completely inconsequential.”
Well, no, it is consequential, because it effects simultaneity. So, because of the apparent length contraction, events can’t happen at the same time for the observer and the observed. Going back to the photon as an example, when one is emitted, we see that it takes a certain amount of time to traverse space. However, for the photon, it appears to take zero time to travel any distance. You can’t say that we are right and the photon is wrong, because in either frame of reference everything behaves as if your observations are correct. So, both of those things are true, even though it seems to be a contradiction.
“Which leads to another part of the discussion - the question over whether turning on a flash light at light speed would project light forward onto something likewise moving at the speed of light”
Well, theoretically, you should see the light project forward. However, that’s completely theoretical, because no physical object with mass that could emit photons will ever be able to reach c. The trickier question is whether an outside observer would see the light beam project forward or not.
“The real question should be - “why is the speed of light...the speed of light?””
Yes that is the real question, and I don’t have much clue as to the answer to that.