That's what special relativity says - in any reference frame, light is always traveling v + c, where v is your velocity and c is the speed of light.
To make this happen, time itself slows down. But how would this actually work? Does this mean electrons would "orbit" within the electron cloud more slowly? (If not, then molecules larger than Z=137 may be possible.)
Yes, all of the particles within that frame of reference slow down. Why? Who knows. Maybe space becomes more "viscous" which slows down all particles within it.
If you imagine every event as having (x,y,z,t) coordinates in a particular reference frame, the Lorentz transformation is a 4x4 matrix which rotates events to show what would be observed in another reference frame. You trade spatial distance for temporal distance and vice versa.
This comes out of the structure of spacetime, rather than viscosity of some kind, which would be visible as a force.
If you're looking for something more than a model that correctly predicts the universe, you're looking for something other than physics.
Edit: Let me see if I can make myself clear. We know that c is constant no matter how fast you are moving. If c is constant then it can be derived that time slows down and distances get compressed, etc. etc. etc. Einstein derived all of this by realizing that c is constant in all frames of reference. Now, if I ask "Why does time slow down?" and I get the answer "because c is constant" then we are just going in circles. It seems that that is what is happening here. Correct me if I'm wrong but are you not using a derivation of the fact that c is constant as an answer? I'm looking for a more fundamental reason as to why time slows down. Which is the same as asking why c is constant.
All solid matter moves forward in time at the same speed, minus the speed in which it's moving in the other 3 dimensions. Light and other particles only move forwards in time.
the speed of light, c, can be violated from your frame of reference, but the external observer doesn't see this - it's your perception of time that has slowed down.
you reach the speed of light (from the perspective of an external observer) when your local velocity is infinite (and then all travel becomes instantaneous).
On the other hand, someone stationary watching you travel near the speed of light would say that your clock slows down more the faster you move, but lengths stay the same.
You are correct. I don't think I said otherwise. I guess I should have been clearer, time slows down in the frame of reference traveling at c when looking at it from a different frame of reference. I'm sure we are saying the same thing.
>>at the speed of light, all distances in the direction of travel would be zero.
Yeah, but a person observing you in a different frame of reference won't see that. The fact that distances are zero is just another way of saying that time has slowed down in your frame of reference. Is just two faces of the same coin.
Indeed. You can see this sort of effect in, say, the muon decay demo in my relativity simulator:
http://www.refsmmat.com/jsphys/relativity/relativity.html
The muon decay lifetime observations can be explained equally well in terms of time dilation or length contraction.
you reach the speed of light (from the perspective of an external observer) when your local velocity is infinite (and then all travel becomes instantaneous).
From your perspective, reaching the speed of light causes all distances in the direction of travel to become zero. Your clock functions correctly and time travels at the ordinary pace. From a stationary observer's perspective, distances are the same but your clock has stopped.