Amazing. I hope to some day wake up and have a deep conceptual understanding of the relationship between velocity and time in relation to the various bodies at play.
I also hope to have an understanding of what it means for a photon to be everywhere at once, from its own point of view.
In the end, I guess I just want to understand the universe just a bit more than I do.
Special relativity is actually quite accessible and really interesting - find a good book or set of lectures on iTunes U or something.
(General relativity, the generalised version including acceleration and gravity, is what makes people think relativity is hard).
This is also why particles traveling at c cannot possibly
decay: no time passes for them. A photon is everywhere at
once, from its own point if view.
Time dilation (special relativity) has nothing to do with wave-particle duality (quantum physics). The infinite time dilation of photons is due to their velocity, not their wave-like nature.
Furthermore, all particles (electrons, protons, quarks, etc.) have wave-particle duality just as much as photons do.
Wave-particle duality is even observable with larger molecules: http://link.aps.org/doi/10.1103/PhysRevLett.88.100404
This is also why particles traveling at c cannot possibly decay: no time passes for them. A photon is everywhere at once, from its own point if view.