Doubly-Special Relativity
I just found out about this new theory called Doubly-Special relativity, which was popularized by Giovanni Amelino-Camelia.
It states that there are actually two observer-independent constants in the universe.
1) The speed of light (as per the standard theory of relativity)
2) A new observer-independent length (the Planck length).
Although I still have trouble grasping the Plank length (~1.6 × 10−35). According to Wikipedia, it is the length scale at which the structure of spacetime becomes dominated by quantum effects, giving it a discrete or foamy structure.
Anything smaller than a plank length, and all bets are off. Essentially, this is a universal pixel. With doubly-special relativity, we know that this “pixel” is a constant size, that any independent observer can agree upon.
This is quite a strange claim, given the premises of special relativity. There is an observed “length contraction” with relative speed. So, if you are on a very fast train (.99 light speed), the landscape around you will look “smooshed” together. If things look “smooshed” to you on the train (but to the farmer in the field they look the normal length) how could you agree on the size of an “inch”? You could not. But if you both zoom to , a hundred-million-trillion times smaller than a proton, then you will see a unit of size that is the same for both of you.
How though? Well, maybe that’s how time and space “curl-up” and warp with your relative speed. They take the beating so that these “pixels” remain constant (along with the speed of light).
So we maintain a constant “resolution” and a constant “frame-rate” even in the face of relativity.

