I am currently reading E=mc^2 by David Bodanis, and a paragraph on the speed of light sparked my interest. It is not particularly relevant to my following idea, but just made me wonder.
If the universe is infinite, then would we not be traveling faster than (or equal to?) the speed of light?
Let me explain.
We live on lowly Planet Earth. Earth orbits the sun in our solar system in the galaxy of the Milky Way. It is my understanding that as other smaller galaxies orbit ours, we in turn orbit other, larger galaxies. And then that mass of galaxies orbits another larger mass of galaxies and so on and so forth. As the universe is supposedly infinite, this would mean that these orbiting masses would be infinitesimally large. Now, if we add up these speeds (the speed of the rotation of the earth + the speed that the earth orbits the sun + the speed that the Milky Way orbits anther larger mass and so on) the total speed would continue increasing to the point of infinity, much surpassing the speed of light. Therefore I would conclude (almost obviously incorrectly) that each person on earth is traveling infinitely fast.
How could this be? Would we not be invisible, as our image would be behind our own being? And so I could perhaps draw the possibility that if the total speed was fractionally smaller than the speed of light, we could calculate the size of the universe.