[Physics] How would night sky look like if the speed of light was infinite

astrophysicsspeed-of-lightvisible-light

Would it be brighter? Different color? Gravitational lensing? Would black holes exist?

Best Answer

In a Newtonian/Galilean world, where $c$ is infinite, you could not escape Olbers' paradox with an infinite universe. Any line of sight would eventually intersect the surface of a star, and so the whole sky would be as bright as the Sun. This is true whenever two hypotheses are satisfied:

  • The universe is spatially infinite (or rather, the distribution of things does not taper off with distance from us),
  • The age of the universe times the speed of light is infinite.

The first condition says all lines of sight terminate on stars. The second says that we see that stellar surface, whether we have to wait an arbitrarily long but finite time for it to get to us (because $c$ is finite, but we have an infinite past during which light traveled), or not (because any finite distance is covered instantaneously, so it doesn't matter how long the universe has been around).

Note by the way that infinitely quickly propagating influences and infinite, homogeneous universes don't mix well at all, not just with regard to light. For instance, the gravitational effect on us by an infinite, uniform distribution of mass is undefined in Newtonian cosmology. So even before Olbers, Newton knew something had to give if one wanted an infinite universe.

Related Question