Why It Slows
Many of you have seen bits of this lecture before, so thanks for your patience. I will conclude with a new way of visualising c change.
An important lesson from Relativity is that Space and Time are really the same phenomenon. Humans are already hardwired to think this way. Few people know exactly how many kilometres are between work and home, yet most know how long it takes to reach work, often down to the minute. We are used to saying "8 minute drive" or "30 minutes away." The conversion factor is the speed limit of your vehicle.
Intervals in Space/Time are either Spacelike or Timelike. The lightcone follows the metric dr = cdt. Outside this cone, the interval is Spacelike. An event at the lightcone's origin can not affect an event outside. Inside the lightcone, the interval is Timelike. The difference is literally a matter of Time. The conversion factor here is Nature's own speed limit, the speed of light.
The local conditions of Special Relativity, which does not allow for gravity, are part of the curved Space/Time of General Relativity. There is no centre in Space, for every bit resembles every other bit. There is a centre in Time, called a "Big Bang." Our timelike separation from this origin is age of our Universe t, about 13.7 billion years. Now we state a simple principle: The characteristic scale, or radius of curvature R = ct. This is why, as t increases, the Universe expands. That is what powered the Big Bang and continues to drive expansion today.
The Universe can't expand at the same rate forever, because mass and gravity slow it down. Gravity then requires that:
GM = tc^3
Where G is Newton's gravitational constant, M is mass of the Universe. When t was tiny c was enormous, and the Universe expanded like a Bang. As t increases, expansion slowed due to gravitation and continues slowing asymptotically to this day. The curvature radius R, the Schwarzhild radius of a Black Hole, photon wavelengths, and even the size of magnetic fields increase at exactly the same rate!
Here's another way to explain c change. Photons can be thought of as satellites orbiting around the "Big Bang" origin. If you were an astronaut in low Earth orbit, satellites whizzing by your altitude in circular orbits would all have the same velocity. As a satellite's altitude increases, velocity goes down. Every photon that passes by at that moment has the same velocity and timelike separation from the Big Bang. As the Universe expands, that separation grows. Velocity of photons thereby decreases at a very small rate.
As you see, these equations are simple enough for a child to understand. Yet it has taken humans centuries to figure this out. Most physicists still can't explain it, leading to "dark energy" and other epicycles. Is it not fun to discover something simple?