Originally Posted by

**Mayflow**
Originally Posted by

**Markus Hanke**
There are 2 choices, one is the speed of light is a constant, the other one is the speed of light is not a constant.
The speed of light in vacuum is neither constant nor varying, it is a

**relativistic invariant**. The distinction is very subtle and is irrelevant in flat space-time, but it is very important in curved space-times, such as extended regions around massive bodies, because then we have to account for the differences in

**coordinate speed** and

**proper speed**. Coordinate speed of light actually does vary ( in fact it drops to zero at the event horizon of a black hole ), but the speed of light being relativistically invariant means that proper speed - which is what is physically measured in a local rest frame - is the same everywhere. Only the latter is physically meaningful since in curved space-times there is no global notion of time. Proper speed to be everywhere locally exactly

*c* just means that all observers experience the same laws of physics, regardless of where they are and how they move. This leads to the very counter-intuitive result that no stationary far-away observer ever sees anything reach the event horizon of a black hole, while at the same time someone in free fall will cross it in finite and well-defined proper time as measured on his own watch; this is

**not** a contradiction, but a simple manifestation of the nature of gravity.

Marcus explained the issue quite nicely and any attempt to elaborate on it would likely make it sound more complicated than it is but I could offer a crude explanation of some of the terms.

The "global notion of time" is what I like to call a "god's view of time." This would be how time might appear to an observer beyond our universe with a time-frame independent of ours. Such an observer would see time in our universe passing at different rates in different parts of the universe.

From a global perspective, the speed of light can vary but there is no such thing as a gods eye view of the universe to tell us which is the "preferred" or "absolute" speed of light.

A local rest frame is the point of view of an observer that is inertially at rest. (Not accelerated in any direction.) A rest frame can be in motion as with passengers on a plane who may be moving but they feel no motion.

Flat space-time is the familiar 3-D space of Euclid, Newton, and Special Relativity where time and space are uniform in all locations and parallel lines never meet. This is our intuitive view of the world.

Curved space-time is the space-time of General Relativity where parallel lines meet at a great distance and cross like the longitude lines on the curved surface of a globe. This is described by the 4-D geometry of Riemann.

The amount of curvature in curved space-time can vary something like a sheet of graph paper made of rubber only the curvature is in four dimensions of space. 4-D space is impossible to imagine and it is hard to think of either space or time as curving but the curvature is what we observe as gravity. The greater curvature about a massive body, the greater its gravity.

I prefer to think of curved space-time as "shorter space and slower time" because that is the effect we observe as space-time becomes more curved. Time slows and distances shorten and these differences cause ponderous bodies to move together in curved paths- gravity.

"Coordinate" speed is the speed of objects observed at a distance and the coordinate speed of light can vary. We can observe the speed of light slowing in the presence of of massive bodies because of gravity.

"Proper" speed is the speed of an object as it is measured from the location of the object itself. Passengers on a plane observe motions inside the plane in proper speed.

It is contrary to ordinary experience to find rate of coordinate speed to be any different from proper speed. A person walking on the ground appears to move just as fast as a person walking on a plane. But, at relativistic speeds close to c or in a gravitational field far from ones own, the two speeds begin to part company.

Even though the coordinate speed of light (that of a remote observer) may vary because of changes in speed or gravity, the proper speed of light (locally observed) never changes because local variations in space and time are always proportional to c.

The speed of light is a constant when measured relative to ones local environment so c is said to be relativistically invariant. This makes c a physical constant.