E=Mc2

[a_lost_packet_]

...How can gravity bend light around a gravitational field, and not change its speed?

Edit: I'll rephrase that. Gravity causes light to no travel in a straight line, therefor changing the lenght of time it take us to see an event. :shock:

But, it is a straight line. It's "spacetime" in which the light is traveling which has been distorted by gravity. There simply isn't any other "straight line" for the light to travel. Gravity has not "bent light" as far as attracting photons like one imagines a rocketship may experience being attracted by (and attracting in exchange) the mass of the planet. The planet has simply curved the spacetime in which the photons travel. They have no other choice in the matter.

If you could make a curlicue helix out of spacetime, light would still go 'round and 'round at the speed of light. Likewise, a black hole distorts spacetime so much that light simply does not have the energy to climb out because, for illustration, the gravity well is "too steep."

 

[ramparts]

a_lost_packet is exactly right. Here's a useful thought experiment:

Imagine you're in an elevator which is accelerating upward at a very high speed. Suppose at one point, someone shines a light beam through a window in the elevator. What will the path of that light beam be? Well, obviously it will appear to curve down, since the elevator has moved up by the time the light (traveling on a straight line) gets to the other side. So you have an instance in which light thinks it's traveling in a straight line - and is obviously still traveling at the speed of light - but is curved in your accelerated frame.

In fact (extra fun bonus) this is exactly how they discovered the gravitational bending of light that you're talking about. One of Einstein's biggest breakthroughs - possibly his biggest - was the equivalence principle, which can be interpreted as saying that an accelerating frame (such as this elevator) is equivalent to one in a gravitational field. So any experiment you run in that elevator will have the exact same results as if the elevator were stationary in an equivalent gravitational field. Naturally that includes the bending of light.

Note that at no point has the speed of light changed - it's following what looks to us like a curved path, but what it thinks is a straight path, called a spacetime geodesic. A geodesic through a curved surface is a curved line which in fact happens to be the shortest distance between two points, which is what a straight line normally does. Think of longitude lines on the surface of a sphere - they're curved paths but they're geodesics because between any two points on the longitude line, a segment of that line is the shortest path between them.