• Question: Does bending of light due to warping of space violate Fermat's Principle or is it that in the principle light goes in a straight line with respect to space(taking space as the reference) and in Relativity that reference itself is bending and so does the light?

    Asked by rajathjackson to Dave, David, Jack on 28 Jun 2013.
    • Photo: Jack Miller

      Jack Miller answered on 28 Jun 2013:

      Hi Rajath,

      Fermat’s principle is best stated as ‘light takes the path of least time’. In ordinary, Euclidean space, this happens to be a straight line — but the whole point about general relativity is that it’s the shape of space itself that is bent. This changes the path that is ‘a straight line’. This is formally encoded mathematically in something called ‘the metric’, which is specifically constructed to measure distances in space — and that metric varies as the shape of your space does.

      Hope that helps,

      — Jack

    • Photo: David Freeborn

      David Freeborn answered on 28 Jun 2013:

      Hi Rajath,

      No, it doesn’t violate Fermat’s principle. Light always does go in a straight line.

      But bending space changes what a “straight line” is!

      You see, mathematically, we define a straight line as the shortest distance between two points. In so-called Euclidian geometry, that’s the familiar type of straight line you are used to. But as soon as we start bending space, the “metric” that defines a straight line varies.

      This leads to an effect called gravitational lensing around very massive objects, like stars: