Light Curve Space: Maintaining Speed Constant

[MNC007]

if light is traveling by a curved space, for example near the sun, how can it maintain speed? shouldn t go slower? to keep the speed constant in a curve you have to accelarate...

 

[G01]

When working with curved spaces, you have to generalize your definition of a straight line path. Specifically, in a curved space, light will travel along a "geodesic" which is the generalization of a straight line to curved space. A geodesic is the shortest path you can take between two points in a curved space, just like a straight line is the shortest path between two points in flat space.

So, You shouldn't think of the light traveling through curved space as if the light was traveling in flat space and turning around a curve. Instead, its the space itself that is bending.

Think about a light ray traveling in flat space. It travels the shortest path between two points, a straight line (the geodesic in flat space) and is not accelerating at all. Agree? Now the presence of the massive sun intrinsically warps the space itself, changing the geodesic the light will travel. But the light still travels along the geodesic, the shortest path.

A more familiar analogy may help: Think about walking in a "straight line" from Boston to Seattle. In reality you are walking along a curved path along the surface of the earth, but to you, stuck in the curved space of the Earth's surface, the path "feels" equivalent to a straight line. i.e. its the shortest path you can find.

 

[_PJ_]

Also note the difference between speed and velocity is that velocity is a vector quantity which refers to direction. Speed only has magnitude.

So light travels at a constant speed, even though its velocity may change.

Consider a threoretical, perfect planet orbiting a perfect star. The planet orbiots at a constant angular velocity, its speed stays the same, although its linear velocity is continually changing with its direction.

 

[MNC007]

Thanks to both. I´ve got it now!