Why Does Light Travel the Shortest Path?

[Cobalt101]

Why does light (or indeed any object) travel the shortest path between two points (whether for flat or curved space/space-time) ?

 

[phinds]

Why does light (or indeed any object) travel the shortest path between two points (whether for flat or curved space/space-time) ?

Well, it DOESN'T travel on a geodesic if there is a force acting on it, only if it is in freefall (no forces).

 

[Cobalt101]

But my question is if there is no force acting on it (i.e. free fall) why does it travel on the geodesic?

 

[PeterDonis]

Why does light (or indeed any object) travel the shortest path between two points (whether for flat or curved space/space-time) ?

Do you mean the shortest path in space or the shortest path in spacetime?

If you mean the shortest path in space, it's not always the case that light, or any object, takes that path. You need to be more specific about what scenario you are talking about.

If you mean the shortest path in spacetime, that concept as you state it has no meaning for light, since the spacetime interval along a light ray's worldline in spacetime is always zero. For ordinary objects, if they are in free fall, then the path they take through spacetime is the longest path between two events, not the shortest.

 

[PeterDonis]

if there is no force acting on it (i.e. free fall) why does it travel on the geodesic?

A geodesic is defined as the path in spacetime that a freely falling object takes. The reason it's defined that way is that that's what makes the spacetime geometry model work correctly, i.e., make correct predictions.

 

[Cobalt101]

Do you mean the shortest path in space or the shortest path in spacetime?

If you mean the shortest path in space, it's not always the case that light, or any object, takes that path. You need to be more specific about what scenario you are talking about.

If you mean the shortest path in spacetime, that concept as you state it has no meaning for light, since the spacetime interval along a light ray's worldline in spacetime is always zero. For ordinary objects, if they are in free fall, then the path they take through spacetime is the longest path between two events, not the shortest.

I guess my question is at the basic end of things, trying to understand how the bending of space actually "works", what is the mechanism- for example, why does a planet follow the geodesic around the sun ?

 

[A.T.]

why does a planet follow the geodesic around the sun ?

Geodesics in space-time is a human made model. It's our interpretation of the world. Why we use that interpretation? Because it works for making quantitative predictions.

 

[Drakkith]

I guess my question is at the basic end of things, trying to understand how the bending of space actually "works", what is the mechanism- for example, why does a planet follow the geodesic around the sun ?

Well, if you consider a classical flat space you could then ask why objects travel on straight lines when not subject to a net force.

 

[Cobalt101]

Yes - that is a subset of the question. Is there any understanding as to why this is the case (ie as no forces are involved)

 

[Drakkith]

I believe it is simply an axiom of physics. Perhaps it would be better to ask what would happen if that principle wasn't true?

 

[PeterDonis]

what is the mechanism- for example, why does a planet follow the geodesic around the sun ?

You're looking at things backwards. Saying that a planet follows a geodesic is our way of modeling what happens; we model it that way because we've found that that model makes good predictions. But the physics comes first, then the model. Asking why planets follow geodesics implies that the model comes first, then the physics; that's backwards.