Gravity bends spacetime, does the amount of lightray-bending correlate?

AlSo

If gravity does not act directly on objects, rather it distorts nearby spacetime, objects falling towards a massive object are just following the geometry of the distorted spacetime. Why is light ray not-so-readily following this distorted spacetime? The "straight line" light ray travels should be along the distorted spacetime curvature, light ray should be the easiest and most ready traveller which follows the curved spacetime, more ready than any other objects. Does the amount of lightray-bending correlate with the amount of spacetime distortion? Thank you.

Passionflower

Yes it does.

AlSo

Thank you Passionflower!

A.T.

No. All free-fallers advance through spacetime according to the same rule, and the bend in their spacetime-paths is comparable. But when you project those spacetime-paths onto the space dimensions, the slow object's space-paths become more bend, then light's. That is because light moves more though space than slow objects, so the projection spacetime->space distorts the slow object's paths more.

In short you have to differnetiate between :
- path-curvature in spacetime
- path-curvature in space

Passionflower

The paths in spacetime are not the same it depends on the object's momenta.

A.T.

Of course not, as I said: light moves more though space than slow objects. So the path in space time is obviously different.

Do you need the object's momentum to predict its worldline in a gravitational field? Isn't the initial velocity and position enough information?

Passionflower

Huh?

So you think that for an observer on A light moves through more space going from A to B than a rocket does?

If that is what you think then you are completely wrong.

A.T.

Nope. Light advances through more space than the rocket in the same observer time.

ETA: Maybe a better way to put this is: The light-path in spacetime is closer to the spatial axes, so it is distorted less when projected onto the spatial dimensions.

Passionflower

Prove it!

From a stationary observer on A both a turtle and a hare travel exactly the same distance from A to B and so does a light ray except when the spacetime is non-stationary.

A.T.

That the rocket travels less distance than light in the same time?

Passionflower

Oh in the same time for a particular observer, yes something that travels faster covers more space than something that goes slower.

AlSo

thanks gentlemen, when a light photon travels through a distorted spacetime/space, does it "see" the spacetime/space as straight lines? If it does it will curve at ease. If it does not it is probably jumping across spacetime/space lines and insists on its own "straight" path according to its own "straight" reference. What I have in mind is, when spacetime/space are wrapped, the idea of "straight" is loss and everything travels through it will see the distortion as "straight" regardless of their speed and momentum. Am I correct?