Curved line shortest distance between two points?

[ChrisisC]

Can someone explain how this is possible? it makes no sense to me. You wouldn't walk along the track surrounding a soccer field if you wanted to get to the other end... you would walk straight across the grass to reach your destination. Why did Einstein propose this?

 

[fresh_42]

Can someone explain how this is possible? it makes no sense to me. You wouldn't walk along the track surrounding a soccer field if you wanted to get to the other end... you would walk straight across the grass to reach your destination. Why did Einstein propose this?

Imagine the field isn't flat, but 200 yards high. Would you still walk over the grass? This is basically what it is about in spaces with curvature: a giant heap in the middle. Or take the earth. There is no way directly through it. Masses bend spacetime and thus it has a curvature and the shortest way isn't a straight line anymore.

 

[Dale]

Can someone explain how this is possible? it makes no sense to me.

Have you ever seen a map showing intercontinental airplane routes? Why do you think the airlines use curved routes if not because they are shorter and therefore save money.

 

[fresh_42]

Have you ever seen a map showing intercontinental airplane routes? Why do you think the airlines use curved routes if not because they are shorter and therefore save money.

Good idea! (black is the shortest way, grey the direct line - it shows at least the principle)

 

[A.T.]

Why did Einstein propose this?

What exactly are you referring here? The concept of geodesics was not introduced by Einstein.

 

[ChrisisC]

What exactly are you referring here? The concept of geodesics was not introduced by Einstein.

In the book "Hyperspace" by Kaku, Kaku says that Einstein said a curved line is less distance than a straight line. I'm assuming Kaku said this because it refers to GR. I could be wrong.

 

[A.T.]

In the book "Hyperspace" by Kaku, Kaku says that Einstein said a curved line is less distance than a straight line. I'm assuming Kaku said this because it refers to GR. I could be wrong.

Could also mean the pseudo-Euclidean line interval in Minkowski space time.