High School Curved line shortest distance between two points?

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The discussion centers on the concept that in curved spaces, the shortest distance between two points may not be a straight line, as illustrated by the analogy of walking across a soccer field versus around its track. This principle is rooted in Einstein's theory of general relativity, which posits that mass distorts spacetime, creating curvature. Participants reference real-world examples, such as intercontinental flight paths, which utilize curved routes for efficiency and cost savings. The concept of geodesics, which describes these shortest paths in curved spaces, is mentioned as not being introduced by Einstein himself. Overall, the conversation seeks to clarify how curvature affects distance and the implications of this in physics.
ChrisisC
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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?
 
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ChrisisC said:
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.
 
ChrisisC said:
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.
 
Dale said:
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)

upload_2017-1-4_3-56-47.png
 
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ChrisisC said:
Why did Einstein propose this?
What exactly are you referring here? The concept of geodesics was not introduced by Einstein.
 
A.T. said:
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.
 
ChrisisC said:
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.
 

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