Geodesics

[Racoon]

Geodesic - Least-energy path between two points in space-time

;)

 

Doing a lil' research, and am wondering (trying to imagine really), how Objects follow these "contours in space" requiring the least expenditure of energy.

 

Einstein talks about "Coordinate systems belonging to accelerated frames are curvilinear; suitabily imagined as grids drawn on rubbery surfaces that can be tugged, stretched, or deformed."

 

So, Matter itself creates and molds the space in which it moves! :)

The behavior of matter in a gravitational field only points up the contours of space in that region.

Gravity, being the accelerating force, means that interval calculations will show timelike seperations for nonequivelent paths through a field.

With increasing acceleration, a stronger field, time slows...

 

Matter shapes Space! :)

 

which brings us close to Black Holes ;)

and Time

 

Kinda' paraphrased a bit...

What do you think of Geodesics?

anyone have embedding diagrams??

[InfiniteNow]

I like the examples given in most texts I've read...

 

Imagine a bed sheet held afloat at all four corners. Put a tennis ball on it, it travels toward center and makes a dimple. Put a heavier (let's say bowling) ball on it, and the dimple becomes an even bigger depression in the sheet. Now, roll the tennis ball around the sheet w/ the bowling ball in the center... it travels toward center much faster than it would if another tennis ball were sitting there. That's an illustration of gravity warping space time...

 

Je le pense...

[HydrogenBond]

There is a slight wrinkle, sorry for the punn. If we look at the earth, the gravity vectors cancel in the center of gravity. The sheet sags around the balling ball but rises in center to the height of the edges. It still amounts to same thing for the tennis ball, but it should keep the tennis ball from ever reaching the center of gravity.