Curved Space

[pgrmdave]

Assuming that the universe is curved through the fourth dimension, is there anyway to measure that curve? To relate it to terms more understandable, the earth is a 2d surface curved through the 3rd dimension, that curve is measurable, even with local anomalies, i.e. mountains, valleys. Is there any way to discover the curvature of the universe, and would we be able to make sure that it wasn't a local anomaly?

[BlameTheEx]

Pgrmdave

 

Not without making unwarranted assumptions about the nature of the universe. For me the hubble constant is a measure of curved space, and not a measure of expansion, but I can hardly claim it as a popular belief.

[pgrmdave]

How would you explain the red shift in galaxies if not by expansion?

[Bo]

yes you can measure such a hypercurvature, because it defines the geometry of the embedded space. To stick with the example of the earth: (or any sphere)

 

Flat geometry (like a sheet of paper) has 2 defining properties:

- parallel lines don't intersect

- then angles of a triangle add up to 180 degrees

 

Sphericle geometry however has:

- parallel lines intersect at at least 2 points

- The angles of a triangle add up to more then 180 degrees

 

(Note: there is also something called hyperbolic geometry, which has the opposite properties)

 

These 2 properties can be easily seen by thinking of the earth.

- picture 2 circles, both starting at the north pole, going over the equator, over the south pole, back to the north pole. Clearly these 2 circles intersect; but at the equator, they are exactly parallel, since they bove intersect the equator with 90 degrees.

- picture a triangle, starting at the equator, going straight up to the north pole, there making a 90 degree angle, going down to the equator, and from there back to the starting point. by the same argument as above, the angles of the triangle add up to 3*90=270 degrees.

 

bo