Is curved space detectable ? how?

Question

i took a thought experiment to the physical level by using a beach ball and a sphere of space the same size as the beach ball, to check the curved space theory. i frist took a string and attached it to the north pole of the space sphere and attached next to a point on the equator, from there i made a right angle turn along the equator and went a quarter of the way around the space sphere and affixed the string at that point from there i turned north and back to my starting point the north pole, all the while making sure the string stayed taught.and according to theory the three angles should add up to more than 180 degrees but every time i try it i only get 180 degrees. i would like to know what i'm doing wrong before i move on to the beach ball. it seems curved space is more complicated than it looks. does anyone know where i'm making the mistake. thank you. gravity guru.

Answer 1

The curvature of space that general relativity predicts is impossible to pick up on small scales on the level you're talking about. When you do that thought experiment, the triangle you draw won't have a sum of 180 degrees, but rather something very close to it. You wouldn't be able to measure the curvature of space with tools like a string on the scale of a meter in length.

However, relativity has been confirmed in a variety of different ways. Perhaps the most famous (and indeed the original one that famous confirmed relativity in 1919) is that we can see our Sun bending light through the curvature of space; we can see light from stars that are normally "behind" the Sun sometimes that we could not otherwise see. Another example is that the orbits of the planets are not quite the same as predicted by Keplerian/Newtonian equations, and the 'correction factor' provided by general relativity exactly predicts the correct orbit of the planets in the Solar System.

Answer 2

Well, I bet you measured wrong.  So, you start at the north pole and move to the equator.  Then you turn by 90 degrees and start moving along the equator.  You go 1/4 the circumference and make a 90 degree turn back toward the north pole.  So, at this point, you made two 90 degree turn, which add up to 180 degree.  When you get back to the north pole, you will end up making a 90 degree angle with your first path, to give you a total of 270 degrees.  This is greater than 180 degrees, just as you wanted.  In fact, you make a 90 degree turn to get onto the equator and a 90 degree turn to get off of it, so no matter how far you travel along the equator, the third angle will have to add with the first two 90 degree turns to make a total of greater than 180 degrees.

And to answer your title, yes it is detectable, and it was first done by looking at stars behind the sun during an eclipse.  They could see stars the sun should have obscured, but because the sun is so massive, its gravity bent light rays from those stars that would have otherwise missed the earth and made those rays hit the earth, allowing astronomers to see these stars that were behind the sun from our viewpoint.  This is called gravitational lensing.  But being a gravity guru, you probably already knew that.