In general relativity, gravity is said to be caused by the curvature of space time. And there are examples that illustrate gravity such as this video https://www.youtube.com/watch?v=MTY1Kje0yLg, and many pictures online. But in these examples space time in essentially just a 2-D plane that sinks down when an object is placed on it. I guess you could say that in these examples gravity is portrayed to be a literal potential well in space time. Also, this is a man on Earth 
. This man could just jump off earth into space since he is above the potential well. Shouldn't the proper illustrations have potential wells all around the object?
Asked
Active
Viewed 215 times
1
PiccolMan
- 741
- 1
- 7
- 17
-
To be precise, space-time is four dimensional. It is the defect of the picture (or cartoon, whatever it is) that it shows space-time to be just 2-D. – SchrodingersCat Feb 18 '16 at 04:32
-
this ( common ) illustration is not relevant. To show a curvature, you need a time coordinate. Or at least a grid representation – Feb 18 '16 at 04:32
-
How would the time coordinate fix everything? Also shouldn't space time be 4d? – PiccolMan Feb 18 '16 at 04:41
-
Possible duplicates: http://physics.stackexchange.com/a/13839/2451 and links therein. – Qmechanic Feb 18 '16 at 07:50
-
@John Rennie can you link the duplicate please. – PiccolMan Feb 18 '16 at 15:56
1 Answers
2
The video you link to is a good illustration of a model of how gravity behaves in two dimensional space cuts of reality, in time. Your diagram above reduces the space dimensions by one and fixes time to t=t1. In doing that the rotational direction is lost. The man can jump ( we do send rockets off the earth after all, no? ) given the energy to do so.
It is illustrating how thinking in terms of potential, as we do in Newtonian physics, is equivalent mathematically in thinking in terms of space distortion.
anna v
- 233,453
-
Just pretend my diagram is of a 2d plane, and that time is not constant. But the problem is that the man is not in a potential well (he is above it), thus, with just one little jump he can go into space. – PiccolMan Feb 18 '16 at 16:01
-
@PiccolMan The potential well of the earth with respect to the size of the potential the man is on is thousands of time deeper than you diagram. The video is showing planets around a sun analogy. man would be the size of an atom on that analogue. – anna v Feb 18 '16 at 16:04
-
but even then the potential well for people on the bottom of earth w/ respect to my diagram would be greater than for people on the top (where the man is). It doesn't make sense for gravity to be stronger on one side of earth. – PiccolMan Feb 18 '16 at 16:13
-
One should not stress analogues to the extreme. It is surprising that it works on lines to give intuition how curvature could show attractive behavior. It is not to be taken instead of newtonian or general relativity mechanics. You should read the answers in the duplicate links. – anna v Feb 18 '16 at 16:25