Grendizer said:
Hello DrewD,
My problem is visualizing how space is curved at gravity and how the light travel in this curvature? Initially I thought there was some sort of "gap in space" or "interruption" at gravity point, which affects the path of light. That's why I made a 2-D universe, just to make it as simple as possible and make my point clear.
I am going to try to rephrase my question differently. As shown in the attached figure, let's imagine space is curved without a body, a glitch in a hypothetical world. My question is then to you, how would the light travel?
Perhaps you mean to say a 2-d representation of the path of light in a 3-d special universe. In a 3-d universe gravity follows a 1/r^2 law according to Newton versus 1/r in a 2-d universe. Best to stick with the 3-d spatial universe with a 2-d picture of the path of light, rather than having to invent new physics where you do not know where it will take you.
If you have an object influenced by a gravitating mass such as a star, then the object follows an orbit which can be elliptic or circular. If the object is not in an actual orbit then the trajectory is parabolic or hyperbolic depending upon whether the velocity of the object is equal to the escape velocity or greater.
Light also follows these rules since it is influenced by gravity, but since its speed is so great you will be hard pressed to find anything other than a hyperbolic orbit due to Newtonian mechanics.
Along comes Einstein with his theories of relativity and gravity and the situation changes somewhat. A famous experiment involving an eclipse of the sun (by the moon) occurring in the beginning of the 20th century( early 1900's WWI). Eddington and his team traveled to the southern hemisphere to observe the positions of stars near the sun using an occult disk with a telescope. Eddington declared the experiment a success for general relativity in that the shift of the stars close to the sun's edge from their "real" position to an "apparent" position due to the gravitational influence of the sun on light was experimentally determined to be twice that as for Newtonian gravity, as calculations had determined. ( due to the errors of the technology at the time, and the physics of the sun, the experiment was not really a "true" verification, but who was to argue with Eddington ).
In any event. light does curve around a massive object, and if you are speaking spacially, then the red curve in one of your previous posts is not correct, but the others paths would be more representative of the lights' spatial path.
In addition, one can consider the massive object as having what is sometimes termed as a gravitational well. The object or light passing by the gravitating mass enters into the well and exits. How far into the gravitational well the object enters would be a function of how close it grazes by the mass, and of how large the mass is. Your red line can then be thought of the path as an object or light entering and exiting the well. One can then see that by doing so the object or light has a longer path that curves in and out a bit than a more straighter path farther from the object. Since a path closer to the large mass has this dip into the well and becomes longer, the time for the light from the object also takes longer to reach you than the straighter path farther out.
So while you have drawn several paths, some straight, some curved, and some with a dip, neither of them is actually correct or incorrect, except for the fact that you have to specify what you are describing ( which was alluded to by the post from Drakith ). You can also see that the stretched sheet does have something in common with the ideas of a gravitational well represented by the dip in the sheet if a mass is placed upon it.
