# How warped spacetime bends trajectories of light and moving objects?

I fail to see why the light follows something like the blue line and not the green line on the attached image.

• Figure 1 - light bends around warped spacetime

Afaik. something similar happens with Earth when it cannot escape from the space warped by the Sun. Otherwise it would leave the Solar System on a straight line.

• Figure 2 - Sun bends the spacetime around itself, so Earth cannot escape - ref

I thought about these space warps. Maybe I am wrong, but I think it is possible to describe them with 4d coordinates, where the 4th dimension is the warp of the spacetime, or the depth of the gravity well, or something like that.

• Figure 3 - Travel in warped spacetime with 4 coordinates

So if we are traveling through warped spacetime, we experience that the distance is longer and the trip takes more time than we expected, because we travel in the 4th dimension as well, not just in the regular 3 dimensions. But with this model we should not end up in a different region of space than we planned if we go forward on a straight line.

What am I missing?

Note that I have not a clue about physics, so please try to explain it on a human language! xD

• To approach this question from a different perspective than my previous answer, what would be causing the green line to bend back towards its initial path? I know that if you covered up the mass in the middle with your hand, you'd assume that there was nothing there and that the line would continue moving in a straight line, but if you can accept that the light gets bent leftwards initially, then you would probably have to place another mass to the right to bend it back, and then a mass on the left to straighten it out to line up with its original path. Does that help? – Ben Sandeen May 2 '18 at 19:03
• @BenSandeen Interesting. So do you say it bends only to one direction? Does it always magnify the background? If so, then negative mass to the (almost) same direction could bend it back or another mass to the opposite direction. – inf3rno May 2 '18 at 23:43

The main idea is that it follows the path of least resistance. The light "wants" to travel the shortest path, which is (almost) always a straight line. However, since spacetime is curved, this straight line happens to be curved as well! Shown in the image are two hypothetical light paths, one that follows the curvature of spacetime and one that doesn't.

Consider the drawing on the left first. Initially, it might appear that the one that goes straight (the yellow line) would be travelling the shorter distance, because it looks like a straight line on the chalk board. However, it isn't a straight line, because the spacetime it's in is curved. Likewise, while the red line appears to be longer, it's not, because it's actually following the straight line in the spacetime that it's in.

If we "uncurve" the spacetime, we can clearly see that the yellow line is actually the longer of the two. Since the light "wants" to minimize the distance it travels, it'll end up taking the red line's path. The reason that it "wants" to take the shortest path is beyond my ability to explain, but it can be solved using the Variational Principle.

• Interesting. What I thought of that we can see objects packed into curved spacetime much smaller than they really are when we enter to the same region of space. For example if something is inside a black hole, we cannot see it from the outside, because the spacetime is so curved there, that light does not have enough time to travel through it. According to your answer curved spacetime works differently than I think, or your left drawing is from the perspective of the outside world, and the right drawing is from the perspective of the inside world, as we would "see" it from the curvature. – inf3rno Jan 15 '16 at 19:46
• I believe the correct way to interpret the drawings is that the left one shows how spacetime looks to us, while the right shows how spacetime itself thinks it is curved. – Ben Sandeen Jan 20 '16 at 17:58

I think once you accept that gravity can bend space-time, it is straightforward to accept that light will just follow these curved lines. the real question to me is why can gravity bend space time ? I mean, I fully understand that when considering two mass bearing objects but it is harder to comprehend when we talk about electromagnetic waves...i think if this mechanism would be understood, that would pave the way of unifying the gravity with electromagnetism

• I think this should be a comment. Ohh I see, with 1 score it is hard to comment. – inf3rno May 12 '15 at 19:28
• Also I may be incorrect but I don't think gravity bends space time. Mass bends space time and that bending is what we call gravity. – jheindel Sep 7 '15 at 19:28