Relativistic Doodles

This post explains how my illustration of general relativistic time dilation works. This is the parent post.

Here is an image of a simple classical timeline:


There are 2 observers: green and red. They have their own watches. The red observer shoots an arrow towards the green observer. The position of the arrow vs. the time recorded by the two observers looks like the picture above. If we take a trace of the trajectory of the arrow, we get:


If we were to take the trace of a 2 signals 1 second apart that travel at constant speed, and 2 signals 1 second apart and traveling instantaneously, we would get:


You will notice that the components of all 4 traces (like the ones drawn in grey) are parallel and perpendicular to the space-time axes. This is always the case. So even when I distort the edge of the red timeline a bit, I get:


So if I am standing with the red observer, and I see him sending out signals, I will not notice a difference even when the red timeline distorts, because to me, the components of the signals are still parallel and perpendicular to my space and time. In the same way, when an observer is falling into a gravity well (like that of a black hole) and sends out signals, the observer does not notice the relativistic effects of gravity on the signal. However, the observer who is standing far away from such distortions notices an altered signal. So even though the signal at t=8 was instantaneous according to the red observer, it reached the green observer at t=9.

If you understood this, then you will know what is wrong with this set of traces of signals that a red observer sends as she falls into a black hole: