In the above image we show a length dilated image of a galaxy as it appears to us from a distance. We make the assumption that the elliptical appearance of the galaxy is the consequence of length dilation which results in a distorted image. Each section of the galaxy is deeper within the gravitational well, and since the force decreases following the Inverse Square Law the shape of space is distorted, since each ring represents equal space.

Light must travel through distorted space to reach us, and the light from the very center of the galaxy must travel through ten of these rings of distorted space (in the simulation above) while the light near the edge only travels through one ring.

Let’s assume that John is one of the outer rings, on the left, and time is running is faster, as symbolized by the wave length, and John’s ruler (in yellow) is also less dilated in length. John measures the speed of light against the ruler (the blue arrow) and of course John gets the result that the speed of light is 300,000 kilometers per second.
On the image on the right time has slowed down, and John’s ruler is also length dilated. John measures the speed of light using a slow clock and a short ruler and gets the result 300,000 kilometers per second.

Now for the sake of simplicity we will assume that the difference is one half, in that the length dilated ruler is dilated by one half and that the clock is running 50 per cent slower on the right. Let’s assume that the ruler on the left is 300,000 kilometers long, and in comparison the dilated ruler on the right is 150,000 kilometers long, relative to the length of the first ruler, since length is relative in this universe. Therefore it takes light one half second to traverse the length dilated ruler, given the slow clock. Therefore the speed of light must be a constant, and not a variable constant.

Therefore my statement that the speed of light slows down like molasses down in some gravitational hole must be incorrect, and I thought I would pose this thought experiment so that others can consider the matter and come to their own conclusions.

Now if I am thinking straight here, this would imply that even though light had to traverse ten rings of distorted space from the center of the galaxy, nevertheless, our view of the galaxy center is not time dilated with reference to our view of the outer edge.