Equivalence Of Inflation And Motion: A Thought Experiment

Imagine two, pure white, snooker balls slowly and steadily moving towards each other from opposite ends of a snooker table. Now imagine if the table and world vanishes so that the two balls are moving in a black void. What do we see?

We see two balls moving towards each other. We can't tell which is moving or both, because we have no background to relate to their motion. All we can see is that they are getting closer to each other. This one moving and the other not, is exactly the same as the other moving and this one not, which is exactly the same as both moving.

Is that all we see? As the balls move closer, we could say that they appear to be getting bigger because the gap between them is getting smaller. This is easier to picture if we fly high up and start the tiny snooker balls one mile apart. They are tiny white dots at either end of our viewpoint. Now, as they move towards each other we move closer to them too. They look like they get bigger and bigger as they, and we, get closer and closer. If we move closer at the same rate as they move, so that we can always keep their central point in the same place in our field of view, the balls don't look like they are moving at all but inflating; they appear to expand from a small dot until they touch each other. Movement of the balls and expansion of their size has become equivalent.

Perhaps we are cheating here, as we are moving too. It is our perspective that makes it look like the balls are expanding rather than moving, but, as in the first example of motion, what if, instead of us moving towards the balls, the balls are moving towards us and we are stationary? As before, the two results would be identical.

Also, if our only view of the scene is from our perspective then any observation from that perspective is valid as truth. The only alternative is a omniscient knowledge that the two balls are moving, versus expanding, and we don't see this from an external perspective, merely know it. Can this ever occur in reality?

Perhaps the expansion effect of the balls is something more fundamental than a illusion, but the perspective is important, so this effect only works in at least two dimensions when the balls are moving along only one.

As well as motion appearing to be expansion, of course the reverse can be true. Two inflating balls could look like they are remaining the same size and merely moving, if we back away at the same rate that they are inflating. So, based on our viewpoint, and with only two balls in an empty universe, we can't tell any difference between motion and inflation.

All of this made me consider the expansion of the universe. Could an expanding universe be visualised as an illusion of motion through a higher dimension? If we were placed inside one of the balls as it moved, assuming its walls were transparent, what would we see as we looked towards the direction of movement? We would see a smaller distant ball get bigger and bigger as it got closer.

Is it fair to think of size in terms of the illusion of perspective? I'm reminded of the joke of toy cows vs. real cows that are far away. Perhaps the word illusion is deceptive. One could argue that if something looks like it is getting bigger, then it is, if we are the sole observer of reality. If we had but one eye and no way to perceive depth, could we tell the difference between small things and distant things? If things were distant in an extra dimension, could these be seen as small, and we remain oblivious to their true nature of being distant in that dimension?

Mark Sheeky, 19 November 2018