Is the universe a conspansive manifold?
There are hints that space and time are discrete. These hints are of mathematical nature: If 1/3 is 0.333..., then 3/3 is 0.999... although 3/3 is the same as 1. So there is not an infinite number of decimals. Sooner or later we will make the step to the next integer.
Another argument is that if a tortoise starts at 1 m after the hare and moves at half speed, the hare will sooner or later catch up. However, if you always divide the distance the hare moves by two, in theory the tortoise will always be ahead, so if you argue like that the hare would never catch up. This shows that in reality when the difference is small enough, the hare will eventually catch up because space is discrete.
Now let us think about the CTMU: Christopher Langan states that the universe is a conspansive manifold. That means that the universe contains everything and therefore it does not get any bigger, but the distances between the objects inside the universe become bigger. This in effect means that the resolution of the universe scales up with time. Is this a contradiction to the observation that space and time are discrete?
Well, one might argue that even if the resolution increases, space remains discrete. The only thing that changes is the smallest size of a distance in space.
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