Finite Infinity Paradox

I have been giving some more thought about my previous post where I stated my belief that the universe is infinite. It has occurred to me that there is a problem  here and it is this: no matter how distant two objects might be apart in the universe, the space between them can only ever be finite. Similarly, if we consider two objects which start off touching, and then start moving away from each other, in order for them to be an infinite distance from each other they need to continue moving away for an infinite length of time. However, this cannot happen because no matter how much time goes by, it will always be finite and so will the distance separating the two objects. It would therefore follow (call this McAdam's Infinity Paradox if you like - I have not read these ideas expressed anywhere else) that in an infinite universe physical objects may only approach a separation of infinite distance, but never reach it.

We now find ourselves in an infinite universe where all distances can only ever be finite.

Perhaps the idea of infinity should be viewed as a concept rather than a physical reality, and that spacial distances are actually an illusion because of our own particular limitations in our perceptive ability. Consider that two particles on the atomic scale which are super-entangled will affect each other instantly and independent of the speed of light no matter how great the separation between them. In what sense can we say that there is a spacial distance between the two particles given that they act as if there is not? Could distance itself be an illusion?

Edge of forever

I have come to the conclusion that the Universe is infinite. My reasoning is that outside of spacetime there is an absence of absolutely everything, including empty space itself. Clearly, this is very difficult to get your head around, a bit like infinity.

It would seem to me that assuming the above to be the case, there can be no boundary or edge to the universe as you have to have something to have a boundary with, and as there is nothing, there is therefore no boundary. However, for the universe to be truly infinite in every sense of the word, then it's geometry has to be open whereby an object travelling through space and not in an orbital trajectory would never return to the start position, or cross it's previous path. The Universe may be curved , but not necessarily curved back upon itself, in other words closed.

If we take the view that the universe is infinite, then it is no surprise that life exists and I am here to write this. In an infinite universe there are infinite possibilities. The fact that life has arisen here means that it is not only likely, but a certainty that it has arisen an infinite number of times in an infinite number of places.