The universe is either finite (i.e. not endless) and so having terminations (edges) in all directions; or the universe is infinite (i.e. endless) and goes on forever in all directions (and probably endless in time also).
Can we get a clue from physics / mathematics as to which alternative is true?
The basis of universal physics - the rules of radiation, electricity (dc + ac) and that force which mysteriously holds matter together; i.e. quantum mechanics - all rests on the square root of minus one.
What? On a simple number?
It's _not_ really a number - more a concept. That's because, by all the rules of ordinary human mathematics - a system invented by humans for counting, adding, multiplying and dividing real things that you can pick up and manipulate - the square root of minus one can't exist!
Because the rules say that +1 × +1 = +1; and -1 × -1 = +1, so there's no way to get -1 by multiplying two identical numbers together (i.e. "squaring").
But it seems that the universe, while allowing human mathematics to work for counting discrete objects (particles and planets), also demands a higher mathematical concept to describe the universal force holding matter together and endowing inertia (i.e. momentum - and hence all the workings of radiation, electricity and particle physics).
And that concept is "root minus one".
That is (and I speculate here), the universal force is radiative (i.e. incoming _and_ outgoing in all directions) and so it consists of a negative (outgoing) and positive (incoming) force at `unity' - so we have -1 × +1, and that gives us -1.
That can also give us a vital clue as to the form of the universe. I.e. if quantum mechanics is true universally, then "root minus one" must be true everywhere in the universe.
But if the universe had `edges' (i.e. if it was finite) then the radiative forces would not be equal towards an edge. That is, the incoming force would decrease (if the nearby `edge' was absorbant), or increase (if the nearby `edge' was reflecting) while the outgoing force in that direction would remain the same.
I.e. a finite universe (with `edges') would only have one central place where "root minus one" was true and therefore where quantum mechanics would work. But that doesn't seem to be the case.
Checking to the extent of the observable universe, which also means looking back in time, we find that the laws of physics - implemented by quantum mechanics and therefore by "root minus one" - are operating normally at all times and places.
So, as quantum mechanics seems to work everywhere in the universe, and backwards in time (far as we can see), the universe looks to be infinite.
14 January 2014
PS - for other details see recent message - and references at index page.