Observations show space time is flat, as close as we can measure - which could mean it is very big, or could mean it is infinite.
But - infinity is a big number! We couldn't tell if space is, say, 10^(10^100) light years in diameter or infinite.
Even if our theories some time in the future show that space has to be infinite - well theories get changed, how can we tell if a future theory won't show that it is finite?
It might behave like an infinite universe for 10^(10^100) light years (that's a number with 10 to the power 100 digits, so a number of light years far too large to write out in decimal inside our Observable universe at one digit per atom) - but beyond that it might curve around on itself and close up - or just stop.
(Note, if somehow you could inscribe the number with a single digit per Planck volume, you'd need a slightly bigger number, 10^(10^200) would do the trick - be to large to write in this way - see Planck units.)
And though that's a huge number compared with ordinary experience, mathematicians work with far far higher numbers than that - and even the largest numbers ever used in maths are tiny compared with infinity.
So - this is surely going beyond the province of science - and into philosophy and metaphysics - and probably has no answer that can be proved one way or another.
Though - if it was finite, that could be proved potentially.
What we can say is that space seems to be very large, and is no reason at present to put any particular limitation on its size.
There are ideas for "finite universes" which might mean that some of the most distant galaxies we see are in fact the same galaxies as the ones close by, seen by light that has gone around the universe more than once. Couldn't be a curved space time to do that - but could be a kind of space time where opposite sides of the universe get identified with each other in other ways - like a room with a door and you walk out of it to the East and find yourself coming back into the same room from the West, go out of ceiling and find yourself coming in through the floor.
There is no evidence yet however that our universe is like this. A 2003 paper came up with a bound of at least 78 billion light years for the diameter of the universe by looking for patterns in the three degree background radiation Observable universe
And - even if our universe did turn out to be finite - then you could still speculate that it is just one of many "baby universes" - in a multi-verse.
But - infinity is a big number! We couldn't tell if space is, say, 10^(10^100) light years in diameter or infinite.
Even if our theories some time in the future show that space has to be infinite - well theories get changed, how can we tell if a future theory won't show that it is finite?
It might behave like an infinite universe for 10^(10^100) light years (that's a number with 10 to the power 100 digits, so a number of light years far too large to write out in decimal inside our Observable universe at one digit per atom) - but beyond that it might curve around on itself and close up - or just stop.
(Note, if somehow you could inscribe the number with a single digit per Planck volume, you'd need a slightly bigger number, 10^(10^200) would do the trick - be to large to write in this way - see Planck units.)
And though that's a huge number compared with ordinary experience, mathematicians work with far far higher numbers than that - and even the largest numbers ever used in maths are tiny compared with infinity.
So - this is surely going beyond the province of science - and into philosophy and metaphysics - and probably has no answer that can be proved one way or another.
Though - if it was finite, that could be proved potentially.
What we can say is that space seems to be very large, and is no reason at present to put any particular limitation on its size.
There are ideas for "finite universes" which might mean that some of the most distant galaxies we see are in fact the same galaxies as the ones close by, seen by light that has gone around the universe more than once. Couldn't be a curved space time to do that - but could be a kind of space time where opposite sides of the universe get identified with each other in other ways - like a room with a door and you walk out of it to the East and find yourself coming back into the same room from the West, go out of ceiling and find yourself coming in through the floor.
There is no evidence yet however that our universe is like this. A 2003 paper came up with a bound of at least 78 billion light years for the diameter of the universe by looking for patterns in the three degree background radiation Observable universe
And - even if our universe did turn out to be finite - then you could still speculate that it is just one of many "baby universes" - in a multi-verse.
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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