@kellyjay saidMay be obvious, but an infinitely large expanse cannot be finite. So, your question does not make sense.
If there is an infinitely large expanse with nothing in it.
The tiniest of all measurable dots appears in it.
Then that dot expands at an infinitely fast rate.
Will it ever fill the expanse? 🙂
If not then does that mean it has edges and is finite?
@KellyJay
One theory has it OUR universe is finite, if you could see it in total including the parts we can't see with telescopes, it might measure some 50 billion light years across whereas we can only see the first 14 billion light years or so.
It is thought our universe is expanding STILL about 3 times faster than light so we will NEVER be able to see the whole thing no matter HOW powerful the telescope. It could have a mirror a light year in diameter and that will not let you see one METER past the point where light cannot reach us because it is too far away for any light to get here so that thought experiment with a mirror one light year in diameter will see LOTS of stuff but not one METER past the point of no return for light past that distance. It's even worse than that. Future scientists will have to take our word and recordings of images because every million years that goes by, less and less of our universe will be able to be seen so in ten or twenty billion years from now it might be the only thing we see is our own galaxy and nothing beyond that.
In that regard we live in a special time where we can see out that far.
We may need to have data that lasts for 50 billion years so intelligent life coming after us can see the universe for the wonder it is and not just our galaxy to be seen in that far far future where there will be no humans.
But some theories have it our universe is just one bubble of universes, in a kind of foamy soap bubble of reality but even THAT is not infinite.
So no telling just how big our universe is OR the other bubble universes thought to exist.
@sonhouse saidThese distances are inherently unfathomable.
@KellyJay
One theory has it OUR universe is finite, if you could see it in total including the parts we can't see with telescopes, it might measure some 50 billion light years across whereas we can only see the first 14 billion light years or so.
It is thought our universe is expanding STILL about 3 times faster than light so we will NEVER be able to see the whole thing ...[text shortened]... inite.
So no telling just how big our universe is OR the other bubble universes thought to exist.
@wildgrass saidI have to agree, it is like the can God make a rock so big He cannot lift it type of question, an infinitely fast anything a bad idea.
May be obvious, but an infinitely large expanse cannot be finite. So, your question does not make sense.
@kellyjay saidyou can imagine a closed space (like the earth's surface): no kinks, no evident limit (if you can't realize another dimension). Then you could ask if we would realize if the webb telescope saw our own galaxy as very faint far out one 😉
If there is an infinitely large expanse with nothing in it.
The tiniest of all measurable dots appears in it.
Then that dot expands at an infinitely fast rate.
Will it ever fill the expanse? 🙂
If not then does that mean it has edges and is finite?
@kellyjay saidWith considerable effort modern hydraulics could probably lift the earth. The machine would need something stable to anchor itself to, though.
I have to agree, it is like the can God make a rock so big He cannot lift it type of question, an infinitely fast anything a bad idea.
@wildgrass saidOr use a really powerful rocket. 🙂 But could we actually lift earth, wouldn't that require a fixed point, we would only be able to move it. LOL
With considerable effort modern hydraulics could probably lift the earth. The machine would need something stable to anchor itself to, though.
@Ponderable
The difference there is if you go out in a spaceship at 0.999999999999X the speed of light, you might run into our galaxy again in some unfathomable future but while that makes a nice thought experiment, the reality is you can't see our galaxy again because of the expansion of the universe going faster that light as we speak making it literally impossible to see anything outside the bubble of about 14 billion light years radius because the expansion of the universe is stripping the speed of light so we can never see past that distance even if you have a mirror a light year in diameter, you would still be able to only see to the edge of the observable universe.
@wildgrass saidIf we had something stable to anchor it too we could just get an Ancient Greek philosopher to use his big enough lever 😉
With considerable effort modern hydraulics could probably lift the earth. The machine would need something stable to anchor itself to, though.
@kellyjay saidSomething expanding at an infinitely fast rate is not expanding, it’s already there (wherever ‘there’ is).
If there is an infinitely large expanse with nothing in it.
The tiniest of all measurable dots appears in it.
Then that dot expands at an infinitely fast rate.
Will it ever fill the expanse? 🙂
If not then does that mean it has edges and is finite?
@moonbus saidIt's kind of indeterminate.
Something expanding at an infinitely fast rate is not expanding, it’s already there (wherever ‘there’ is).
If the "universe" is the real number line, and the "point" is the set containing the integer 0 (denoted by {0}), and the "point" in one instant "expands" to become the set of all integers, then the "point" expanded at an "infinite rate" by growing by an infinite number of objects (all the integers) in an instant.
And yet the real number line will not be filled, simply because not all the real numbers are integers.
With a different scheme we could even contrive to keep the expansion going forever at an infinite rate. In the 1st second throw into the set {0} all the rational numbers between 0 & 1, in the 2nd second put in the rationals between 1 & 2, and so on. The set is growing at an infinite rate (an infinite number of objects are being poured into it per second), and this continues for an infinite number of seconds. But once again, the real line will never be filled since not all real numbers are rational (such as the square root of 2, pi, and the cube root of 7).
And we don't have to add just rational numbers. 1st second: include in the set {0} all real numbers between 0 & 1; 2nd second: throw in all real numbers between 1 & 2, etc. We never fill the real line.
Other schemes could be contrived to actually fill in the real line eventually. 1st second: put into the set {0} all reals within a distance of 0.1 of an integer; 2nd second: throw in all the reals within a distance of 0.2 of an integer. It takes just a few seconds to fill the whole real line. How many? 😉
@soothfast saidIt's hard to think about infinity. One easily gets into a mind cramp. Regarding numbers, there are countable infinities and non-countable infinities. You know this already, but for the benefit of other readers here: the integers are countable, and any set which can be put into 1:1 correspondence with the integers is also countable. The even numbers, for example, are a countable infinity: 1 maps to 2, 2 maps to 4, 3 maps to 6, and so on. It is tempting to think that the integers must be a bigger infinity than the set of even numbers, since the latter is missing half the numbers (all the odd numbers), but this is a mistake. The set of even numbers is infinite in exactly the same sense as the set of integers.
It's kind of indeterminate.
If the "universe" is the real number line, and the "point" is the set containing the integer 0 (denoted by {0}), and the "point" in one instant "expands" to become the set of all integers, then the "point" expanded at an "infinite rate" by growing by an infinite number of objects (all the integers) in an instant.
And yet the real number l ...[text shortened]... stance of 0.2 of an integer. It takes just a few seconds to fill the whole real line. How many? 😉
Rational numbers are not countable. For every integer, there is a next integer: 1,2,3,4 etc. Whereas for rational numbers, there is no next rational number -- between any two fractions, 17/32 and 18/32, there are infinitely many other fractions, 35/64 etc. So it is not possible to put the rational numbers into 1:1 correspondence with integers. It easy to make the assumption that the set of rational numbers is a bigger infinity than the set of integers. But this is a mistake.
I find it not helpful to think of infinity as a quantity at all, not even the biggest possible quantity. I find it more helpful to think of countable and not-countable infinities as having different characteristics or properties, rather than different quantities; properties such as 'nextness'.
So, now, relative to KellyJay's question, the issue seems to me to be whether the concept of 'filling' applies to one or the other of these infinities, and if so, what would it mean to say that the numbers of one set 'fill' a numerical space whereas the others do not. I guess one could say that the integers do not 'fill' the numerical space of the rational numbers. For, between any two integers, there is a finite number of other integers (i.e., the concept of 'filling' applies because there are two 'edges' namely the smaller and the larger of the two integers), whereas between any two fractions there are infinitely many other fractions (hence, no such thing as 'filling' for this case). One might say that the rational numbers are more 'densely packed' than the integers. And this is a property of the rational numbers, not a quantity. Real numbers too have properties which fractions do not have...
I believe KJ's thought experiment postulates a point physically expanding in extended space, not merely in an abstract numerical space. If we're not careful here, we may run headlong into one of Zeno's paradoxes. This was the point of my original comment, that an infinitely fast process isn't a process -- it must already have arrived, the start and the finish are identical. For example, if you postulate a body of water heating up infinitely quickly, the question does not arise 'when does it boil?' If it is heating up infinitely quickly, it is already boiling.
Food for thought: is extended space physically divisible infinitely, like real numbers (no such thing as the next voxel or unit of volume)? Or is there a smallest voxel (volume of physical space with nothing in it)? But now we really do have old Zeno breathing down our necks.