Can there be an infinity of stars in the Universe?
I have a mind puzzle.
Can there be an infinity of stars in the Universe ?
I have 2 opposed reasonings, yet I don’t find any flaw in them. Can you help me here ?
Answer A : No, the number of stars cannot be infinite.
In the whole Universe, at an instant t, there are W molecules of water. This number may be very big, but it has a definite value. The same goes for stars. Each of all the stars at the instant t has her own size, and we can give her a name. We can list all of them, and we can sort them from nearest to farthest — if we are omniscient, of course.
Answer B : Yes, the number of stars can be infinite.
Space has no finite volume. Space has no ending wall. If I advance into space, I can always go further. Wherever I go, space is by default filled with… vacuum. But it could be otherwise. [I am not sure of this point.] Space could be by default filled with… air. So there would be +∞ molecules of air in the Universe. We can apply this reasoning to stars. Let’s say there is, in average, 1 star / 1060 m3. So, in the total infinite volume of space, there would be +∞ stars. When I advance into space, I would keep meeting new stars, without end. Like in these video games in which mountains keep appearing as far as you walk.
Your 'Answer A' assumes that $W$ is a finite value and then concludes that it's a finite value. It's a clear case of begging the question.
Related question: *astronomy.stackexchange.com/questions/6031/can-there-be-an-infinity-of-humans-in-the-universe*
I don't think there is a way of judging which answer is best, as this is based primarily on your opinion of what lies outside the observable universe.
Theoretically yes, there can be infinitely many stars. Since this space you're talking about is better described by general relativity and Einstein's field equations. One of its solutions describes the universe as being spatially infinite.
+1, though under the assumptions of large-scale homogeneity and isotropy (which are motivated mainly by cosmic background radiation), there are *four* qualitatively different kinds of possible spatial geometries, two of which are infinite (Euclidean $3$-space and hyperbolic $3$-space).
You can check out Olbers' paradox, also known as dark night sky paradox.
In short, it argues that the universe can't be a static one (ie. no time component = no beginning and no ending, infinite in size, etc), because if it were that way, than in this infinite universe, there should be an infinite amount of stars and the light of those stars would had an infinite amount of time to reach us. This would mean, that we should see the light of all (infinite) stars at all times, which is definitely not the case if you go out at night and look up.
But we know the universe has a finite age, so this has little bearing on the question.
@RobJeffries and since we 'know' that the universie has a finite age, we conclude that it also has a finite amount of stars
Your logic is incorrect. Nobody knows whether the universe is spatially finite or not. The finite age has no bearing on that. The question does not ask about the *observable* universe (which is certainly finite and has about 1e22 stars in it).
But if the Universe were to be infinite, there would not be an observable universe. The light of all possible sources would have had an infinite amount of time to travel and therefore would have reached every point in the universe and therefore we should 'see' the whole universe. Where is the error in this thinking?
@t.rathjen If you read the article you linked about Olbers' paradox, you would see that it is resolved by redshift.
There is an uncountable amount of stars from our perspective, but space does have a limit of size which is the distance which subatomic particle and matter as traveled since the big bang and with that limit of stars. Although stars die and form beyond our ability to count so observably we can never have an exact count of stars at anytime as well.
I would bet on answer B because The universe does have a total mass of about 25 billion galaxies. We can mathematically calculate the mass of our universe.
Space does not necessarily have a limited size. The universe *could* be infinite. Nothing needs to have travelled anywhere since the big bang - space expanded.
@RobJeffries Was space expanding before the big bang? Can space expand at he speed of light?
That space has expanded to the extent that most of the universe lies outside the *observable* universe is a critical component of modern cosmology. We do not know the size of the universe, and it could be infinite.