There is literally not one aspect of the universe that is provably finite. Not in any direction, not at any scale, not in any way you can think to look at it.

And yet the vast majority of physicists treat infinity in the equations as a sign of them being incomplete, and dismiss the possibility of the universe being infinite in any way

I would like to point out that there is no proof of God not existing either

Except you I suppose.

Maybe I misunderstand you, but I don’t think I agree with that.

E.g. the observable universe is finite. Its observable age is finite. The number of known elementary particle types is finite. The number of particles within the observable universe is finite (according to the current understanding). Etc.

There are many examples.

Do we disagree on this, or am I perhaps misunderstanding your position here?

Key word is provably. We can assume the universe is finite because we don't have evidence against it, but no one knows if it's possible to prove or reject that for good.

Infinity is an abstraction. The universe cannot be "infinite" in the mathematical sense, as the mathematical infinity is an abstraction. The only meaningful question is "is mathematical infinity required to produce good models of the universe/physics?" and the answer so far is "no". We use infinity because it is convenient, but it is not really needed.

There is no reason to think that "infinity" will be essential to describing the universe any more than any other possible abstraction that we have not so far constructed.

Why can the universe not be infinite and go absolutely indefinitely in every direction?

> The universe cannot be "infinite" in the mathematical sense

Why not? An infinitely large universe goes against our intuitions, but our intuitions were formed by the experience of living on a finite planet and have no bearing on what's true on a galactic scale – just like they have no bearing on what's true at the quantum scale. There is no objective reason to assume that the universe isn't infinite.

Observable universe is just the part of the universe from where light had time to hit the Earth already. It is growing pretty much at the speed of light, not because of physical changes to the space-time, but because the light from farther away finally arrived. So while it's definitely finite, I wouldn't say it disproves the claim that nothing about the universe is known to be finite.

> It is growing pretty much at the speed of light

The observable universe is growing much faster than that, because space itself is expanding.

Because of inflation, there is a distance at which the objects not already in our light cone are moving away faster than the speed of light. So the amount of stuff that we will be able to observe is limited.

besides the other points raised, even within the observable universe there are some assumed infinities as well as things that might be infinite, might not be.

e.g. time and space likely aren't quantized, you have an infinite amount of points in between any two arbitrary points in spacetime. don't mention planck scale black holes, it's a meme and even most phycisists who like to cite it haven't actually thought about it for more than 5 minutes.

I have the exact opposite experience. There nothing I can think of that is infinite in nature. Not only is it impossible to prove infinity empirically ("in the universe"; the only thing that actually matters) but there are exactly zero actual things with an infinite nature of any kind that I can think of. It's a useful imaginary construct that makes fancy math work, that's all.

This isn't really true.

For example, the special theory of relativity doesn't work if space-time has any "lowest scale" (i.e. if the distance between any two events can be expressed as n * min_dist, where n is an integer and min_dist is a constant that has the same value for all observers), it you can't infinitely sub-divide it, since then lengths couldn't contract the way that the Lorrentz transforms predicts. Lots of math in QM and QFT also requires space and time to be continuous for other reasons as well.

Also, none of our current laws put any kind of limit on the life span of the Universe as a whole, so space-time is also infinitely increasing, even if heat death or big crunch models are correct.

Of course, none of this is provable per se - it is fundamentally impossible to run an experiment in finite time that proves whether something is finite or infinite. It could be that SR and QFT are wrong in their continuous space assumptions, but only in ways that are too subtle to measure. Still, as it stands, we don't have any theory of how the world works which allows for a discrete space-time, even as an approximation - we need space-time to be continuous for our current theories to work at all.

Well, our physics is famously incomplete and even if it weren't: math needing infinity is in no way shape or form proof of anything but the nature of math which itself could be nothing but a highly particular construct.

I always find it interesting nobody seriously questions why something so extraordinarily basic as geometry pervades "the universe". I'd say it's much more likely we are mathy creatures and cannot do anything but perceive logical building blocks somewhat reminding me of a guy using a flashlight proclaiming the universe comprises various configurations of spherical lights.

I can imagine infinity just fine and I'm sure many useful things can be inferred from it, but that doesn't mean it exists. Lots of math is possible but does not exist in reality and that's fine, I'm just being honest about the very real boundaries here. I get the feeling many people confuse the map for the territory.

> there are exactly zero actual things with an infinite nature of any kind that I can think of

That's because your imagination is bounded by being a monkey that has spent its entire life in a finite environment — no offense. The universe, however, isn't bounded the limits of our imagination or intuition.

Yes, that's all very interesting (truly) but where does your actual lived experience come into play? That's the part I am talking about, the "in the universe" part, not the "could be" or "in imaginary parts of the possible universe" but the actual, experience-able universe. That's what separates math from physics and IMO math is the one that has to prove its worth not the other way around. I can construct endless internally consistent imaginary worlds with zero bearing on (any) reality.

> There is literally not one aspect of the universe that is provably finite.

Or provaly infinite.

On the other hand, every single observation anyone has ever made was a finite value of something.

Even when things are potentially infinite, there seems to be a conspiracy of the universe to make it finite. The size of space may be infinite, but due to a finite speed of light and the finite age of the universe we can only ever observe a finite slice. When attempting to zoom in to an infinite degree onto supposedly point-like particles, quantum mechanics makes everything fuzzy and finite again. Black holes appear to have infinite curvature at the center, but it's unobservable due to the event horizon.

This principle seems so natural that we even apply it in advance: In quantum field theory, there are infinities in the equations when done naively, which we deem so unnatural that we apply funny tricks which make mathematicians cringe, but they miraculously work out so well that we get theory and experiments to agree to an astonishing degree.

And not one aspect that’s provably infinite, either. Many things though that are finite to the best of our understanding. As in, any infinities that crop up in our models are properly understood to be cases where the models are wrong or incomplete.

Good luck with calculus tho.

So you're going to always only do numerical computations only? Good luck solving even simple optimization problems that have a few parameters.

Who needs calculus anyways? I'd rather focus learning linear algebra especially after realizing a derivative is just a linear transformation and integration problems share a lot with determinants (areas).

Maybe so many more people would engage with mathemathics when they realize this.

> Who needs calculus anyways?

I can't really think of anyone. Maybe just mathematicians, physicists, economists, computer scientists, chemists and engineers. Apparently they even use something called back propagation in AI training, which is nothing but chain rule from ... calculus.

But yeah, I can't see it being relevant since we have linear algebra already.

Applied calculus doesn't need infinities. No computer can represent a real real number. Only truncations of them, only finite versions of them.