Does Infinity Exist in Nature?
No, no it does not. It's a good thing too. If we somehow had a choice, we wouldn’t want it to.
So, why not? The easiest way to frame why we wouldn’t want infinity to exist in nature comes from algebra. If you replace any variable with infinity or add an infinite list of unknown variables to your problem then your problem will stop making sense and become unsolvable.
We solve problems about what the world looks and acts like using algebraic variables or linear algebra. Physics makes heavy use of algebra but it goes by a different name, dimensional analysis. They have different names but they are identical. Since the language of physics is written in algebra, then infinity in any form, makes these systems of equations unsolvable.
This is exactly why the hypothesis that infinity does exist in nature is not falsifiable and why falsifiability is important. Non-falsifiable claims add unsolvable unknowns to our systems of equations making them unsolvable.
Why could we think infinity exists in nature?
Ever hear about infinite parallel worlds or infinitely dense singularities? These can’t literally be true because these ideas rely on the idea that infinity exists in nature. They aren’t falsifiable. So, where does this intuition come from and why do some physicists think infinity does exist?
What makes this problem tricky for physicists is that the infinity problem originates deep in our mathematics and physicists aren’t necessarily mathematicians. Physics is built atop mathematics and in our math infinity exists as an axiom (axioms are fundamental and self-evident truths). Physicists try to get rid of infinities as much as possible but since infinity is written into the language of mathematics getting away from it is tricky. However useful it is, and it is useful, infinity makes our math less realistic.
Why do mathematicians think infinity exists? Mathematics is humanity's most abstract human language. It is used to describe both reality AND the things we imagine. They just leave the reality stuff to the physicists. So sure, infinity exists, but only in our minds which is where everything starts so it is important. However, the hypothesis that infinity exists inside, as well as outside the mind, is the line where we go wrong. This same line is where physics starts.
Our modern math is an effective tool but fundamentally an imperfect one. I think of mathematics as a fundamental human language. But, just like any other language, it was invented. And so far, we haven’t found a way to make our math/language match or accurately characterize our physical world. It may be quite a feat to find an effective way around infinity but our math will never be more accurate than a mathematics that doesn’t assume infinity at the start. With infinity, mathematics will always be at least one step away from a snug fit on reality.
