Jokes about human stupidity aside, has any physical thing had a physical property that is literally infinite?
From time to time I read about properties of the big bang such as heat or density that are described as infinite. Were they actually infinite or just so ridiculously large (like Graham’s number large or larger) that we play fast and loose with the definition of infinite?
Is there anything else that is actually infinite?
It’s possible that the universe is infinite. If so, it has always been infinite from the instant of creation. Whether that means it was ever at an infinite physical density is a different question and not known.
Other than that, no.
The density and time required to reach a black hole’s singularity are both considered “infinite.” Probably not what OP meant, though. Not the same has having an “infinite” quantity of jellybeans.
Black holes may have an infinite density… but it’s also possible that they’re just incredibly dense. We don’t have a way to know yet. The answer that applies to black holes will probably also apply to the Big Bang in regards to density.
This. It is common for physical theories to have infinities when applied in extreme situations. It is not common for users of those theories to assume that those infinities represent actual infinities in the universe. Rather, it is assumed that the infinities just indications that the theory is only approximately correct and the infinity corresponds to a situation where some simplifying assumption is not valid.
As **Exapno **points out, it’s possible that the universe is infinite in extent, and, if so, it must have been infinite in extent at the moment of the Big Bang.
By the same sort of reasoning we can know that the universe could NOT have been infinitely dense or hot at the moment it came into existence because it’s not infinitely hot or dense NOW. Infinity is not something you get to or come back from.
To explain the reasoning for leahcim’s post:
The reason may not be clear to laypeople. After all, if a thing isn’t infinite, its obviously nothing like infinity, right? Why would you use an infinity sign unstead of an actual number, even if the number was rather suspect. By definition, it would have to be more accurate than a big 'ole infinity sign.
This is completely true.
However, there is a concept in mathematics of a limit. This is just what you think: a barier beyond we we cannot get past no matter how much we try. This is important because it applies to physics as well, and everyday life. If you are doing things a certain way, there are parts you must miss. No “equation”, or work process, can handle everything.
Limits are the concept that points out where these are, and very often as we approach these limits, we get very close to infinity. In math, the infinite value can exist in any direction - up, down, left, right, forward, back - whatever. It’s created on paper by a graph, and tells you that no matter what values you use in your equation, you can never ever reach that point. It’s infinite.
But, there’s a few tricks you can do with it. For one, you can get arbitrarily close to that point. And this is why it’s important to physics. There are a lot of stuff in the universe which is too big, or too small, or too hot, or whatever, to categorize properly. We simply can’t judge it. But, if you have the right forumla, you can basically substitute for the real values. Often, you’re not working with infinity, but something so close to it as to make the difference irrelevant.
Coastlines are infinitely long.
http://blogs.nature.com/barbaraferreira/2010/10/is_the_coastline_of_britain_infinite.html
http://www.bbc.co.uk/learningzone/clips/the-problem-of-measuring-coastlines/11229.html
In theory, yes, coastlines and fractals are infinite. In practice, they’re not because you get to a point where the stuff that physical things are made of is indivisible.
Optics is a good example of this - the old ‘focus at infinity’ thing - and it’s actually possible to construct a lens system that really is focused at infinity - in practice, it just means that anything ‘this side of infinity’ is a little bit unfocused, but to such a small extent that it doesn’t matter.
But it’s not possible for a real physical value (such as the number of widgets in the universe, or the distance between A and B) to transition from finite to infinite. There isn’t any way to increment a finite value to infinity, in the real world.
IF the “singularity” within a black hole does have infinite density, then it got there by incremental addition, didn’t it?
It got there by means of a division-by-zero error, I think. Infinite density because it’s got finite mass, but zero size.
I was always taught that division by zero was undefined. Is that interchangeable with infinite?
Ok, but still. You had an object that had a defined mass and size, and over time, became an object with a defined mass and zero size. So it went from finitely dense to infinitely dense over a period of time. So that would be an example of something that didn’t start out infinite becoming infinite over time.
That is, IF black holes truly do have an infinitely dense singularity at their center. But it’s at least theoretically possible that they do, so it is at least theoretically possible that non-infinite quantities can become infinite quantities over time in given circumstances.
Does a black hole singularity form with a size of zero? Because using that “can’t get here from there” arguement would seem to imply that it couldn’t go to zero, it would have to from that way.
Density isn’t a ‘thing’ - it’s not a quantity - it’s a ratio.
It’s an attribute or quality of things.
If you can achieve infinite density by incrementing the number of objects in a finite space from a finite to infinite value, I’ll have been wrong.
Not as far as I know. Division by zero is undefined, because it’s not a reversible calculation.
i.e:
8 / 2 = 4
4 * 2 = 8
but
8 / 0 = ?
because 0 * x = 8 has no solution for x
According to last night’s episode of Person of Interest, pi has an infinite number of nonrepeating digits.
Come to think of it, don’t a lot of divisions result in an infinite number of digits? 10 / 3 = 3.333… on to infinity, right?
Not just a lot, but an infinite number of them.
You said no “real physical value” could go from infinite to finite or vice versa, and I hold that density is a “real physical value.” If you want to backpedal and claim that density is not a “real physical value” then I accept your backpedaling.