Calvin Lin posted a query which was supposed to be about whether or not "completion of an infinite sequence" could have meaning.

but the subject ended up dwelling on the nature of infinity. Now I'm asking why do we need infinity at all? Here's the question being posed:

Imagine that we have two universes, one that **necessarily** involves the concept of infinity, the other not needing any such notion of infinity at all, but relying instead on "very large numbers". Is there any way we could tell the difference between the two? What experiment could we conduct to show that the universe that we live in is in one or the other?

Note: The concept of infinity doesn't have to be restricted to time or size, i.e., "infinitely old universe", "infinitely large universe". There are many other things that can involve infinities, such as, for example, quantum field theories.

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## Comments

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TopNewestThe hard part of this question is finding a physical phenomenal that requires an infinite amount of something (\(n\)) to have the result \(A\) as compared just a very large number of (\(n\)) which would give the result \(B\). And that (\(n\)) must be measurable, so it cannot be, for example, time or space (or can it?)

My guess is that we can't tell because there is nothing (or is there?) such that we can measure it as truly infinite rather than just a very large number

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One example would be black holes, which, in theory, has a singularity of infinite density. But do we really need that to have real black holes? Many physicists don't think so, especially when considering other factors such as quantum physics, which makes it moot.

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Wait, do black holes necessarily have a singularity of infinite density? Can't we have, say, just a body with such a high (bit finite) density that light (which has a finite speed) can't escape it?

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That is, if you strictly go by general relativity as worked out by Einstein. If you are asking if it's possible, per general relativity, to have a black hole without a singularity with infinite spacetime curvature, the answer is basically no.

However, alternative models, using variations of Einstein's general relativity or extensions of it using quantum physics, for example, of black holes have proposed that such a singularity need not exist. These models need observational verification, like other models in physics such as string or supersymmetry theory in particle physics. Sure, it's been possible to devise a mathematical model that avoids such singularities.

Here's such a paper that attempts to do just that, without straying far from general relativity

Black Holes Without Spacelike Singularities

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Anyway, we don't necessarily need to try to measure "infinity" directly. There are some models in physics where infinities seem unavoidable, like quantum field theories. Feynman, Schwinger, and Tomonago jointly won the Nobel Prize in physics in 1965 for their work in quantum electrodynamics which entailed finding a way to deal with infinities that threatened to make any computation of probability amplitudes impossible. As Feynman himself explains frankly, they went with a process called "mass renormalization" which involves making an arbitrary "cut-off", akin to leaving out a infinity of decreasing terms in an

divergentinfinite sum. He was said to be deeply unsatisfied with that process, which he considered to be a desperate move--and yet, such computations yielded some of the most accurate ever verified by physics. So, are infinities needed, or maybe it is just an illusion?Log in to reply

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\[\color{blue}{\huge{\mathrm{Zeno's \ Paradox}}}\]

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That's the problem of infinity. I firmly believe it's just human exaggeration if it exists then we should bother only when its needed like in black holes and the universe. I read in The Universe in a Nutshell that many infinities cancel out each other like the positive energy needed for creation of galaxies cancel with the negative gravitational potential. However more complex theories include more infinities about which I am not sure. If infinity were not there we would have crossed the speed of light

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I was thinking of time. We consider "TIME" as a physical quantity. Sir, don't you think time can be infinite. Although I must say that my way of seeing time is not very much developed.

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Not only your way of seeing time may not very much be developed, physicists still haven't quite figured out what time either is or why we have it, and many believe it to be an emergent property. Indeed, some theories about black holes say that time could be conflated with space. In that case, if we cannot even measure when time starts and end, we probably can't even speak of time as being finite or infinite. That may ultimately not have much meaning, to try to make that distinction.

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Well... conflating space and time is a theory. It hasn't been experimentally proven ( as far as I know). The time we're living in, is this real ? Isn't it measureable and if we take the big bang as the starting point of time, then it must be having some value in some units till now and that value would be increasing continuously. By saying this, I'm actually visualizing time as an endless string, one end of which is at a fixed point but the other seems to be at infinity.

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practicalreality, staring right in the face of engineers trying to develop such systems.Log in to reply

Time has not been defined and probably can't be defined because of its odd nature. Even if it were infinite we should not care much about before the big bang

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Well... I think its just our lack of knowledge that leads us to the concept of infinity. Mathematics is yet to develop to define it. Its same as when the concept of Quantum mechanics was coined. When people didn't understand something they called it quantum. But now it has been defined and rules have been set, though we're still making progress in it.

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Yeah. I agree with Julian sir's argument. We might expect time to be never ending. But space may be considered to end at some point, but we do not know whether it ends. It's a hypothetical question. If someone asks,

"what's the biggest number you know?", he may reply a \(100\) or \(1000\). But this doesn't mean there are no numbers exceeding \(\text{100 or 1000}\).to a grade \(1\) kidBut, if the same question was asked to you,

Some may saywhat would you reply?While others may argue, if givenI honestly do not know.(as in the case of Calvin sir's post). A better question, might be to ask, what exactly is meant by \(\text{"relying on very large numbers"}\). Again here, it may depend on the person as to what exactly he considers \(\text{"very large numbers"}\) to be.infinite time I'll tell you infinitely many numbersWe may consider the case of never ending decimals such as the one post by Jake Lai, which proves that: \[0.999999 . . . . . . \infty = 1\]

This may show that the thing the other universe consider as \(\text{"very large numbers"}\) is actually nothing but infinity(or is it?).

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