Does infinite actually occurs?

Question

I tend to deny any claim that $X$ is infinite, where $X$ is anything from our observable universe. For instance:

• The number of grains of sand on Earth is infinite? No, it is a big number but not infinite.

• The number of seconds I would take to count to infinite is not infinite, because I would die sooner or later without achieving this goal.

• Numbers are not observable (you can't see a "number", just a representation of it, like two apples or the number 100 written in a notebook).

• The universe is infinite? I'm not aware of current theories stating so, then in my opinion it would be very big, even indefinitely big, but how come could it be infinite? It would result on the non-sensical consequence of this question If the universe is spatially infinite, and if something (A) is possible, does that mean the thing (A) happens?

Is there any measurable infinite in our universe discovered so far?

Answer 1

I think you ask some good questions here, though many have been asked before.

I tend to deny any claim that X is infinite, where X is anything from our observable universe. For instance:

This is correct. Nothing in our observable universe is infinite. The observable universe is very large, but not infinite.

The number of grains of sand on Earth is infinite? No, it is a big number but not infinite.

This is true.

The number of seconds I would take to count to infinite is not infinite, because I would die sooner or later without achieving this goal.

You're splitting the question here a little, but you're right, there's no mechanism by which it would be possible to count to infinity.

Numbers are not observable (you can't see a "number", just a representation of it, like two apples or the number 100 written in a notebook).

I agree with that too.

The universe is infinite? I'm not aware of current theories stating so, then in my opinion it would be very big, even indefinitely big, but how come could it be infinite? It would result on this non-sensical question:If the universe is spatially infinite, and if something (A) is possible, does that mean the thing (A) happens?

Couple of points here:

1) see Timaeus' answer. It's possible that the universe is infinite. You might not be aware of any "theories" and theory is perhaps not the right word, as it can have more than one meaning, but as I understand it, there are proposals and mathematical and astronomical studies that suggest the universe might be infinite - strange as that sounds.

2) it's bad form to call another person's question "non-nonsensical", besides, the question is valid. If you have an infinite number of solar systems and each solar system has a finite number of atoms, then, there is a mathematical quandary that suggests there could be other earth's out there, but it only works if the universe stretches on forever and the distance between 2 similar earths would be an unimaginably large distance.

But as to your essential question "how could the universe be infinite?", that's a good question, and, a surprisingly complex question.

The simplest answer is, every test performed has failed to measure or prove a finite universe. Do we "know" the size of the universe - no. Not with any certainty at all, but what's been studied so far implies that an infinite universe is possible and, somebody said in a similar question that it's the "theory du jour". But it's still not known. (theory du jour might suggest it's wrong, but that's not what I'm trying to imply)

For longer, deeper answers read: Here and Here and Here. Point is, an infinite universe isn't junk science. There is some real research backing it up.

Now as to the "it can't be true" theme of your post, I'd like to remind you that "It can't be true" has gotten a lot of scientists in trouble over the years. Einstein's special relativity was one such "it can't be true" idea that was met with skepticism. Michael Faraday was met with that as well, and quite a few others.

As far as not liking ideas, Einstein didn't like quantum mechanics. A scientist probably shouldn't trust his feelings or his beliefs, but should approach the evidence with an open mind.

Answer 2

Is the universe infinite?

We don't know, we can't know. And we never will know. But there are some solid reason to think it is, and some solid counter arguments.

One argument is based on the fact that we look out at things far away and notice they are all moving away from us. We argue that it is unlikely we happen to be at a unique place in the universe so we ask ourselves how the universe would look if that same observation came out the same way in many places in the universe, so if it were a generic real estate feature.

When we restrict ourselves to such models we cab design models of how our universe looks and then on large scales it looks pretty uniform, sure there is a planet right under us and a star pretty nearby but when you look at large enough regions it looms pretty similar here there and everywhere (those this is still a conclusion from the model, we don't actually see what it looks like elsewhere).

When we make models about how universes that are super uniform look like we find three major types, ones that are positively curved, ones that are negatively curved, and some that are flat. And then we can try to measure the large scale curvature and we get a number that could be zero.

Every measurement has error so either it is zero or else it is smaller than our error. It is possible to have a flat and finite universe, but is does make our motion rather special so some people reject it (of course over time a geodesic motion has its peculiar velocity become closer and closer to the Hubble flow plus we are made out of neighbors so of course we aren't moving terribly different than them if they are moving together). So I admit I fail to see how this is evidence for an infinite universe, but I understand this global large scale flatness is the essential reason many scientists think the universe is infinite.

But there is a problem with this evidence. When we look very far away we look at earlier times (it takes time for light to get to us) and things that are too far away seem too related. So people postulate that maybe the universe went through a growth spurt so those places used to be closer together.

However this growth spurt (called inflation) causes the large scale curvature to change over time and to become numerically close to zero even if it is actually positive or negative. So that might be why it is so small now. If the curvature were positive or negative no one would seize that as evidence that the universe is infinite.

So there are people that think the universe is infinite, they'll cite the "we don't live in a special place" principle (which is great) and the possibly zero curvature (which might be explained by inflation) and then there is some hand waving where they conclude the universe is infinite.

But we can't test that anyway, so few people bother to argue. The part that could affect us now is finite and the last we can affect is finite. So whether it is infinite or finite doesn't affect our predictions so it is a bit out of scope for science.

But its not like it is better if you claim the universe is finite. After all even if you walked a huge distance and came to a place that looked just like your house including all the views from your house did you walk around an finite universe or does the universe have a regularity where it tends to looks similar if you go a certain distance. If it was really finite and you walked around again you'd get back to your starting point but if it is just likely to be regular then any of those trips might end up someplace that looks different.

It's like some ants going down a long street of identically built identically landscaped identically furnished row houses. Near the middle of the street the universe might look finite and rather small. But as they get near the edge they can start to see the view looks different. As they get to the end of the street it is very different looking.

So even if you saw evidence that was 100% exactly like what you'd expect for a finite universe the universe still might be bigger or even infinite.

So no evidence is good enough to show it is infinite and no evidence is good enough to show it is finite.

But making some choice for your model might make it easier or harder. But don't get too excited either way. You only make finite measurements, and from them you will never know whether the universe is infinite or finite.

You can definitely rule out it being tiny and we've done that. You can even rule out is being medium sized.

So the universe is big, and that's good enough.

Answer 3

You don't need (currently strongly suspected but unproven) size of the universe to find a whole lot of infinities all around you.

There are alternate representations of quantities that are inverse of others, and "true zero" occurs in the nature. If something has frequency of zero, then its period is infinite.

When the quantum state of two entangled photons collapses, it happens instantaneously - with time being a discrete, quantized quantity, one Planck time being the smallest possible unit, the collapse doesn't happen a multiple of Planck Times apart - it happens absolutely simultaneously. That means the speed of the state propagation is infinite. Not "huge" or "enormous" - time is not something that can be arbitrarily small, there's the smallest one Planck Time, and then there's a flat zero time. Divide finite, non-zero distance by that, you get an infinity.

Nuclear decay/fusion time of nuclei of atoms grows the more stable they are, approaching from two sides, hydrogen fusion, radioactives fission, both tending towards iron squat in the middle; half-life of iron is infinite; it has nothing to decay into. It may undergo other transformations, but not spontaneous nuclear decay. No matter how many iron atoms you take and how long you observe them, this won't happen, period.

Superconductors have a flat zero resistance, thus infinite conductance. Drop-off of current in a superconductor loop over time is zero. Not over infinite time as the superconductor may be destroyed eventually, but the momentary value is a perfectly valid physical quantity, and the fact that the current in ten minutes will be exactly equal to the current now, not an electronovolt of difference, means that at this moment conductance is infinite.

In a small volume of a vacuum chamber currently there are no particles. In a second a neutrino may pass, or an electron-positron pair may manifest, or the walls of the chamber may emit a photon, but currently it's infinitely empty.

Generally, on the other side of each "zero" an "infiniy" is lurking - and absolute zeros aren't all that uncommon in the nature.