Are there any real examples of Infinite, or possible infinite, in our universe?

Question

infinite small or large, infinite slow or fast, infinite long time or short, any kind of infinite counts. Are there any real-life example out of Math, that is infinite?

This is the whole knowledge I know now:

size: I know Planck length is the observation size limit, so, are there 0 point particles exist?

Electrons don't have size, but is it the same to say "don't have size " and "size is 0"?

Observable universe have a 45 Billion light year radius, so there is a maximum size limit, right?

time: Planck time is the shortest time; the life span of the universe is the longest time.

speed: Light speed is the fast limit; 0 kelvin does not exist, so 0 speed does not exist.

mass: The energy of our universe is finite so the mass is finite, information is finite too.

difference: not only 0 speed does not exist. all rational number are not exist, all number are not constant, in real life. Can you find exactly 3 apples? no matter how did you define what is "a apple" you always get more or less amount of your definition in real world.

Did I made mistakes? Are there any examples that are infinite?

P.S. I don't know which tag this question belongs to. help me to add them please.
P.S. help to Solve the question, not Block the question, please.

Answer 1

Answering your question depends on our models. In classical physics, we can talk about zero velocity. If you don't count it, as its not quantum and relativistic, then we can ask whether QM and GR are fundamentally true to all orders of magnitude. They don't seem to be. So would any example count?

Some other examples could be:

• The zero mass of the photon (to our best experimental knowledge)

• The zero difference between the speeds of light and gravitational waves

• The infinite ratio between the mass of the electron and the mass of the photon

• We can, in fact, take the inverse of any observable with value zero, and get an infinite observable.

Answer 2

Our senses can't sense something infinite, or a infinitesimal difference. Similarly with any instruments we use to measure things.

Our theories and mathematics may work out more smoothly if we assume such things are possible.

So for example, one way to measure waves is in cycles per second. Imagine you have a use for the inverse measure, seconds per cycle. Then the slower something cycles the bigger the number, and something that has no cycle would have an infinite measure.

Is it more convenient to be able to record the absence of a cycle as an infinite value, or to not be able to?

It isn't about reality, it's just about how we want to organize our thinking.

Answer 3

IMHO, it's a very hard question. At first, everything is a concept in our head, because we process outer world information given by our sensory organs (eyes, ears, etc.) and filtered / reconstructed by our brains. What we actually perceive is a "brain model" of the world, not the world itself. Some concepts can be "harder" than others, such as $0$ or $\infty$. One can argue that zero is more realistic than infinity, but I do not agree on that. At last, they are closely related : $\boxed {\infty = \lim_{x\to 0} 1/x}$ and $\boxed {0=\lim_{x\to \infty}1/x}$.

Another interesting fact is that we can arrive to indeterminate forms, manipulating with zero or infinity alone or with them both in conjunction :

$$ {\frac {0}{0}},~{\frac {\infty }{\infty }},~0\times \infty ,~\infty -\infty ,~0^{0},~1^{\infty },\infty ^{0}. $$

The fact that indeterminate forms ties together zero and infinity also means something.

Can you prove to me that you really have zero apples ? Maybe you have one under your back or wherever you want it to hide ? Is it realistic, that you note that you don't have something ($0$ amount) ? You may have 0 apples, but 0 dragons as well. Finally if we agree that zero has some "realistic sense" then so does the infinity too. Because zero is what is left to you when you pass 1 apple to infinite amount of people for tasting it. Line is just an infinite amount of co-linear points. Circle - polygon with infinite amount of edges, etc. So in my opinion, either we have both notions $0,\infty$ in reality or none of them.