Where is Infinity? Answers to Unsolved Mysteries

[Misr]

Where is infinity??

Hello ,

This is an extract from my book about my problem.

http://img98.imageshack.us/i/infinityc.jpg/

I was rold before on this forum that this article is wrong

so can u define more what's wrong with it and explain it in a better manner??
Thanks in advance

 

[Naty1]

It is NOT correct as you properly note. Not all infinities are created equal; but that's complicated. Let's keep it simple here and maybe I can help you "imagine" a little about infinity. .

Your quote is based on a simple inverse square law, meaning 1/r² for idealized point charges. That's a dot without any size, a mathematical approximation, not a physical reality; that let's us do a lot of math, but not all, rather simply and with great accuracy. As r approaches zero (distance,say) both 1/r or 1/r² approaches infinity...but not quite the same way.

An infinity just might occur within a "small space" such as the center of a black hole, where space is completely curved...it's so curved it "disappears" and there is no distance...so there is no "distance", there is not space, there is not time..it's called a singularity which is a theoretical type of infinity...but this "singularity" has different theoretical mathematical characteristics than another type of singularity, that which might have initiated the big bang which might have started this universe from "nothing"...

Maybe you can begin to imagine a point singularity this way...take a piece of paper, crumple it up into a "ball" shape...points on that paper are now closer together...unless they have to travel the surface of the crumpled paper...crumple it more and more and more...distances from point to point get smaller and smaller and the crumples get more and more curved...more disttorted...there are mathematical ways to measure such changes...

Try this idea of infinity: If the universe is infinite then there is no beginning nor an end...it extends "forever" . I might well be infinitely distant from you, and you might be infinitely distance from someone else who is also infinitely distant from me. But no one knows if the universe is infinitly large.

Just keep in mind the above descriptions might not be EXACTLY accurate...but they might help you imagine a little about infinities as long as you don't take the analogies (approximate ideas) too far.

You might also try reading something more advanced, like fractals:

"...The structure of a fractal object is reiterated in its magnifications. Fractals can be magnified indefinitely without losing their structure and becoming "smooth"; they have an infinite perimeter resp. an infinite surface area. An example for a fractal curve of infinite length is the Koch snowflake..."

http://en.wikipedia.org/wiki/Infinity#Geometry_and_topology

I'm pretty sure infinites are ideas; so far, I do NOT think there is experimental proof (incontrovertible evidence) of any infinities in this universe.

 

[Rasalhague]

I think it's just using sloppy language. It's probably treating "undetectable"or "insignificant" as synonymous with "zero". Since field strength goes to zero at an infinite distance, it then uses the word "infinity" to mean (not an infinite distance but) the distance at which field strength becomes undetectable.

 

[jnorman]

in regard to your specific question, "where is infinity?":

it is three doors down on the left, just past the rectangle of futility.

 

[Frame Dragger]

The issue here is that 'infinity' is usually the byproduct of a flawed theory (see renormalization) or an incomplete one. There is no billiard ball consuming endless energy as it tried to reach c .

So... I go to my favourite reaction from the author of a fine book called "Prime Obsession." which I've used in another thread here.

Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, ‘What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers."

 

[Misr]

I tried to rephrase this stupid article so Am I on the right way ??

Infinity is where the electric field intensity and the electric potential is vanished., where the electric field intensity = K q /d^2 and electric potential = Kq/d
Some people think that infinity is far awat from planet earth. In fact infinities are created different , they may be as small as the dimensions of the atom or far away from planet earth.

Its obvious that the electric field intensity is inversely proportional to the square of distance and the electric potential is inversely proportional to the distance from the charge , yet when this distance becomes so far the intensity of the electric field become so weak till it vanishes at infinite distances, where the intensity = K q/0 , which is undefined.Right ?right?? but why do we consider the distance zero at infinite distances?

 

[Misr]

could u help?

 

[Cantstandit]

There is no general definition of infinity, if that's what you are trying to find. Infinite distance is often used to define something "distant enough to be neglected", in case of electric charges (electrons) you can say that charges are infinitely far away from each other when they are 10m apart, because when you calculate force acting on them its 0.(30 zeros)3 so you can safely say that for all the purposes the force is 0, and because force is 0 only in infinity, you treat 10 meters as infinity IN THIS PARTICULAR CASE of two electrons.

Similarly you could say Physics Forums have infinite number of posts, because there are so many of them and their number grows so fast that you won't be able to read them all even if you quit your job ;)

So infinity is often used but it must be always in context of some force or number of interest.

Its obvious that the electric field intensity is inversely proportional to the square of distance and the electric potential is inversely proportional to the distance from the charge , yet when this distance becomes so far the intensity of the electric field become so weak till it vanishes at infinite distances, where the intensity = K q/0 , which is undefined.


Right ?right?? but why do we consider the distance zero at infinite distances?

This, you got it wrong, when the distance approaches zero force reaches infinity, when the distance is infinity force reaches zero.

 

[Frame Dragger]

There is no general definition of infinity, if that's what you are trying to find. Infinite distance is often used to define something "distant enough to be neglected", in case of electric charges (electrons) you can say that charges are infinitely far away from each other when they are 10m apart, because when you calculate force acting on them its 0.(30 zeros)3 so you can safely say that for all the purposes the force is 0, and because force is 0 only in infinity, you treat 10 meters as infinity IN THIS PARTICULAR CASE of two electrons.

Similarly you could say Physics Forums have infinite number of posts, because there are so many of them and their number grows so fast that you won't be able to read them all even if you quit your job ;)

So infinity is often used but it must be always in context of some force or number of interest.



This, you got it wrong, when the distance approaches zero force reaches infinity, when the distance is infinity force reaches zero.

We shouldn't bring the Colour charge into this, should we? I'm guessing Confinement is a bad idea to discuss at the moment...

 

[Misr]

and because force is 0 only in infinity

en the distance approaches zero force reaches infinity

I'm confused about these two sentences

 

[mate0]

infinity is just a concept, as long as you have the basic idea an exact definition is unnecessary, and probably impossible because it is used (misused?) so many different ways. in most cases the context it's used in will tell you the meaning.

 

[Misr]

I can't download files from my internet .
But i want to know...

This, you got it wrong, when the distance approaches zero force reaches infinity, when the distance is infinity force reaches zero.

What is the difference between force reaches zero and force reaches infinity?
Isn't force zero at infinity??

 

[Doc Al]

What is the difference between force reaches zero and force reaches infinity?

What's the difference between having zero dollars and having a whole bunch of dollars?

Isn't force zero at infinity??

In some contexts, the force goes to zero as the distance goes to infinity.

 

[Misr]

The article was just really stupid but i got what you are tryin to say
Thanks so much.

 

[Tac-Tics]

Students are introduced to "infinity" in a very informal way. It's bigger than the biggest number you can say (except for "infinity plus one", of course). It's the "all-est" of them all. It contains anything and everything. When you put two infinities head to head (God cannot create a stone he cannot lift), your head gets dizzy. It's THAT BIG!

The reality is that infinity is a tricky, nuanced notion. It's proper domain is logic and mathematics. In those domains, there isn't just a number called "infinity". Infinity isn't a number in the conventional sense. However, the word "infinity" is used in various contexts to suggest that unbounded, bigger than the biggest idea we all agree on.

In physics, "infinity" is almost always the "infinite limit" in the calculus sense. Calculus is the study of a bunch of closely related notions of infinity -- but all through the context of a powerful mathematical notion called a limit. The limit is used for when we want to explore the behavior of some function arbitrarily close to some value, but for technical reasons, never equal to that value.

The definition of a derivative, in a bastardized sense, is just \frac{f(0)}{0}. But since division by zero isn't defined, we can't do that. However, \frac{f(a)}{a} is defined for all nonzero values of a no matter how small.

What you're dealing with here is just the opposite of that. You want to take \frac{f(\infty)}{\infty}, but you can't, because \infty isn't a number. However, \frac{f(a)}{a} is defined regardless of how big a is.

In physics, infinity is often (ab)used to mean "large enough that we don't care any more" (and similarly, infinitesimal is "small enough we just call it 0").

The point the article is making is that "far enough away that it might as well be infinite" for an electron is a very small distance. (Less than the width of a human hair). The actual potential of an electron is indistinguishable from the potential of an electron as measured an inch away from your face.

I would disagree with whoever told you the article is "wrong". It's not rigorous enough to be wrong.

As a rule, none of the mathematics used in physics should be taken as "exact". Physicists use the math to guide their theories, but if a rule needs to be broken to match up with the data, you break the rule and continue as if nothing happened. Later on, if a mathematician is so inclined, he might study the legitimacy of breaking that rule. (And it often is).

 

[mate0]

i think the original question has been answered, and now we are just repeating what has already been said.
can a mod please lock this thread?