Researchers from the Complutense University of Madrid (UCM, Spain) have mathematically shown that particles charged in a magnetic field can escape into infinity without ever stopping. One of the conditions is that the field is generated by current loops situated on the same plane.

At the moment this is a theoretical mathematical study, but two researchers from UCM have recently proved that, in certain conditions, magnetic fields can send particles to infinity, according to the study published in the journal *Quarterly of Applied Mathematics*.

"If a particle 'escapes' to infinity it means two things: that it will never stop, and "something else", Antonio Diaz-Cano, one of the authors, explained to SINC. Regarding the first, the particle can never stop, but it can be trapped, doing circles forever around a point, never leaving an enclosed space.

However, the "something else" goes beyond the established limits. "If we imagine a spherical surface with a large radius, the particle will cross the surface going away from it, however big the radius may be" the researcher declares.

Scientists have confirmed through equations that some particles can escape infinity. One condition is that the charges move below the activity of a magnetic field created by current loops on the same plane. Other requirements should also be met: the particle should be on some point on this plane, with its initial speed being parallel to it and far away enough from the loops.

"We are not saying that these are the only conditions to escape infinity, there could be others, but in this case, we have confirmed that the phenomenon occurs", Diaz-Cano states. "We would have liked to have been able to try something more general, but the equations are a lot more complex".

In any case, the researchers recognise that the ideal conditions for this study are "with a magnetic field and nothing else". Reality always has other variables to be considered, such as friction and there is a distant possibility of going towards infinity.

Nonetheless, the movement of particles in magnetic fields is a "very significant" problem in fields such as applied and plasma physics. For example, one of the challenges that the scientists that study nuclear energy face is the confinement of particles to magnetic fields.

Accelerators such as Large Hadron Collider (LHC) of the European Organisation for Nuclear Research (CERN) also used magnetic fields to accelerate particles. In these conditions they do not escape to infinity, but they remain doing circles until they acquire the speed that the experiments need.

**An infinite mystery**

The existence of infinity has been debated since the times of ancient Greek civilisation. The fact that the idea can lead to logical contradictions developed the "fear of infinity", a doubt that has remained over the course of centuries. At the beginning of the twentieth century, the great German mathematician David Hilbert (1862-1943) said that mathematic literature is "riddled with mistakes and absurdities, largely due to infinity". Some experts believe that it has not advanced much since ancient Greek times because debate remains open about current or real infinity (understood as a whole) and potential infinity (which grows or divides with no end) as Aristotle considered. However, it is also true that mathematicians have learned to handle infinity with certain skill, above all the work of the Russian Georg Cantor (1845-1918), which introduced different types of infinity. For example, a countable infinity, with natural numbers, is not the same as a straight, he continued. In any case, infinity is an elusive concept that has also stimulated research in many areas of mathematics, such as infinitesimal calculus. One of this science's big problems during the twentieth century was the "continuum hypothesis". It essentially means knowing if there is an 'intermediate' infinity between countable and continuous infinites. In addition, as well as mathematical infinity, there is a physical one that, at the same time, can have two meanings, one practical and the other cosmological: Is the universe finite or infinite?

**Explore further:**
The sum of digits of prime numbers is evenly distributed

**More information:**
A. Díaz-Cano and F. González-Gascón. "Escape to infinity in the presence of magnetic fields". *Quarterly of Applied Mathematics* 70 (1): 45-51, March 2012.

## Star_Gazer

## TS1

I think this article needs a rewrite. One issue with it is that it does not provide much context for the statements (thus making their meaning difficult to determine). Besides that the way it is written makes it look like the author did not understand what he/she was writing about.

## kaasinees

Lol, they got nothing better to do?

## indio007

How to compute whether it is possible for an electron ejected from the sun can "tunnel" the gap between it and the closest star. Or an other star for that matter.

## infinite_energy

Great question.

If the universe is finite that means that it definitely can be simulated. If it is infinite? ... we will never know because there are no limits to knowledge :)

## Vendicar_Decarian

## krundoloss

## Mastoras

I suggest a reading about the contributions of the mathematicians mentioned. Cantor, and the others. You will also need some set theory.

-.

## Deathclock

Yeah, you are.

## Deathclock

At least they aren't trolling the comments section of an obscure science news site...

## Mastoras

Then, we consider another set B, made from the members of the first set which are labeled with an even number. So, set B will contain members of the first set with labels 2, 4, 6,...

Which set has more members?

For every member of set A with label n, there can always found a corresponding member in set B, and this will be the one with label 2n. On the other hand, for every member of set B with label 2n, there can always found a corresponding member in set A, and this will be the one with label n.

So..., each set is not greater than the other. And the number of their members is infinite.

The members of set A were infinite, and from them we were able to select a subset of members, forming set B. But although members of B were selected as a subset of A, the two sets are still equal.

This is one of the non-intuitive characteristics of infinity.

-.

## Mastoras

Still, I think it worths a bit more than what you payed for it!!

-.

## Husky

## Jotaf

They missed the word "line", so it should be:

Which is the concept of cardinality of infinities. A great documentary that explains these topics (and other very interesting ones) in an intuitive way is "The Story of Maths" by Marcus du Sautoy. Here's a link to the wikipedia article on the relevant episode:

http://en.wikiped..._problem

As for the article, what they mean by "sending a particle to infinity" is that you can make a particle go as far away as you want. This has obvious implications for whether the Universe is finite or not...

## panorama

## LariAnn

## panorama

Sounds like you'd enjoy I'm Sorry I Love You...maybe Love is Like a Bottle of Gin...

## El_Nose

by infinity they mean .. and iquote

not other dimensions not out of the universe -- then the scientist goes on to say this is provable in the real world -- BUT often there are other forces at play that prevent this that the research can not account for that would stop this from happening such as friction.

Reading is fundamental.

and the non math people suggesting that math doesn't deal with infinity well never took a discrete math course -- or an analytical math course such as calculus. Because all college level math is about make things so general infinity is not an issue, as long as the prerequsites are met the statements hold.

Please look up proofs by induction as a starting point to understand.

## UberGoober

## axemaster

I guess the biggest problem is that magnetic fields do no work. So the result presented here would probably mean that at an appropriate starting angle, the particle would have nonzero divergence through an infinite gaussian surface.

## axemaster

## Urgelt

This is a weakness in set theory.

We must not forget that mathematics relies on arbitrary rules invented by humans. When we use rules which nature also seems to use, mathematics seems to describe reality. When we use rules which nature does not use, we get paradoxes. (See "Russell's Paradox.")

The problem isn't the nature of infinities, but our insisting on rules for them which nature doesn't use, leading us to head-scratching paradoxes like "infinity times two is equal to infinity divided by two."

Say the universe is infinite. Draw an infinite plane through it to divide it. Now you have two infinities, one on either side of the plane. Is a half infinity equal to both halves together?

In set theory, yes. But not in nature, it isn't. If it were, then your home would be in both halves when you divided the universe. Nature allows your home in only one of the halves.

## Urgelt

"A man of Seville is shaved by the Barber of Seville if and only if the man does not shave himself. Does the Barber shave himself?" If he does then he doesn't, but if he doesn't then he does!"

This paradox is permitted by set theory rules. It is not permitted in nature. Or, far as I know, in Seville.

So. If, in a divided universe, your home can be in only one of the two infinite parts, then the sum of the parts - an infinity - must be larger than either of the two infinities added to make the larger infinity. Because in one of the half-infinities, your home is absent. Added back together, the larger infinity includes it.

You *can* add and subtract infinities in nature.

Until set theory refines the concept of infinity, it's going to spew out all sorts of paradoxes that are impossible in nature.

## Jotaf

About the more esoteric concepts of infinite vector spaces and other related ones, their applications are less obvious but aren't entirely imaginary. For example, we've been building classifiers that work on infinite-dimensional Hilbert spaces for 15 years now (see Kernel Trick). Think about that the next time your picture is automatically tagged on facebook!

I don't get this argument, why can't it be in one infinite space and not in the other?

## Urgelt

Perhaps you're thinking that "infinite" means "everything." It doesn't, not even in set theory.

What it actually means is "limitless in one or more dimensions."

In the example I gave, the hypothetically infinite universe is divided into two infinite subsets. The two sets do not overlap. Each is unique. Your home can be in one or the other, but not both.

Both sets are limitless - but only in certain directions. Both have a limit: the plane separating them. Neither includes "everything."

Limited infinities are used in mathematics all the time. There's actually not much use for an unbounded infinity that includes everything.

Hope this helps.

Set theory is all about limits: drawing boundaries around sets, then working with them. Without boundaries, you don't have sets.

## Isaacsname

WINNING

:P

## Isaacsname

Who really wants to know ?

Would they believe if they were told ?

## indio007

## MandoZink

Would termination of the magnetic field end this journey to the beyond? Or is this "path to infinity" irreversible and forever independent of the field that sent it there? (exactly where?)

## Au-Pu

What a load of nonsense.

## determinist

Be a lamp unto thyself...

## markeagleone

I also believe that the universe being infinite is up for debate and that there are alternate universes(string theory) is also up for debate. The main problem is that science is based on observation. The backward thinking that the use of math can solve everything is a joke. You write a mathematical equation and (in theory) say this is how the physical world should be is too big of a guess without physical observation. What is being stated here is that if I build a chair out of steel, I can say it will last forever.

## markeagleone

## antonima

You would think that the magnetic field drops off according to an exponential equation, but its not always like that with magnetic fields. They must always travel from North to South, which leads to some strange cases. That is why such simple sounding research like this gets done.

## uhjim

so you say

## Cave_Man

This type of thinking leads me to believe in a holographic universe. The whole thing is in all it's component parts in the form of information, that's why all the matter in the universe was in one atom so to speak at the big bang. All particles remember all interactions since the beginning of time and therefore the information of all other particles.

Stored in string vibrations somehow I would assume kinda like an interference pattern. Makes me think the whole universe is an interference pattern. Spacetime God=Cosmic ripples in the lake of quantified meaning.

## Standing Bear

## jibbles

3) cantor and the continuum hypothesis do not seem very relevant to the result. the space wasted on them here could well have been used to give more detail about the result.

2) it's funny how a phrase like "to infinity" can set people's heads spinning. if it bothers you, just replace it with "arbitrarily far".

-- arbitrarily far and beyond!

## jibbles

## taniana

## Jotaf

I know that, I asked that question because I thought you were implying the opposite! Analogies like that one about the house are not great for explaining these things. That's why we have math, spoken/written language has its limitations.

## Jotaf

I've explained this in my previous 2 posts. You can prove that infinities are of different nature with very simple arguments. See the episode "To infinity and beyond" of the documentary series "The Story of Maths" by Marcus du Sautoy for a nice explanation.

Also, if infinity were abstract with no relation to reality, engineers and scientists wouldn't use the concept on an almost daily basis. It would break down fast and people would quickly recognize it as the bunch of hocus-pocus that you believe it is. It's clearly not the case.

I just hate it when people are so dismissive of something, just because they have an oversimplified mental picture of it.