# Magnetic fields can send particles to infinity

##### April 17, 2012

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 to , 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 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 and nothing else". Reality always has other variables to be considered, such as 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.

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Adjust slider to filter visible comments by rank

##### Star_Gazer
2.6 / 5 (7) Apr 17, 2012
Way over my head.. What does all that mean?
##### TS1
2.7 / 5 (6) Apr 17, 2012
Way over my head.. What does all that mean?

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
1.3 / 5 (14) Apr 17, 2012
"At the moment this is a theoretical mathematical study"

Lol, they got nothing better to do?
##### indio007
2 / 5 (4) Apr 17, 2012
I've been wondering something like this recently myself....
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
1.8 / 5 (5) Apr 17, 2012
"Is the universe finite or infinite?"
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
1 / 5 (4) Apr 17, 2012
Mindless
##### krundoloss
4 / 5 (4) Apr 17, 2012
What are they talking about. What does it mean to "send a particle to infinity"?
##### Mastoras
4 / 5 (3) Apr 17, 2012
Obviously, you need a certain background to understand the mathematical subjects mentioned in the article. Beyond this, the article does seem to have some lines written in a less that clear way.

I suggest a reading about the contributions of the mathematicians mentioned. Cantor, and the others. You will also need some set theory.
-.
##### Deathclock
1.7 / 5 (6) Apr 17, 2012
Mindless

Yeah, you are.
##### Deathclock
3.4 / 5 (10) Apr 17, 2012
"At the moment this is a theoretical mathematical study"

Lol, they got nothing better to do?

At least they aren't trolling the comments section of an obscure science news site...
##### Mastoras
5 / 5 (2) Apr 17, 2012
Suppose you have a set A with an infinite number of members. We label each member of the set with one of the natural numbers: 1, 2, 3,...

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
3 / 5 (2) Apr 17, 2012
Folks, the previous leaves many things unproved or loosely stated. So, it has many flaws. But it is intended as an introductory note to satisfy the reader's curiosity about infinity that aroused from the article. It is not a mathematical paper.

Still, I think it worths a bit more than what you payed for it!!
-.
##### Husky
3 / 5 (2) Apr 17, 2012
does the article suggest that a particle can escape to some hyperdimensional plane, with the same polarisation as the magnetic field ? now there would be a candidate for dark matter....
##### Jotaf
5 / 5 (2) Apr 17, 2012
This article is about math, and unfortunately assumes a bit of background. There's one mistake that makes it much more difficult to understand for the casual reader:

For example, a countable infinity, with natural numbers, is not the same as a straight, he continued.

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

For example, a countable infinity, with natural numbers, is not the same as a straight line, he continued.

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
not rated yet Apr 17, 2012
I Thought You Were My Boyfriend is my favorite by them...anyone anyone...?
##### LariAnn
1 / 5 (6) Apr 17, 2012
My viewpoint on infinity is that the mathematics involved are not the same as what I call "finite mathematics". An example of what I'm describing is what I call "fractions of infinity". That phrase sounds like an oxymoron, but it is not, as a line of infinite length is a fraction of a plane of infinite area, yet both are infinite! So everyday mathematics doesn't work when dealing with infinity. This includes infinitesimals as well. Trying to mix finite mathematics and the mathematics of infinity leads to insoluble problems. IMHO, when technology can be derived from the mathematics of infinity, we will travel to other galaxies with no power source issues.
##### panorama
not rated yet Apr 17, 2012
My viewpoint on infinity is that the mathematics involved are not the same as what I call "finite mathematics". An example of what I'm describing is what I call "fractions of infinity". That phrase sounds like an oxymoron, but it is not, as a line of infinite length is a fraction of a plane of infinite area, yet both are infinite! So everyday mathematics doesn't work when dealing with infinity. This includes infinitesimals as well. Trying to mix finite mathematics and the mathematics of infinity leads to insoluble problems. IMHO, when technology can be derived from the mathematics of infinity, we will travel to other galaxies with no power source issues.

Sounds like you'd enjoy I'm Sorry I Love You...maybe Love is Like a Bottle of Gin...
##### El_Nose
4 / 5 (4) Apr 17, 2012
did anyone asking question stop to read the entire article ...

by infinity they mean .. and iquote

"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"

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.

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
3.7 / 5 (3) Apr 17, 2012
I told me girlfriend I loved her infinity times infinity. She's so gullible.
##### axemaster
5 / 5 (1) Apr 17, 2012
So are they saying that a particle can escape a magnetic field - meaning that when B->0 it would have a nonzero kinetic energy? If so... well it would seem to violate conservation of energy in a continuous vector field, so I'm wondering what they really mean.

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
not rated yet Apr 17, 2012
Also, just for those who wonder: this research is physically relevant to the design of electromagnetic thrusters, because they require that exhaust ions not return to the engine.
##### Urgelt
3.5 / 5 (4) Apr 17, 2012
Mastoras wrote, "So..., each set is not greater than the other. And the number of their members is infinite."

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
4.3 / 5 (3) Apr 17, 2012
I'll take a moment and restate Russell's Paradox here, for convenience of readers.

"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
5 / 5 (2) Apr 17, 2012
Many people assume infinity is an abstract and useless concept. In reality it's useful every day, in real-world engineering problems. Analyzing he behavior of systems in the limit as time approaches infinity is commonplace, and can be done reliably. Without that analysis your computer wouldn't work, and the industrial processes used to manufacture it wouldn't either.

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!

If it were, then your home would be in both halves when you divided the universe.

I don't get this argument, why can't it be in one infinite space and not in the other?
##### Urgelt
4 / 5 (2) Apr 17, 2012
Jotaf asked, "I don't get this argument, why can't it be in one infinite space and not in the other?"

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
not rated yet Apr 18, 2012
Sweet ! I was born in infinity !

WINNING

:P
##### Isaacsname
1 / 5 (1) Apr 18, 2012
" Is the universe finite or infinite ? "

Who really wants to know ?

Would they believe if they were told ?
##### indio007
1 / 5 (3) Apr 18, 2012
"Consider the set of all sets that are not members of themselves. If such a set exists, it will be a member of itself if, and only if, it is not a member of itself."
##### MandoZink
not rated yet Apr 21, 2012
I do not have a problem with infinity, but I do not understand the path/direction that this infinity is heading. Its not the math, but the physical concept that needs a little more explanation.

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
1 / 5 (3) Apr 21, 2012
TSI was correct. The article needs a rewrite. They say it is a theoretical mathematical study, which is fine. Well postulated theories often lead to valuable lines of research. But in this theoretical study they claim to have proved it and later claim to have confirmed (is that somehow different to proved?) that the phenomenon occurs.
What a load of nonsense.
##### determinist
not rated yet Apr 22, 2012
Why is the square root of -1 a variable? Humans have small windows through which we view the objective reality. Scientific method is of great service to our understanding of the O.R. "Mathematics" is a human contrivance (a scientific theory)which has proven to be useful in a terrestrial sort of way. But even mathematics may need to evolve.

Be a lamp unto thyself...
##### markeagleone
1 / 5 (1) Apr 22, 2012
So this is what the great learned brains here are up to. You can't have a infinite greater than an infinite. That is like saying 10 is greater than 10. Secondly,the concept of infinite is an abstract concept. In math,it works because the numbers are only in relation to other numbers at a set equation. In reality, such things as gravity, entropy, and countless other forces are in action. If you are to derive an equation in math, the equation should fit the physical world.
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
1 / 5 (1) Apr 22, 2012
What they are saying here is a part of everyday science that most people have been taught. If you put something into motion it will tend to stay in motion unless otherwise acted upon by other forces. I would suppose you could use that law and say if there are no other forces acting on it,it would go forever. We all know that will never be the case, so why are they wasting time and money just to restate a known physical law? I could have told them that a lot cheaper,in a faster amount of time. Of coarse, I would use the word infinite in its rightful place-probably would have said as far as we know or can calculate. Infinite has not been or will ever be a confining number.
##### antonima
not rated yet Apr 22, 2012
I would think that a particle traveling away from a dipole magnet would eventually return since all lines of force travel from one pole to the other, much like the photo for the article!

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
1 / 5 (1) Apr 23, 2012
"Mathematics" is a human contrivance (a scientific theory)"

so you say
##### Cave_Man
1 / 5 (3) Apr 23, 2012
I'll take a moment and restate Russell's Paradox here, for convenience of readers.

"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!"

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

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
1 / 5 (1) Apr 23, 2012
You mean a magnetic field of sufficient strength and/or configuration is like a 'warp field'?
##### jibbles
5 / 5 (1) Apr 23, 2012
1) did they use google translate to write this?!
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
not rated yet Apr 23, 2012
again, this is one vague and terribly "written" report with rambling, irrelevant material. who gets paid to write/vet/republish these hack jobs?
##### taniana
1 / 5 (2) Apr 25, 2012
as Eddie implied I'm blown away that a person able to profit \$7977 in four weeks on the internet. did you look at this site NuttyRich.com
##### Jotaf
not rated yet Apr 28, 2012
Perhaps you're thinking that "infinite" means "everything." It doesn't, not even in set theory.

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
5 / 5 (1) Apr 28, 2012
So this is what the great learned brains here are up to. You can't have a infinite greater than an infinite. That is like saying 10 is greater than 10. Secondly,the concept of infinite is an abstract concept.

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.

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