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?

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**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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