By NASA [Public domain], via Wikimedia Commons

There are two people standing 1 m apart in space. If their electrons magically turned into positrons, how strong would the electromagnetic repulsion force between them be?

Short answer: About 1029 Newtons.

Long answer: Let’s suppose a wizard suddenly decides to curse two astronauts in orbit by magically switching all of the electrons in the atoms in their bodies with their antimatter counterpart, the positron. The positron is just like the electron in almost all ways, except it has a positive electric charge like a proton. Without the electrons, these people are no longer electrically neutral. They carry enormous positive charge, and as we know, like charges repel.

The force between the two, now incredibly positively charged, people is easily calculable from the Coulomb force law. All you need to calculate the force between two charged objects is the amount of charge they carry and the distance between them.

So, what’s these peoples’ charge? Again, normal neutral people like you and me have an equal number of protons and electrons in our body, which result in zero total charge and no long range electrostatic forces between us. But if all those electrons magically and inexplicably turned into positrons? Then the net charge becomes enormous.

The human body contains about 4×1028 nucleons (a science word meaning protons and neutrons). Only about half of those are protons (the other half are neutrons), but for every proton there is now a positron with equal charge, so the total charge of our people is about 4×1028 elementary charges.

To you give a sense of scale, an average lightning bolt carries about 100 Coulombs of charge, which is about 1020 elementary charges. These people contain the electric charge of nearly a billion lightning strikes. Move over, Thor.

So the force between them is enormous, about 1029 Newtons. That’s ten million times the force of gravity between the sun and the earth. The energy of the electric repulsion between them is a million times the energy of the asteroid that killed the dinosaurs. You might think that this means these people blast away from each other in a horrifically violent explosion, due to the enormous electric repulsion.

And you’d be right. But somehow, it gets worse.

The people themselves are packed densely with positive charge. All those protons and positrons don’t just want to push away the other person, they want to push away from every other particle around them. The positive
people explode too! … I’m now thinking ‘positive people’ wasn’t the best name of them.

The explosion sends protons and positrons streaming out at nearly the speed of light, forming a shell of expanding positive charge. At the end, every single one of these particles all carry the energy of a typical tennis ball. They spread through the universe as high energy cosmic rays.

In fact, their energy is incredibly close to that of the Oh My God particle, the fastest cosmic ray ever observed. Until now, the origin of that cosmic ray was not understood, but after working this out, I think I have a pretty good guess about where it came from.



asked by anonymous

cover image credit: Wikimedia Commons


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