Electron Handedness

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A comic about how chirality and mass are related.

Electron handedness

Would the mirror image of our universe behave in the same way as our universe? The short answer is “no”: particles that are “reflected” have slightly different properties than their counterparts, which means that our reflected universe would be slightly different than the universe itself. To understand why, we need to talk about a property of electrons called “chirality” or “handedness“, which can be seen as a quantity that tells us in which side of the mirror they live.

Imagine an electron that is moving towards a mirror, like in the comic below. Apart from this, the electron is also spinning around itself in the clockwise direction. Physicists usually represent this with an arrow going forward, because that’s the direction a screw would go if spun that way. Now we can ask ourselves whether the arrow of the spin and the arrow of the movement point in the same direction: if they do, we say the particle is “right-handed.”

electron-handedness-chirality-particle-physics-comic

We could now take a look at the mirror and see what the electron on the other side looks like. Of course, he’ll be moving in the opposite direction: however, he is spinning in exactly the same way! This means that now the arrow of its spin and the movement point in opposite directions. We say the particle is “left-handed.”

Chirality vs. Helicity

Here comes a little subtlety that complicates things a bit. It turns out that, if I look at the electron from the point of view of a particle travelling in the same direction but faster, I get that the spin and the movement now point in the opposite way! However, there is still a very real way in which the electrons from both sides of the mirror are different from each other. The good news is there is still a way of determining whether the electron is right- or left-handed: the bad news is we can’t look at the pictures any more, but we need some complicated mathematics.

Physicists call the property of the spin pointing in the same way as the movement “helicity.” The problem with helicity is that it depends on who’s looking at the particle, so it’s not great for distinguishing between left- and right-handed electrons. The property that allows us to distinguish between those is called “chirality.” The beauty of chirality is that it does not depend on who’s looking; the disadvantage is that there’s no easy way to show it in a picture. However, imagining the left- and right-handed particles as mirror images of one another is a good enough analogy.

Right-handed, Left-handed and the Higgs

So why is it important to distinguish between left- and right-handed particles? It turns out there are many good reasons. For starters, some forces will only interact with right-handed particles, a bit like teachers in the 1950s. This creates a noticeable difference between the mirror universe and ours and is why the W+ boson in the comic is ignoring the poor left-handed electron.

So are actual electrons right- or left-handed? It turns out they are neither. In fact, electrons are a combination of two particles: a right-handed and a left-handed electron. Right- and left-handed electrons are massless: they weigh nothing. Because of this, they travel at the speed of light, just like photons. But real electrons do have mass and do not travel at the speed of light, so what’s going on?

Right- and left-handed electrons are massless and travel at the speed of light. In fact, they travel at the speed of light because they are massless. But we can turn this reasoning around: they are massless because they travel at the speed of light, they are massless. Only massless things travel at the speed of light. So the reasoning doesn’t go like this:

Massless → Speed of light

Or this:

Speed of light → Massless

But rather this:

Speed of light ↔ Massless

In a similar way, we can deduce that, if a particle does not travel at the speed of light, it has mass:

Less than the speed of light ↔ Mass

This is how the electron acquires mass. A right-handed electron travels at the speed of light and then bumps into a Higgs boson, which turns it into a left-handed electron travelling at an angle, at the speed of light. Then the left-handed electron bumps into another Higgs boson and turns into a right-handed electron, and so on. The result is a random zig-zag motion that, looked at from large enough distances, appears to be a negatively-charged particle travelling at less than the speed of light and therefore with mass. It also implies that the particle is not right- or left-handed but a combination of both.

Summarizing: handed electrons have no mass, but “real” electrons do because they are a combination of left- and right-handed electrons. This combination can only happen because of the Higgs boson. That’s why we say the Higgs boson gives particles mass.

This post in Quantum Diaries was a great source of inspiration. Read it for a much more detailed and rigorous explanation of chirality and helicity, including some nice diagrams for showing what chirality looks like mathematically.

One Response

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