Supersymmetry, the Whys and the Hows in Understandable Terms

I wrote this piece while I was working on thesis project in theoretical physics, as a way to wrap my mind around supersymmetry. Hopefully, it is written in a way that is understandable to most readers.

A few years ago, in a class on modern physics, I listened to an astronomer complain about his colleagues. He probably talked about a lot more but since the man was boring beyond belief I don’t remember anything from the hour-long lecture, apart from the skepticism in his eyes when talking about the people he worked with. You see, he had been forced to start collaborating with particle physicists, and particle physicists have a weird way of doing things that, especially to an outside observer, seems to consist of assuming that what they consider to be the “prettiest” option is the correct one. Infuriatingly, nature almost always agrees with them; “it seems to have worked out OK for them before”, in the words of my boring astronomy professor.

For a particle physicist, supersymmetry is one of the prettiest thing possible, so pretty  that a lot of theoretical physicists (string theorists for example) assume that it must be correct. I will be trying to give a somewhat easy-to-grasp explanation of supersymmetry, of why it is so beautiful, how physicists found it and what consequences it has for the universe. Unsurprisingly, it starts out with regular “non-super” symmetry.

Space-time

Arguably, the greatest act of Albert Einstein was to explain how space and time where not separate things, but two sides of the same strange coin. How 2036 is far away in time, in pretty much the exact same way that Kuala Lumpur is far away (at least from Sweden) in space. If you move very quickly, your image of reality will change, distances will contract and time will change speed. Suddenly, picturing the universe as three-dimensional becomes unpractical and we need a new mathematical object that combines space and time. Physicists call that space Minkowski Space. I will simply call it the Universe.

It’s not quite obvious why we would need to combine space and time into one thing, but it has to do with one of the fundamental ways in which mathematics work. When we use mathematics to analyze mathematical things, we often don’t actually look at the objects themselves, we look at how we can transform it, more specifically: how we can transform it without changing certain things about it.

Symmetries

Take a standard, blank, rectangular piece of paper and put it on a table in front of you. You can lift it up, twist it around and put it down again in a lot of different ways, but there are very few ways to do that, that doesn’t change the way the paper looks afterwards. In other words, we want it to seem like we were never there and we call those special kinds of “ways to move a paper around” symmetries. After some examination, we can find that there are four ways to do that. The boring way, not moving the paper at all, and three other ones:

figur 1

Flip it right-to-left.

Figure 2

Flip it top-to-bottom.

Figure 3

Rotate it 180 degrees

With this knowledge, if we forget the paper but remember these symmetries we still know quite a bit about what we are dealing with. We see that all the corners are identical, since we can mirror the paper both horisontally and vertically, and since we can only rotate it 180 degrees (and not 90 degrees, or any degrees we want) we know that it is not square (or circular). We don’t know everything, but in some mathematical sense we know enough.

That same process leads to supersymmetry. Now, instead of the paper we have the universe, and instead of it looking the same, we require the laws of physics to be the same after we have “manipulated” it.

But what does it mean to “manipulate the universe”? The easiest way to think about it is as “tranformations” between two people observing the universe in different ways. For example, if I am standing twenty meters away from you, looking in the same direction, “my universe” (or the way I see it) is shifted twenty meters compared to yours; if I am looking in another direction, the universe seems rotated to me and so on. In both of those cases the laws of physics are preserved (the laws of physics are the same wherever you are, and in whatever direction you are looking, or let’s assume that they are) but not all do. If the universe I see is twice as big as yours, you would need to throw a ball twice as hard to get to the same place, and if forces don’t act in the same way we can’t say that the laws of physics do; if the universe I see is all red, something strange has happened to the wavelengths of light.

So stretching and color-shifting doesn’t work, but simple movements and rotations do. We can also move in time (let’s assume that the laws of physics will look the same tomorrow as they do today). There is one more kind of transformation that works as a symmetry, and that is changes in speed. As we talked about earlier, Einsteins special theory of relativity tells us that at high speeds the universe looks very differently, which might make us think that it shouldn’t be a symmetry. But the important part is that it tells us just in what way it looks different. Basically, since we have rules for how the world works at high speeds, we can put changes of speed into our little group of symmetries.

With that addition we have found all transformations that doesn’t change our understanding of the laws of physics, or in other words: the symmetries of the universe. Together, we call them the Poincaré Group, after the french genius Henri Poincaré.

The word “group” in Poincaré Group is important, and in mathematics it means something different from similar words like “set” or “family” or “category”. A group is a collection of things that we can add together in a certain way, just like how we can add numbers and get new numbers (1+3 = 4) we can add tranformations (moving ten meters + turning 90 degrees = first moving ten meters and after that turning 90 degrees). A branch of mathematics called “Abstract Algebra” deals with objects like groups, so now that we have the symmetries collect in one, we can draw on centuries of mathematical knowledge to analyze it.

To summarize, symmetries are ways to “transform” an object in ways that does not change some important thing about it. We found the symmetries of the universe by considering how we can transform the universe without changing the laws of physics, and grouped it together in to an object that we can analyze with mathematics.

Supersymmetry

So now that we used the way we think of the universe and its laws of physics to get this handy mathematical object, the Poincaré Group, what if we could make this group bigger, add some more parts to it and then go backwards through the process and get a new model of the universe? What would these new supersymmetries look like?

It turns out that it is possible, but it is such an unusual kind of transformation that for a long time we were convinced it couldn’t be done. The only way to do it, it seems, is to build a symmetry that turns bosons into fermions, and vice versa.

Lets explain that a little.

According to the Standard Model of Particle Physics the universe is built by fermions and bosons; fermions are the particles that builds up matter, like electrons and quarks (quarks are tiny fundamental particles that combine into protons and neutrons to form atoms which builds up all matter around us) and bosons are particles that transfer forces, like photons that carry electromagnetism (like light) and the evasive Higgs boson.

The supersymmetries that we have found connect these different kinds of particles; electrons, quarks, protons and neutrons would be tranformed into “supersymmetrical” particles we call selectrons, squarks, sprotons  and sneutronsThese particles would be bosons, energy carriers like photons, and bosons like the photon would have their own corresponding supersymmetrical particles, photinos, that work in a similar way to our normal electrons.

It is like a different world of particles, where every part of our world has a supersymmetrical counterpart, just the kind of symmetrical, beautiful solution that particle physicists love.

Conclusions and Experiments

In summary: physicists search for symmetries, ways to transform objects without losing their important characteristics. Looking at the universe, we can see that there could be more symmetries, symmetries that connects materia-particles to energy-particles. That would mean a whole new system of particles like our own except that the particles would have “swapped places”. The hypothesis that such a symmetry exists is called supersymmetry.

We call that an hypothesis, because so far we have not found any supersymmetric particles, but the particle accelerator LHC in Switzerland will soon reach high enough speeds to perhaps start producing these particles, and after the Higgs boson, this is the next goal.

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