Supersymmetry for the masses

Introduction
Since the times of the Ancient Greece, Natural Philosophers (they had several names, from time to time) have often asked themselves what the “world” is really made of. The first answer was “atoms” (“impossible to divide further”), and, as today, we still can’t prove if it’s true or not. Nowadays, this word has the different meaning of “minimal entities of chemistry”, but chemical atoms are not impossibile to divide since now we know they are made of more fundamental constituents called quarks and electrons.

The best description we (I mean the western Natural Philosophers) have found so far is called “Standard Model”, and it’s based on a more deeper cookbook called “quantum field theory”. While nobody has yed proved the latter to be wrong, we know the former to be an incomplete description of the world we live in. For some aspects it’s even flawed, since it predicts that some elusive objects called neutrinos are weightless, but experiments show they are not. This is not bad news: after all, it suggests that there’s still a lot of work to do. In physics, greek atoms are called elementary particles.

Relativistic Quantum Field Theory
At the beginning of the XXth century, physicists (mainly Planck, Einstein, Heisemberg, Schroedinger) discovered that our world, when considered at very short length, behaves differently from, let me say, at our “scale of distances”. They discovered the “quantum mechanics”. A famous physicist once noticed that we are all well accustomed to quantization: for example, when we order a beer at the pub, we buy it in pints, even if the beer flows continuously from the cask.
Basically, in the atomic world, energy is sold in glasses of different size. But always in glasses.

What does it mean the word “field” in the name of this theory? A field is an entity defined everywhere in the space. For example, when we watch forecasts on tv, we actually observe the “temperature field” or the “wind field”. We define the temperature to be a “scalar” (it can be measured with some kind of scaler), while the wind is a “vector” (wind has a magnitude and a direction, like “from south to west”: this makes a vector). There can be more uncommon type of fields, and they turn out to be very important for our discussion.
Anyway, the whole thing is that when you mix up “quantum” and “field” you discover that the particles are fields of waves. When two bodies exchange energy they do this through waves of the field that we recognize as particles.

Let’s talk about the word “relativistic”. Again, at the dawn of the previous century, Albert Einstein proved that the laws describing electrical and magnetic phenomena imply that space and time must be considered in a particular combination as a single entity (the so-called spacetime). This is inavoidable if we believe that everyone, independently of their place and speed (and possibily religious beliefs).
What followed from this discover has been an incredible breakthrough in Natural Philosophy: the speed of light in vacuum is the fastest speed that everything can reach, and it is the same for everyone, independently of their place and speed. Experiments boldly confirmed this theory. It’s so difficult to understand how it can be, that I suggest you to accept it as a fact, until it will be proven false. But don’t get crazy, nobody can understand it: We can only describe this weird thing with math.

Now, relativity let us toss and turn object in 4 dimensions: time and space. When we rotate something in space we call this operation…well, rotation. When we rotate something in 2 spatial dimensions and time we obtain a “Lorentz boost”. It has no obvious meaning in everyday life, but scientists discovered that it can explain a property of particles called “spin”: when placed in a magnetic field, electrically charged particles behave like they’re rotating, but they are not.
Particles can be classified according to the numerical value of their spin, which is always the same for each one. In fact, if you put together relativity and quantum mechanics, you discover that the spin is quantized (“sold in glasses”). If you measure the spin in a unit called “Planck constant”, it turns out that all the particles can have a spin that is either an integer multiple of this unit (let’s say 1, 2, 3…), or a semi-integer multiple (1/2, 3/2…). The first kind is called “boson” after the indian physicist Satyendra Bose, while the second is called “fermion” after Enrico Fermi. From calculations, it turns out that spin-0 particles are scalars, spin-N/2 are “spinors”, spin-1 are “vector bosons” and spin-2 are “tensors”. Don’t be afraid of spinors and tensors: you don’t need to know exactly what they are.

The Standard Model
Ok, now we have all the ingredients. What can we do with them? Let’s assign a kind of field for each particle discovered so far.
Experiments show that bosons are responsible of forces (like electromagnetism and nuclear reactions), while fermions are the “building blocks” of the world called quarks and leptons, let’s say, they form atoms, molecules, human beings etc. It is still experimentally unproven, but very likely, that gravitation is due to a spin-2 boson called “graviton”, but remember: gravitation is not a part of the Standard Model!

Now, a main issue is: “how come that particles have mass?”. Despite the fact that we can fancy several ways to get this results, the more simple and elegant is through the so-called “Higgs mechanism”, after the physicist who proposed it. Basically, Standard Model states that there is a field (a scalar one) that interacts only with some particles, but not all. Heavy particles interact very strongly with the Higgs field, while photons do not at all (light is “weightless”). It act, more or less, like putting a sheet of paper on a wet table top: paper absorbs water and it gets heavy. If you try doing the same with a plastic card it doesn’t work.

The problem is that nobody has ever officially seen a Higgs particle (some rumors from Fermilab). So far. Moreover, this theory doesn’t predicts the value of the masses, and other parameters.

So we’ve got:

  • Spin-0: scalar particles (Higgs)
  • Spin-N/2: “spinor” fields (quarks, electrons, neutrinos..)
  • Spin-1: vector boson fields (electroweak interaction)

Is this all?

Beyond the Standard Model: Merits and flaws

Despite some rumors, the SM is a magnificent theory. Of course, it’s not perfect. For example, a lot of parameters are put in “by hand” (like the value of the masses, which is, IMHO, the biggest flaw), but it let us explain why the sun is so hot and so long-lived, and a lot of other important stuffs. Moreover, gravity is not included. Nobody tells us that we will eventually find a “Theory of everything”, but it is so attracting that it’s worth trying.

In the past 30 years (or more) a lot of effort has been made in this direction. Einstein has tried, too, but without much success. Actually, Grand Unification is the Tree of Life of particle physics, and it seems to have a large number of limbs. But only one trunk. Supersymmetry is one branch that is very promising.

You can see SUSY from different points of view, anyway, it states that fermions and bosons are two faces of the same coin, if you knew how to see it properly. Of course, in our world, they are not the same thing: fermions are the bricks of the Cosmos, and bosons act like glue. So what has SUSY to do with out world?

In Field Theory there’s an important operation called “commutation”. Commutation is made of “operators”, which are mathematical objects describing some kind of transformation.

The point is that if you apply SUSY twice and then come back to the initial state, you get a shift in one direction.

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