"Simple," you may say. "All you have to do is test the theory against experimental data and, if predictions don't work, toss the theory in the garbage can." In practice, however, things are way more complicated.
Take it from the start: a hypothesis is proposed to explain a known phenomenon, say, the orbit of the moon or the cause of a disease. The hypothesis can also propose the existence of something new, for example, the existence of a particle or global warming. The first case, a hypothesis that explains what's out there, is easier to deal with. Experiments are set up to test the hypothesis. Does it explain what it's supposed to explain? Are there rival hypotheses that do a better job, that is, explain more with less? Assuming the hypothesis passes the tests, it is then accepted until something better comes along.
It's the second case, a hypothesis that predicts new phenomena, that is more challenging. What if the particle isn't found? Or global warming is deceptively subtle?
The complication, at least in the physical sciences, comes from the way predictive hypotheses are built. In general, and especially in physics, chemistry, and astronomy, hypotheses are based on mathematical models, descriptions that attempt to approximate the workings of Nature. Every model is thus an incomplete replica of what's really trying to explain. As a consequence, no model is complete or perfect.
In particle physics, the branch of physics that tries to find the most basic constituents of matter and studies how they interact with one another, all that we know up to now is condensed in the so-called Standard Model. According to the model, there are 12 fundamental particles of matter arranged into three "families" with four members each.
For example, the matter we are made of, atoms, is composed of electrons, protons, and neutrons. Protons and neutrons are, in turn, composed of two types of a different particle called a "quark." So, the family of particles that dominates the world around us is composed of the electron and the up and down quarks. In addition, there is the electron-neutrino, an elusive particle that shows up in radioactive decays and at the core of the Sun.
The other two families have a similar structure, but the particles are heavier. Their members are found mostly (but not exclusively) through high-energy collisions in particle accelerators such as the Large Hadron Collider (LHC), famous for the discovery of the Higgs boson this past July. By the way, the Higgs is the newest member of the Standard Model, although we still need to understand a few of its properties to know exactly where it sits. (Sean Carroll just published a book on the Higgs, which I highly recommend, The Particle at the End of the Universe.)
Since every model is incomplete, there are gaps in the Standard Model. To fill them, physicists propose extensions, new models with new particles. The main test of these extensions is to find out if the particles they predict exist. Of the extensions, the most popular by far is called supersymmetry.
Proposed in 1974, supersymmetry is indeed super: if the world is supersymmetric there should be twice as many particles out there. The reason is that supersymmetry transforms every particle into a new one by changing a fixed amount of its internal rotation, or spin. (For the experts, by ½ of Planck's constant, equivalent to the spin of the electron.)
There are many possible extensions of the Standard Model that invoke supersymmetry; they make different predictions for what kinds of particles experiments should find. The simplest predict that all supersymmetric particles (the extra ones that double the count) should be unstable but for the lightest of them all. This fellow should be around if these models are correct. Supersymmetry has also been proposed as an explanation to the cosmological dark matter problem, or why galaxies seem to rotate faster than what simple Newtonian gravity predicts. The lightest supersymmetric particle would gather on the outskirts of galaxies, creating an invisible dark cloak that changes its rotation speed.
Physicists at the LHC and dozens of other experiments have been avidly hunting for supersymmetric particles. Up to now, they found no trace of any. Recently, LHC physicists looked at the decay of a particle called the B-meson, further complicating things for supersymmetry. (Particles are usually unstable and decay, or disintegrate, into lighter ones.) Different models predict different types of decay. Of these, the B-meson has a particularly rare one, at least according to the Standard Model, where it decays into two muons, heavier cousins of the electron. For every billion times the B-meson decays, it only follows this path three or four times. Observations of B-meson decay at the LHC have fallen in line with Standard Model predictions, not with the decay predictions of most supersymmetric models.
Given the lack of data in support of supersymmetry after all these years, why is the theory still considered viable?
The complication comes from the way mathematical models depend on various adjustable parameters. For example, the decay rate of a particle may depend on its mass and the way it interacts with other particles; if certain types of decays aren't seen, parameters can be changed to reflect that. The model may be made to hide from available experiments. And given that technology has more concrete limits than the imagination of theorists, a model may always be beyond the detectable.
How, then, can such types of models be ruled out? Well, simpler versions may be ruled out when the tweaking of parameters becomes so extreme that the model loses its original motivation: it explains nothing and becomes too cumbersome. Or a forbidden particle is discovered. Then there are always the more complicated versions, with more parameters that are harder to rule out.
The point is that there isn't a clear-cut answer. The physicist Max Planck used to say that wrong ideas don't die out, their proponents do. It will be interesting to watch what will happen in the next few years with supersymmetry and its proponents if tests keep producing negative answers.
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