system
Given the following post, respond as if you're commenting on Reddit:
human
How does supersymmetry work and can we measure/see the superpartners?

How does supersymmetry show itself, what suggests that it is real? And finally, the potential superpartners, are they measurable in any way and how would we know if we find them?
gpt
Supersymmetry has many attractive qualities. Supersymmetric theories are often free from dangerous quantum corrections as the contribution to them from the fermions cancels with that from the bosons.

For example, the vacuum energy of a non-supersymmetric theory such as the standard model includes contribution from the vacuum fluctuations of all the different fields at all energy scales up to the Planck scale. The vacuum energy turns out to be *huge*. We know it experimentally to be minuscule. In a supersymmetric theory, it's zero.

Same thing for the Higgs boson mass. It should receive giant contributions from scales up to Planck yet it is incredibly small compared to what you'd expect. Supersymmetry would explain that as the quantum correction from the top quark cancels with that from the stop.

And supersymmetry makes beautiful things work. Supersymmetry is very constraining and so allows you to deduce a lot of information about a supersymmetric theory, informations that for complex theories would be absolutely impossible to obtain by standard techniques. This information is valuable as it can often be extrapolated to complex non-supersymmetric models sufficiently similar to those.

And string theory is able to do most of its magic with supersymmetry.

However, the world is not supersymmetric. Supersymmetry wants at the very bare least the particles to be grouped in "supermultiplets" including each equal number of fermions and bosons with the same mass and quantum numbers. This is clearly not the case. So if SUSY is real, it must be spontaneously broken at a certain energy scale. Above that energy, supersymmetry is manifest; below, it's invisible.

Now the point is you'd like that scale to be as low as possible, because the positive qualities SUSY has in terms of taming quantum corrections only hold in the unbroken phase. Basically if the breaking happens at energy X, then the quantum corrections only appear below X. So instead of the corrections = 0 you expect in a fully supersymmetric theory, or the corrections ~ Planck you expect in a non-supersymmetric theory, when SUSY is broken at X you get corrections ~ X. 

However, X just cannot be too low. All the superpartners are now invisible because they acquire masses of the order of X. We haven't found sparticles yet, so X must be higher than what we've looked. That's hugely simplified but basically that's the general idea: we're not seeing SUSY in accelerators, not yet at least.

Now either you hope the SUSY breaking scale is behind the corner (low energy supersymmetry) and so you have both a prediction for a bunch of new particles, a partial explanation for the hierarchy problems, and so on, or you think it's actually really big, perhaps GUT (10^(16) GeV) or even Planck (10^(19)GeV) scale, making it unaccessible to experiments. Both are possible. And both include millions of other subcases.

So the most important thing is that talking about supersymmetry does not necessarily mean stops at the LHC. And the claim that theories that predict supersymmetry (such as string theory) need superpartners at the TeV scale is false. There is no need for the SUSY breaking scale to be low.

Now how would you recognize a superpartner in a collider? Easy: it shares the quantum numbers of its partners, but with different spin. For example squarks would be scalars that are coloured (interact with the strong force like quarks) and have the same electric charge, etc etc.