The following questions and answers are copied from questions posted and answers I wrote at the Physics Forum (with some significant editing, expanded text, and reformating):
What is the point of sparticles? What will they prove? How will they work? I've read about supersymmetry, but don't really get it. I know it is to unify quantum mechanics and relativity, but how?
Sparticles are particles beyond the Standard Model of particle physics that are necessary for supersymmetry which is a generalization of the Standard Model of particle physics that is attractive for reasons of interest to theoretical physicists.
Standard Model Fundamental Fermions and Bosons
In the Standard Model of particle physics, there are two basic kinds of particles.
In the Standard Model, fundamental fermions are the building blocks of what we crudely in layman's language think about as "matter". For example, a hydrogen atom is made of three quarks that combine to form a proton with an electron orbiting around it. The six kinds of quarks are fundamental fermions, and these fundamental fermions combine to make protons, neutrons and more exotic composite particles called hadrons which are made of two (mesons) or three (baryons) or more quarks. Particles made up of quarks are often accompanied by orbiting electrons, or muons (heavy electrons), or taus (really heavy electrons). When muons and taus and other fundamental particles decay into lighter particles they spew out one of three kinds of neutrinos (which are very light, but non-zero mass particles that interact barely at all except via the weak force and gravity). Electrons, muons, taus and the three kinds of neutrinos combined are fundamental fermions that are similar in certain ways and are collectively called leptons.
In the Standard Model, fundamental bosons are we crudely think of in layman's language as the particles that make up force fields. Electromagnetic fields are made of bosons called photons. Protons and neutrons and other particles made of quarks (which are fundamental fermions) that are held together by bosons called gluons which carry the strong force. The weak force is carried by bosons called the W boson (for "weak") and the Z boson (because they needed to give it a name and didn't have any other good ones). Gravity, if it is a field carried by a particle is carried by a hypothetical boson called a graviton. The Higgs boson carries the "Higgs field" which gives fundamental particles their mass (it isn't clear whether or not the Higgs boson interacts with neutrinos which may get their mass in a different way, how neutrinos get their mass is an unsolved problem in physics).
Supersymmetry Is A Balance Between Fundamental Fermions and Fundamental Bosons
Without getting into all the technical details, supersymmetry (also known as SUSY) is basically about the idea that there are technical reasons that makes it desirable for there to be a fundamental balance between fundamental fermions and fundamental bosons.
The theoretically easiest way to get that balance is to imagine that every fundamental fermion has a new fundamental particle boson counterpart (squarks and sleptons), and that every fundamental boson has a new fundamental fermion counterpart, which have their own special names.* These partner particles are "sparticles."
This then gets jumbled a bit because some of these counterparts have very similar physical properties that cause them to blend into each other and look like different particles (something that happens in the Standard Model as well in the way that the electromagnetic force and weak force are related to each other in very deep ways call electroweak unification), and the theory also requires at least four extra Higgs bosons to work out (a positively charged one, a negatively charged one, an extra heavy one, and one with a different parity - i.e. left handedness v. right handedness than a usual Higgs boson).
More complicated "non-minimal" versions of supersymmetry assume even more new particles.
* It could be that a balance between fundamental fermions and fundamental bosons already exists in the Standard Model in a much more subtle way than the crude and obvious balancing present in supersymmetry theories, which would explain how seemingly "unnatural" aspects of the Standard Model "miraculously" balance out, but so far only the vaguest hints that this might be the case have been worked out by theoretical physicists and only as conjectures and hypotheses, not as proven theories.
Supersymmetry is a GUT and SUGRA is a TOE.
Supersymmetry itself does not unify quantum mechanics and relativity. Instead, it unifies the three forces of the Standard Model (electromagnetism, strong force, weak force) into forms of the same underlying force that is unified at high energies, making it what is known as a Grand Unified Theory (GUT). Supersymmetry also ties in naturally to some mathematical structures known as "groups" in a more elegant way than the Standard Model does (which takes at least three different groups crudely "glued" together to summarize).
If you add quantum gravity to the supersymmetry mix by adding the graviton (a fundamental boson) and a superpartner called a gravitino (a fundamental fermion), you get supergravity also known as SUGRA which is a low energy approximation of a Theory of Everything (TOE), and supergravity, in turn is usually a foundation of string theory.
Why Isn't Supersymmetry Noticeable In Daily Life?
We don't notice any of this in everyday life, or even in high energy physics experiments (if the theory is true) because all of the particles created by supersymmetry except one (which explains dark matter and interacts with other matter no more strongly than neutrinos do) are unstable and decay into ordinary matter before we have time to see it, and also because they only form at all in very high energy situations.
If this sounds familiar, it should. Most of the particles we do know exist decay extremely rapidly into ordinary matter and only form at all in very unusual high energy situations, or are always found confined in composite particles and never seen in isolation, or are neutrinos which are extremely hard to detect because they interact so weakly with everything else.
In daily life, we see mostly protons and neutrons (which are made mostly out of up quarks and down quarks bound together by gluons so tightly that we never see free quarks or free gluons), electrons, and photons. The force that connections protons and neutrons in the nucleus of an atom is carried mostly by pions which are made up of two up and down quarks bound by gluons which are themselves short lived and travel only short distances before decaying (with the quarks and gluons never visible in isolation). All other particles in the Standard Model are too ephemeral or ghostlike to notice without high technology instrumentation in carefully constructed lab experiments.
The vast majority of physics (except radioactivity and high energy physics) can be explained with protons, neutrons, pions, electrons and photons (the first three of which are not actually fundamental), without knowing about the huge menagerie of fundamental particles and composite particles needed to describe the last 0.1% of reality.
Supersymmetry just adds more exotic, ephemeral fundamental particles and particles that are very hard to detect (a dark matter candidate called a WIMP) to the mix for relative obscure theoretical reasons set forth in the next section.
Supersymmetry is attractive as a theory for many reasons, some of which are now obsolete:
(1) It provides natural candidates for dark matter particles of a variety called "WIMPS".
(2) It makes the constants of the Standard Model such as the Higgs boson mass seem more "natural".
(3) It makes it much easier to do math that sheds light on how particles interact at very high energy, because the balance between fermions and bosons makes lots of terms in calculations that would otherwise have to be calculated cancel out.
(4) It unified the three fundamental forces into one master force at high energies called the GUT scale.
(5) It provides a way to explain where the matter in the universe came from that are unexplained in the Standard Model.
(6) It sheds some light on the kind of reasons that Standard Model constants might have the values they do although not particular clear guidance.
(7) Supersymmetry is so mathematically similar to the Standard Model of particle physics, it is easy to tweak properties of particular versions of supersymmetry like particle masses in such a way that it predicts essentially the same things as the Standard Model down to the limits of experimental error. So it is hard to reject outright.
(8) Before we knew the mass of the Higgs boson, lots of Standard Model predictions in high energy situations were nonsense answers where the likelihood of all possible events didn't add up to 100% if Higgs boson mass is not just right, but this doesn't happen in supersymmetry. This is less of a big deal than it used to be because the mass of the recently discovered Higgs boson is "just right" and prevents the Standard Model from becoming pathological mathematically at high energies in the way that it would if the Higgs boson where much heavier or much lighter than it is in reality.
(9) Supersymmetry is also a very natural low energy approximation of string theory. Many versions of string theory require, for mathematical reasons, that fundamental fermions and fundamental bosons have counterparts for each other for reasons related to the way a fundamental superstring in that theory can vibrate.
Theoretical physicists are very reluctant to abandon supersymmetry because that would mean giving up hope that their best shot at a good theory of quantum gravity through string theory as explained below. So they'd have to start over from scratch trying to merge quantum mechanics and general relativity.
Why String Theory?
The Standard Model and general relativity are mathematically incompatible with each other. The reasons that the Standard Model (i.e. quantum mechanics) and general relativity are incompatible are quite mathematical and technical but include, for example, the fact that point particles which are assumed in quantum mechanics would instantly turn into black holes in general relativity.
The Standard Model and supersymmetry are both fully compatible with special relativity, however.
Scientists from Einstein onward have been trying very hard to unify gravity and other forces of nature ever since general relativity and quantum mechanics were conceived in the early 1900s. So far, no one has even come close to succeeding.
A potential connection to string theory is attractive because string theory offers a reasonable hope that it could provide a mathematically consistent way to create a theory of quantum gravity that could be consistent with the rest of quantum mechanics which is called the Standard Model.
String theory is pretty much the only game in town that creates a potential theory of quantum gravity with particle based force fields like those used in the rest of quantum mechanics so it is very tempting to find a way to connect what we know to it.
There is another approach to quantum gravity that involves applying quantum mechanical concepts to the nature of space-time itself, which includes approaches known as Loop Quantum Gravity (LQG), rather than using the force field carried by particles approach of string theory, but that is a story for another day that doesn't involve supersymmetry.
Why Not Supersymmetry?
The obvious problem with supersymmetry is that nobody has ever seen any of the supersymmetric particles, either because they are not real, or because the new particles are simply too heavy to see in colliders, or because they are otherwise not visible due to something called "R-parity" (a property that basically keeps sparticles and regular matter separated).
(1) If superpartners exist, the LHC has determined that they are much heavier than they were expected to be. At some point, if they are not found at low enough masses, they would be so heavy that they would lead to predictions that are contrary to experimental evidence.
(2) "Naturalness" which is an important reason for supersymmetry is being questioned as a useful theoretical concept.
(3) The evidence of force unification that should have showed up by now has not appeared.
(4) And, the LUX experiment has pretty much ruled out the kinds of WIMP dark matter particles that supersymmetry predicted.
Why Not String Theory?
String theory has all of the problems of SUSY and SUGRA and also lots of problems of its own. Basically, there are thousands or millions or more versions of string theory (called "vacua") and nobody knows which version is remotely close to our reality.
Where Does This Leave Us?
The Standard Model, in contrast, has no obvious generalizations that could for example be used as a basis for a version of string theory. So figuring out how to meld it with quantum gravity is even more difficult.