What is the difference between symmetric, asymmetric and supersymmetric particles?
I don’t think any particles are symmetric in and of themselves. Rather theories can incorporate various kids of symmetries. For one, physics looks the same no matter what time we perform an experiment. This means that physics is symmetric under changes in time. Special relativity states that physics is symmetric under “Lorentz transformations”. That is, any two observers who are related by such a transformation (say, in uniform rectilinear motion with respect to each other) see the same laws of physics.
Electromagnetism starts getting closer to what you’re looking for. Particles are described by complex-valued functions, but only the magnitude of the complex number really matters. Multiplying the function’s value everywhere by the same complex number of unit length (and the functions of all the other particles) gives the same physics, thus physics is symmetric under this group of transformations.
Some particles behave in a way that obeys the normal commutative law of multiplication (called bosons) while others obey an anticommutative law (fermions). There have long been theories with symmetries mixing up various bosons with each other and various fermions with each other. For one, it’s known that the proton and neutron are both different states of the same particle (the nucleon) in a similar way to how an electron spinning up and one spinning down are different states of the same particle. Supersymmetric theories are ones which somehow mix up bosons and fermions. Why this is so surprising is a very deep result, though.
As Mathochist said, one doesn’t refer to a particle itself as symmetric or antisymmetric. Supersymmetry is a different animal, though…
Symmetry (in various forms) is the root of the standard model of particle physics. Even with all its symmetry, the standard model has a property that some consider annoying: bosons and fermions act quite differently. In particular, the quantum mechanical wavefunction describing a system of identical bosons stays the same if you swap two of the bosons around. Swapping two identical fermions, in contrast, flips the sign of the wavefunction. (Mathochist alluded to this property.)
So to “fix” this, many theories have been formulated that posit the existence of a set of partner particles to the bosons and fermions we know today. The partners to the bosons would behave like fermions and the partners to the fermions would behave like bosons. Such a theory is usually called a “supersymmetric” theory, and the partner particles are usually called “supersymmetric” particles (or sometimes: sparticles. Also: sbosons and sfermions (and squarks and selectrons and…)) There is currently no experimental evidence for supersymmetry, but a lot of people are looking. (Many have high hopes that the LHC at CERN will shed some light on the issue when it turns on.)
This isn’t quite right. Before there was a standard model (or even a quark hypothesis), it was noted that the neutron and proton seemed to have identical strong force interactions. Because of this, folks thought that the neutron and proton were actually two states of a single particle, and they called the “neutron-ness/proton-ness” property isospin (from “isotopic spin”) since the formalism looked identical to the one that described electron spin. Today, we know that the neutron and proton are actually different particles with different quark constituents. We also know that they don’t act identically under the strong force (due to the slight difference in the up and down quark masses.) Nonetheless, the isospin concept is a handle tool for some calculations, and it can be extended (although somewhat less successfully) to baryons made up of any of the known quarks.
Yes, the two were conjectured to differ by the action of isospin-SU(2), but now we see they have different quark constituents. However, the up and down quarks differ by the action of isospin-SU(2). If you apply a certain transformation, you swap ups for downs and turn a (uud) proton into a (ddu) neutron. Further, the difference in masses and resulting difference in strong interaction behavior is explained by the fact that flavor-SU(6) (the symmetry exchanging quark flavors) is a spontaneously broken gauge symmetry. Incidentally, this also explains why the gauge bosons of the strong and weak interactions have mass.
The reason I bring it up, is because I saw a program on Nova recently about the Elegant Universe-The program was all about String Theory and its mathematical and scientific implifications. But how are the particles in question associated with String Theory? And since I’m on the topic, how is Superstring Theory different than String Theory? I would assume, as the name implies, that the former is a more advanced version of the latter? Is it a higher level of physics than String Theory, or just a variation of it?
The variation is that superstring theory includes a symmetry that mixes bosonic modes of vibration and fermionic modes of vibration. As for how particles work into string theory, try this analogy:
Imagine a stretched wire, like a guitar string. As was known to the ancients, there are various ways for this (classical) string to vibrate, but they are all combinations of sine waves and those sine waves are characterized by their wavelength and amplitude. Now, since the ends of the wire are fixed, half the wavelength must evenly divide the length of the length of the wire, giving a number of “states” indexed by the quotient. Further, when we look at quantum mechanics we find that for each wavelength, only certain amplitudes are allowed to actually occur, which are all multiples of a fundamental amplitude for that state (yes, this is very handwavy). Thus we can look at a vibrating stretched wire and decompose it into the individual sine waves (one for each state) and for each one determine what multiple of the fundamental amplitude for that state the observed amplitude comes out to be.
Now, this turns out to look very much like a quantum field theory of a particle we’ll call the “wiron”. A wiron is a mode of vibration of the stretched wire. The wiron has various states, indexed by the number of times its half-wavelength divides the length of the wire. Multiple wirons can exist in the same state (incidentally making it a boson) and the state of the “wiron field” (the wire itself) is given by adding up all the fields of all the wirons present.
Admittedly, this works out a lot better on a chalkboard. For more information, go get the book Brian Greene wrote that they based the Nova show on. Someone should be along shortly with the Amazon link.