|Fractals like the one above have a property known as scale invariance. Some exotic forms of matter may also be scale-invariant.|
The first property of matter that was known to be quantized was not a surprising one like spin — it was mass. That is, mass only comes in multiples of a specific value: The mass of five electrons is 5 times 511 keV. A collection of electrons cannot have 4.9 or 5.1 times this number — it must be exactly 4 or exactly 6, and this is a quantum mechanical effect.
We don’t usually think of mass quantization as quantum mechanical because it isn’t weird. We sometimes imagine electrons as tiny balls, all alike, each with a mass of 511 keV. While this mental image could make sense of the quantization, it isn’t correct since other experiments show that an electron is an amorphous wave or cloud. Individual electrons cannot be distinguished. They all melt together, and yet the mass of a blob of electron-stuff is always a whole number.
The quantization of mass comes from a wave equation — physicists assume that electron-stuff obeys this equation, and when they solve the equation, it has only solutions with mass in integer multiples of 511 keV. Since this agrees with what we know, it is probably the right equation for electrons. However, there might be other forms of matter that obey different laws.
One alternative would be to obey a symmetry principle known as scale invariance. Scale invariance is a property of fractals, like the one shown above, in which the same drawing is repeated within itself at smaller and smaller scales. For matter, scale invariance is the property that the energy, momentum and mass of a blob of matter can be scaled up equally. Normal particles like electrons are not scale-invariant because the energy can be scaled by an arbitrary factor, but the mass is rigidly quantized.
It is theoretically possible that another type of matter, dubbed “unparticles,” could satisfy scale invariance. In a particle detector, unparticles would look like particles with random masses. One unparticle decay might have many times the apparent mass of the next — the distribution would be broad.
Another feature of unparticles is that they don’t interact strongly with the familiar Standard Model particles, but they interact more strongly at higher energies. Therefore, they would not have been produced in low-energy experiments, but could be discovered in high-energy experiments.
Physicists searched for unparticles using the 7- and 8-TeV collisions produced by the LHC in 2011-2012, and they found nothing. This tightens limits, reducing the possible parameters that the theory can have, but it does not completely rule it out. Next spring, the LHC is scheduled to start up with an energy of 13 TeV, which would provide a chance to test the theory more thoroughly. Perhaps the next particle to be discovered is not a particle at all.