Measuring systems are almost always arbitrary - even the orderly metric system is chopped up into random little pieces we call grams, kilograms, and tons. With the increased need for precision, it's necessary that everyone use the same random unit of mass for a kilogram. After a Nobel winning discovery, and decades of tireless research, scientists have managed to pin down a kilogram and an ampere.
In order to get everyone on the same page, mass-wise, people have to be able to use measuring units that are the same wherever they go. They also need to be able to use units that won't degrade over time. This is a tough thing to do, and so far people haven't managed it with a kilogram. The standard kilogram, used by every company and institution serious about measuring things, is a lump of platinum-iridium. That lump, although it's being carefully maintained, is vulnerable to damage, loss, or general degradation over time. In order to measure a kilogram again and again, no matter what, it has to be tied to universal constants.
A Plank mass is a unit of mass defined by Planck's constant, h, the speed of light, and the gravitational constant. Two of those are already universal constants, but one, Planck's constant, is tied to another constant, e. This is the charge of an electron. The charge of an electron could be measured in amperes - unfortunately we don't have a universal constant that can help us define the ampere.
There is one phenomenon, the Quantum Hall Effect, that relates one of these constants to the other. It can help determine both as always constant, and set up a universal standard for both the amp and the kilogram. The Hall Effect is simple. First run a charge through a wire - imagine the wire running directly away from the center of your body. Then they apply a magnetic field perpendicular to the charge - imagine it radiating up and down. When this happens, a voltage builds up on either side of the electric flow. So on your left side there would be an abundance of positive charges. On your right would be a build up of negative charges. Since these charges are only separated by a conductor - the wire - they're not really separated at all. They create a current across the wire, as the electrons rush over to the positive side of the wire. This, in turn, creates a resistance to the original flow of charge flowing down the wire.
In the eighties people noticed that this Hall Resistance, at low temperatures and high magnetic fields in two dimensions, hit certain consistent levels. It drops directly between these plateaux, and those are measurable. Hall resistance is equal to h/(ie^2). The 'i' is a random integer. This equation has both the constant h and the constant e in it, allowing scientists to measure both to a high degree of accuracy. We may be able to measure it to higher degrees of accuracy - right now we have a disgraceful uncertainty of 86 parts per trillion - but it can't change itself. And at last, both the amp and the kilogram may both be safe for future generations.
Via IOP Science, Warwick, Hyperphysics, and JHU.