Suppose I have a few "weights". Half of them, and I know which half, has a mass EXACTLY, to infinite precision, twice the other half. I know that very quickly the weights will not be exactly related to each other, due to say dust from the air landing on them unequally. Taking that into account, what practical uses can I do with these weights that takes advantage of the fact that some are twice the mass of others?
The ways you can take advantage of these weights is really dependent on what kinds of advantages you are looking for. You can't make money in the stock market with them. You can't go to war with them. You can't make money in a casino with them (or can you?). You really have to figure out what sort of things you're interested in doing.
You may be interested in the IPK and its six official copies. Metrologists define the kilogram from the IPK. It's so special that it's never used to measure anything other than to compare it against the clone IPKs. And it has been drifting for some reason yet unknown to metrologists. They're about 50 micrograms off of being the same 1,000 grams masses.
So what can you do with these masses? Well, you can look at what metrologists do with their IPKs. If there was anything more valuable to be done with them, you'd see them doing it.
Of course, next May, we are finally shifting off of this standard. Instead, the kilogram will be fixed precicely to Planks constant.
Avagadro's number is also getting fixed, which means the number of atoms in a kilogram mass like this is fixed:
So at the very least, your masses should be good for one heck of a good guess for "how many jelly bean atoms are in this jelly bean jar!"
Nothing. Perfectly precise weights are only useful if you intend to build a standard based off of it like the current SI units and the definition of a Kilogram (before they changed it). Of course the biggest issue would be getting everyone to agree to your perfectly precise standardized weight (Stares at America in particular) and your weight can't change. So that's no touching and no decaying checked off. Outside of that, your weight is just a weight.
Things you can do with a weight:
- Hold down paper
- Lift it for sick gains
- Throw it
- Tell people how perfect it is and have them proceed to touch or breath on it changing the weight
- Hold open a door
- Compare it to yourself and figure out how much you weigh
- Compare it to other products to determine how much they weigh
- Do some math problems involving X, 2X and 1/2 X