And that’s why these are such an important part of mass metrology. But you sort of pay a price for that, because each time you do this subdivision, the uncertainty increases a little bit, right? So what is the uncertainty in say the milligram there? If you do it with a subdivision, it will be maybe a part in 10 to the four, one part in 10 to the four. So like 0.01 percent-ish range.
But there is a way to do better, and that’s thanks to the fact the kilogram is no longer defined by the platinum-iridium cylinder in Paris. Over the course of a century or so, the replica kilograms were brought back to Paris a few times to be weighed with each other. And from those measurements it became clear that their weights were diverging by up to 75 micrograms. No one could say if the replicas were getting heavier or if the original was getting lighter. But it was unacceptable to have mass standards with changing masses.
So the solution was to eliminate the kilogram’s dependence on a physical object and instead define it based on a constant of nature, Planck’s constant. So how does that work? Well, Planck’s constant is best known for relating the frequency of a photon to its energy by E=hf. But energy and mass are related through E=mc2. So you can see how mass is related to Planck’s constant.
In 2019, scientists officially set the value of Planck’s constant to be this number in Joule-seconds which, along with the definition of the meter and the second, now defines what a kilogram is. The real advantage of this definition is how it can be applied in fancy scales.
This is a Kibble balance. It can balance the weight of an object with an electromagnetic force. What’s great about that is that the electrical quantities used in this balance can be read out very accurately, and in units of Planck’s constant. So you get direct traceability by weighing something in this balance.
This is kind of the smaller cousin of the Kibble balance. It’s called the electrostatic force balance or the EFB. And this is a balance that was designed, specifically to measure mass sort of in the milligram range. The Kibble balance uses an electromagnet, I use a capacitor, which is basically two metal electrodes that you apply a potential to. And when you apply a potential, there’s an attractive force between those two electrodes. I apply an electrostatic force by applying a voltage here at this you can see the cylinder here. There’s this cylinder and there’s inside of this there’s another cylinder, and they’re close together. So you have this concentric cylinder like this. And when you apply a voltage, it pulls that moving cylinder down in there. And by measuring the properties of the capacitor and measuring the voltage that we apply, we can know exactly how much force we get here. And then up here, we drop our mass on. So we compare our gravitational force from the mass to the electrostatic force from our capacitor.
To get the best accuracy, this lab is located deep underground and they keep the air temperature a constant 20 degrees Celsius to avoid any thermal expansion or contraction of the devices. And all measurements in this balance are made in a vacuum. So there are no air currents and no buoyant force on the object from the atmosphere. They’ve even carefully measured the acceleration due to gravity in the lab. Here it is, it’s under the chair. Right there, that triangle, that is where the USGS measured absolute gravity with an absolute perimeter 9.801-ish meters per second.
Does this lab measure small forces the most accurately in the world? At the milligram level, so 10 micro newtons-ish of force. Yes, this measures force the most accurately in the world. I’m confident in saying that, but of course, you can go lower than that. This is the smallest weight and you can’t see it here. This is 10 micrograms. So when you think about the uncertainty in a kilogram, when you take Planck’s constant at a Kibble balance and you realize the kilogram, you’re at that level of about 10 micrograms. And so they need to measure very, very small forces to measure the mass of those particles.And then in the biomedical field, there are a lot of applications where you need to measure very small forces.For example, if you’re looking at the mechanics of a cell, you need to measure forces of a piconewton to understand how the cell is responding to different stimuli.So, those are two of the more common applications for measuring forces of this small. If you, like me, are fascinated by precision measurement, then you would probably love Brilliant. Brilliant is a learning tool that helps you master STEM concepts such as foundational math, computer science, and quantum physics. It offers interactive, hands-on lessons that build on each other, and questions throughout the lessons to test your knowledge. You can even learn about how to design measurements for quantum entanglement using polarizers on an optical table.
For the holiday season, Brilliant is offering 20% off an annual premium subscription to the first 200 people who use this link. So if you’re looking for an easy and fun gift for friends or family who love learning, try a Brilliant subscription.