How We're Redefining the kg

What do I have to push, sub-basement?

Woman: Sub-basement. [Buzzing safety alarm] I'm at the National Institute of Standards & Technology in Washington D.C. and I'm going to the sub-basement. It's getting dark down here. We're going to find out how they're going to redefine a kilogram.

The kilogram is in trouble. Since 1799, it's been defined as the mass of a metal cylinder, in a locked vault in a basement in Paris. But over the last century, careful measurements of this international prototype kilogram and in-theory-identical national standards from around the world have shown that their masses are diverging. The spread has grown to around 50 micrograms, or 50 parts per billion.

And having a standard of mass that changes is unacceptable. Plus, the kilogram is the last of the base SI units to still be defined by a physical object. The metre, for example, used to be defined as the length of a platinum bar in Paris, but in 1983 it was redefined as the distance light travels in 1/299,792,458 of a second.

This definition means that the speed of light is set to exactly 299,792,458 point 00000... et cetera, metres per second. Note how this works: first, you take the existing definition, say, the length of that metre bar, and you measure as carefully as you can how it relates to a physical constant of the universe: the speed of light.

Then you set the exact value of that constant and use it to redefine how long a metre is. I know this might seem circular, but, importantly, it moves the point of truth off of the physical object, and onto the unchanging constant of the universe. So, naturally, the thought is to do the same thing with the kilogram.

But... using which constant, and how? [Heavy mechanical noises] Well, there are a number of different strategies that were attempted but the two that achieved the greatest success were: 1) using a silicon sphere to determine and set Avogadro's number and 2) to use a Watt balance to determine and set Planck's constant.

DEREK: Hi, how ya' doin'? I'm Derek.

JON: Pretty good.

DEREK: Nice to meet you.

DEREK: Where is the Watt balance?

STEPHAN: The Watt balance is behind these closed doors, and...

DEREK: It's in there?

STEPHAN: It's correct, and right now the problem is that... We are in a crunch to get a number by the end of May.

DEREK: What's the number?

STEPHAN: The Planck's constant. This is what we measure with the Watt balance. In 2011, the General Conference on Weights and Measures decided that the kilogram should be redefined based on Planck's constant, but that doesn't mean that the Avogadro approach was futile.

I mean, you can use Avogadro's number to calculate Planck's constant and vice-versa. So, ultimately, both approaches are going to be used to redefine Planck's constant and Avogadro's number simultaneously.

STEPHAN: One good thing about having silicon spheres, is that you only want to redefine if you have agreement between different numbers, right? And the silicon sphere method is a method in my mind that comes out of chemistry. You measure Avogadro's constant, which is a constant that comes out of chemistry.

This method comes out of physics, we measure Planck's constant. So if they both agree, it's a pretty strong sign, right? Because you know chemistry and physics agree. Now, since I've already discussed the Avogadro approach in a previous video, here I want to focus on the Watt balance.

It's actually now called a Kibble balance in honor of its inventor, Bryan Kibble, who actually passed away in 2016. You know, traditional balances work by equating the gravitational forces on objects in two pans. The Kibble balance looks kind of similar, but all of the balancing happens on the left-hand side, where a mass pan is attached to a coil of wire in a magnetic field.

On the right-hand side is a motor. The whole apparatus is sealed and operated in vacuum. The balance operates in two modes: weighing mode and velocity mode, and both are required to determine Planck's constant.

In weighing mode, a kilogram mass standard is placed on the mass pan and then current is passed through the coil in the magnetic field and adjusted until the weight of the kilogram is equal and opposite to the electromagnetic force on the coil.

The equation for this is Mass times the local gravitational acceleration is equal to the Magnetic field, times the length of wire in the coil, times the current flowing through it. In this equation, the variables that are difficult to measure exactly are the magnetic field strength, and the length of wire in the coil.

But luckily the Kibble balance allows us to get around this problem using velocity mode. In velocity mode, the kilogram mass is lifted off the mass pan and now the motor on the other side of the balance is used to move the coil back and forth at constant velocity through the magnetic field.

This motion induces a voltage in the coil which is equal to the magnetic field, times the length of wire in the coil, times its velocity. Now we have two equations which we can solve for B times L and so we can set them equal to each other and eliminate these variables without having to know precisely what their values are and if we rearrange a little bit you get voltage times current equals mass times gravity times velocity.

On the left-hand side, there is electrical power and on the right-hand side, mechanical power, and that's why this was called the Watt, the unit of power, balance. But how do you go from this to Planck's constant, the number that relates a photon's frequency to its energy?

Well it turns out there's actually a way of measuring voltage accurately using a macroscopic quantum effect that involves Josephson junctions. So a Josephson junction consists of two superconductors separated by a thin piece of insulator. Now if you apply a microwave radiation to that junction, you create a voltage across the device and its value is precisely known to be hf over 2 e.

Where h is Planck's constant, f is the frequency of the radiation, and e is the charge on an electron. Now by tuning that frequency and stacking as many of these Josephson junctions as you want in series you can create virtually any voltage you like very very precisely.

The way this is used in the Kibble balance is a stack of hundreds of thousands of Josephson junctions are put into the circuit with the coil as it is moved through the field and so you exactly balance the voltage which is induced in the coil using those Josephson junctions. So you can measure that voltage very very accurately.

But how do we measure current? Well, it turns out this voltage measuring method is so good that instead of trying to measure current directly we instead measure V on R which is the same thing. So this current is passed through a resistor, and we measure that voltage again using Josephson junctions.

And then to measure resistance we use another macroscopic quantum effect called the quantum hall effect. Which is beyond the scope of this video but, suffice it to say that the resistance measurement will be an integer fraction, one over p times Planck's constant divided by the charge on the Electron squared.

So if we sub all of this into our equation and solve for h, we have that Planck's constant is equal to four over p n squared, those are all constant numbers that we know, times the local acceleration due to gravity times velocity divided by frequency squared times the mass which is one kilogram.

So here we have a very precise equation for Planck's constant in terms of the mass of one kilogram. Now to get an answer that's good to say, ten parts per billion.

You need to know all of these values very accurately. So to measure V for example the velocity of the coil as it moves through the Magnetic field, we use a laser interferometer as the distance to the coil changes the interference Fringes pass over a detector.

And essentially by counting how many fringes go past in a certain period of time you can determine the speed of the coil very accurately. To measure g, a device called a gravimeter was used to map out the local acceleration due to gravity in the balance room before it was built in there.

The gravimeter actually drops a corner reflector down a vacuum tube and measures its acceleration again through interferometry, counting the fringes as they pass. This is a 3D printed map of the acceleration due to gravity in the Kibble balance room.

The bump is due to the mass of the powerful and very heavy permanent magnet that's in the balance. The acceleration due to gravity must continually be measured because it can be affected at this level of precision by the positions of the sun and moon and even the water table underneath the building.

In 2018 the kilogram will no longer be defined by an object in Paris. Instead, it will be defined based on the fixed value of Planck's constant which is being finalized right now as a result of all these measurements from the Kibble balances and silicon spheres.

So right now what we do is, we put the mass in, and we get h out and in 2018, after redefinition, h will be fixed and you use that to realize the unit of mass.

STEPHAN: Easy.

DEREK: Yeah, just that-- just that easy.

STEPHAN: Yeah -

DEREK: Just that simple.

STEPHAN: Simple.

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