How To Measure The Tiniest Forces In The Universe

This is 10 micrograms. You think that I might be able to see? I think you might be able to. Oh boy. It's an arrow right there. Yeah, yeah, yeah. This flashlight will help. I feel like I need to get video of this.

[Dr. Shaw] I don't know how. (Dr. Shaw laughing) It kinda looks like a hair, like a tiny— Yeah. like a smaller than an eyelash.

If you wanna measure a force like the weight of an object, the way it has always been done has been to balance it with some known standards. And the most precise standard weight people ever created was the kilogram, a platinum-iridium cylinder stored in a vault on the outskirts of Paris.

(gentle music) Replicas of this kilogram were sent to countries around the world to use as their mass standards. Here is K20, the United States Mass Standard. And yes, the US is secretly metric. They just apply a conversion factor to get to "freedom units". It's just a little translation that we do here, but our country is actually on the metric system.

Doesn't that seem crazy? Yes, it's stupid. The uncertainty in the mass of a standard kilogram is on the order of tens of micrograms. So that's tens of parts per billion or about 0.000001%. It's pretty good. But there's a problem if you want to weigh something lighter than a kilogram, the uncertainty increases.

This little object here is a 50 gram test weight. So it's a reference mass. Can I pick it up? Maybe with tweezers? Yeah, if you don't mind? Sure. [Dr. Shaw] We try to keep the fingerprints off. so it's got a little bit of heft. You can feel that. A little, yeah. What about this one, what's this?

[Dr. Shaw] This is 10 grams here. Yeah, that's pretty light. That's pretty light. And paperclip here is about one gram. And so, how you might use one of these test masses. So, if you're working in a laboratory or something like that you could take one of these little weights and put it on here and you could look at the scale and say, oh, okay, my scale is reasonably well calibrated here.

That last digit might change a little bit. But you could sort of make some statement about whether or not your scale is accurate. When we're talking about the kilogram, these are obviously much smaller than a kilogram. How do we think about getting from that large object down to something that's this size here?

One of the ways to do it is using conventional mass metrology, which is that you take the kilogram and you use a process called subdivision. Where you compare other smaller masses against the kilogram. You take two 500 gram masses and you make sure that they're equal on your balance. And then you put both of those on your balance and compare that against a kilogram.

Would you go like two 500's and then two 250's and then two 125's? like you just... Yeah, yeah, yeah. So you could do like one common arrangement is something like we have here. This is a 500 milligram mass, these are two 200 milligram masses, and that's a 100 milligram mass. So these three sum up to this.

Okay. So you can compare those two against each other. The smallest we have here, is down there. That's a milligram. That is a milligram? [Dr. Shaw] That is a milligram right there. What are they made out of? Okay, these are made outta stainless steel.

And we have to do things like you see this little lint free brush here. If you have a speck of dust on here or something like that, it can be a problem, if it's a big speck of dust. So every time we do weighings with these, we'll take a lint free cloth and a brush and clean them off a little bit.

Why are they this sort of curious wire kind of shape? The shapes? Yeah. It helps you remember which one is which. The five-sided one is 500 milligrams. One of the interesting things from my perspective about this is that you can really subdivide over a large range of these masses from a kilogram.

This is one millionth of a kilogram is a milligram. So you can subdivide the kilogram by a million times. 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 that is what 10 micrograms, I mean you can't, I had to put the little arrow here so you can. If you were here in the laboratory, you could look and peer down there maybe. I feel like I need to to get video of this so people can see what 10 micrograms.

[Dr. Shaw] I don't know how. It kinda looks like a hair, like a tiny, like a smaller than an eyelash, right? [Dr. Shaw] It is really much, yeah, that's about the... Much thinner. [Dr. Shaw] Yeah, that's about the scale you're looking at there, yeah. I'm almost certain I can capture this on video.

We brought a special lens with us. Ooh yes. We brought a special, Special lens. 2024 mill macro, 'cause I was like, we're gonna need it for this. Try to find this thing. Oh, I can see it. Oh yes. Do you see it there? Yeah, yeah, yeah, yeah, you got it.

You made this? Yes, with great trouble and then calibrated it on a balance. It was, man, I'll tell you, it was not easy. When you have that thing, you can imagine what it's like trying to work with something like this, right? And this is about as small as you can reasonably expect to make something as a test weight.

And if you wanna measure a force smaller than that, so I have these little tiny chips here. These are atomic force microscope cantilevers. There're little tiny force sensors on the end of these. There're little tiny cantilever beams with a sharp tip. And you can use that sharp tip to press against things and apply nanonewton to piconewton forces.

But I mean the tip is so small it's very, very difficult to see. It really requires a microscope. Is it like there's a little diving board on there? Yeah, exactly. There's a little diving board, that's right. It looks like a little diving board. It's like a spring, right? And if you push on it, the more it bends the larger the force.

What is the smallest force that you want to measure? Do you have a... Yeah, I can show you, I can show you. This is one of the sensors we used to do the smallest forces that I can confidently say we've measured that are traceable in some way to the International System of units.

And that is a femtonewtons of force at about a piconewton would be like if you're stretching out a DNA molecule. So, if you take it a DNA molecule and stretch it out end to end, that's a piconewton. So back to a factor of a thousand less than that was what we were measuring. So, this is an example of one of the sensors we use to get to the sort of femtonewton level.

This is a fused silica parallelogram flexor. You can't see it really well. So let me, I have a big version right here. So what we can do is we can set this vibrating and it'll vibrate with really pure tone. And we can see very, very small changes in force based on how far this vibrates up and down.

I would have a little laser interferometer, which measures the motion of this. So we measure the displacement of this end here and then right next to it we would have a little tiny optical fiber that would deliver a known optic laser power to this.

So this would be a photon pressure force, whereby reflecting the light off the surface here we actually get a very small force. If we vary that force sinusoidally, we vary it in time, we can get this to move up and down and we can get it to vibrate. And we can see differences as small as femtonewtons in our force.

So you're saying you could measure the force from a laser pointer? Yeah, oh yeah, yeah, definitely. Yeah, we've done that. My pointer was shining on that. That's right, that about approximately seven piconewtons of force. And once again, that's enough to stretch out a DNA molecule.

Can I ask you the big question? Yeah, yeah. Why does anyone need to measure forces this small? Yeah, that's a good question. So a couple of things. there are a couple of different answers to that. One is sort of the industrial relevance.

Automotive manufacturers need to measure the mass of particulates that come off their exhausts, particularly in diesel systems. Particulate contamination is a really kind of a big deal. So, you need to be able to measure 50 micrograms of these particulates for those environmental standards to be met.

The laser power measurements for people who are doing industrial processes with lasers, because you can actually use the measurement of a small force to calibrate laser power. Pharmaceuticals, you have milligram doses, microgram doses sometimes.

The other thing that's important I think kind of goes to the heart of why NIST is so cool, in my opinion. Is that it really helps us push the frontiers of science. The new scientific discoveries benefit from the new measurement capabilities, which then feed into new precision metrology capabilities.

And so, that is really one of the things to me that makes NIST really special is that we're very good at sort of creating that environment where that can happen.

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