Ep. 336: Units of Measure

How heavy is a kilogram, how long is a second? How warm is a degree? We measure our Universe is so many different ways, using different units of measurement. But how do scientists come up with measurement tools which are purely objective?

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This episode is sponsored by:  Swinburne Astronomy Online, 8th Light, Cleancoders.com

Show Notes

  • A Brief History of Measurement Systems — NASA (pdf)
  • History of the Metric System — Science Made Simple
  • Imperial and USA Measurement Systems and History
  • Fubar
  • International Bureau on Weights and Measures
  • Mass VS Weight
  • Natural Logarithms
  • Transcript

    Transcription services provided by: GMR Transcription

    Female Speaker 1: This episode of Astronomy Cast is brought to you by Swinburne Astronomy Online, the world’s longest running online astronomy degree program. Visit astronomy.swin.edu.au for more information.
    Fraser Cain: Astronomy Cast, episode 336, units of measure. Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos, where we help you understand not only what we know, but how we know what we know. My name is Fraser Cain. I’m the publisher of Universe Today, and with me is Dr. Pamela Gay, a professor at Southern Illinois University Everettsville and the director of Cosmo Quest. Hey Pamela, how are you doing?
    Dr. Pamela Gay: I’m doing well. How are you doing, Fraser?
    Fraser Cain: Good. Now you have been traveling. You’ve got more traveling coming in the future?
    Dr. Pamela Gay: Unclear at this point. I was at Pensacon last week. I contracted the creepy crawly flu. I’m going to go to the doctor before I decide about getting on an airplane again, because I value my eardrums.
    Fraser Cain: Right. Now let’s give a quick shout out to the upcoming Cosmo Quest hang-out-a-thon.
    Dr. Pamela Gay: Yes. On April 26, 27, we are going to do 36 straight hours of astronomy goodness. We have a whole bunch of different things planned. We’re still working on getting the confirmations in from everybody, so bear with us before we start announcing the schedule, but we wanted to let you know that this is coming and you can watch us all slowly lose our minds in the name of science on April 26th and 27th.
    Fraser Cain: It is always hilarious. Good. Well, I’m looking forward to it. I’m in. I know you’re going to sequester me for a couple of hours. I’ll be happy to help out.
    Dr. Pamela Gay: Likely more than a couple of hours.
    Fraser Cain: Yikes.
    Dr. Pamela Gay: Let’s go for a few hours.
    Fraser Cain: All right. Let’s get rolling with the show.
    Female Speaker 1: This episode of Astronomy Cast is brought to you by 8th Light Inc. 8th Light is an agile software development company. They craft beautiful applications that are durable and reliable. 8th Light provides disciplined software leadership on demand, and shares its expertise to make your project better. For more information, visit them online at www.8thlight.com. Just remember, that’s www.8thlight.com. Drop them a note. 8th Light; software is their craft.
    Fraser Cain: So how heavy is a kilogram? How long is a second? How warm is a degree? We measure our universe in so many different ways using different units of measurement, but how do scientists come up with the measurement tools which are purely objective? All right Pamela, so now I’m a Canadian, and so I think in metric. I, fortunately, or maybe unfortunately, am also able to think in imperial most of the time, but there’s one thing that I just can’t think in imperial, which is temperature.
    Dr. Pamela Gay: Really?
    Fraser Cain: Yeah. I am incapable. And I try, and so somebody goes, “Oh, it’s like 70 degrees out,” and I’m just like, “What is this gibberish?” I don’t know what that means. I don’t know what it means. I’m not even going to listen to you know, because I don’t want to find it. So if you say that it’s -40, then I’ve got some common ground, but most of the case, I actually have no idea. I don’t know if it’s warm or if it’s cold, and of course if it’s 100 degrees, I don’t know. Is that boiling water? I don’t know. I don’t know.
    Dr. Pamela Gay: So I have to admit that temperature is one of those things that my brain gets broken with, because I deal so much with people like you, who think in Celsius, and so much with – Well, my weather comes in imperial, sadly. And for whatever reason, my brain automatically switches to Celsius when it hits 32 degrees Fahrenheit and zero Celsius. So suddenly it’s like, if it’s below freezing, it needs to be a negative number as far as my brain is concerned. And so I have this weird – I have to be careful what comes out of my mouth because the units may be randomized.
    Fraser Cain: And units of measurement are a bugbear. If you’ve been going through high school, going through university, dragging units of measure along is awful, and that’s how you lose your marks, because you forgot to remember that it’s meters per second squared or it’s, I don’t know, kilonewtons per arc second.
    Dr. Pamela Gay: And this is a really important thing because saying, “I’m going to get 12,” what does that mean? I’m going to get 12 pies? 12 apples? $12.00, $12,000.00 – “
    Fraser Cain: 12 academy awards – yeah.
    Dr. Pamela Gay: So the rule that I’m teaching is if you don’t put units in, I automatically make it units of cow to amuse myself, and write the word “cow” in and take off points.
    Fraser Cain: So 12 cow, 13.6 cow?
    Dr. Pamela Gay: It’s always in units of cow. That’s what my default unit is: cow.
    Fraser Cain: Right. So what are the, I guess – Could we boil the entire universe down into some basic measurements?
    Dr. Pamela Gay: If you start with a unit of distance and a unit of mass and a unit of time, you can pretty much get everywhere else from there.
    Fraser Cain: Wow. So what is the basic measurement for distance?
    Dr. Pamela Gay: The basic measurement for distance is the meter. This is an oddly defined unit, because it was initially defined based on the distance between the earth’s equator and the North Pole, but that’s not entirely a constant number with plate tectonics and all that. So it was originally one 10 millionth the distance from the earth’s equator to the North Pole, assuming sea level the entire time, and then it was realized that was silly, or at least not constant and really hard to work with. So it became the length of a path travelled by light in a vacuum during a time interval of one over 299,792,458ths of a second. And yes I had to read that, because I would get it wrong otherwise.
    Fraser Cain: Right. Okay. So I sense some ret-conning here, where there – Because that doesn’t sound like a very precise number of seconds for light to be travelling, or fractions of a second. So why wouldn’t it be the amount light travels in, I don’t know, one 100 thousandth of a second or one 10 millionth of a second? Strange that it’s such a weird number, right?
    Dr. Pamela Gay: Well, it was a matter of, they started out with what they wanted to have as a basic unit, the one 10 millionth of the distance from the Earth’s equator to the North Pole. That seems nice. But when it was realized that that was problematic, they figured out, “Okay, so what can we do that’s a round number and pretty close and doesn’t change things up too much?” And in the process of trying to come up with a repeatable definition that could be repeated in multiple laboratories, they ended up with this crazy fraction of a second.
    Fraser Cain: Now what’s great about this is that it’s based on a law of physics. It’s based on something that – You could send a – Well, okay. I’m trying to think. If you sent a message to the aliens and you said, “We measure in meters. Here’s how we measure meters,” you’d have to tell them how we measure a second. And you could also tell them second, which we’ll get to shortly, that is also a basic measurement of the universe, and they could then have the exact same yard stick that we do, which is different if we say that we measure in the foot and the foot is about the size of a grown adult’s foot. Right? They would have a problem with that, or a yard, or a mile, or whatever. But if you say, “Light speed, however far light goes in this fraction of a second,” then that never goes away.
    You will never lose your original yardstick, because it’s light-speed, and you can always go back and just re-measure light.
    Dr. Pamela Gay: And the convenient thing is that time, seconds, is also defined somewhat naturally. In this case it’s a bit more complex. It’s defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyper fine levels of the ground state of the cesium 133 atom.
    Fraser Cain: Perfect. All right, let’s just move on. That one is pretty straight forward. I think we all understand that. What?
    Dr. Pamela Gay: So a lot of people mis-think that time is defined using how long it takes for a half-life to decay or occur or something else because they hear the word radiation. That has nothing to do with this. Light has wavelengths. The wavelengths vary depending on the color of light. Different atomic transitions have distinct colors that correspond to that transition. So the energy needed for a hydrogen atom to go from two to three we see as bomber red. In this case, in the cesium atom, in the ground state, there’s a hyper fine transition, which gets into all sorts of crazy quantum mechanics, but it’s an energy transition. That’s the key point. In 133, at a given temperature, in this case zero kelvin, the radiation emitted, the color of light emitted, the amount of time it takes for nine billion yadda yadda yadda periods to go by, that is defined as one second.
    Fraser Cain: Right. So it is like the cesium atom is – Isn’t it – it’s its oscillations, right?
    Dr. Pamela Gay: Well, it’s the wavelength of the light emitted by this transition. So cesium undergoes a hyper fine transition, emits a photon, and the photon goes flying away. That photon has a given frequency, has a given wavelength. So if you wait for nine billion yadda yadda wavelengths to go past, the amount of time that it takes those wavelengths to go past, that is defined as the second.
    Fraser Cain: So now we’ve got our meters and we’ve got our seconds, and these are, as I mentioned, we could e-mail, we could broadcast to the aliens, and we could say, “You know, cesium, okay, well, cesium atom, you know that atom that’s on the periodic of table of – well, you don’t have a periodic table of elements. But you know the one with that many protons? Okay, that one, and then you know light and the speed light takes for that much time? Okay, great,” and then we could translate and they could have the same yardstick and they could be measuring the universe just like us. They could be figuring out meters per second, meters per second squared, they could be calculating parsecs, they could be doing all this kind of thing.
    Dr. Pamela Gay: Parsecs? No.
    Fraser Cain: Or arc second?
    Dr. Pamela Gay: Because that’s defined off the planet Earth.
    Fraser Cain: Okay fine. Fine. Light years, um, but you’re right. A parsec they wouldn’t know. But we could tell them the size of the planet earth and we could tell them, based in meters. I mean, as you mention, all this comes back down to meters and seconds. So those are two of those basic measurements. Then what was the third?
    Dr. Pamela Gay: Kilograms. Well, you have to have a unit of mass.
    Fraser Cain: Yeah, you’d need to have a unit of mass.
    Dr. Pamela Gay: So pick a gram, pick a kilogram. It doesn’t really matter which one you pick. Here’s where things get FUBARed, for lack of a better term. The kilogram is actually based off of a thing. So can’t so much transmit that one to the aliens until we get intergalactic transporter technology.
    Fraser Cain: So the kilogram is a thing somewhere, right?
    Dr. Pamela Gay: It is. There are multiple kilograms locked away in meteorological laboratories, kept under very precise conditions. Interestingly, if the proton does decay, these will gradually decay over time. Luckily we haven’t noticed the proton decaying, but there’s other chemical things that is the reason they have to be so precisely maintained. Yeah, it’s kind of problematic.
    Fraser Cain: Right. So there are these – I guess there is a chunk of metal, I don’t know what it’s made out of, that is in the International Weights and Measures place and it’s kept in this really pristine environment and nobody ever touches it. All they do is occasionally make copies of it and weigh it, and that’s it.
    Dr. Pamela Gay: And the really annoying thing is this isn’t what it was intended to be. Initially it was planned that one cubic centimeter of water would weigh one gram, and that’s easy. But the problem is that when they actually compared their standard of measured kilogram to weight of water, they got 1.000025. A liter of water weighed that instead of one kilogram, which was what was anticipated.
    Fraser Cain: But couldn’t we go back and just say, “No, no. From here on out, a liter of water weighs a kilogram?”
    Dr. Pamela Gay: You’d think. You would think that. But I suspect the reason, and this is pure guesswork, if you think about it, so much of our monetary system is based on who has how much of this or that precious metal. And so if you go and you re-define the kilogram, which has been this wrong compared to liters of water amount for hundreds of years, what do you do with the amount of gold in Fort Knox?
    Fraser Cain: You just say it’s a different number and everyone agrees and we all just get along and we all just live together with the new international standard. But –
    Dr. Pamela Gay: I agree with you. I agree with you. It seems like in that many decimal places, we could just say, “Deal. Define it off of water.”
    Fraser Cain: But I’ve heard that there are ideas that you could go back and try to define the weight or the mas from, again, from the universe, right? There are various ideas, like detecting how strongly weight is pulled by gravity, just count the number of atoms in your item.
    Dr. Pamela Gay: So you’re mixing nomenclature in the most charming of ways. Mass and weight are not the same thing.
    Fraser Cain: Right, I understand. I understand. But if you know the gravity of the place then that could help you get back, and you know how hard it’s being pulled, you could calculate the mass, right?
    Dr. Pamela Gay: Right, so mass is something that definitely should have a natural way to define it. And this is where it was nice and convenient to say, “Based on water at a given temperature filling a given volume,” that the volume is based off of naturally defined numbers. That was a good way to do this.
    Fraser Cain: Yeah, it’s going to be approximately the right number of molecules of water in that liter.
    Dr. Pamela Gay: Exactly.
    Fraser Cain: Right. And again, we can tell the aliens, we can call the aliens and say, “Count up 42 quadrillion water atoms and you’ve got a liter.” Or, “You’ve got a liter and that makes a kilogram.”
    Dr. Pamela Gay: And it could have been even done more simplistically by using something that took on a crystalline form so you didn’t have to worry about pressure. As long as it’s solid, nominally it should be the same volume, it’s just not how they did it.
    Fraser Cain: Okay, so we’ve got our units of time, we’ve got our units of distance, we’ve got our unit of mass. So how come we didn’t derive things? I mean, I think about things like temperature.
    Dr. Pamela Gay: Well temperature – Okay, I forgot. There’s one more because I like to forget temperature. Temperature we can’t get from those, you’re right. Temperature is another one that, in this case, Celsius units that we use were defined off of the freezing point and boiling point of water at sea level under standard pressure. So there we have nice mathematically derived, divide it by 100 and you get the size of a degree, zero to 100, based on a phase transition at a given pressure at a given –
    Fraser Cain: As a Canadian I might know that it’s not – Oh, it’s not sea water. It’s regular water.
    Dr. Pamela Gay: Yes.
    Fraser Cain: At sea level, though. Right. So again, we can transmit that. We can say, “Take water, boil it, that’s 100 degrees Celsius. Take water, freeze it, that’s 0 degrees Celsius. Feel free to break that into 100 units in between. We can talk the same language.
    Dr. Pamela Gay: And here the catch starts to be that the temperature that water boils and freezes is also dependent on the pressure that it’s being held under. But pressure is something that we can get from force over area. Force has to do with mass and acceleration, so all of that can go back to our original numbers. But this is where we start to get to everything derived from everything else, that starts to get a little bit messy.
    Fraser Cain: Oh. How?
    Dr. Pamela Gay: So force. This is the one that leaves most people who think in the imperial system completely FUBARed. We like to be confusing in imperial units here in the United States and the five other places on the planet that use imperial units, and we say things like, “I have a mass of 100 pounds,” which makes absolutely no sense because my weight is 100 pounds. And that means that I have a mass that’s in slugs, and personally I don’t want to think of my mass in terms of slugs. And so no one really uses –
    Fraser Cain: Banana slugs? Black slugs? Which kind of slugs are we talking about here?
    Dr. Pamela Gay: Banana slugs.
    Fraser Cain: Banana slugs. Okay. But we have the same thing here which is that my scale; I measure my weight in kilograms and so, if I try to explain to someone they’re going to Mars, they’re going to stand on the surface of Mars, their weight on their scale here might say 50 kilograms, and then they go to Mars, their weight is going to say whatever, 15 kilograms, or whatever the percentage is.
    Dr. Pamela Gay: Yeah, so the thing is, your weight isn’t measured in kilograms. Your weight is measured in newtons.
    Fraser Cain: My scale says otherwise.
    Dr. Pamela Gay: Your scale has the wrong terminology.
    Fraser Cain: I know.
    Dr. Pamela Gay: Your scale is giving you your mass, because it’s taking into consideration the gravitational acceleration at sea level, where your scale assumes that you are located.
    Fraser Cain: Right. There’s no Newtons button on my scale. So this is where we really screw ourselves up with nomenclature. Mass, which should be measured in kilograms or slugs, depending on which units you like – Let’s go with kilograms, because no one wants to know their equivalent number of slugs. Your mass has to do with how easy it is to move you around. So if I were to plop you down in a wheelchair that has completely frictionless wheels in a room where air resistance is not something I need to consider, I have to exert a certain amount of force to move you around. I take you into outer space; I have to exert force to move you around. That force is what it takes to get you accelerated from zero to in motion. That has everything to do with your mass. Now, gravity on the planet Earth is trying to accelerate you through the floor.
    Luckily the floor has a normal force that is pushing back up, so gravitational force down and normal force of floor, chair, whatever you’re on, balances out so you’re not actually accelerating downward. But your scale, because it has a spring in it, it can measure how much Earth is pulling on you, and so it’s actually measuring your mass, taking into account gravity by measuring the force of the planet Earth on your body solving for mass. My scale here, in pounds, ignores the whole gravitational acceleration part and just says, “This is the force that you’re experiencing.” So mass is how much of you there is for me to try and exert a force on to get you moving. Weight is the total force that’s needed.
    Fraser Cain: And if I recall, force is mass times acceleration. So we derive mass, acceleration is distance –
    Dr. Pamela Gay: 9.8 meters per second squared for the force of gravity.
    Fraser Cain: Right, so this gives us meters, seconds, so boom, we’re deriving force. So what else of the basic measurements in the universe are we able to derive? Density?
    Dr. Pamela Gay: So density, that is the amount of mass in a volume, so here you have kilograms per meter cubed. Pick your units. We have energy to deal with. Energy, when we look at energy, we’re looking at, you’re taking a mass and it has a force over a distance, so take your object, move it some distance. It had a mass that had to get moved that distance using a certain force. The units are kilograms meter squared per second squared. That’s energy. It’s measured in joules, named after the dude.
    Fraser Cain: So you literally could derive, you could take all the equations that you work in and bring them all the way back to those four basic measurements.
    Dr. Pamela Gay: And this is part of why physics teachers yell at students, or at least get very terse and do things like write “cow” a lot, which is what I do, when students don’t use units. I don’t know how many times I’ve forgotten equations and BSed my way through to the right answer when I was a student because I knew what units I needed to get. So it’s like, “Throw in the speed of light. That will get me where I need to go.” That works when you’re in some classes. And it’s because of the units that you can often figure out what you forgot in your equation, because everything goes back to kilograms, meters, seconds, and then when you start getting into gas laws, you throw in temperature.
    Fraser Cain: And what about some of the really extreme stuff? You think about all of these crazy calculations about black hole event horizons and decay of radiation –
    Dr. Pamela Gay: It all comes down to the units. And what’s kind of awesome is in relativity, there’s special units that you can work in depending on what you’re doing that put everything in terms of the speed of light, and you define the speed of light as one and your math becomes easy.
    Fraser Cain: Now what do you think about the actual counting system? I know you’re not a mathematician, but the fact that everything even just comes back to 10, because it matches the digits that we have on our hand. Would we have trouble explaining that to the aliens, that we run in base 10?
    Dr. Pamela Gay: That one is actually a bit problematic because the universe likes to work in natural logs, and that is a completely different set of numbers. If you’ve ever seen, instead of using L-O-G for log, using ln, and instead of raising something to the power of 10 you use E. That’s, you’re working in natural logs when you do that. It’s also a lot of times when you’re dealing with computational stuff, it all falls out to base two, base eight, base 16. There’s a lot of different ways to do numbers. Base 10 is just one of them, and I think if we want to actually consider communications with other life forms, we need to be more fluid in how we think about numbers the way we need to learn to be fluid about how we think about temperatures if we travel a lot.
    Fraser Cain: It’s interesting, and probably just a coincidence, that we live in a three special dimension one time dimension universe, when you think about the measurements. But that’s just me making completely irrational coincidences. So cool. I think we sort of ran through that. That was great, Pamela. Thank you very much. Thanks for listening to Astronomy Cast, a non-profit resource provided by Astro Sphere New Media Association, Fraser Cain, and Dr. Pamela Gay. You can find show notes and transcripts for every episode at astronomycast.com. You can email us at info@astronomycast.com. Tweet us @astronomycast. Like us on Facebook, or circle us on Google Plus. We record our show live on Google Plus every Monday at 12:00 p.m. Pacific, 3:00 p.m. Eastern, or 2000 GMT. If you missed the live event, you can always catch up over at cosmoquest.org. If you enjoy Astronomy Cast, why not give us a donation? It helps us pay for bandwidth, transcripts, and show notes. Just click the donate link on the website.
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