I wish he would spend a bit more time exsplining were some of the constants come from, although that would probably make the video a bit weaker overall. Wasting time on such information.
Is there any compelling reason why the US should switch to the metric system for daily use?
Metric is already used universally in science and engineering, which seem to be the main fields in which consistency across countries matters. I completely agree that in physics, chemistry, engineering, medicine, etc., it is important to use standard units. But what harm is it doing in practice if in everyday life, Americans say things like "I weigh 180 lbs" instead of 81 kg?
The argument that the metric system makes unit conversions easier (e.g., the fact that it's immediately obvious how many meters are in 20 km, but not how many feet are in 12 miles) is true, but not very compelling to me. I virtually never find myself wanting to do these conversions in a non-scientific or non-engineering context, and on the very rare occasions where I need to, I can always look them up on Google.
A good comparison is degrees Celsius, which are just as arbitrary/unscientific (the standard metric unit is the Kelvin). Somehow people around the world get along fine using Celsius.
Celsius is a particularly bad metric unit. It doesn't have enough units in the range most commonly encountered by humans, and it goes negative, which is also to be avoided in a good unit.
Yes, and water freezing is a totally arbitrary value.
Fahrenheit is scaled such that 0 is about the coldest it gets where I live, and 100 is about the hottest. (Very approximately, but close enough). That strikes me as a lot nicer in practice (since 99% of the time people are talking about temperature, it’s related to weather) than something based on the physical properties of a particular substance.
Also water freezing at 0 and boiling at 100 is only valid for a specific, non-metric, air pressure.
A good comparison is degrees Celsius, which are just as arbitrary/unscientific (the standard metric unit is the Kelvin). Somehow people around the world get along fine using Celsius.
You don't realize how arbitrary Fahrenheit and Celsius are until you try cooking at altitude. When I make breakfast in a particular town I frequent, it takes almost an extra minute to boil an egg.
My Jeep is a bizarre combination of metric and SAE. ISS needs to have two sets of tools[0]. NASA lost the Mars Climate Orbiter due to confusion over the units of measure[1]. Patients are given the wrong dosages[2].
It seems safe to say it's a point of ongoing friction, especially on things like international trade.
I already made it clear that I totally agree metric should be standard in engineering or scientific applications. I wasn’t aware that this isn’t the case in the US — thanks for the info. I believe it is at least 95% the case in the US and I think we should make every effort to get that to 100%.
I still stand by my argument that it does not matter much for everyday life.
Well, the point I was arguing was "why not" have two separate systems ?
As for "why" to have them, well there isn't a good reason intrinsically -- if there were a way to magically convert the US to metric overnight, it wouldn't bother me. It just seems very unlikely and difficult in a country as huge and culturally diverse in the US. Especially since, by the standards of the rich/developed world, the US is pretty poorly educated, and also very difficult to govern (Obamacare, a law that would have seemed like a moderate reform, relatively simple to pass in any parliamentary system, is the most radical change in any area of policy enacted by the US federal congress in the last decade).
The thing a lot of people miss about the ultra-gridlocked US system is that there's a huge gulf between it being obvious to most people that "we should enact some policy" and anything actually changing. The best answer to "why doesn't the US do this or that" is often just "its political institutions can't".
Since it's so unlikely to change, and given my argument that it isn't a big deal in practice, I guess my main point is that we rationally-minded people should stop worrying/complaining about it so much.
Why should there be any separation between science and daily life?
Think about it not for the benefit of the current generation who would be forced to burden the switch, but for the next generation who could reap the benefits.
I think one issue is that by growing up with US units and then using a second system for science and engineering, it can make American students studying those topics feel like they are in an unfamiliar territory and interfere with their intuition. Most will eventually overcome this through practice and become fluent in both systems, but it's still a barrier. Science becomes a Special Discipline requiring Special Language different than what your family uses at home. Like if all science were still done in French or Latin, and you needed to study those to read a paper.
Until you have met people who grew up abroad measuring their height in cm and their weight in kg, preparing food from recipes listing ingredients in grams and mL, to whom those units are completely natural for daily life and are also the same ones they use at work when designing machines and filling test tubes, it's easy to feel that US units simply "are" the units suitable for daily life, as though that were a universal truth and not just a local cultural oddity.
Not to mention the massive net costs of having suppliers worldwide making extra sets of almost identically sized components that nonetheless aren't interoperable. Screws with 3 mm and 3.175 mm diameter, etc.
> Science becomes a Special Discipline requiring Special Language different than what your family uses at home. Like if all science were still done in French or Latin, and you needed to study those to read a paper.
You realize this is still a problem for most of the world and needing to learn English, right? :P I'm hoping we can solve this in my lifetime with everyone knowing one standard language through education as a child, but as it stands the struggle is real for many of my fellow non native English speakers.
That said I agree with you, all these differences are a pain and I'm confronted with them way too often in my daily life.
Absolutely! America is very lucky to have come out on the right side of that lottery. But then it unnecessarily goes and handicaps itself by making measurements into a foreign language.
> is that apparently the metric system was opposed in the US based on religious reasons.
As you will discover people often use religion as an excuse for things they anyway want to do. Usually they are people who only pay lip service to their religion.
Someone didn't want to use Metric. Religion doesn't actually have anything to do with it.
> That is mind-boggling.
It shouldn't be. I assume you are surprised that religion is involved in this, but actually it is not. If they were Atheist they would have the same objection, just using different words.
Basically you need to distinguish between people being people, and people acting in a certain way because of religion. This is an example of the former.
I've actually become quite fond of liquids being powers of 2 and lengths being broken fractionally. The base unit doesn't really matter (and you can always use decimal length, as is often done when building precision items).
So, for liquids,
2 tablespoon = 1 ounce
2 ounce = 1 jack
2 jack = 1 gill
2 gills = 1 cup
2 cup = 1 pint
2 pint = 1 quart
2 quart = 1 pottle ( ½ gallon)
2 pottle = 1 gallon
I find it much easier to switch units and do conversions in my head, especially when scaling recipes.
With respect to base-2 fractional length measurements, I just find it much easier to work with fractions than than with decimals. Half of ⅛ is ¹/₁₆ with next to no thought. I don't need to do division of 25 to get 12.5. It's a personal thing, but I find it nice.
Fractions are nice when the numerator is always 1. They're a pain when it isn't; sorting drill bits or buying material from McMaster Carr, you constantly have to sort out whether 17/64 is larger or smaller than 3/8, and by how much, and it becomes quite burdensome.
It's not immediate like it would be with decimals, but ⅜ -> 6/16 -> 12/32 -> 24/64 is still something I find I can do (and track) in my head with ease. Yeah, doing it repeatedly on a task would get a little tiresome. Also, who knows where the numbered and lettered series drill bits fit in without a chart.
The fractional system isn't perfect for all use cases by any means. (My understanding is that a lot of machining just deals with decimal inches directly.) I just find it convenient for many everyday tasks. I'm also weird, I guess, in that arithmetic on fractions feels easier than on decimals.
Thinking more about my original statement, a lot of it has to do with halving (e.g. finding a center) being a common operation for many tasks. It also helps that most things are sold in those fractional increments too :)
Fun (?) anecdote - metric apparently has been used in US engineering for quite a while; a petrolhead buddy of mine was puzzled as to all the fractions used on the drawings of his (I think) Chrysler Hemi V8 from the fifties - on a hunch, we converted a few to metric. Bingo.
(Just making up a number here) 3.937" stroke? Why on Earth... Ah. 100.0mm. That's why.
Another anecdote - In structural engineering, US units are way easier to work with, and even in Canada, about 90% the buildings I work on use kips, ft, ksi, etc.
In Australia, we use metric. On the odd occasion, you will find both imperial and metric depending on the application. Our wood sizes are metric, nuts and bolts can be either, nails metric, screws metric, tape measures generally have both imperial and metric, pipes are generally metric though you can get imperial if needed.
I have been using metric since the seventies. About the only things I still use imperial for are people's height and the length of fish (for undersize/oversize determination). In regards to woodworking, I much prefer metric over imperial and the millimetre over just about all other base units.
They aren't easier to work with for any reason other than that sizes of standard components (pipes, beams, etc) are sized conveniently in US units and have US units printed on the spec sheets.
If you go overseas outside of North America, you find that the sizes of everyday objects are conveniently sized in metric, and building codes and standards and material strengths and densities are specified in SI units, and suddenly working with the metric system in those industries is easy and convenient.
Do you deal with building insulation? How would you interpret a material spec of "1 BTU ft/(in^2 hr °F)"? I had to work with these units in the US and it was not at all convenient.
I don't deal with building envelope. Its not surprising or unexpected that there are differing opinions among various professions on which set of units are more convenient.
In Canada, all our building code, material design codes, etc are in metric, and yet we are still using US units for day to day design.
What lengths and widths of wood can you buy from the lumberyard?
What is the common width and thickness of drywall sheet you can buy and the hardware store? What door sizes are available? What size of screws are cheaply available in Canada?
I think these factors are far more likely to affect what unit of measure is commonly used in construction, rather than any intrinsic merit of the measurement system. If you were shopping at a Japanese or German hardware store, you'd probably suddenly find all of those 12 foot dimensions quite frustrating and not be at all surprised to find the hard-hat-wearing locals happily using the metric system for the same tasks.
> a cylinder of a platinum alloy stored at the BIPM in France, will now be retired. It will be replaced by the Planck constant – the fundamental constant of quantum physics.
I recently ordered a picture frame from Amazon. It came in its packaging box, which was placed in a box by the manufacturer. That box was put in another box by Amazon and shrink wrapped to a large piece of cardboard, which was then put inside yet another box.
On the surface, it seems crazy, but Amazon did manage to get it to me undamaged.
My wife recently ordered five storage boxes. They arrived in two packages on the same day. One package neatly fit four of the boxes. The other package was large enough for five, and contained one storage box and a excessive amount of packing material. Not an Amazon purchase, so it must be an industry issue.
I have already sent an email to the Norwegian bureau of standards to inquire about buying one of their secondary kilogram standards - presumably they'll want a couple for displays and museums, but it would make for a great letter weight. (Just hoping the secondary ones are NOT also made from platinum. That is a tad too extravagant, even for a measurement nut.)
I do happen to have the previous generation time standard in my garage, though, a HP 5061A Cs clock.
Also the tertiary ones? (I was -poorly- trying to indicate I was after a secondary /national/ standard - the ones calibrated against the national reference which is in turn calibrated against the Paris one.
Considering they have measurement history on that particular object going back over a century, I guess they will continue to regularly measure it to see what happens.
Last I heard, the original Big K, along with (some of) the secondary copies, will not be sold. Instead, they will be observed/studied in an on-going basis, in order to better understand why their masses appear to have drifted apart over the years (which is partially the reason for this re-definition).
As I understand it the problem was not so much to find a mathematical definition of the kg based on other units but rather to find a definition suitable for experiments. If you can't practically use the definition to reproduce the prototype then it's not a very good definition indeed.
It seems that they settled on this definition because a Kibble balance[1] has shown to be precise and practical enough:
> Accuracy criteria were agreed upon in 2013 by the General Conference on Weights and Measures (CGPM) for replacing the current definition of the kilogram [...] with one based on the use of a Kibble balance. These criteria have since been met, and the definition of the kilogram and several other units will change on May 20, 2019, World Metrology Day, which celebrates the establishment of the SI, or metric system, in 1875, following the final vote by the CGPM on November 16, 2018.
This is probably the dumbest thing I'll type on HN.
In university I just gave up trying to understand why we even needed the Avogadro constant / mole as a fundamental constant. It still confuses me. Why have a difference between molar mass and mass? Why couldn't it just be "1" and everything else change around it?
Isn't this something essentially tautological though?
When we discuss the mass of a neutron and we say "one neutron weighs one u" then we discuss the mass of an electron and we say "one electron is 5.4858×10−4 u" and "one proton is 1.0072764 u" then we add them up and say "one hydrogen atom is 1.00794 u while one helium atom is 4.002602" (forgetting some complications for a moment) are we not just summing likes?
Or is it just that since mass is defined in Planck and time / distance terms that we need to relate it to counts of things? Theres a gap there I don't understand. Can we not just say "we measured a proton's mass and it is u"? Am I making a jump there?
In my opinion it is because a mole is a numerical amount of atoms vs the mass of the substance, so it makes reactions, formulas, and measurements easier to determine. Avogadro's number is useful just as a baseline to use (number of carbon-12 atoms in 12 grams of carbon-12), like there are 12 inches in a foot or 100 centimeters in a meter...
In a meta-sense, I don't think your question is dumb at all.
There's a complicated technical topic which you're still not understanding. There's no indication it's a question you could easily answer yourself, and you're posting it in a forum of people likely to find the topic interesting, some of whom might give an answer that clicks for you.
> the Avogadro number was initially defined by Jean Baptiste Perrin as the number of atoms in one gram-molecule of atomic hydrogen, meaning one gram of hydrogen. (from Wikipedia)
(It's since been refined to be 12 grams of carbon-12.)
So a mole is defined to be approximately one gram worth of protons and neutrons. We use it because grams are a significantly easier unit of mass for humans to work with, than like individual particles.
No, it's not. Avogadro's number is a constant, but it's not fundamental - the only difference is that it's defined in terms of fundamental constants (namely, the Planck constant) now. It's still an arbitrary number defined in terms of the mass of a gram.
Nope, it is fixed to be N_A = 602,214,076,000,000,000,000,000 exactly (6.02214076x10^23 to units precision).
It used to be the case that the mole was an experimental value equal to the number of atoms in a certain mass of a certain something. That is no longer the case with this revision. It is a fixed, never changing integer constant.
This does mean that 1 mole of carbon-12 is no longer exactly 12 grams. But it is approximately 12.0000000 grams, which is within the best we can experimentally measure today, so nothing changes in practice as a result of this update except first chapter of an introductory chemistry textbook (good excuse to push out a 9th edition for $250!).
Therefore it is accurate to say now that whereas before the Avogadro's number was experimentally determined based the exact expressed mass of a carbon-12 atom relative to a platinum-iridium cylinder in Paris (the old kg), it is now the case that the expressed mass of the carbon-12 atom must be measured relative to the a kg definition based on Planck's constant.
(I say "expressed mass" because this situation is a little confusing... I'm talking about the numbers we write down expressing the mass as a multiple of some standard kilogram. That reference mass changed, not the actual inertial mass.)
EDIT: Or you can just read the draft of the agreement that was voted on. The definitions are on the first page:
A fundamental constant isn't just any fixed constant. It's specifically a constant that describes a fundamental property of the universe.
For instance, c describes the speed of light in a vacuum, and is a fundamental physical property of the universe.
Avogadro's constant isn't the same thing. It's just a number that humans decided would be useful. We could have fixed it to any other number; there's nothing fundamental about the number ~6.022e23.
I thought it was just a ratio. Mass per mole. I admit I have never used this in my day to day life and college was 20 years ago. So maybe I am clueless.
Nah, I think that's just it. It's easier to write down certain calculations in mole in a chemical context, because you're concerned with atoms reacting with each other. You don't have 12 grams of carbon and 4 grams of hydrogen, but 1 mole of carbon and 4 mole of hydrogen.
My understanding is that the cause is error propagation. We can measure certain kind of masses really accurately in unified atomic mass unit. With better relative precision than the Avogadro constant. But if we used kilograms to write down these quantities then they would carry the error of the Avogadro constant needlessly.
Edit: I think your question boils down to "Why do we have two separate units for mass, u and kg, connected by the Avogadro constant?" Most answers dismiss your original question as Avogadro constant is not a unit. But u is a unit and it's the point why we have this constant.
Edit2: To further emphasize my point look at the mass of neutron[1]. It's listed both in kg and u. Note the number of decimal places.
Right, I get that, and if anything I feel less dumb now that I've asked it publicly and people seem to think that it's a non-dumb question, but when talking about fundamental constants I understand there is a practical nature to it all, but just as we have a nano-meter and a light-year I figured we'd have the same for mass.
Why do I need both kg and u as fundamental constants?
I believe the comments here have answered it. It isn't something weird, like quantum gravity or some such. If I understand everyone correctly it's just a practical decision we made at some point because we didn't want mass to be in u and that's that.
They aren't fundamental constants, they are fundamental units. The system is ultimately about allowing people to compare measurements (not describing the universe in abstract), and is only tied to fundamental physical constants where it makes that more reliable.
That's not a whole answer, but it may be helpful for your thinking.
As others have noted, knowing the count of entities (note: not atoms, entities - i.e. it can also be molecules) in relation to actual mass is very useful for the physical sciences - at a molecular level the quantities of molecules and atoms interacting matter, not their masses - but mass is the unit I do experiments with.
EDIT: A simple example would be if you were trying to make water - H2O, from hydrogen (H2) and oxygen (O2). The molar ratio is 2:1 - but in doing a practical synthesis, that doesn't tell me how much mass/volume of gases to actually mix up. Avogadro's number and molar mass is what I need to turn those into practical units to work with.
I mean that really comes back to the "practical units" thing (and that chemists were the ones doing the work) - a kilogram of anything in chemistry is a huge amount, whereas a gram is about right to make "a lot" of something (in synthesis research people get excited about gram-scale synthetic yields).
So it's pretty much chosen to get integer-ish units with common things you work with like carbon - i.e. 1 mole of carbon of is ~12 grams.
No I agree, it seems stupid. What we did is take a block of metal and call it a kilogram, figure out how many atoms are in 1/1000 of it (a gram) and call that a mole. What we should do is redefine the gram to be whatever 1e10 atoms of Hydrogen weighs, or something similar. When I read the headline I thought thats what they did, and I admit first reaction was "oh god I'm going to be dealing with conversions and associated errors for the rest of my life".
> What we should do is redefine the gram to be whatever 1e10 atoms of Hydrogen weighs, or something similar.
That was actually an alternative proposal for redefining the kg. The kg would have been 1000/28 the weight of a mole of silicon-28; you could build a sample by counting 6.023x10^26/28 atoms of silicon-28, and making a sphere out of them.
Initially the watt balance seemed to be less precise than atom counting, but then it was improved to a point where defining the kg on top of the mole became less convenient than the definition they are adopting now.
In chemistry, the molar “mass” plays a more important role than the mass proper. Why has its unit not been chosen to be equal to 1? For the same reason as why the gram is not defined to be the mass of, say, proton. (Chemistry doesn’t normally deal with single molecules.)
For the same reason that we use both temperature and energy and find them both useful. We can talk of the energy of an electron. On the other hand, temperature, is an statistical property defined for many particles.
Using mole (based on Avogadro constant) makes it easier to do statistical mechanics, but it's not a microscopic property like mass.
Understanding mass in molar terms is necessary to do a lot of chemistry correctly. The mole is effectively a count of the number of molecules kicking about, although the count is large enough that terms like "quadrillion" don't cut it. (One mole is about 600 sextillion molecules). Knowing how many molecules are around lets you actually compute how much stuff can react in a given chemical environment, and other aspects of chemistry end up being pretty related to molecule counts. Vanilla mass doesn't cut it since an atom of iodine weighs about 6.6 times that of fluorine but can still only react with one other molecule.
The flip side is that the molecular count is less useful to us in the everyday world. We can gauge the weight of a kilogram much more than we can gauge a septillion molecules. And if we're trying to figure out how much stuff a shelf can hold before it collapses, it's the weight that matters, not the actual molecular count. (Note for pedants: in the familiar environment of Earth's surface, mass and weight can be treated as the same quantity in most cases.)
So mass and molecular count are both very important quantities that have importance in different fields of science, and they don't have a trivial relationship to each other. Avogadro's constant and molar mass is a way to express their relationship.
trying to use kg instead of moles when calculating a chemical reaction would be like trying to set up a speed dating event by taking the weights of all the men and women instead of matching them up pairwise. Sometimes it is much easier to calculate based on scalar quantity than it is to calculate based on mass.
The argument there is that avogadro's constant is just an arbitrary number and mol is not an unit, but weird case of SI prefix.
On the other hand it is fundamental-ish constant, because it is defined as arbitrarily scaled result of inherently uncertain measurement. And the new definition of kilogram had significantly increased the attainable certainity of such measurement (to the extent that it is uncertain due to practical issues, not by definition). The other proposed replicable definition of kilogram (ie. mass of Si monocrystal wih particular geometry) would fix the definition of mole as some known and defined number, but would be significantly harder to replicate (because it would define how to produce an artifact in contrast to how to directly measure the mass as the ratified definition does)
Yeah, I think that's his idea. So, instead of tables of molar mass in g/mol, you would have tables in terms of "amount of substance"/g. E.g. number of atoms or number of molecules.
An Avogadro's constant number of molecules is one mole. One mole of hydrogen has much less mass than one mole of iron. You have to choose an arbitrary mass of a single element as the base quantity. Hydrogen might be the best theoretically, it's just a proton and an electron, but it is tricky to work with because it's a gas at room temperature. So instead the mole has been defined as the number of molecules in a specific mass of carbon-12.
I think this is exactly the rationale. But, from a more practical perspective...
If instead of g/mol, we referred to molecules/g -- we would end up populating tables and charts with really big numbers. This would make lookup tables hard to read, difficult to publish, and hard to work with. Imagine if you had to do math with a bunch of 10^23 exponents all of the time.
Instead, it was agreed to effectively pull out a constant value from each of those to make the math significantly easier. Now, instead of dealing with a lot of big numbers, all of the lookup tables could now list smaller g/mol values. And we would be left with just the one single large (Avogadro's) number in the equations.
Honestly, we don't need a set mole constant, but it makes chemistry significantly easier to do so. Unlike the other constants mentioned in the OP, Avogadro's number is completely arbitrary. It could be '1' as the parent suggested, except then it makes the rest of the math more difficult.
Even for this SI overhaul, we didn't really even need to redefine the mole, except for the fact that it was previously defined in terms of the old kg. This was just "fixing a glitch".
> Imagine if you had to do math with a bunch of 10^23 exponents all of the time.
What if it was just set to 10^24 then? Much easier to remember and serves the same purpose.
If it was 1 it would work too, since the SI system already has a way to deal with large numbers: prefixes. So we might wrote Ymol for yotta mole = 10^24 mol.
> Even for this SI overhaul, we didn't really even need to redefine the mole, except for the fact that it was previously defined in terms of the old kg. This was just "fixing a glitch".
I came to complain about the article calling the mole a "base unit of the SI", and this seems like an appropriate thread.
Why is the mole a defined unit at all? As far as I understand things, "one mole" is the same thing as Avogadro's number -- neither can be a unit, because they're both dimensionless constants (well, they're both one and the same dimensionless constant). Applying actual units, "one mole of water molecules" is the same thing as "Avogadro's number of water molecules". Avogadro's number, and therefore the mole, is the conversion factor between atomic mass units and grams. Similarly, 3 is the conversion factor between feet and yards, but nobody thinks 3 is a fundamental base unit of the imperial system. The foot is a base unit of the imperial system, measuring length, the yard is a non-base unit also measuring length, and 3 is a number with no special relationship to the system at all. It would be total nonsense to say that yards are defined by reference to 3. How is Avogadro's number different?
Wouldn't "fixing the glitch" be abandoning the idea of calling the mole a unit in the first place?
I'm pretty sure the mole is not defined as 6 * 10^23 mol^{-1}.
There is a concept of "the Avogadro constant", which is defined to have units of mol^{-1} (at least, according to a cited statement on wikipedia), but that is not a coherent concept -- since mol is dimensionless, mol^{-1} is also dimensionless.
> Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole as a unit like the metre or the second have arisen:
> the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity
> the mole is not a true metric (i.e. measuring) unit
> One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.
amu and g are both units of mass, so 1 amu = 1 g/mol is an explicit statement that mol is dimensionless.
Calling mol a unit won't accomplish anything except corrupting your dimensional analysis. mol is not analogous to the SI units meter, second, ampere, gram, kelvin, etc. -- it is analogous to the SI prefixes kilo-, mega-, milli-, micro-, nano-, etc.
Why does it need to be based on the mass of an arbitrary molecule? Can't it just be 10^23 or 10^24? Most of the time, you're going to have to look up constants to convert moles to mass anyways.
Avogadro's constant is not itself a heavily-used value in chemistry. Its derivation is obvious if you think in a different way:
You need to convert from mass to numbers of molecules, which means you need to divide it by the mass of a molecule. The mass of a molecule is determined by the sum of the weights of each of the atoms, themselves the weights of their constituent nucleons [1]. If you fix the weight of a nucleon to be 1 (that is, we measure in daltons), then computing the weight of a molecule such as glucose (aka C₆H₁₂O₆) in daltons is a trivial formula. All you need is a periodic table that lists atomic weights, which is every copy you find a chemist using. It's worth noting that the resulting molecular weights are going to be independent of whatever measuring system you want to use [2], whether it be grams, ounces, alien flits, what have you.
Now you need to convert the mass of your substance into a count of "stuff-loads" of molecules. The simplest and most idiotic thing to do is to define a "stuff-load" to be the amount of molecules in a unit mass if it weighs 1 dalton--in other words, you make this formula be exactly one. In SI, the unit mass for this equation is grams and the "stuff-load" is the mole. If we were using US ounces as the unit mass, we'd define an ounce-mole and use that instead of SI moles.
Put another way: we define a mole such that the constant in the computation of moles from molecular weight and mass is exactly 1. Avogrado's constant itself is merely the inverse of the mass of a nucleon when expressed in grams.
[1] Okay, there's a lot more that goes on into the computation of mass. In terms of the mathematical error, though, other sources of error (e.g., wrong isotopic ratio) are going to matter before these come up.
[2] Up to the slight adjustment (about ±1%) of what you consider the weight of a nucleon to actually be.
The one that made it click for me as incredibly useful was Avogrado's Law (now part of the Ideal Gas Law):
> Equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.
This law, for example, explains why hot air rises. Take two equal quanties of the same gas at the same pressure. They will have the same volume. Now, heat one quantity of gas. By this law, that gas will have a larger volume at the same pressure. Because it has the same amount of mass distributed over a larger volume, it must be less dense. Therefore, it rises.
> By this law, that gas will have a larger volume at the same pressure.
It will have larger volume, but that is not implied by Avogadro's law. That law is about the surprising property of all gases: no matter the chemical nature of the gases, if they all have same T and P, they all will have same number of molecules per unit volume.
We need a means of converting mass to number of atoms so that we can predict how much mass of a specific product will be formed, what the limiting reägent will be, &c.
It also helps to define concentrations based on number of moles in a L of solvent (Molarity vs g/L) for the same reason.
Historically, the mole predates the acceptance of atomic theory. Stoichiometry of various reactions let you work out that there was some mass of oxygen that would entirely react with some mass of carbon to form carbon monoxide. They didn't have the same masses, but the relative amounts for each element were constant (or small integer multiples, such as twice as much oxygen to carbon for CO_2).
So Dalton took the lightest one, hydrogen, and defined a mole as the stoichiometric amount equivalent to that in 1g of hydrogen. Looked at that way, it's a pretty solid choice.
Well, now you could do that. At least you could next March when these rules take affect. But before you could not because the conversion between atomic mass and SI/kg mass depended on that experimental constant. Two mass systems were required because we couldn’t conver between them with atomic accuracy.
I don't believe the Avogadro constant needs to be an SI unit. It's like having 12 as an SI unit, or a million, or 1. Sure, it's a useful constant scaling factor, but it doesn't need to be canonized at the heart of the SI system. It doesn't actually express anything fundamental about how we measure our universe.
And if nothing else, it can be derived: a mole is the number of atoms in a kilogram of carbon-12. Done.
> why we even needed the Avogadro constant / mole as a fundamental constant(...?)
It serves as a link between human-scale and atomic-scale observations, classically needed for chemistry performed on Earth by humans. This link must exist, as others mentioned, for stoichiometric calculations (e.g. air/gas mixture in a internal combustion engine). For much of modern scientific history, it was deemed useful to scale into an easily eye-visible human scale (the gram). [0]
The number of things in a mole is arbitrary. It's a dimensionless unit. However, since many things are already measured in moles in chemistry, there's no real reason to remove it. Dealing with numbers on a more practical macroscopic scale is probably more convenient than dealing with large powers of 10.
I don't know about trade, but kilo standards were deviating by tens of micrograms from eachother, some things are sold at prices which warrant accounting for those micrograms, so a completely stable international definition seems helpful.
Certain types of scientific instrument will need to be recalibrated to meet the new definitions.
Is there any scale in the world that can measure a kilogram to within the accuracy of a microgram?
And if you buy a kilogram of something and they accidentally short you by a few micrograms, haven't you only overpaid by a few parts per billion? Even on a billion dollar order you've only overpaid by a few dollars...
Mostly yes, it does seem over-stated. I guess if you squint "wide-reaching" does not necessarily mean "important" just, you know, "wide-reaching". Like the "wide-reaching" effect of dropping a pebble into an otherwise undisturbed swimming pool maybe? The ripples go pretty far, they don't really matter, but they do go far.
With the old definitions, the values of the known constants were just approximations, but now that the unit is defined based on the constants, we can consider the constant as being the exact value, no matter how imprecise it was when it was measured using old definitions of the units.
I guess the next redefinition will happen if and when there's detectable drift in "fundamental" constants?
And until then, all the metric fanbois will constantly tell you that metric is superior to imperial because its measurements are immutable. Until suddenly they are.
There are no other standards. Metrology is expensive and doing it over again would offer no benefit whatsoever. All prior standards in widespread use were abandoned during the 20th century in favour of defining the relevant units in terms of SI units.
Specifically the international yard equals 0.9144 meters and the international pound equals 0.45359237 kilograms
There literally isn't another definition, in the US when you say "100 yards" the only legal meaning that has is 91.44 metres, which is whatever CGPM / BIPM says it is.
This is why imperial makes more sense to me than metric. If we had a base-12 number system, metric would be perfect, but base-10 is terrible under division. For practical divisors like these, imperial shines.
If you're doing science, metric makes more sense because units work out. But most all US science has already adopted metric.
I won't disagree with you on this because you'll always feel more comfortable with something if you've been using your whole life. For example, I would never understand why you think 1/2ft = 6in is simpler when you have to know in advance that 1ft = 12in. It could be because I'm not used to it.
Using the metric system you'll rarely write 1/2m, as fractions are not what a person used to metric would default to. That is why 1/6m looks so weird as no one would use it like that, but if you write it 0.5m now it's obvious we are talking about 50cm, or 500mm.
BUT,
In those examples you are not using the system, you are just using one unit. If the question were, for example, what is the mass of the water contained in a 1m x 1m x 1m box, then the answer is obvious which system is by far the most sane one.
> If the question were, for example, what is the mass of the water contained in a 1m x 1m x 1m box, then the answer is obvious which system is by far the most sane one.
You're not disagreeing, the GP said
> If you're doing science, metric makes more sense because units work out. But most all US science has already adopted metric.
Your question asks for mass of a cubic meter of water, presupposing a typically scientific quantity (mass, instead of weight) and presupposing that a cubic meter (why not a cubic foot?) of water is a useful collection of water for some purpose. Fine, use metric. But imperial units as a system are made for practical everyday utility, which your example doesn't presuppose. On the other hand if we imperial users run across a situation where metric seems more useful, fortunately we can precisely convert, so it doesn't really matter.
In other places of utility (such as engineering disciplines) adopting a unit agnostic approach is the best. Some fields don't use either imperial or metric units but their own domain specific things, and software can always present units in whatever preference someone has or whatever is the most useful for the moment.
You are confused, arguments about the benefits or lack thereof of metric are based on internal consistency, not standards and metrology.
Nobody is arguing against more precise definition of standard values, which is why Imperial units these days are themselves defined in terms of SI units. So if the meter were to change, for example, so would the US foot.
The meter was originally an actual physical rod (you can see the prototype on display at the fascinating French Musée des Arts et Métiers). Now it's based on the speed of light in a vacuum.
The kilogram was a physical mass (and, yes, it was evaporating). Now it's finally defined in terms of the Planck constant, the second, and the meter.
The second was originally 1/86400th of Earth's day. Now it's based on the radiation of cesium-133 (I don't really understand how this is measured).
The ampere was originally defined based on depositing milligrams of silver from a solution of silver nitrate; it's now based on newtons and meters.
The kelvin was originally defined based on water; it's still defined based on water.
The mole hasn't really changed much? It's based on the number of atoms in a kilogram of carbon.
The candela was originally based on a literal standard amount of light emitted by candles made from dead whales; now it's based on radiation from light sources of a specific frequency and an intensity based on the watt (which relies on kilograms, meters, and seconds).
Mole was just redefined as exactly 6.02214076e23 — the number of Si-28 atoms in a perfect 1 kg sphere. This was an intentionally check against the kibble balance measurement.
Seconds are the metric unit of time if I understand it correctly. It doesn’t make any sense to say “kiloseconds” or something like that because days are the time that the sun is up (ish), months are roughly based on moon cycles, and years are approximately the time it takes us to go around the sun.
It’s also historical and pretty hard to change the basic units of time.
FWIW, while scientists don't usually use kiloseconds, it's pretty common to see 1.437e4 seconds, rather than 3h 43min 20sec, used as units in time series etc. Similarly one uses milliseconds, femtoseconds, and soforth.
Years (or more specifically millions of years) gets used sometimes when talking about astrophysics, evolution or continental drift. (I am not a researcher and definitely not in any of those field though, so this may just be in material aimed at non-scientists). But I guess there's enough orders of magnitude of different that they rarely cross over so no one cares about the odd ratio, similar to J vs eV.
There has been a proposal during the French Revolution with 10 hours a day, 100 minutes an hour and 100 seconds a minute. But it has only been in use for a few years beginning in 1792: https://en.wikipedia.org/wiki/Decimal_time
Presumably, the second was shorter, rather than the day was longer.
EDIT: More specifically, if you take an average rotation of the Earth as 86164.1 seconds, and divide by 10, then 100, then 100, you get 0.861641, which would be the conversion from our seconds to the metric second in that scenario. Likewise, the metric minute would be 86.1641 of our seconds or about 1.43607 of our minutes, the metric hour would be 8616.41 of our seconds or 143.607 of our minutes or 2.39345 of our hours. The day would be slightly shorter than our day, reducing the need for leap seconds to keep our time aligned with the sun.
You could just define the second to be a 1/100,000 of a day and go from there. Aside from screwing with literally everyones perception of time, it could work.
But which day? Such a second would probably work for everyday purposes (just like to most of us a second is 1/86400 of a day) but it would be woefully inadequate as a universal fundamental unit of time. And defining the second in terms of something like "the length of the solar day at Greenwich meridian on Jan 1 2020" prevents anyone from ever reproducing the exact value based on their own measurements, which is one of the big reasons for defining fundamental units in term of physical constants.
Yep, things leap seconds have been used for. The moon also constantly robs Earth angular momentum via tidal interactions.
But an even bigger issue is that the sidereal day (one 360° rotation of Earth as measured against distant stars) is not 24 hours but roughly four minutes less. And the length of the solar day also varies over the year due to the slight eccentricity of Earth’s orbit—days near perihelion are slightly longer than near aphelion. And then there are the higher-order effects caused by gravitational interaction with other planets...
One can arbitrarily define a second as anything and then say that one UTC day usually has 100000 seconds and some are longer or shorter. It is just a matter of scaling few unit definition constants by 10000/86400.
Yeah, I don't think it's really an issue. Physicists only convert things to hours/days/years when disseminating results to a broader audience, when doing the actual physics everything is microseconds or megaseconds or whatever.
I would say most people prefer the one they learned first. For doing science metric is usually better. Easier unit conversions. I think inches/feet are better for construction as you have more options at what level of accuracy you want to work with and splitting things up unless you need to have a fifth of something.
That's actually exactly why I like working in Imperial when woodworking. You're composing and dividing things by 2 all the time, so a base-2 fractional system is great.
12 and 60 are superior highly composite numbers¹ — as is 360, the number of degrees in a circle and the number of days in a year (with a little engineering work TBD).
Speaking of circles, SI hasn't fixed Hz vs rad, have they?
> Speaking of circles, SI hasn't fixed Hz vs rad, have they?
I don't think so.
Anyone who hasn't heard of the Hz/radian issue should see the "Hz" definition in the units definition file shipped along with Frink - if you like finding interesting rants in unexpected places, it's delightful:
Heinlein's "Starship Troopers" has the space marines using "kiloseconds" and "megaseconds" conversationally, and it was always tricky for me to convert those to hours and minutes in my head accurately.
$ units --verbose
Currency exchange rates from FloatRates (USD base) on 2018-10-25
3070 units, 109 prefixes, 109 nonlinear units
You have: 1 megasecond
You want: 1 day
1 megasecond = 11.574074 * 1 day
1 megasecond = (1 / 0.0864) * 1 day
Gee, I never knew about units, thank you. Very cool. It can convert meters/s to furlongs/fortnight, cm^3 to gallons.. Write fractions like '1|2'. And you can add your own units to the units file.
Also in the book "A Deepness in the Sky" by Vernor Vinge. In the beginning of the book there was a convenient chart for converting to our customary earthly time units.
And in Dukaj's "Perfect Imperfection" [1] occasionally multiples of Planck time are used (with metric prefixes), as the post-humans and "out-of-space computers" can operate on very small time scales.
In scientific literature we do typically use one particular preferred time unit (second being the SI units) and then exponentiating properly (eg optically driven metal to insulator transition in V2O3 occurs in 1.3 picoseconds (10^-12 s), desorption of atmospheric gasses from CoPc thin film in vacuum takes ~10^5 s (~1 day)).
Calendars are hard because you've got multiple inconveniently disparate sources of information you want to unite: universal constants on the one hand (such as the second being tied now to atomic vibration) and more "local" concerns such as the orbital position of the earth with reference to the sun, the moon, other neighboring objects in the solar system.
Vernor Vinge's novels, as one example, use metric prefixes and seconds exclusively (this is referred to as Metric time [1]), which is a fun thought experiment. The biggest complaints are that the units aren't necessarily great for human activities and definitely don't align well with minutes/hours/days/weeks/months.
Hectosecond is close to a minute, but slightly larger (1.666 minutes). Kilosecond is about 16.666 minutes long, which is the closest unit to an hour. It's almost a useful quarter-hour (but again it doesn't line up that well). But then you hit the order of magnitude wall and the next prefix up is Megasecond which is nearly, but not quite a fortnight (~11 days), and Gigasecond is just shy of 32 years. You long at that point for more prefixes between Kilo-, Mega-, and Giga- if you are using seconds as base unit at that point, especially living on Earth and trying to coordinate calendar weeks, months, years. (There are non-standard prefixes Myria- (10^5), also from the French revolution, and Hebdo- (10^7) which are almost useful enough here to beg them to be standardized.)
In Vernor Vinge's fiction, spacefaring humans even measure time in kiloseconds and megaseconds. 1 ks is slightly more than a quarter of an hour; 1 Ms is about eleven and a half days.
> Instead of hours and minutes, the mean solar day is divided into 1000 parts called ".beats". Each .beat is equal to one decimal minute in the French Revolutionary decimal time system and lasts 1 minute and 26.4 seconds (86.4 seconds) in standard time. Times are notated as a 3-digit number out of 1000 after midnight. So, @248 would indicate a time 248 .beats after midnight representing 248/1000 of a day, just over 5 hours and 57 minutes.
just set the timezone of your devices to UTC, and you're done! Actually getting other people to schedule meetings with you in UTC is going to be a bit trickier though.
>The mass of the international prototype of the kilogram m(K) is equal to 1 kg within a
relative standard uncertainty equal to that of the recommended value of h at the time this Resolution was adopted, namely 1.0 × 10-8 and that in the future its value will be determined experimentally,
Is the Planck simply the most standard deviation the kilogram can stray from now?
It is still not apparent to me. Is a kilogram of something now it's joules x seconds or something? Does the kilogram now vary depending on what the kilogram is of? Like, is a kilogram of Iron a different mass from a kilogram of Aluminum?
>The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.
So mass is now some sort of length times a given elapsed time?
Given the definition of metre and the definition of second, the kilogram is whatever value that makes the Planck constant h precisely 6.62607015×10−34 kg m^2 s^(-1).
There is only one value a kg could be in that example, everything else is constant. The question I think you're trying to ask is "why 6.62607015×10−34 instead of some other simpler value" and the answer is a bit longer.
Original 1 kg was the mass of a cubic decimeter of water at 4 C at 1 ATM. Why a cubic decimeter at 4 C? Water is densest at 4 C and a cubic decimeter of it is a weight that people can work with on a day-to-day scale. Unfortunately this was a bit hard to measure so they made the IPK (international prototype kilogram) which was a lump of metal. Fast forward 100 years and the lump of metal proved to be too unreliable for modern standards as it kept losing very small amounts of mass, also it Earth's gravity isn't even so it requires you average it out and then calculate the local offset and a whole bunch of other weird things that can mean a microgram or two. This is inconvenient but we still needed a way to say "1 usefull measurement of mass" but unfortunately in the universe 1 Planck's constant is far too small to ever use daily. Thankfully it has become easier to accurately measure Planck's constant against the IPK so now we have solidified 1 kg to be exactly what we measured.
The nice thing is 1 kg will forever be the same thing now and is easy to measure to extraordinary accuracy. The downside I think you're asking about is 1 kg by itself isn't some significant relation of the physical world, it's just a useful-in-daily-life multiple of mass as defined by Planck's constant.
According to the new definitions, some of the fundamental constants can no longer be wrong. We could even have defined them as 1 (which is what physicists have been doing for a long time already.)
If you do that, magnitudes of resulting units will either be huge or very tiny, depending on the composition of fundamental constants in said measure. The constants are very carefully chosen to match old units.
There are some theories of physics that imply that the value of "constants" like the speed of light actually vary slightly over long distances or times. This would be very inconvenient for the new system if it turned out to be true.
How would you use the new definition to calibrate instruments? My current understanding is that there is a lineage of artifacts calibrated against another artifact until one of those was calibrated against the one true artifact. So how would NIST or another certifying source say that my 1kg standard is 1kg +/- tolerance?
Is it anyone with a kibble balance can now certify calibrations? How do you know your kibble balance is as accurate as the next guy's kibble balance?
Essentially this brings it one more step away from using another artifact for calibrating things. Instead this lets us define the kilogram against what we believe are universal constants, in this case properties about the electromagnetic force.
It's much simpler to understand looking at it with a watt balance, even though it's not going to be as precise or accurate as a kibble balance [1]. Basically now anyone with access to a kibble balance and the right set of numbers/information can make an exact 1kg object.
I'm pretty sure a watt balance and a Kibble balance are the same thing. Regardless, that YouTube video is so good! I was just about to post the same link.
Or potentially more usefully, ascertain an accurate measurement of how closely a given measuring device is to the target to calibrate it's use in actual measurements (outside of the expensive validation mechanisms).
It will still mostly work the same way, except that instead of someone having the "one true artifact", anyone with enough equipment can measure their kilogram against natural constants and know it's correct.
It means the right answer is freely available to anyone (with a bunch of scientific equipment).
The pictures in that article about NIST reminds me of the adage, "The smaller the measurement, the bigger the lab."
I like to use metrology labs as an example of something people often take for granted (measuring things) and showing how deep that invisible rabbit hole goes.
The NIST explanation of Kibble balance calibration includes this:
> Everything on the right side of that equation can be determined to extraordinary precision: The current and voltage by using quantum-electrical effects that are measurable on laboratory instruments; the local gravitational field by using an ultra-sensitive, on-site device called an absolute gravimeter; and the velocity by tracking the coil's motion with laser interferometry, which operates at the scale of the wavelength of the laser light.
Current is measured in amperes, derived from the charge (in coulombs, defined from the charge of a proton) and time (in seconds, defined from the vibration of a Cs atom). Gravitational acceleration is measured in ms^-2, derived from length (in metres, defined from the distance travelled by light in a vacuum in a second) and time. Velocity is also derived from length and time.
With these new defined constants (including the Planck constant), all of the instruments could now be calibrated by observing natural phenomena and a whole lot of counting.
It was metricized with all the rest before that. What happened in 59 was harmonization with other countries including Canada, who had a different agreement on the metric yard. The older american definition was 1 yard = 3600/3937 meter. The international metric yard is exactly 0.9144m. (A difference of 0.002mm)
Can anyone tell this poor ignoramus whether the kg is getting heavier or lighter - and how much by (approximately, I know it's not going to be an exact figure given the reason they are changing it)?
> These changes don't affect the "size" of any of the units.
The size of electrical units is changing slightly. According to this BIPM document [1]: "The transition from the 1990 convention to the revised SI will result in small changes to all disseminated electrical units. For the vast majority of measurement users, no action need be taken as the volt will change by about 0.1 parts per million and the ohm will change by even less. Practitioners working at the highest level of accuracy may need to adjust the values of their standards and review their measurement uncertainty budgets".
That doesn't make sense to me, the definition has changed.
The IPK was 1 kg and the copies of it were all slightly heavier or lighter, for argument let's say IPK1 was 1.1 kg and IPK2 was 0.9 kg. Now that we have a constant for the mass of 1 kg, all of those IPK's will now have a new mass relative to the new definition.
Unless the new definition was based on the current IPK and set its mass as of today as the standard, and that standard now will be unchanging?
> Unless the new definition was based on the current IPK and set its mass as of today as the standard, and that standard now will be unchanging?
Correct. The current IPK will still be 1kg to within margin of error at the time the new definition comes into effect, but any further changes to it will make it, for the first time, drift away from that value.
It's probably better to think about the other way around. Despite heroic efforts, the "old" kilogram was getting (a tiny big) lighter every time it was handled.
The "new" kilogram will finally be a constant. To a reasonable approximation it hasn't changed at all at this moment time.
>The definition of the kilogram for more than 130 years, the International Prototype of the Kilogram (IPK), a cylinder of a platinum alloy stored at the BIPM in France, will now be retired. It will be replaced by the Planck constant
Maybe I interpreted it wrong (non-native English speaker), but does it say that the Kilogram will be equal to the Planck constant? Shouldn't it be that the definition of the Kg will be based on the Planck constant?
>Although the size of these units will not change (a kilogram will still be a kilogram)
Are our current measurements of the IPK that exact so the old kg is exactly equal to the new Kg? How can they measeure it with 0 error?. It doesn't make any sense to me.
> but does it say that the Kilogram will be equal to the Planck constant?
No, this statement means that Kilogram will give up its place as a fundamental unit to Planck constant. Earlier, Kilogram was used as a fundamental unit, defined by a physical object. Not anymore.
The kilogram will be defined by Planck constant. Namely, m = E/c^2 = hf/c^2.
> How can they measeure it with 0 error?
We can't, all measurements have errors. But we can measure things better than a physical object, which has changed with time. So we only have to measure Plank constant with precision higher than variation of physical object's mass for the purpose of replacing the definition of mass.
I guess it means that we are fixing the value of the Planck constant and deriving measure of kilogram from it. Given the measure of second and metre, a kilogram is the mass so that the value of plank constant is observed to be exactly 6.626x10^−34.
So there was a definition of a kilogram based on an actual physical thing with an arbitrary amount of mass.
Does this new definition essentially try to approximate that mass as close as possible? What is the margin of error there?
I would love to know this for a second as well, although I don't know what we used to measure a second before we locked it to the vibrations of a cesium atom.
First, the assumption was that the Earth's rotational period was 86400 seconds. Mechanical clocks had given us no reason to doubt this was so.
By the mid-20th century quartz timers were able to discern that the Earth has longer and shorter days, as numerous factors cause the spin to speed up or slow down. Instead of a single day the second was taken to be one 86400th part of an average day over the whole year.
A few decades later the availability of atomic clocks made this seem silly and we uncoupled the second from the variably spinning Earth. The completely arbitrary seeming atomic clock definition of a second was basically chosen to be indistinguishable from our last guess at the "averaged over a year" second.
So now packages relying on older values would have to be updated, right? In that case, wow, all those ancient - but usable FORTRAN/C code. Correct me if I am wrong.
Ideally the weight of a kilogram defined by the new definition should be identical to the weight of the old physical "the kilogram" object. The goal of this isn't to change how much a kilogram weighs, it's just to change how it's defined.
For a comparison, it used to be that we measured the speed of light as being 299,792,458 meters/second. Since then, we have defined the meter to be 1/299,792,458 of the distance that light travels in one second. An object that was 1 meter long before is still 1 meter long, but the way we communicate how long a meter is has gone from "it's how long this particular stick in France is" to a precise definition based on fundamental properties of the universe.
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[ 4.0 ms ] story [ 8349 ms ] thread[0] https://youtu.be/c_e1wITe_ig
https://en.wikipedia.org/wiki/United_States_customary_units
What surprised me reading that wiki page is that apparently the metric system was opposed in the US based on religious reasons. That is mind-boggling.
Metric is already used universally in science and engineering, which seem to be the main fields in which consistency across countries matters. I completely agree that in physics, chemistry, engineering, medicine, etc., it is important to use standard units. But what harm is it doing in practice if in everyday life, Americans say things like "I weigh 180 lbs" instead of 81 kg?
The argument that the metric system makes unit conversions easier (e.g., the fact that it's immediately obvious how many meters are in 20 km, but not how many feet are in 12 miles) is true, but not very compelling to me. I virtually never find myself wanting to do these conversions in a non-scientific or non-engineering context, and on the very rare occasions where I need to, I can always look them up on Google.
A good comparison is degrees Celsius, which are just as arbitrary/unscientific (the standard metric unit is the Kelvin). Somehow people around the world get along fine using Celsius.
Celsius is literally the same scale as Kelvin, just shifted so that 0c = water freezing.
So you end up needing negatives, and decimals.
Fahrenheit is scaled such that 0 is about the coldest it gets where I live, and 100 is about the hottest. (Very approximately, but close enough). That strikes me as a lot nicer in practice (since 99% of the time people are talking about temperature, it’s related to weather) than something based on the physical properties of a particular substance.
Also water freezing at 0 and boiling at 100 is only valid for a specific, non-metric, air pressure.
You don't realize how arbitrary Fahrenheit and Celsius are until you try cooking at altitude. When I make breakfast in a particular town I frequent, it takes almost an extra minute to boil an egg.
It seems safe to say it's a point of ongoing friction, especially on things like international trade.
[0]: https://space.stackexchange.com/questions/12391/iss-nuts-and... [1]: https://mars.jpl.nasa.gov/msp98/news/mco991110.html [2]: https://www.chihaklaw.com/Articles/Confusion-over-metric-mea...
I still stand by my argument that it does not matter much for everyday life.
As for "why" to have them, well there isn't a good reason intrinsically -- if there were a way to magically convert the US to metric overnight, it wouldn't bother me. It just seems very unlikely and difficult in a country as huge and culturally diverse in the US. Especially since, by the standards of the rich/developed world, the US is pretty poorly educated, and also very difficult to govern (Obamacare, a law that would have seemed like a moderate reform, relatively simple to pass in any parliamentary system, is the most radical change in any area of policy enacted by the US federal congress in the last decade).
The thing a lot of people miss about the ultra-gridlocked US system is that there's a huge gulf between it being obvious to most people that "we should enact some policy" and anything actually changing. The best answer to "why doesn't the US do this or that" is often just "its political institutions can't".
Since it's so unlikely to change, and given my argument that it isn't a big deal in practice, I guess my main point is that we rationally-minded people should stop worrying/complaining about it so much.
Think about it not for the benefit of the current generation who would be forced to burden the switch, but for the next generation who could reap the benefits.
I think one issue is that by growing up with US units and then using a second system for science and engineering, it can make American students studying those topics feel like they are in an unfamiliar territory and interfere with their intuition. Most will eventually overcome this through practice and become fluent in both systems, but it's still a barrier. Science becomes a Special Discipline requiring Special Language different than what your family uses at home. Like if all science were still done in French or Latin, and you needed to study those to read a paper.
Until you have met people who grew up abroad measuring their height in cm and their weight in kg, preparing food from recipes listing ingredients in grams and mL, to whom those units are completely natural for daily life and are also the same ones they use at work when designing machines and filling test tubes, it's easy to feel that US units simply "are" the units suitable for daily life, as though that were a universal truth and not just a local cultural oddity.
Not to mention the massive net costs of having suppliers worldwide making extra sets of almost identically sized components that nonetheless aren't interoperable. Screws with 3 mm and 3.175 mm diameter, etc.
You realize this is still a problem for most of the world and needing to learn English, right? :P I'm hoping we can solve this in my lifetime with everyone knowing one standard language through education as a child, but as it stands the struggle is real for many of my fellow non native English speakers.
That said I agree with you, all these differences are a pain and I'm confronted with them way too often in my daily life.
It seems like this is rapidly becoming the case in the Western world, and that that language is English.
As you will discover people often use religion as an excuse for things they anyway want to do. Usually they are people who only pay lip service to their religion.
Someone didn't want to use Metric. Religion doesn't actually have anything to do with it.
> That is mind-boggling.
It shouldn't be. I assume you are surprised that religion is involved in this, but actually it is not. If they were Atheist they would have the same objection, just using different words.
Basically you need to distinguish between people being people, and people acting in a certain way because of religion. This is an example of the former.
So, for liquids,
2 tablespoon = 1 ounce 2 ounce = 1 jack 2 jack = 1 gill 2 gills = 1 cup 2 cup = 1 pint 2 pint = 1 quart 2 quart = 1 pottle ( ½ gallon) 2 pottle = 1 gallon
I find it much easier to switch units and do conversions in my head, especially when scaling recipes.
With respect to base-2 fractional length measurements, I just find it much easier to work with fractions than than with decimals. Half of ⅛ is ¹/₁₆ with next to no thought. I don't need to do division of 25 to get 12.5. It's a personal thing, but I find it nice.
The fractional system isn't perfect for all use cases by any means. (My understanding is that a lot of machining just deals with decimal inches directly.) I just find it convenient for many everyday tasks. I'm also weird, I guess, in that arithmetic on fractions feels easier than on decimals.
Thinking more about my original statement, a lot of it has to do with halving (e.g. finding a center) being a common operation for many tasks. It also helps that most things are sold in those fractional increments too :)
(Just making up a number here) 3.937" stroke? Why on Earth... Ah. 100.0mm. That's why.
I have been using metric since the seventies. About the only things I still use imperial for are people's height and the length of fish (for undersize/oversize determination). In regards to woodworking, I much prefer metric over imperial and the millimetre over just about all other base units.
That's just my opinion.
If you go overseas outside of North America, you find that the sizes of everyday objects are conveniently sized in metric, and building codes and standards and material strengths and densities are specified in SI units, and suddenly working with the metric system in those industries is easy and convenient.
Do you deal with building insulation? How would you interpret a material spec of "1 BTU ft/(in^2 hr °F)"? I had to work with these units in the US and it was not at all convenient.
In Canada, all our building code, material design codes, etc are in metric, and yet we are still using US units for day to day design.
What is the common width and thickness of drywall sheet you can buy and the hardware store? What door sizes are available? What size of screws are cheaply available in Canada?
I think these factors are far more likely to affect what unit of measure is commonly used in construction, rather than any intrinsic merit of the measurement system. If you were shopping at a Japanese or German hardware store, you'd probably suddenly find all of those 12 foot dimensions quite frustrating and not be at all surprised to find the hard-hat-wearing locals happily using the metric system for the same tasks.
I thought they did that long time ago.
I recently ordered a picture frame from Amazon. It came in its packaging box, which was placed in a box by the manufacturer. That box was put in another box by Amazon and shrink wrapped to a large piece of cardboard, which was then put inside yet another box.
On the surface, it seems crazy, but Amazon did manage to get it to me undamaged.
I do happen to have the previous generation time standard in my garage, though, a HP 5061A Cs clock.
They are. They are made identically to the primary.
Fingers crossed. :)
It seems that they settled on this definition because a Kibble balance[1] has shown to be precise and practical enough:
> Accuracy criteria were agreed upon in 2013 by the General Conference on Weights and Measures (CGPM) for replacing the current definition of the kilogram [...] with one based on the use of a Kibble balance. These criteria have since been met, and the definition of the kilogram and several other units will change on May 20, 2019, World Metrology Day, which celebrates the establishment of the SI, or metric system, in 1875, following the final vote by the CGPM on November 16, 2018.
[1] https://en.wikipedia.org/wiki/Kibble_balance
Are other units still tied to physical measures, or is this all of them?
As you stroll Paris, you can still find various meter secondary standards - bolted onto public buildings to aid in commerce back in the day.
https://xkcd.com/2073/
In university I just gave up trying to understand why we even needed the Avogadro constant / mole as a fundamental constant. It still confuses me. Why have a difference between molar mass and mass? Why couldn't it just be "1" and everything else change around it?
When we discuss the mass of a neutron and we say "one neutron weighs one u" then we discuss the mass of an electron and we say "one electron is 5.4858×10−4 u" and "one proton is 1.0072764 u" then we add them up and say "one hydrogen atom is 1.00794 u while one helium atom is 4.002602" (forgetting some complications for a moment) are we not just summing likes?
Or is it just that since mass is defined in Planck and time / distance terms that we need to relate it to counts of things? Theres a gap there I don't understand. Can we not just say "we measured a proton's mass and it is u"? Am I making a jump there?
There's a complicated technical topic which you're still not understanding. There's no indication it's a question you could easily answer yourself, and you're posting it in a forum of people likely to find the topic interesting, some of whom might give an answer that clicks for you.
Well done, IMHO.
> the Avogadro number was initially defined by Jean Baptiste Perrin as the number of atoms in one gram-molecule of atomic hydrogen, meaning one gram of hydrogen. (from Wikipedia)
(It's since been refined to be 12 grams of carbon-12.)
So a mole is defined to be approximately one gram worth of protons and neutrons. We use it because grams are a significantly easier unit of mass for humans to work with, than like individual particles.
It used to be the case that the mole was an experimental value equal to the number of atoms in a certain mass of a certain something. That is no longer the case with this revision. It is a fixed, never changing integer constant.
This does mean that 1 mole of carbon-12 is no longer exactly 12 grams. But it is approximately 12.0000000 grams, which is within the best we can experimentally measure today, so nothing changes in practice as a result of this update except first chapter of an introductory chemistry textbook (good excuse to push out a 9th edition for $250!).
Therefore it is accurate to say now that whereas before the Avogadro's number was experimentally determined based the exact expressed mass of a carbon-12 atom relative to a platinum-iridium cylinder in Paris (the old kg), it is now the case that the expressed mass of the carbon-12 atom must be measured relative to the a kg definition based on Planck's constant.
(I say "expressed mass" because this situation is a little confusing... I'm talking about the numbers we write down expressing the mass as a multiple of some standard kilogram. That reference mass changed, not the actual inertial mass.)
EDIT: Or you can just read the draft of the agreement that was voted on. The definitions are on the first page:
https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN...
https://en.wikipedia.org/wiki/Fundamental_constant
A fundamental constant isn't just any fixed constant. It's specifically a constant that describes a fundamental property of the universe.
For instance, c describes the speed of light in a vacuum, and is a fundamental physical property of the universe.
Avogadro's constant isn't the same thing. It's just a number that humans decided would be useful. We could have fixed it to any other number; there's nothing fundamental about the number ~6.022e23.
Edit: I think your question boils down to "Why do we have two separate units for mass, u and kg, connected by the Avogadro constant?" Most answers dismiss your original question as Avogadro constant is not a unit. But u is a unit and it's the point why we have this constant.
Edit2: To further emphasize my point look at the mass of neutron[1]. It's listed both in kg and u. Note the number of decimal places.
[1] https://en.wikipedia.org/wiki/Neutron
Why do I need both kg and u as fundamental constants?
I believe the comments here have answered it. It isn't something weird, like quantum gravity or some such. If I understand everyone correctly it's just a practical decision we made at some point because we didn't want mass to be in u and that's that.
I feel better about it now.
That's not a whole answer, but it may be helpful for your thinking.
EDIT: A simple example would be if you were trying to make water - H2O, from hydrogen (H2) and oxygen (O2). The molar ratio is 2:1 - but in doing a practical synthesis, that doesn't tell me how much mass/volume of gases to actually mix up. Avogadro's number and molar mass is what I need to turn those into practical units to work with.
So it's pretty much chosen to get integer-ish units with common things you work with like carbon - i.e. 1 mole of carbon of is ~12 grams.
Disclaimer: I took high school chem, that's it.
Cf binding energy, electron excitation, E=mc^2 (the m there is m0, the rest mass; the full equation includes the momentum and "relativistic mass").
The situation is actually worse for hydrogen (cf hydrogen bonding).
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.htm... is a pretty coherent and readable approach to the subject.
That was actually an alternative proposal for redefining the kg. The kg would have been 1000/28 the weight of a mole of silicon-28; you could build a sample by counting 6.023x10^26/28 atoms of silicon-28, and making a sphere out of them.
Initially the watt balance seemed to be less precise than atom counting, but then it was improved to a point where defining the kg on top of the mole became less convenient than the definition they are adopting now.
Because the SI system is redundant anyway one constant more or less doesn’t matter much.
If you want a truly minimalist system you can use CGM or MKS.
Using mole (based on Avogadro constant) makes it easier to do statistical mechanics, but it's not a microscopic property like mass.
The flip side is that the molecular count is less useful to us in the everyday world. We can gauge the weight of a kilogram much more than we can gauge a septillion molecules. And if we're trying to figure out how much stuff a shelf can hold before it collapses, it's the weight that matters, not the actual molecular count. (Note for pedants: in the familiar environment of Earth's surface, mass and weight can be treated as the same quantity in most cases.)
So mass and molecular count are both very important quantities that have importance in different fields of science, and they don't have a trivial relationship to each other. Avogadro's constant and molar mass is a way to express their relationship.
On the other hand it is fundamental-ish constant, because it is defined as arbitrarily scaled result of inherently uncertain measurement. And the new definition of kilogram had significantly increased the attainable certainity of such measurement (to the extent that it is uncertain due to practical issues, not by definition). The other proposed replicable definition of kilogram (ie. mass of Si monocrystal wih particular geometry) would fix the definition of mole as some known and defined number, but would be significantly harder to replicate (because it would define how to produce an artifact in contrast to how to directly measure the mass as the ratified definition does)
If instead of g/mol, we referred to molecules/g -- we would end up populating tables and charts with really big numbers. This would make lookup tables hard to read, difficult to publish, and hard to work with. Imagine if you had to do math with a bunch of 10^23 exponents all of the time.
Instead, it was agreed to effectively pull out a constant value from each of those to make the math significantly easier. Now, instead of dealing with a lot of big numbers, all of the lookup tables could now list smaller g/mol values. And we would be left with just the one single large (Avogadro's) number in the equations.
Honestly, we don't need a set mole constant, but it makes chemistry significantly easier to do so. Unlike the other constants mentioned in the OP, Avogadro's number is completely arbitrary. It could be '1' as the parent suggested, except then it makes the rest of the math more difficult.
Even for this SI overhaul, we didn't really even need to redefine the mole, except for the fact that it was previously defined in terms of the old kg. This was just "fixing a glitch".
What if it was just set to 10^24 then? Much easier to remember and serves the same purpose.
If it was 1 it would work too, since the SI system already has a way to deal with large numbers: prefixes. So we might wrote Ymol for yotta mole = 10^24 mol.
I came to complain about the article calling the mole a "base unit of the SI", and this seems like an appropriate thread.
Why is the mole a defined unit at all? As far as I understand things, "one mole" is the same thing as Avogadro's number -- neither can be a unit, because they're both dimensionless constants (well, they're both one and the same dimensionless constant). Applying actual units, "one mole of water molecules" is the same thing as "Avogadro's number of water molecules". Avogadro's number, and therefore the mole, is the conversion factor between atomic mass units and grams. Similarly, 3 is the conversion factor between feet and yards, but nobody thinks 3 is a fundamental base unit of the imperial system. The foot is a base unit of the imperial system, measuring length, the yard is a non-base unit also measuring length, and 3 is a number with no special relationship to the system at all. It would be total nonsense to say that yards are defined by reference to 3. How is Avogadro's number different?
Wouldn't "fixing the glitch" be abandoning the idea of calling the mole a unit in the first place?
There is a concept of "the Avogadro constant", which is defined to have units of mol^{-1} (at least, according to a cited statement on wikipedia), but that is not a coherent concept -- since mol is dimensionless, mol^{-1} is also dimensionless.
Just look at https://en.wikipedia.org/wiki/Mole_(unit)#Criticism :
> Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole as a unit like the metre or the second have arisen:
> the number of molecules, etc. in a given amount of material is a fixed dimensionless quantity
> the mole is not a true metric (i.e. measuring) unit
Or look at https://en.wikipedia.org/wiki/Atomic_mass_unit :
> One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.
amu and g are both units of mass, so 1 amu = 1 g/mol is an explicit statement that mol is dimensionless.
Calling mol a unit won't accomplish anything except corrupting your dimensional analysis. mol is not analogous to the SI units meter, second, ampere, gram, kelvin, etc. -- it is analogous to the SI prefixes kilo-, mega-, milli-, micro-, nano-, etc.
>>> Avogadro's number, and therefore the mole, is the conversion factor between atomic mass units and grams.
But that doesn't intertwine anything with grams. I went on to say
>>> Similarly, 3 is the conversion factor between feet and yards, but nobody thinks 3 is a fundamental base unit of the imperial system.
>>> It would be total nonsense to say that yards are defined by reference to 3.
You need to convert from mass to numbers of molecules, which means you need to divide it by the mass of a molecule. The mass of a molecule is determined by the sum of the weights of each of the atoms, themselves the weights of their constituent nucleons [1]. If you fix the weight of a nucleon to be 1 (that is, we measure in daltons), then computing the weight of a molecule such as glucose (aka C₆H₁₂O₆) in daltons is a trivial formula. All you need is a periodic table that lists atomic weights, which is every copy you find a chemist using. It's worth noting that the resulting molecular weights are going to be independent of whatever measuring system you want to use [2], whether it be grams, ounces, alien flits, what have you.
Now you need to convert the mass of your substance into a count of "stuff-loads" of molecules. The simplest and most idiotic thing to do is to define a "stuff-load" to be the amount of molecules in a unit mass if it weighs 1 dalton--in other words, you make this formula be exactly one. In SI, the unit mass for this equation is grams and the "stuff-load" is the mole. If we were using US ounces as the unit mass, we'd define an ounce-mole and use that instead of SI moles.
Put another way: we define a mole such that the constant in the computation of moles from molecular weight and mass is exactly 1. Avogrado's constant itself is merely the inverse of the mass of a nucleon when expressed in grams.
[1] Okay, there's a lot more that goes on into the computation of mass. In terms of the mathematical error, though, other sources of error (e.g., wrong isotopic ratio) are going to matter before these come up.
[2] Up to the slight adjustment (about ±1%) of what you consider the weight of a nucleon to actually be.
> Equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.
This law, for example, explains why hot air rises. Take two equal quanties of the same gas at the same pressure. They will have the same volume. Now, heat one quantity of gas. By this law, that gas will have a larger volume at the same pressure. Because it has the same amount of mass distributed over a larger volume, it must be less dense. Therefore, it rises.
The law as quoted doesn't say what happens when the temperature change. Maybe it gets more dense? Be more specific.
It will have larger volume, but that is not implied by Avogadro's law. That law is about the surprising property of all gases: no matter the chemical nature of the gases, if they all have same T and P, they all will have same number of molecules per unit volume.
We need a means of converting mass to number of atoms so that we can predict how much mass of a specific product will be formed, what the limiting reägent will be, &c.
It also helps to define concentrations based on number of moles in a L of solvent (Molarity vs g/L) for the same reason.
So Dalton took the lightest one, hydrogen, and defined a mole as the stoichiometric amount equivalent to that in 1g of hydrogen. Looked at that way, it's a pretty solid choice.
And if nothing else, it can be derived: a mole is the number of atoms in a kilogram of carbon-12. Done.
No longer is. Not quite.
It serves as a link between human-scale and atomic-scale observations, classically needed for chemistry performed on Earth by humans. This link must exist, as others mentioned, for stoichiometric calculations (e.g. air/gas mixture in a internal combustion engine). For much of modern scientific history, it was deemed useful to scale into an easily eye-visible human scale (the gram). [0]
[0] https://en.wikipedia.org/wiki/Avogadro_constant#General_role...
https://en.wikipedia.org/wiki/Mole_(unit)#Criticism
"the new changes will have wide-reaching impact in science, technology, trade, health and the environment, among many other sectors."
Am I missing something?
Certain types of scientific instrument will need to be recalibrated to meet the new definitions.
And if you buy a kilogram of something and they accidentally short you by a few micrograms, haven't you only overpaid by a few parts per billion? Even on a billion dollar order you've only overpaid by a few dollars...
For your second question, agreed - no trade deals care about the accuracy of the new kilogram vs old.
According to the first result in Google https://brightside.me/wonder-curiosities/the-16-most-expensi...
> 1. Antimatter — $62.5 trillion per gram
> 2. Californium — $25-27 million per gram
So the difference is a few dollars per milligram of antimatter, and less than a cent per kilogram of Californium.
From https://en.wikipedia.org/wiki/United_States_Bullion_Deposito...
> As of November 2017, Fort Knox holdings are 4,582 metric tons (147.3 million oz. troy), with a market value of over $100 billion.
So the difference is a few hundred dollars.
$100 million dollar rounding error.....
Hint: not by one microgram.
https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN...
And until then, all the metric fanbois will constantly tell you that metric is superior to imperial because its measurements are immutable. Until suddenly they are.
Specifically the international yard equals 0.9144 meters and the international pound equals 0.45359237 kilograms
There literally isn't another definition, in the US when you say "100 yards" the only legal meaning that has is 91.44 metres, which is whatever CGPM / BIPM says it is.
1/3 m = 33.33 cm, 1/3 ft = 4 in
1/4 m = 25.00 cm, 1/4 ft = 3 in
1/6 m = 16.67 cm, 1/6 ft = 2 in
This is why imperial makes more sense to me than metric. If we had a base-12 number system, metric would be perfect, but base-10 is terrible under division. For practical divisors like these, imperial shines.
If you're doing science, metric makes more sense because units work out. But most all US science has already adopted metric.
Something is 3m x 0.3cm, what area is that?
If that's one internal face of a container what width will hold a pint/litre respectively?
Using the metric system you'll rarely write 1/2m, as fractions are not what a person used to metric would default to. That is why 1/6m looks so weird as no one would use it like that, but if you write it 0.5m now it's obvious we are talking about 50cm, or 500mm.
BUT,
In those examples you are not using the system, you are just using one unit. If the question were, for example, what is the mass of the water contained in a 1m x 1m x 1m box, then the answer is obvious which system is by far the most sane one.
You're not disagreeing, the GP said
> If you're doing science, metric makes more sense because units work out. But most all US science has already adopted metric.
Your question asks for mass of a cubic meter of water, presupposing a typically scientific quantity (mass, instead of weight) and presupposing that a cubic meter (why not a cubic foot?) of water is a useful collection of water for some purpose. Fine, use metric. But imperial units as a system are made for practical everyday utility, which your example doesn't presuppose. On the other hand if we imperial users run across a situation where metric seems more useful, fortunately we can precisely convert, so it doesn't really matter.
In other places of utility (such as engineering disciplines) adopting a unit agnostic approach is the best. Some fields don't use either imperial or metric units but their own domain specific things, and software can always present units in whatever preference someone has or whatever is the most useful for the moment.
Nobody is arguing against more precise definition of standard values, which is why Imperial units these days are themselves defined in terms of SI units. So if the meter were to change, for example, so would the US foot.
The meter was originally an actual physical rod (you can see the prototype on display at the fascinating French Musée des Arts et Métiers). Now it's based on the speed of light in a vacuum.
The kilogram was a physical mass (and, yes, it was evaporating). Now it's finally defined in terms of the Planck constant, the second, and the meter.
The second was originally 1/86400th of Earth's day. Now it's based on the radiation of cesium-133 (I don't really understand how this is measured).
The ampere was originally defined based on depositing milligrams of silver from a solution of silver nitrate; it's now based on newtons and meters.
The kelvin was originally defined based on water; it's still defined based on water.
The mole hasn't really changed much? It's based on the number of atoms in a kilogram of carbon.
The candela was originally based on a literal standard amount of light emitted by candles made from dead whales; now it's based on radiation from light sources of a specific frequency and an intensity based on the watt (which relies on kilograms, meters, and seconds).
More info from an older Veritasium video: https://www.youtube.com/watch?v=ZMByI4s-D-Y
https://youtu.be/VHd4HPmz5aE
I guess for science seconds are basically the only measure of time that usually matters?
I'm not sure why a metric hour didn't catch on.
a 7 day week gives two days weekends every 5 days, so you quickly lose personal time on the 4 day week.
It’s also historical and pretty hard to change the basic units of time.
Our biggest revolution yet: extending the length of the day by 16%!
EDIT: More specifically, if you take an average rotation of the Earth as 86164.1 seconds, and divide by 10, then 100, then 100, you get 0.861641, which would be the conversion from our seconds to the metric second in that scenario. Likewise, the metric minute would be 86.1641 of our seconds or about 1.43607 of our minutes, the metric hour would be 8616.41 of our seconds or 143.607 of our minutes or 2.39345 of our hours. The day would be slightly shorter than our day, reducing the need for leap seconds to keep our time aligned with the sun.
[0]: https://www.nasa.gov/topics/earth/features/japanquake/earth2...
But an even bigger issue is that the sidereal day (one 360° rotation of Earth as measured against distant stars) is not 24 hours but roughly four minutes less. And the length of the solar day also varies over the year due to the slight eccentricity of Earth’s orbit—days near perihelion are slightly longer than near aphelion. And then there are the higher-order effects caused by gravitational interaction with other planets...
Speaking of circles, SI hasn't fixed Hz vs rad, have they?
¹ https://en.wikipedia.org/wiki/Superior_highly_composite_numb...
I don't think so.
Anyone who hasn't heard of the Hz/radian issue should see the "Hz" definition in the units definition file shipped along with Frink - if you like finding interesting rants in unexpected places, it's delightful:
https://futureboy.us/frinkdata/units.txt
Really? :)
[1] https://en.wikipedia.org/wiki/Perfect_Imperfection
Rounding up to 4Ks is a reasonable substitute for an hour. Also gives you the convenient 15min ~ 1Ks or "a quarter of a metric hour."
(Just kidding.)
Calendars are hard because you've got multiple inconveniently disparate sources of information you want to unite: universal constants on the one hand (such as the second being tied now to atomic vibration) and more "local" concerns such as the orbital position of the earth with reference to the sun, the moon, other neighboring objects in the solar system.
Vernor Vinge's novels, as one example, use metric prefixes and seconds exclusively (this is referred to as Metric time [1]), which is a fun thought experiment. The biggest complaints are that the units aren't necessarily great for human activities and definitely don't align well with minutes/hours/days/weeks/months.
Hectosecond is close to a minute, but slightly larger (1.666 minutes). Kilosecond is about 16.666 minutes long, which is the closest unit to an hour. It's almost a useful quarter-hour (but again it doesn't line up that well). But then you hit the order of magnitude wall and the next prefix up is Megasecond which is nearly, but not quite a fortnight (~11 days), and Gigasecond is just shy of 32 years. You long at that point for more prefixes between Kilo-, Mega-, and Giga- if you are using seconds as base unit at that point, especially living on Earth and trying to coordinate calendar weeks, months, years. (There are non-standard prefixes Myria- (10^5), also from the French revolution, and Hebdo- (10^7) which are almost useful enough here to beg them to be standardized.)
[1] https://en.wikipedia.org/wiki/Metric_time
In Vernor Vinge's fiction, spacefaring humans even measure time in kiloseconds and megaseconds. 1 ks is slightly more than a quarter of an hour; 1 Ms is about eleven and a half days.
> Instead of hours and minutes, the mean solar day is divided into 1000 parts called ".beats". Each .beat is equal to one decimal minute in the French Revolutionary decimal time system and lasts 1 minute and 26.4 seconds (86.4 seconds) in standard time. Times are notated as a 3-digit number out of 1000 after midnight. So, @248 would indicate a time 248 .beats after midnight representing 248/1000 of a day, just over 5 hours and 57 minutes.
And really, you can use kilo seconds or terra seconds just as easily as micro seconds. Its just harder to relate to as human time-scales.
>The mass of the international prototype of the kilogram m(K) is equal to 1 kg within a relative standard uncertainty equal to that of the recommended value of h at the time this Resolution was adopted, namely 1.0 × 10-8 and that in the future its value will be determined experimentally,
Is the Planck simply the most standard deviation the kilogram can stray from now?
>The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.
So mass is now some sort of length times a given elapsed time?
Given the definition of metre and the definition of second, the kilogram is whatever value that makes the Planck constant h precisely 6.62607015×10−34 kg m^2 s^(-1).
Original 1 kg was the mass of a cubic decimeter of water at 4 C at 1 ATM. Why a cubic decimeter at 4 C? Water is densest at 4 C and a cubic decimeter of it is a weight that people can work with on a day-to-day scale. Unfortunately this was a bit hard to measure so they made the IPK (international prototype kilogram) which was a lump of metal. Fast forward 100 years and the lump of metal proved to be too unreliable for modern standards as it kept losing very small amounts of mass, also it Earth's gravity isn't even so it requires you average it out and then calculate the local offset and a whole bunch of other weird things that can mean a microgram or two. This is inconvenient but we still needed a way to say "1 usefull measurement of mass" but unfortunately in the universe 1 Planck's constant is far too small to ever use daily. Thankfully it has become easier to accurately measure Planck's constant against the IPK so now we have solidified 1 kg to be exactly what we measured.
The nice thing is 1 kg will forever be the same thing now and is easy to measure to extraordinary accuracy. The downside I think you're asking about is 1 kg by itself isn't some significant relation of the physical world, it's just a useful-in-daily-life multiple of mass as defined by Planck's constant.
Is it anyone with a kibble balance can now certify calibrations? How do you know your kibble balance is as accurate as the next guy's kibble balance?
https://www.nist.gov/si-redefinition/kilogram-kibble-balance
Edit: Found some information explaining this from NIST: https://www.nist.gov/si-redefinition/kilogram-disseminating-...
https://www.nist.gov/si-redefinition/nist-do-it-yourself-kib...
It's much simpler to understand looking at it with a watt balance, even though it's not going to be as precise or accurate as a kibble balance [1]. Basically now anyone with access to a kibble balance and the right set of numbers/information can make an exact 1kg object.
[1] https://www.youtube.com/watch?v=ewQkE8t0xgQ
It means the right answer is freely available to anyone (with a bunch of scientific equipment).
I like to use metrology labs as an example of something people often take for granted (measuring things) and showing how deep that invisible rabbit hole goes.
> Everything on the right side of that equation can be determined to extraordinary precision: The current and voltage by using quantum-electrical effects that are measurable on laboratory instruments; the local gravitational field by using an ultra-sensitive, on-site device called an absolute gravimeter; and the velocity by tracking the coil's motion with laser interferometry, which operates at the scale of the wavelength of the laser light.
Current is measured in amperes, derived from the charge (in coulombs, defined from the charge of a proton) and time (in seconds, defined from the vibration of a Cs atom). Gravitational acceleration is measured in ms^-2, derived from length (in metres, defined from the distance travelled by light in a vacuum in a second) and time. Velocity is also derived from length and time.
With these new defined constants (including the Planck constant), all of the instruments could now be calibrated by observing natural phenomena and a whole lot of counting.
[0]: https://en.wikipedia.org/wiki/Mendenhall_Order
> "[...] the size of these units will not change (a kilogram will still be a kilogram) [...]"
The size of electrical units is changing slightly. According to this BIPM document [1]: "The transition from the 1990 convention to the revised SI will result in small changes to all disseminated electrical units. For the vast majority of measurement users, no action need be taken as the volt will change by about 0.1 parts per million and the ohm will change by even less. Practitioners working at the highest level of accuracy may need to adjust the values of their standards and review their measurement uncertainty budgets".
[1] https://www.bipm.org/utils/common/pdf/SI-statement.pdf
It used to literally be defined as the mass of "IPK" - the international prototype kilogram. https://en.wikipedia.org/wiki/Kilogram#International_prototy...
This switch now defines it in terms of the force equivalent of the energy exerted by a single photon - if my understanding is correct.
Theoretically a more scientifically sound way of keeping 1 kg a constant permanently.
The IPK was 1 kg and the copies of it were all slightly heavier or lighter, for argument let's say IPK1 was 1.1 kg and IPK2 was 0.9 kg. Now that we have a constant for the mass of 1 kg, all of those IPK's will now have a new mass relative to the new definition.
Unless the new definition was based on the current IPK and set its mass as of today as the standard, and that standard now will be unchanging?
Correct. The current IPK will still be 1kg to within margin of error at the time the new definition comes into effect, but any further changes to it will make it, for the first time, drift away from that value.
The "new" kilogram will finally be a constant. To a reasonable approximation it hasn't changed at all at this moment time.
Maybe I interpreted it wrong (non-native English speaker), but does it say that the Kilogram will be equal to the Planck constant? Shouldn't it be that the definition of the Kg will be based on the Planck constant?
>Although the size of these units will not change (a kilogram will still be a kilogram)
Are our current measurements of the IPK that exact so the old kg is exactly equal to the new Kg? How can they measeure it with 0 error?. It doesn't make any sense to me.
Further down, the article says: "The kilogram – will be defined by the Planck constant (h)."
No, this statement means that Kilogram will give up its place as a fundamental unit to Planck constant. Earlier, Kilogram was used as a fundamental unit, defined by a physical object. Not anymore.
The kilogram will be defined by Planck constant. Namely, m = E/c^2 = hf/c^2.
> How can they measeure it with 0 error?
We can't, all measurements have errors. But we can measure things better than a physical object, which has changed with time. So we only have to measure Plank constant with precision higher than variation of physical object's mass for the purpose of replacing the definition of mass.
Does this new definition essentially try to approximate that mass as close as possible? What is the margin of error there?
I would love to know this for a second as well, although I don't know what we used to measure a second before we locked it to the vibrations of a cesium atom.
First, the assumption was that the Earth's rotational period was 86400 seconds. Mechanical clocks had given us no reason to doubt this was so.
By the mid-20th century quartz timers were able to discern that the Earth has longer and shorter days, as numerous factors cause the spin to speed up or slow down. Instead of a single day the second was taken to be one 86400th part of an average day over the whole year.
A few decades later the availability of atomic clocks made this seem silly and we uncoupled the second from the variably spinning Earth. The completely arbitrary seeming atomic clock definition of a second was basically chosen to be indistinguishable from our last guess at the "averaged over a year" second.
https://www.youtube.com/watch?v=Oo0jm1PPRuo
For a comparison, it used to be that we measured the speed of light as being 299,792,458 meters/second. Since then, we have defined the meter to be 1/299,792,458 of the distance that light travels in one second. An object that was 1 meter long before is still 1 meter long, but the way we communicate how long a meter is has gone from "it's how long this particular stick in France is" to a precise definition based on fundamental properties of the universe.