Yeah, moles are just a crutch for folks who are afraid of scientific notation, and candelas as a base unit serve no useful purpose whatsoever that I can discern.
There’s something called history. The SI system attempted to replace an even messier non-system of everyone using local or personal units. It did so by the best means available at the time and was a big success, but it was not globally accepted and is still not accepted in a couple of recalcitrant countries. Some new units were added over time, and the base definitions of some changed, but now we have serious inertia behind the units themselves and replacing the system with a philosophically purer one makes no more sense than teaching 1st graders 1 + 1 by way of Bertrand Russels’ proof.
Because the SI system isn’t meant to be a statement about physical laws. It’s a base system for scientific communication and practical metrology.
But why didn’t you choose 1 second, or 53 seconds, or 0.000007 seconds? You chose something arbitrary, so you’d better give that choice a name. Let’s call it a “meter”.
I don’t get what you propose as an alternative to defining an ampere. How would you express 1 A using only kg, m, and s? It’s true that you need to have kg, m, and s already defined to make the SI definition (as indicated by the arrows in diagram at the top of the SI units wiki page). But that doesn’t get you a unit for current. Arbitrary choices about an arbitrary physical system are needed, and those need to be agreed upon and conveyed.
Moles are defined because it’s much easier to measure mass than it is to count 10[sup]22[/sup] of something. If the mole were defined as a fixed number, then we would have poor understanding of how much a mole of something weighed (massed). As it stands, we know that 1 gram of something weighs 1 gram exactly, at the expense of not knowing exactly how many atoms/molecules that corresponds to. But that’s okay, because we can’t count all those atoms/molecules anyway (though folks are getting close to making the inverse definitional path sufficiently precise and practical).
Oh, I don’t deny that moles are useful. They’re just not fundamental.
And the candela as a base unit opens up a whole can of worms with other human-based units. If we’re recognizing the candela, how about the rem, for instance?
The rem? What you mean the unit that’s now defined in relation to the SI unit sievert?
OK, then, the sievert. It’s a good and useful unit, sure, but nobody claims that it needs to be a base unit.
And it’s exactly analogous to the candela. If we want to talk about radiation in general, we can use the gray, which is equal to 1 m[sup]2[/sup]s[sup]-2[/sup]. If we want to talk about radiation’s effect on human tissue, we use the sievert, which is like the gray but weighted according to various factors relating to human tissue. If we want to talk about light intensity in general, we can use the watt, and if we want to talk about light’s effect on the human eye, we use the candela, which is weighted according to various factors relating to the eye.
I think what I said was misconstrued slightly. I’m not saying that the meter (or amp, or whatever) isn’t a useful unit. I just don’t get why it’s a base unit, as contrasted with derived units. I’m not trying to say we should switch to Planck units.
I get the history behind this; the units were largely set before we even knew the proper physical relationships. And they have made some progress in “philosophical purity”, in particular for the meter, which is defined in terms of the second. They just forgot to stop calling the meter a base unit when it’s clearly a derived unit.
As mentioned, for most (all?) of the others there are efforts underway to make the definitions more explicit. So eventually we’ll fix the Avogadro constant and then the mass of a mole of carbon will be the experimental value, just as it should be. But honestly, I don’t see why we can’t do that now. For whatever chemistry calculation you’re doing, the error term is going to divide out in a way that it doesn’t matter which way you do it.
Ultimately, I’m just arguing in terms of “degrees of freedom”. The meter and second, despite being two base units, only has one degree of (physical) freedom–if someone were to swap your cesium 133 for an atom of cesium 135 as a prank, both units would change in equal proportion. Mass is another degree of freedom, but not so with the remainder.
(and yes, I second Chronos’ arguments about the candela)
Are you sure that’s not what you’re saying? When you say that the meter is derived from the second, you’re saying to treat one particular physical constant, c, as inherent. Similarly, when you’re calling the ampere derived, you’re effectively saying to treat the magnetic coupling constant (closely related to the electric coupling constant and c, of course) as inherent. And that’s not an unreasonable thing to say: Physical constants like those appear to be about as inherent as we can get. But why stop there? hbar and G are equally inherent… and once you’ve got hbar, c, and G, you’ve got the Planck units, and everything is derived.
No, wait, I think I’ve got it now: You’re not talking about how the units could be defined, just in terms of how they actually are now? I guess I see the point, though one could still argue that the kilogram is the only “degree of freedom” left: If someone swapped your Cs-133 for a Cs-135, you could still get a Cs-133 and fix the prank (hence why we use a definition like that). But if someone swapped out a different hunk of precious metal, we wouldn’t really have any way of knowing, much less fixing it.
“Base” as used in “SI base units” is not the antonym of “derived” as you are using it. Sticking with the ampere example, how are you suggesting to express “1 ampere” using kg, m, and s? Note that you can express “1 joule” in terms of kg, m, and s. It’s simply “1 kg m[sup]2[/sup] / s[sup]2[/sup]”. Thus, joule is an SI derived(*) unit and not an SI base unit. You cannot do the same with “1 ampere”. Thus, it is a base unit.
(*) “Derived” in my “SI derived unit” has a meaning different from your use.
I echo Chronos here.
That just makes velocities stay constant. Suddenly people start living to be 150 years old, and we can’t explain why. It’s still a problem.
I suppose I could have just stuck with meter instead of ampere. If you have seconds already defined, how do you get to meters? You can’t. The speed of light happens to be a handy, measurable physical quantity that involves both time and distance, so you could define a meter by injecting that quantity into the definition. But that’s an arbitrary choice of physical system (though a natural one to pick) that had to be injected. Some arbitrary connection is needed, and so a meter becomes a base unit.
I like the ampere example better just because it is more obvious that an arbitrary physical system has been introduced.
In contrast, the SI unit for area is m[sup]2[/sup]. That is purely a mathematical combination of other base units. Thus, m[sup]2[/sup] is an SI derived unit (which happens not to have a fancy name).
Right. The metric system is immensely useful and we’ve got an tremendous amount of infrastructure based on their current values. There are big practical reasons to have a second as a different unit from the meter, partly due to history and partly due to the fact that at low speeds, we move through time at a high rate (nearly c) and space very slowly, making the “mixing constant” large.
That’s true, but I think that’s just an argument about what kind of physical artifacts we want to use. A cesium atom is just as arbitrary as a lump of platinum-iridium, but it has the practical advantage that there are lots of identical ones out there and it’s ok if we lose one. Cheaper, too.
Here’s another way of making the point I was trying to make. Looking at Planck units, the advantage is that all the major relevant physical constants are 1.0. That’s really nice feature, but it has the disadvantage that it makes the units themselves very large or very small (usually–there are some exceptions).
On the other side of the spectrum we have SI, where most of the physical constants are empirically determined. G, Avogadro’s number, Boltzmann’s constant, etc.–they have to be measured. But it does have the nice feature that the units are of usable magnitudes.
So, why not try to get most of the advantages of each? Keep the SI units at approximately their current values, but fix the relationships so that the physical constants are actually constant? Sure, it’s not as nice if they were 1.0, but there is at least no experimental error.
Of course this was already done with the meter. c used to be empirically determined, but now it’s not. There is zero uncertainty in c because the ratio is fixed.
As far as I can tell, you can fix everything relative to each other with only two required (physical) degrees of freedom. Everything else can be defined relative to those two physical artifacts (whether cesium atoms or otherwise). One could reduce this by giving up on our existing units (as done with Planck units), or have more but with the side effect of overconstraining the system and causing superfluous unfixed physical constants (as is done with SI).
At any rate… I guess there’s really not much to argue, since SI is already moving in this direction, and once they’ve finished then it’ll just be quibbling about terminology. Maybe my complaint is that they aren’t moving more quickly.
But that’s unrelated to how many base units you need. Just because the meter is defined by fixing the speed of light doesn’t remove the meter as a base unit. That’s the erroneous leap. It just changes how you go about defining how big a meter is.
The number of base units in SI has nothing to do with the number of physical constants you want to use when defining their sizes. That’s arbitrary. At the end of the day, you still want to say how tall some tree is, and you can’t do that using only seconds (assuming, as we have been here, a non-Planck-units style system). Thus, you need to have a meter in your base unit system, even if it’s defined in an elegant way.
Going back to your original point:
You need more than two base units if you want to report anything. This is separate – essentially unrelated – from how you choose to define the sizes of those units.
But even in SI, I can always say a tree is 100 light-nanoseconds tall. The meter is really just a convenience unit–a fixed scaling factor. We don’t say that a megameter is a different base unit than a meter. It’s a base unit times a scaling factor.
You agree, I hope, that if you write down a bunch of formulas with units, then any time you see an “N”, you can paste in “kg-m/s[sup]2[/sup]” and still have a perfectly correct set of formulas. Right?
Well, you can do the same with the meter. You do a global search and replace, where every instance of “m” is replaced with “(1/299792458 s)”. Your formulas will look a little weird: joules don’t exist anymore, so the only unit of energy is the kilogram. But it works perfectly; every formula is still correct.
Of course you can also replace any instance of “m” with “42 schleems”. But that doesn’t get you anywhere; you still have the schleem to deal with. The meters can actually be reduced to seconds and you end up with one less unit.
I’m not quite sure what you mean here. Again, I’m not denying the utility of the meter or otherwise. It just doesn’t seem like it should be called a base unit when it has no existence independent of the second.
Amps are, granted, a little harder to deal with. You have to fix the coulomb, and then the fine-structure constant makes an appearance, which obviously can’t be fixed (being dimensionless). So your unit is still subject to experimental error unless you relax the constraint about the force being exactly so-many newtons/meter.
Right. “Light-nanoseconds” is a fine unit for distance. Notice, though, that you said “100 light-nanoseconds” and not “100 nanoseconds”. They are difference things. The former is defined by the latter and the introduction of a chosen physical quantity. A “light-[nano]second” exists as it’s own thing in the unit system, separate from a “[nano]second”.
If you want to elevate c to a unitless quantity, you can, but in doing so you are moving to Planck units, and…
Indeed, Planck units (or similar unit sets) make for a terribly impractical system for experimental science, for reasons that go well past history or familiarity. They are beautiful in the right theoretical situations, but I’m working with the assumption here that we are not trying to do that. SI certainly isn’t. It’s trying to serve as a useful set of units for experimental science, metrology, and communication.
Agreed. “N” is indeed a direct shorthand for the more cumbersome combination of SI base units “kg m / s[sup]2[/sup]”.
And this is where the catch is. “Meter” is not equivalent to “1/29979248 s”. Instead, “meter” is equivalent to “the distance that light travels in 1/29979248 s”. The second string is a distance. The first is not. And, because defining that distance is arbitrary (particularly in the choice of the reference physical system), it cannot be obtained just by knowing what a second is.
The newton, in contrast, is truly just a search-and-replace shorthand notation.
It should be called a base unit because you cannot get it from seconds alone. The meter requires knowing both how long a second is and how fast some reference velocity is. One can discuss a unit system in which that reference velocity (and/or other reference quantities) are taken to be unitless, but those are Planckian systems, and they aren’t useful for what SI is useful for. Thus, SI needs more than two base units.
There’s a potential misconception here that I think you’re probably not making, but just in case someone else has the misconception: People still do the same sorts of experiments that we used to do to measure the speed of light. All that’s changed with those experiments is how we describe what we’re doing. It used to be that we would say that we were measuring the speed of light with better precision than before, but now we would say that we’re measuring the length of the meter with better precision than before.
So it’s unanimous that the order is arbitrary?
The consensus seems to be “it’s complicated”. A particular order for a given set of units is often fixed as a matter of convention, with “fixed” depending on the units in question and the field of study. These conventions bring with them all the benefits that linguistic and notational conventions always do, even if violating those conventions doesn’t render the expression useless. Analogy: Yoda speak is understandable, but it’s not how things are usually done in daily life. (“Have one coffee, I will.”)