# The Ampere as a base unit?

I know there are seven base unit and the rest are derived. Wherever I look I see the Ampere as the base unit of electrical current. How can this be when an Ampere = 1 Coulomb/second and is therefore clearly a derived unit?

The ampere is actually defined as the amount of current which would produce a certain force between two conductors in a vacuum. It is the coulomb which is defined as the charge in one amp per second, so that is the derived unit.

ETA: Here’s the proper definition of an ampere from Wikipedia:

Yeah, what he said.

And then I suppose the coulomb would be officially defined as an ampere-second? I guess that makes sense.

Interestingly, there are many ways one can define a base system and its derived units, including ways with different numbers of degrees of freedom. Combining the various measurements of the relations between units to minimize error and maximize error, and trimming the system over time as new measurements are made, is fascinating stuff.

What bugs me is that SI purports to have a base unit for luminosity, when there’s already a perfectly good unit for that derived from the others, the watt.

Not so. Luminosity is weighted by wavelength to closely match the sensitivity of human vision. N watts at one wavelength will generally have a different luminosity than N watts at some other.

Yeah, but we don’t need a base unit for every other possible weighting function one might apply to power. What’s the SI base unit for luminosity as perceved by dragonflies? Or as perceived by an H-alpha filter on a solar telescope?

Well, there is bolometric luminosity (the total of all radiant energy, not just just visible), the SI unit of which is, in fact, the watt.

Luminance is a measure of light as perceived by a human visual system. If you are not interested in human perception then the measurement you want is something other than luminance. Funnily enough humans have found that perception by humans is important enough to standardize measurements for them. Dragonflies are free to choose their own system of measurement.

Sure, human perception is interesting enough to justify a standardized unit. I’m not disputing that. I’m just disputing that it should be a base unit. Resistance of a particular circuit element to the flow of current is interesting, so we give it a unit, the ohm. But the ohm isn’t a base unit; it’s derived from the ampere, the kilogram, the meter, and the second. Likewise, I would assert that the lumen is also a derived unit.

To express a luminance value in watts you need to apply a luminance function which takes into account the variation in sensitivity of the human eye with wavelength. This function cannot be derived from any other SI unit, it must be agreed upon based on measurements. In essence the SI standardization of luminance is the definition of this function.

Going back to the original question I’d like to know: Why is current taken as the base unit when charge is more fundamental.

Like friedo already told: ampere is defined to be…

So it’s not a base unit but a derived unit defined by …

Historical reason is ok. But now that SI-system is going to be revamped anyways, why not change the base unit in electricity to something that is scalar. Charge is an attribute of substance, just like mass is an attribute of substance, amount is an attribute of substance and temperature is an attribute of substance.

Yes, charge does seem more “fundamental” than current, at least to this physics major. The reason is of course historical, because it was easy to measure current but not to measure charge (using the term easy relatively of course).

Hopefully they’ll redefine the kilogram as well. I hate that kilogram is the base unit of mass, but that no other base unit uses the kilo- prefix. It’s stupid. Also, it’s based on an actual kilogram of platinum in France. Dumb.

I don’t see why charge is more fundamental than current.

But even aside from that, units need to be practical, and specifically there needs to be a way for independent laboratories to rederive a unit from a practical experiment.

For instance, there is currently a debate as to how to define the kilogram. The “fundamental” approach seems to be to take X atoms of an isotopically pure substance, where X is just a fixed constant chosen to be consistent with the current definition (which is just a hunk of metal in France).

This is in fact one of the proposed approaches, but it’s difficult to do accurately. So there are alternate approaches, such as one that uses the definition of current to exert a magnetic force on a test mass, and use this force (along with the definition of G) to compute a mass. This sounds more complicated and much less fundamental, but it’s easier to do accurately. So there’s a chance that will be used instead.

Yes I always keep two infinitely long wires of negligible cross section lying around so I can accurately re-derive what an ampere is.

(Not to mention a very good stopwatch so I can measure the distance light travels in 1 ⁄ 299,792,458 of a second to figure out exactly how long a meter is, so I know how far apart to place the wires)

Is G known all that accurately–compared to other physical constants, I mean?

(I seem to remember that someone else wanted to define the kilogram in terms of Planck’s constant.)

I know you’re having fun, but the fact is that laboratories can and will do this. The current approach is to actually move the physical specimens around to compare them, which obviously invites a whole host of risks. With this approach, any laboratory in the world can produce a standard as good as the “main” one (which actually isn’t that good for the kilogram–the sample in France has changed mass over time).

Now that I think about it, you don’t actually need to know G. You do need to know the local gravitational acceleration (little g), though, but that can be very accurately measured (much better than the ~50 ppb for Planck’s constant).

And for the record, G is about the least-precisely measured of any of the fundamental constants (or at least, any of them that you’ve probably heard of). We can measure the product of G and the mass of the Sun (or of the Earth, or of Mars, Jupiter, or Saturn) extremely well, but it’s hard to break those apart.