Did anyone ever figure out why the weight (or mass) of the Paris kilogram cylinder was drifting? IIRC it was gaining weight, maybe a few hundred micrograms per decade. Rich ---------- Quoting "Keith F. Lynch" <kfl@KeithLynch.net>:
"Adam P. Goucher" <apgoucher@gmx.com> wrote:
There seems to be a lot of recent excitement about the redefinition of the kilogram, but I'm more worried about the candela.
Kilograms are more fundamental. I'm surprised they even keep the candela in SI. Lots of old metric-system units aren't in SI, for instance the calorie.
I'm interested in the philosophical implications of the several changes. They aren't just changing the values of the various units, they're subtly changing what they're units *of*.
For instance an earlier change in SI had the side effect of defining the vacuum speed of light as a specific constant. Before, people could debate whether that speed was constant, and could measure it. Today, it's constant by definition and any attempt to measure the speed is actually measuring the length of the meter.
Since the fine structure constant is dimensionless, SI can't, and didn't attempt to, define its value. Its value depends on the speed of light, Planck's constant, the charge of the electron, and the permeability of space. Suppose that it's discovered that the fine structure constant isn't constant. Is it meaningful to say which of the four things it depends on has changed, or is it completely arbitrary? Previously, the speed of light and the permeability of space had defined values, so we'd have the choice of saying that Planck's constant or the charge of the electron had changed. With this week's change in SI, Planck's constant and the charge of the electron have been given defined values, and the permeability of space has lost its defined value, so we'd be required to say that if the fine structure changes, the permeability of space had changed.
Getting back to the kilogram, there are several definitions of mass: Energy divided by the square of the speed of light. Resistance to acceleration (which can be subdivided into resistance in each of the X, Y, and Z directions). Tendency to attract other masses (which again might vary with direction). Tendency to be attracted by other masses (which again might vary with direction). Resistance to torque (which might vary with direction of the axis). Quantity of atoms of a specified type or mixture of types. Formerly the last definition was used, now the first one is being used.
General relativity implies that those definitions are all equivalent. SI now implicitly assumes that general relativity is correct.
(Nitpick: This week's changes won't actually take effect until next May.)
Now, back to the candela:
On the face of it, it seems to have a relatively simple definition:
"The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540*10^12 Hz and that has a radiant intensity in that direction of 1/683 watt per steradian."
where luminous intensity is defined as:
I_v = 683 V(gamma) I_e
where I_e is the radiant intensity (in watts per steradian) and V(gamma) is the 'standard luminosity function' (which must be equal to exactly 1 when gamma = 540*10^12 Hz, for these definitions to be consistent).
But this raises the question: what is V(gamma) in general? I've found a tabulation of values for integer * 10^-9 metre wavelengths in the visible interval:
but no indication as to how to compute V(gamma) for any of the 2^(aleph_null) other wavelengths beside the 401 provided. Any ideas?
It can't be computed, only measured. Unlike other SI units, it's subjective. That table came from asking volunteers which spots of colored light, of various wavelengths and luminous fluxes, appeared brighter.
It varies between individuals. The table even mentions that younger people generally see better in the blue. (That's because eye lenses turn yellowish with age, much as many clear plastics do.) It varies strongly with luminous flux (Purkinje effect). And it would be unethical to measure it outside the range of that table, since a light bright enough to be seen might be bright enough to damage the eye.
Of course anyone can come up with a heuristic formula based on that table. Or based on another table made by testing a different set of people.
At first I thought that that table isn't consistent with SI, since SI implies that V(gamma) is 1 for 540 THz, and the table states that it's 1 for 555 nm, which is not the same. 540 THz is about 555.171 nm, which has a lower value in the table, and 555 nm is about 540.167 THz. But then I realized that I was assuming a vacuum. Obviously, these tests were done in air (again, for ethical reasons). To make those numbers consistent would require an index of refraction of about 1.0003, which is indeed reasonable for typical comfortable temperatures and pressures of air.
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