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On 12-10-2009 18:27, Warp wrote:
> Neeum Zawan <m.n### [at] ieee org> wrote:
>> Perhaps they could _change_ the definition to that, but I'm willing to
>> bet that it's off by a bit from the current definition.
>
> AFAIK kilogram *was* originally defined as the weight of 1 liter of water,
> but for whatever reason they changed it to the weight of a specific object
> (I really can't understand why).
Standards are defined on whatever can be most accurately measured. So if
you can measure distance and light speed more accurate than time you
define time as a the interval it takes light to cross a certain length.
If you increase the accuracy of your clock, you might want to define a
length as velocity times time, etc. At some point the accuracy of
quasars was approaching our best clocks, if they would have passed that
we would now have time defined in heaven.
The standard kilogram can be more accurately measured than a liter of
water. When we are able to count a specific number of atoms of a known
isotope and weight those with sufficient accuracy that will probably
replace the standard kilogram. ATM we are not that far, but only just,
as this article explains.
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Invisible schrieb:
> ...and here I was thinking that 12g of C12 was *defined as* one mole of
> C12 atoms...
No, the /mole/ is defined on this basis.
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Orchid XP v8 schrieb:
>>> ...and here I was thinking that 12g of C12 was *defined as* one mole
>>> of C12 atoms...
>>
>> Hence the definition of 'mole' depends on the definition of 'kilogram',
>> not the other way around.
>
> Ah, I see.
>
> Couldn't they just reverse it? I mean, just say that 1 Kg = the mass of
> XXX C12 atoms?
That's one attempt to it (except that they appear to intend to use
silicon instead of carbon).
However, at present (or at least until very recently) measuring the mass
of the Grand K can still be done with greater precision than counting
atoms, so they don't know /exactly/ how many atoms make up a mole.
Definitions of SI units change over time depending on how they can be
measured with highest precision.
For instance, the SI unit of distance (1 metre) was, like the kilogram,
initially (*) defined based on a physical entity - the "International
Prototype Metre". (* Actually, even before, for a few years the metre
was based on other properties, including being a 10,000-th of the
half-meridian through Paris, but those didn't last long.)
Later, scientists managed to measure wavelengths at precisions that
exceeded that of the Prototype Metre, and therefore it was decided in
1960 to redefine the metre as the vacuum wavelength of a particular
emission of krypton-86.
Some two decades later, both time and the vacuum speed of light could be
measured even better than wavelengths, and the metre was redefined in
1983 as the distance travelled by light in vacuum within a certain
period of time.
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Warp schrieb:
> Why can't the kilogram be defined as the weight of exactly 1 litre of
> pure water at a certain temperature? After all, that has been the de-facto
> definition for forever.
That was only the /initinal/ definition.
What reason would be there to stick to it - or choose a different
definition, for that matter?
There's only one: Reproducability.
If you can find a definition for a kilogram that /matches/ the initial
definition, but can be reprocuded with /higher precision/, then that
definition is both superior and "backward compatible".
It turned out that measuring the mass of 1 litre of water at a certain
temperature was subject to more error (possibly due to issues with
producing /really/ pure water, and reproducing /exactly/ the desired
temperature) than "copying" the mass of some sample entity made of a
robust, non-corrosive material.
Note that while it was found that the "primary copies" of the kilogram
exhibit a "drift" relative to the Grand K, but nobody is presently able
to tell whether the Grand K also exhibits an /absolute/ drift. If pure
water would provide a reference of adequate precision (or even anywhere
close), I guess scientists would already have checked for absolute
drifts using this method.
Also note that there is no such thing as a "de-facto definition"; there
are "practical realizations" that differ from the official definition,
but I guess none is based on the initial definition these days, except
maybe as makeshift references for low-precision applications.
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Warp schrieb:
> According to wikipedia, one liter of pure water at 4 degrees celsius (the
> standard temperature for measuring SI units) is 0.9999720 kilograms.
That's because the /initial/ definition of the kilogram was one liter of
pure water at /zero/ degrees celsius.
> If they changed the definition of kilogram back to its original form, the
> change would be less than 0.003% from the currently accepted value. Would
> that be a huge catastrophe?
There would be no change at all, because they'd define it as something
along the lines of:
"1 kilogram is the mass of 1.000028 liters of pure water at 4 degrees
celsius"
And yes, a /change/ of 0.003% would be a /tremendous/ catastrophe. Note
that they're currently worried about /imprecisions/ of less than 100
micrograms (0,0000001%).
See also
http://en.wikipedia.org/wiki/Kilogram#Importance_of_the_kilogram for all
the units of measurement that would be affected by such a change.
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Warp schrieb:
>> It may be that it's too difficult to measure "pure water" at "exactly 4
>> degrees celsius" for modern measurement precision.
>
> Not more difficult than measuring the exact speed of light (which is needed
> to define the unit of length) or an exact magnetic force (which is needed to
> define the unit of electric current).
It's not a matter of /exact/ measurement, but of /precise/ measurement
instead.
Vacuum speed of light is (comparatively) simple to measure at high
precision; it seems to me there are not many sources of errors in
experiments except the vacuum (scientists are pretty good at that
nowadays), the stability of the distances in your experiment (which will
be what you'll measure), and the quality of your time reference (note
that the second is the SI base unit that can presently be measured with
the highest precision of all).
With a liter of pure water at exactly 4 degrees celsius, one problem
you'll have is to exactly hit the 4 degrees celsius. Another problem is
to /get/ really pure water, and /keep/ it pure. Yet another problem is
that you'll have to define the exact isotopic composition of the water.
Pressure is another thing, as I guess even pure water is only
theoretically incompressible.
Then there's the shape of the container. You need to make sure that it
/precisely/ holds 1 litre when it is at 4 degrees celsius /and/ filled.
Note that you must also account for any openings used to fill it with
water: If you want them to be completely filled with water when
measuring, you need to know their precise dimensions up until the valve,
while making sure you have no residual water outside the valve. If you
choose to not have such openings to be completely filled, you must take
into account capillary effcts to compute the actual volume of the water,
which then depends on the material and even surface structure of the
container...
Sounds like quite some fun.
> Given that the object which is currently the measurement of 1 kg changes
> weight every time it's measured, does it really matter? It would simply be
> one more change, but then it would be fixed, and that's it.
Nobody /knows/ whether if it actually changes weight. All they know is
that the "primary copies" do change weight with respect to one another
and the Prototype.
And then look at the order of magnitude of those changes.
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Darren New schrieb:
> 0K is unreachable even in theory.
It may provide just as good a base for actual experiments as specifying
any other temperature; I guess the systematic error introduced by a
deviating temperature is comparatively easy to "compute away", and I
also guess that it might be easier to measure an actual temperature than
to achieve a certain reference temperature, so the math to compensate
for the deviating temperature might be needed anyway, making 0K just as
good as any other reference temperature (maybe making the math even
slightly easier).
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On 10/12/2009 12:57 PM, Darren New wrote:
> Plus, of course, if you make *everything* circular, then you have
> nothing. If a kilogram is the weight (well, mass) of a liter of water,
> and a liter is 1000 cubic centimeters, and a centimeter is the length of
> one gram of carbon atoms lined up (or some such) then the whole thing
> falls down.
I wonder if a sphere is the optimal packing of silicon atoms. I doubt it.
-Mike
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On 10/12/2009 10:45 AM, Mike Raiford wrote:
> http://blogs.ngm.com/blog_central/2009/10/a-grander-k.html
"They’ve gone into high gear to redefine the kilo as a universal
constant based on nature instead of an object vulnerable to distortion."
I bet that the new unit will also be proven susceptible to "distortion"
over very large amounts of time, like with the density of space changing
over thousands of millennia or something. (Just a hunch.)
-Mike
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clipka <ano### [at] anonymousorg> wrote:
> With a liter of pure water at exactly 4 degrees celsius, one problem
> you'll have is to exactly hit the 4 degrees celsius. Another problem is
> to /get/ really pure water, and /keep/ it pure. Yet another problem is
> that you'll have to define the exact isotopic composition of the water.
I don't see how that is different from the current method, ie. measuring
the weight of that one object at 4 degrees celsius.
Except that with water you don't have to rely on one specific object which
is unique and there exists only one in the world.
> Then there's the shape of the container. You need to make sure that it
> /precisely/ holds 1 litre when it is at 4 degrees celsius /and/ filled.
Not much different from defining length in relation to the speed of
light. If you want to measure it, you need precise timing and precise
length measurements.
> > Given that the object which is currently the measurement of 1 kg changes
> > weight every time it's measured, does it really matter? It would simply be
> > one more change, but then it would be fixed, and that's it.
> Nobody /knows/ whether if it actually changes weight. All they know is
> that the "primary copies" do change weight with respect to one another
> and the Prototype.
At least with the water the definition would be fixed to one single
weight. Then it's only a question of how accurately it can me measured,
which is no different from all the other units.
--
- Warp
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