How do they compare the difference between the two weights to that accuracy?
Presumably even changes in g across the planet must come into the calculations at that level?
The world's official kilogram has put on weight according to boffins who fear the mass needs a new-year diet. Researchers at the University of Newcastle reckon the reference kilogram artefact, kept at the International Bureau of Weights and Measures (BIPM) in Paris and used to calibrate the world's weights, has put on less …
By definition, it's not possible for the mass of the reference kilogramme to change. Its mass is always exactly 1.0000000000000000000 kg, even if its physical composition changes and it adds or loses atoms.
By definition it's mass must be 1.0000...kg but that does not mean its mass can't change. Mass is a fundamental physical property independent of the system of units used to measure it. If contaminants are added but the mass measured in kilograms is still the same that means that the value of the kilogram has changed, not that its mass hasn't.
A fair point, mathematically, but there is a convention in science that says you retain trailing zeroes where the precision of the measurement justifies the additional digits. So 1.0000000000000000000 is 1 plus or minus 1e-19, whereas 1.0 is 1 give or take 10%.
For our standard kilogram, the claim is that it has "put on" 100 millionths of a gram, so we should quote its current mass as 1.0000000kg.
Just how do you convert a physical entity to a mathematical scribble?
This sounds like those definitions of the value of money where 'it means whatever we agree it means regardless of whether it makes sense or not'. As Mike Scott says above, the definition is the definition. Where the problems arise is in producing a physical representation of that definition. If you cannot achieve it then which is at fault, your definition or your real world?
The Kilogram is really no more of a specific physical entity than a Meter, what is important is that as a unit of measurement it should be constant such that measurements taken today hold true tomorrow.
Because of this such a unit of measurement should be based upon universal constants rather than a single physical object subject to the tender ministrations of entropy. This chunk of metal may be a physical entity, but the conceptual kilogram (which is vastly more important than some historical conglomeration of atoms) is a mathematical entity.
In the case of the kilogram, with remarkable ease. If a metre is fixed by the speed of light, then a kilogram is also fixed because a kilogram is the weight of a volume of pure water 0.1m x 0.1m x 0.1m. The trick is getting pure dihydrogen oxide, of course, which is why the reference kilogram is made of platinum and iridium.
" the weight of a volume of pure water 0.1m x 0.1m x 0.1m"
There remains a problem even if you can get pure 1H216O and that is water has this nasty habit of changing it's density with pressure and temperature and is most dense around 4 degrees C at "normal" atmospheric pressure.
Yeah, another reason to use the metal kilo instead of water, although you could specify the pressure and temperature conditions for the water. On the other hand, water's freezing and boiling points can be altered and even the speed of light changes under certain conditions so the metre and degree Celsius really aren't any better.
We should all go back to Imperial measures. The area one man can plough with one ox in a day may be variable, but by gum, at least it's got history!
"a kilogram is the weight of a volume of pure water 0.1m x 0.1m x 0.1m. The trick is getting pure dihydrogen oxide, of course"
And because that was the original real definition of a kilogram (the current reference kilogram made of platinum and iridium is only an approximation of this) we have a simple way of defining a proper kilogram by mathematical means: calculate how many dihydrogen monoxide molecules fit into one litre and multiply that number by the mass of one molecule.
>>The metre is defined in terms of physical constants.
>>The litre is defined in terms of metres.
>>One litre of pure water weighs 1kg.
>>Where's the problem?
One problem is that a litre of pure water AT STANDARD TEMPERATURE AND PRESSURE weighs 1KG,
Pressure is measured in Pascals, which is defined in terms of Newtons - which is itself defined in terms of Kilograms. And there's the big problem - you are trying to define a kilogram in terms of something that is (indirectly) defined in terms of kilograms. Clearly, that's totally bogus.
You make a good point, but a circular definition isn't necessarily totally bogus. Since the density of water is rather insensitive to pressure the problem of "what mass of water has a volume of one litre at a temperature of 273.15 K and a pressure of (x * 1e5 m^-1 s^-2), where x is the mass of the water" can have only one solution in the vicinity of 1 kg. If there are, or might be, other solutions then you'd have to add a clause to specify which solution you mean, but you would then have a perfectly meaningful definition of the kilogram, even if it is a rather impractical one.
the problems are
- purifying water to the required degree of purity (accuracy), even dissolved gases (oxygen, nitrogen and others are all soluble in it to varying degrees) will affect the density of the water.
- 1 litre of water doesn't have a mass of 1 kg (density at 4 Celcius is 0.99997 g/ml, this is at it's densest)
- the density of water varies with both temperature & pressure
It's a nice idea but utterly unworkable in practice.
The purity and temperature of the water are where the problem is.
You can dissolve 100 grams of salt in a litre of water. It now weighs 1.1 kg., while still occupying only 1 litre of space.
Alternatively, you can heat 1 litre of water to 80 degrees. It still weighs 1 kg., while occupying more than 1 litre of space.
Maybe I am missing something, but couldn't we just define the kg by saying something like 'a kilo is the rest mass of X number of Carbon-12 atoms'? Or, the mass-equivalence of the energy of X many photons of frequency Y?
Why are we using physical measures -- is there any good reason other than it is too hard to calibrate to the definitions given above?
That is exactly the reason, multiple groups have been working for years trying to figure out a new measure which can be reproduced.
Current attempts include. perfect silicon spheres with a precise radius and current required to lift a mass using an electromagnet but no one has come up with a reproducible one just yet.
If the kilogram standard is now heavier than it was, that must mean that I now weigh less kilograms than I used to. Hurrah for basing weight measurements on an physical object.
Now, can we do something to get the metre back to a physical object as well? - preferably one that also increases. After Christmas my waistline badly needs a re-definition of standards.
Since the weight is a reference kilogram, then they cannot know whether it has put on weight or not as it is the reference, how can they test that their measuring equipment is accurate if not by checking with the 1 kilogram reference?
If the scales say 1.00000001KG then recalibrate the scales to 1.0Kg job done.
There are several copies held in various countries around the world. The copies all still weigh the same as each other. The original seems to be heavier. You can either claim that the original has put on weight or you can claim that *all* the copies have lost *the same* amount of weight. Occam's Razor favours the former hypothesis.
For the sake of interest, pure water is never pure. It's always reacting with itself (self-ionized) as Hydroxonium. In principle if it began as pure H2O you'd have a 50/50 mix, but this gets rather circular...
@AJStiles when you add salt to water the solution undergoes roughly a 2% volumetric change.
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