# A SI meter definition changed?

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#### Mister T

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I think the new defintions may be a bit more confusing to students at the introductory level, eing a bit more abstract. I suppose we'll see.
Yes. It'll be interesting to see how it's presented in the newer introductory college-level texts. And the response in the literature.

#### Orodruin

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Yes. It'll be interesting to see how it's presented in the newer introductory college-level texts. And the response in the literature.
The old definition is still equivalent so I see no reason why you could not first present the new definition first and then give something like the old definition as clarification:
"The meter, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s-1, where the second is defined in terms of ΔνCs. This means that the metre is the length of the path travelled by light in a vacuum in 299 792 458 of a second."

#### HallsofIvy

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The "radian measure" of an angle is defined as the length of the arc cut off by that angle with vertex at the center of a circle of radius r, divided by r. The numerator and denominator are both linear measurements with the same linear units. The ratio is dimensionless. That is why radians are (and should be) dimensionless.

#### PAllen

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Still not convinced. Do you also want a separate physical dimension for oranges?
Silly fact: at current worldwide annual production, it would take a bit more than a million times the age of the universe to produce a mole of oranges.

#### DrDu

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(Although personally I think amount of substance is a silly dimension to introduce ...)
As a chemist, I always wonder why we need the Coulomb. You can express it easily via the Faraday constant in terms of the mole :-)

#### Dale

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The "radian measure" of an angle is defined as the length of the arc cut off by that angle with vertex at the center of a circle of radius r, divided by r. The numerator and denominator are both linear measurements with the same linear units. The ratio is dimensionless. That is why radians are (and should be) dimensionless.
This is the SI convention, but it is not the only convention possible. The angle in some system of units is not necessarily equal to the ratio, but in general it is proportional to the ratio: $\theta = k \frac{s}{r}$. For radians k is a dimensionless 1 making radians dimensionless, but for degrees $k=180^{\circ}/\pi$ which could be considered dimensionful if degrees were given a dimension. Hence the dimensionality of angles is a convention. SI could have chosen k to be a dimensionful 1 rather than a dimensionless 1.

#### Vanadium 50

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, it would take a bit more than a million times the age of the universe to produce a mole of oranges.
But in 2008-2009 Zimbabwe was able to produce a mole of Zimbabwe dollars overnight.

#### HallsofIvy

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"Degrees"? What in the world are "degrees"? Every one knows that radians are the only way to measure angles!

#### pervect

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"Degrees"? What in the world are "degrees"? Every one knows that radians are the only way to measure angles!
That's somewhat amusing - I am assuming that it was intended to be, of course.

But, being serious, I do have to say that people do use degrees. We can generalize this by saying that a statement that starts with "Every one knows" is generally false, usually there is someone that doesn't know something, and/or is willing to argue some particular point.

Exactly what to replace a statement about "what everyone knows" with is somewhat unclear.

#### Orodruin

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Exactly what to replace a statement about "what everyone knows" with is somewhat unclear.
Oh come on! Everybody knows that!

#### maline

Once we are listing our pet peeves with the SI, here is mine: I think it's awful that Avogadro's number is now an arbitrarily chosen constant. This number, or rather its reciprocal, once represented an important physical quantity: the mass of a baryon in grams. Of course both "baryon" and "gram" require further specification, but the choice of Carbon-12 selects the baryons in a satisfactory way, and we had just gotten around to a solid definition of the gram. So Avogadro's number should be an experimental fact, not open to definition by fiat.
If they would have gone the other way and set a number for $N_A$ while keeping the Carbon-12 standard, thereby defining the gram and kilogram, I would be happy with that too. But fixing both the kilogram and the mole numerically removes the physical meaning of the mole/amu/Avogadro number, and so makes the system more arbitrary rather than less.

Of course, I am also offended that they used $h$ rather than $\hbar$ for the kilogram definition. Can you imagine, $\hbar$ is now an irrational number!

#### Dale

Mentor
This number, or rather its reciprocal, once represented an important physical quantity: the mass of a baryon in grams.
We can now write the mass of a baryon directly in the new kilogram standard. Why does Avogadro’s number need to be tied to the mass of a baryon?

#### maline

We can now write the mass of a baryon directly in the new kilogram standard. Why does Avogadro’s number need to be tied to the mass of a baryon?
Of course it doesn't need to be. But it pains me that something that once had physical meaning has been redefined as a mere convention.
The mole is not just "some big number that we divide our quantities by to make them manageable". It is the conversion factor between amu and grams, and amu is/was (a more rigorous form of) "number of baryons". The new definitions lose contact with that structure.

#### Orodruin

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Of course, I am also offended that they used $h$ rather than $\hbar$ for the kilogram definition. Can you imagine, $\hbar$ is now an irrational number!
In SI base units, yes. In reasonable units $\hbar = 1$.

#### DrDu

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Once we are listing our pet peeves with the SI, here is mine: I think it's awful that Avogadro's number is now an arbitrarily chosen constant. This number, or rather its reciprocal, once represented an important physical quantity: the mass of a baryon in grams. Of course both "baryon" and "gram" require further specification, but the choice of Carbon-12 selects the baryons in a satisfactory way, and we had just gotten around to a solid definition of the gram. So Avogadro's number should be an experimental fact, not open to definition by fiat.
The mass difference between different nucleons (not to speak of baryons in general) and even between the mass for the same nucleon in different nuclei is far greater than the deviations of the true mass of N_A C-12 atoms from 12g. Hence, I don't see a problem here.

#### maline

The SI didn't knowingly change the values of any of the units, so I expect that the mass of 1 mol of Carbon-12 is still exactly 12g, to within current measurement accuracy. What bothers me is that this fact no longer play any definitional role.
I think that as much as possible, units should be values with specific physical relevance. Of course we are limited by the need to keep fixed the values currently in use, so we are forced to use large, ugly multiples of the physical values. The mole was the one case where the old value actually did have significance, and they went and stuck in a big ugly number anyway!

#### Dale

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I think that as much as possible, units should be values with specific physical relevance.
As far as I know none of the SI units satisfy that criterion. I think only natural units would.

#### maline

As far as I know none of the SI units satisfy that criterion. I think only natural units would.
They don't now, but they were originally intended to. The metre was $10^{-7}$ times the length of a curve from the Earth's equator to its north pole. The gram was the mass of a cubic centimeter of water at standard atmospheric pressure and freezing temperature. And the (older) second, of course, was $\frac 1{24\times 60\times 60}$ of the Earth's mean solar day.
The ideal of choosing units based on Nature is what gave us the SI in the first place. Unfortunately the old definitions failed, due to the values involved not being truly fixed nor easy to measure, and the newer definitions were constrained to be equal to the old ones in value. if we were creating new units today, we would probably use natural units times powers of ten, and perhaps the Cesium hyperfine transition frequency times a power of ten. We certainly would not use numbers like 299,792,458!

#### Orodruin

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They don't now, but they were originally intended to. The metre was $10^{-7}$ times the length of a curve from the Earth's equator to its north pole. The gram was the mass of a cubic centimeter of water at standard atmospheric pressure and freezing temperature. And the (older) second, of course, was $\frac 1{24\times 60\times 60}$ of the Earth's mean solar day.
Honestly, those were horrible definitions as they relied on arbitrary artefacts and resulted in units that were not very well defined.

#### maline

Honestly, those were horrible definitions as they relied on arbitrary artefacts and resulted in units that were not very well defined.
Of course we know they didn't work well, and perhaps people should have foreseen that. But the motive was to make the units as non-arbitrary as possible, and I think that's still an admirable ideal.
And yes, nowadays our perspective is so broad that we think of the planet Earth as an "arbitrary artifact". So much the better!

#### cmb

To argue that the 'Mole' is not dimensionless is like arguing that the number 1 is not dimensionless, because you have to have one of something?

Errr... no, not really.

A Mole is dimensionless, whereas a mole of [something] has the dimension [something].

#### Mister T

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The mole is not just "some big number that we divide our quantities by to make them manageable". It is the conversion factor between amu and grams, and amu is/was (a more rigorous form of) "number of baryons". The new definitions lose contact with that structure.
No, they don't. All they do is make the conversion factor exact.

If you had an apparatus that you used to measure the conversion factor you would continue to use the same apparatus in the same way. It's just that the apparatus now calibrates rather than measures. There's nothing less physical about that.

#### Dale

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They don't now, but they were originally intended to. ...
You and I have very different opinions on what constitutes a physically meaningful quantity. To me all of those quantities you have identified as being physically meaningful are not, while the fundamental constants of nature are physically meaningful.

I mean, the mass of a cubic centimeter of water is only physically meaningful to me if I am weighing a volume of water. Planck’s constant is physically meaningful then, but it is also physically meaningful if I am measuring other things besides a volume of water.

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