However, Newton’s definition of mass is not an operational, but a quantitative definition.

And what does that mean? Can you, with this definition, go to the laboratory and get a quantity of mass of exactly 1 kg?

kkwan - 31 October 2011 08:15 AM

Incidentally, there are ongoing projects to define the kilogram (the base unit of mass) as a certain number of atoms, i.e. quantity of matter.

I was afraid this would pop up in your Googlings.

Let me just say this: the constant of Avrogado is again not independent of mass, it is found by comparing atomic masses with macro masses. And how are these measured? Just guess again…

Now one can turn the whole thing upside down, and e.g. define the constant of Avrogado as say 6.10^24 particles, and then create objects with exactly this amount of particles, and say that exactly this amount of silicon is 1 kg, per definition. This would give a possibility to reconstruct 1 kg of matter, even when the ‘standard kilogram’ weights in Paris were lost. Then we have an operational definition. But it is nothing more than ‘setting a standard’.

If you want to know if an object of yours has exactly the same mass as the ‘Avrogado-mass’, then you must test if it behaves the same under the same force. You can do this with a balance (and suppose that gravity is uniform where you are measuring), or apply another force to it, and see if the force needed to give it the same acceleration is the same. So again: you need force.

And what does that mean? Can you, with this definition, go to the laboratory and get a quantity of mass of exactly 1 kg?

No, but that does not make Newton’s definition of mass fundamentally circular.

Let me just say this: the constant of Avrogado is again not independent of mass, it is found by comparing atomic masses with macro masses. And how are these measured? Just guess again…

Now one can turn the whole thing upside down, and e.g. define the constant of Avrogado as say 6.10^24 particles, and then create objects with exactly this amount of particles, and say that exactly this amount of silicon is 1 kg, per definition. This would give a possibility to reconstruct 1 kg of matter, even when the ‘standard kilogram’ weights in Paris were lost. Then we have an operational definition. But it is nothing more than ‘setting a standard’.

If you want to know if an object of yours has exactly the same mass as the ‘Avrogado-mass’, then you must test if it behaves the same under the same force. You can do this with a balance (and suppose that gravity is uniform where you are measuring), or apply another force to it, and see if the force needed to give it the same acceleration is the same. So again: you need force.

The core idea of the Avogadro project is simply to count silicon atoms and redefine the kilogram as a certain number of silicon atoms (quantity of matter) which is Newton’s definition of mass.

Regarding Avogadro’s constant, from this article HERE

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope.

Notwithstanding the use of force in comparing masses, it is not an issue wrt the definition of mass per se.

No, but that does not make Newton’s definition of mass fundamentally circular.

It does. To see this, remember that in Newton’s time it was not known that matter is composed of atoms. So from Newton’s view point it would have been perfectly possible that it in his future some discovery would be made that a mass could be split up endlessly. Would that invalidate Newton’s mechanics? Of course not, but we would still have no idea what a ‘quantity of matter’ would be.

kkwan - 31 October 2011 07:18 PM

The core idea of the Avogadro project is simply to count silicon atoms and redefine the kilogram as a certain number of silicon atoms (quantity of matter) which is Newton’s definition of mass.

But to know that this procedure works, you must know the atomic weight of silicon, and what 1 kg is. The Avogrado constant is derived from these. So one is able to make preciser definitions, but they are in terms of each other, i.e. circular.

It does. To see this, remember that in Newton’s time it was not known that matter is composed of atoms. So from Newton’s view point it would have been perfectly possible that it in his future some discovery would be made that a mass could be split up endlessly. Would that invalidate Newton’s mechanics? Of course not, but we would still have no idea what a ‘quantity of matter’ would be.

Newton would know about Democritus and his atomic theory of matter. Whatever was his philosophy of nature (whether it was atomistic or continuum), how does this indicate circularity?

But to know that this procedure works, you must know the atomic weight of silicon, and what 1 kg is. The Avogrado constant is derived from these. So one is able to make preciser definitions, but they are in terms of each other, i.e. circular.

However, the measurement is not the definition and has no implication of circularity on it per se.

The point is, counting atoms to determine mass is tantamount to determine quantity of matter.

Tautology (from Greek tauto, “the same” and logos, “word/idea”) is an unnecessary or unessential (and sometimes unintentional) repetition of meaning, using different and dissimilar words that effectively say the same thing (often originally from different languages).

An example of a self-referential situation is the one of autopoiesis, as the logical organization produces itself the physical structure which creates itself.