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The best part about this batch of changes is they push the mole and Avogadro's constant out on their own where the belong, not linked to any other units. Now we'll have only a single mass unit (kg) instead of two (kg and unified atomic mass unit) that we do now. This will knock carbon 12 of its perch as the definition of the "other" mass unit that's been essential to use SI's mole but was not actually SI itself.

But wouldn't the most straightforward definition of a base mass unit (kg) be linked to the mass of an atom?

Yes. I believe Asbostos is commenting that they currently are not linked.

("Yes", with the proviso that the proposed silicon atom definition is a more obviously direct link than the watt balance.)

What I mean is, the proposed new definition defines kilogramm using a relationship to Planck constant. Instead, I think that a more intuitive definition would be something like "the mass of {huge number} of C or Si atoms".

The proposal is to define all fundamental physics constants, and derive all the units from them.

The Avogadro number isn't a fundamental physics constant, it's just a unit conversion constant, and thus, didn't get to define any basic unit.

> The Avogadro number isn't a fundamental physics constant

That's a pretty arbitrary assertion. Who defines what "fundamental" is? The number of periods of <something> of Caesium atoms used to define the duration of one second doesn't sound very fundamental either.

In fact, the second and candela aren't choices aren't that fundamental, mostly reflecting how those are measured. All the others come from the speed of light, fundamental charge, Plank's constant, and gases constant; those are pretty fundamental to physics.

Avogadro's number is used to define the atomic units, what makes a lot more sense than pushing it into metric calculations.

The wikipedia page is great: https://en.wikipedia.org/wiki/Metric_system#Future_developme...

You seem to be assuming that the atom is fundamental. It's not. Why not base things off the mass of an electron instead?

What you want, is to go down to the smallest unit possible, which is apparently Planck's Constant.

It's an arbitrary physics constant.

The mass of a chunk of atoms depends on their temperature and their purity, which are things you can't measure very accurately the more atoms you have.

Essentially, that's what they were doing with Le Grande K. It's unstable because molecular properties are unstable in aggregate.

The second depends on a specific isotope at a specific temperature, 0K, so it's all theoretical anyways. How you define something doesn't need to coincide with how you measure it.

It's far easier to measure a single isotope at a specific temperature limit than it is a whole rod of them. Just because they're both theoretical doesn't mean there isn't a huge practicality component to the decision.

How exactly mass depends on a temperature?


You may be thinking "Oh, you fool--E=mc^2 is for fission and fusion, and certainly doesn't apply to things like the energy in the heat of an object". But weirdly, it does. https://physics.stackexchange.com/questions/87259/does-decre...

It also applies to things like gravitational potential energy, or velocity. Climb a flight of stairs, and you gain energy. Gaining potential energy really means that you've gained mass, and so you're heavier at the top of the stairs than at the bottom. The amount that you are heavier depends on the amount of energy you gained, converted into mass. Similarly, as you gain velocity, you gain kinetic energy, which also makes you heavier. If you wave your hand in front of your face, your hand's motion causes it to gain mass. Velocity also dilates time, so time passes ever so slightly slower than for the rest of your body.

This typically only matters in a relativistic context, and doesn't impact day to day life. The difference in passage of time can be measured by an atomic clock if you put it on a rocket into space, but is otherwise insignificant. It's unlikely any scale could measure your weight-gain from climbing stairs, since the amount of energy you gain is insignificant when converted into mass. You can compute the mass gain by solving for "m" in the formula E=m*c^2, so m=E/(c^2).

The speed of light c is a really big number, and so to compute the mass you gain, you're dividing the energy by c^2, which is a much bigger number. Thus a gain to kinetic or potential energy does not noticeably affect your mass in day to day situations. Conversely, if you can convert any meaningful part of your mass into energy, then it's an absolutely tremendous amount of energy: atomic weapons.

> Gaining potential energy really means that you've gained mass

I've never heard this before. Can you link to some further explanation? Intuitively, if anything, you'd lose mass, because you're in a place now where space is less curved than where you were before.

The system composed of you + planet gains mass. You can not measure a different rest mass for yourself at either situation, so you'll probably attribute the extra mass to the planet (and the planet to you).

And yes, there's also some change due to changes in gravity. I'd expect that to be much smaller.

But IANAP, and not that good with relativity.

Mass is constant in this equation. It is absolutely incorrect to talk about a "rest" mass and a "relativistic" mass, only energy and momentum are relativistic, while mass is always a constant. Algebraically it may make a tiny bit of sense, but there is no physical meaning behind it.

Citation, please. Everything I've ever read says “E = mc2 applies to all processes that release or absorb energy.”

Basically, there are two schools of thought. An outdated one, which merges γ into m, and the current one (e.g., the Landau lineage) which leaves m alone. You won't find any "relativistic mass" in any decent source published since the famous theoretical minimum ( https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics ).

There is a very good reason for this approach. In the simplest, most classic way of deriving the special relativity from the first principles, the 4-velocity is introduced before the 4-momentum. I.e., γ and m are coming from different places and are not connected in any ways whatsoever.

"In general, relativistic and rest masses are equal only in systems which have no net momentum and the system center of mass is at rest". This is the case of a system being heated. I'm still led to believe that the mass is still increased by the increased motion of the particles in that system. https://en.wikipedia.org/wiki/Mass_in_special_relativity

Btw., even the Wikipedia article contains a nice explanation of what I'm talking about (and, yes, I'm of the Landau-Kapitsa-Okun school of thought, naturally): https://en.wikipedia.org/wiki/Mass_in_special_relativity#Con...

As I said, algebraically both approaches are equivalent, so there is not much harm in using this notion. But the "relativistic mass" does not have physical meaning and does not make any sense because of the way relativity theory is defined. And I would not count wikipedia as an authoritative source, anyway. 2nd volume of the Course is a bit more legit.

Measured mass is a function of total energy.

It is not a mass (or a "rest" mass, if you want to use this incorrect and unnecessary notion) that you measure.

That's what the new definition does, using Si(28) as the "reference atom". In the current definition the kilogram is not related to atomic mass.

No, the new definition defines kg using Planck constant (according to Wikipedia).

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