Does the Earth move around the Sun?

[D H]

The unit of mass can be made precise. Even today, in mass spectroscopy, there is a unit of mass called atomic mass unit and is denoted by u. It's definition is that it is exactly \frac{1}{12}th of the mass of the isotope ^{12}C.

Yep. An atomic mass-based mass standard certainly is one of the contenders. Unfortunately, physicists do not yet know what 1/12 of the mass of ¹²C is. As you noted, the published value, which is the value that you cited, has a 50 ppb uncertainty. This is largely due to the uncertainty in Planck's constant. Then there's the uncertainty in Avogadro's number. An mass standard that is only usable to particle physicists is of limited value. An atomic mass-based standard would require better definition of Avogadro's number (One solution: Just give it an ad hoc value), a way to accurately count the atoms in a largish sample, repeatability, cost, and all that.

There are a number of efforts underway to do the prototype-based mass standard in. One of them almost certainly will pay off, sometime. One thing is certain: It ain't going to happen any time soon. This is an international standard we're talking about, after all. There are claims to be validated, committees to be organized, documents to be written and reviewed, votes to be taken, ... Years.

 

[Dickfore]

Do you think a replication of the mass standard can be done with precision greater than 50 ppb?

 

[D H]

An order of magnitude better.

From http://www.bipm.org/en/scientific/mass/calibrations_mass/

1 kg prototypes in Pt/Ir
The primary role of the Mass Section is to provide traceability to the international prototype of the kilogram. We do this by maintaining a number of prototypes and other standards in Pt/Ir. A subset of these is used as working standards to calibrate national prototypes upon request. The remainder are used for quality control. The combined standard uncertainty currently assigned to the calibration of a national prototype is typically 0.005 mg.

1 kg mass standards in stainless steel
The BIPM offers a calibration service for 1 kg standards in stainless steel. This service is available free of charge to NMIs of Member States of the Metre Convention. The volume of the standard will be determined by hydrostatic weighing at the BIPM if this parameter is unknown (typical combined standard uncertainty obtained at the BIPM is 0.4 mm3 at 21.7 °C). However, the volumetric thermal expansion near room temperature must be supplied by the NMI or the manufacturer of the standard. If not already in our database, the BIPM will determine the location of the centre of gravity of the standard as well as its magnetic properties (volumetric magnetic susceptibility and axial permanent magnetization). The combined standard uncertainty currently assigned to the calibration of a 1 kg standard in stainless steel is typically 0.013 mg.​

The BIPM has long wanted a replacement for the prototype-based definition of the kilogram, but only if this replacement is accurate to within 20 ppb. In the case of an atomic-based standard, that 50 ppb error in the atomic mass unit itself is only a part of the error. Error will also creep in when the atomic mass unit is scaled up to human size. How do you know if you have 5×10²² atoms in a sample, versus 5×10²² plus 10¹⁷ atoms?

 

[Dickfore]

Ahh, I see. It's because the prototype has such a "big" mass compared to u that the relative error is much smaller.