the kilogram

                If the Planck is not a constant then definition of the kilogram cannot be based on it.
Einstein took constancy of the speed of light in vacuum as a working hypothesis a hundred years ago. Such constancy is not proven and the special theory of relativity may be understood as the speed of light being the same for all moving observers at a certain time and a certain place.
New theory of Vasily Yanchilin in his book "The Quantum Theory of Gravitation" (2003) considers a relationship between c and the potential of the total mass of the universe. This potential decreases with the expanding universe and then so does c, becoming zero at the "edge" of the universe where everything looses speed and direction, gets into a totally quantum mechanical state. Then also correction should be made for the supernova Ia and accellerated expansion of the universe vanishes. Note that in a quantum mechanical world an Initiative from Outside can be compared with a photon hitting an electron and reducing its uncertainty. The general theory of relativity is based on constant c but reflect on electro- magnetic aspects which are not unrelated to other things. Radiation has a mass equivalent and nowhere in the universe exists absolute vacuum. Read more in the book starting at page 188 where a logical question is put: The general theory of relativity dating from before the era of quantum mechanics maintains that when a second passes in empty space then only parts of a second are noticed near mass. However everybody agrees that near mass the unit of lenth becomes smaller and thus atoms shrink. Which means that electrons need more energy for transfers. They get higher frequency  of radiation and as time is connected to physical processes the second will run faster near mass. This is in agreement with fast processes around presumed Big Bang. Also the principle of least action favours the new theory, for a photon will try to make as big steps (oscillations with low frequency) and a minimum of these when passing a mass. So it takes a parabolic route. If Einstein were right a hyperbolic trajectory would be observed.
It appears however that the Galileo satelite clock ticks faster than an atomic clock on Earth. Research is necessary whether this is caused  by higher Heisenberg uncertainty in accordance with the hypothesis that mass reduces it; and by less energy required for transitions of electrons. Can NIST handle this?

Yanchilin presents a new formula for an interval based on wave theory and resulting in non-existence of black holes. These being just big masses. He rejects the 1919 "proof" by arguing that change of potential amounts to 2mgh, of which half is due to change of internal energy according E = m.c quadrat. Last but not least the russian scientist gives a qualitative explanation of gravity as a pure quantum mechanical phenomen: In the half of a particle nearest to an external mass there will be less quantum mechanical transitions to the farthest half than from the latter to the nearest one since the latter is more distant from the external mass. Net result is movement of the particle towards the external mass, which in common language is called gravitational attraction.

Consequences of the new theory are that negative energy, inflation, black holes, a cosmological constant become phantasy. And that the Planck in relation with the speed of light is not a constant, therefore not fit to serve sec for definition of the kilogram.

Mass is not well understood. It is not felt in the absence of other masses as if there is balance in quantum mechanical transitions. In the mathematical model of curved space mass stays present always. Dark mass might be in the view of Yanchilin relic of light and to get the idea one should consider that around Earth all the time there is plenty of sunshine with lots of energy. At large distance light waves spread and do not react unless adjusting curvature is added like with a telescope. If possible add some lines to this and try to answer whether spread of potential may have radiation as a carriage.