I heard a speech about the changing SI unit, but then it got me concerned with a bunch of questions. Basically, they switched from sticks to some "fundamental constants".

  1. What is $h$?

In the Metric SI unit, $h$ can be measured. However, in the new SI, it became a unit and had always be "1". But then, it seemed to me that this brought the question about the magnitude of $h$ itself. i.e. with different measurement methods, instrument, and precision, people will get a different understanding towards the magnitude.

But how could they report such difference then? Or say how could they report weather they agree with the value and precision of $h$? After all, $h$ was defined to be unite "1".

  1. Question about locally.

As shown, in the past, a meter was measured from a stick, quite literately. This had yet another benefits along side the intuition, that was, they tricked the locally. For example, even one assumed there's no variation in the law of physics in terms of orthodox physics or required precision, even if one assume there's no non local effect and causality disturbance, the micro gravity, gradient difference, e.t.c. could still make changes to the experiments.

By using a fixed stick, they by passed/tricked this constrain by transforming copy of sticks around the world, which regulated the global effect by the action of transforming the sticks.(i.e. the transforming of stick actually carried information of the transforming of global model) If they using the "fundamental constants", which means measurements could be carried out anywhere, the definition of fundamental units would then become local, or at least local in the sense of the measurement. There's no way for them to simply communicate or determinte the possible global effect or noise on the local definition of "fundamental units". So, eventually, are they going to start to send "sticks"(i.e. mirrors) around the world anyway?

  • $\begingroup$ “However, in the new SI, it became a unit and had always be 1.” You are badly misinformed. It is not a unit, and it is not 1. It is now exactly $6.62607015×10^{−34}$ joule-second, which is consistent with its previous value. There is no way that “people will get a different understanding towards the magnitude” unless they misunderstand that it now has a defined value. $\endgroup$ – G. Smith May 31 '19 at 4:26
  • $\begingroup$ @G.Smith I used "1" to represent whatever the value they were choosing, i.e. $1h= 6.62...15\times 10^{-34}$(now jole-second was defined by this $1 h$). It still wasn't clear about how they can produce that $1 h$, i.e. they may produce $6.62...15\times 10^{-34}$ differently, or say their exact $6.62...15\times 10^{-34}$ (now defined by $1h$) may be different? $\endgroup$ – ShoutOutAndCalculate May 31 '19 at 4:46
  • $\begingroup$ Sorry, I can’t understand what you are asking. This is no different from defining the speed of light to be an exact value. Did that bother you? $\endgroup$ – G. Smith May 31 '19 at 4:51
  • $\begingroup$ @G.Smith The_Sympathizer's answer solved many of my doubts. But speed of light was exact(in a sense from the wave solution and now defined to be) only for plane wave in vaccume. (I think read a paper somewhere demonstrated even a single photon could be treated as a wave pack and thus had a group velocity, not even mention permittivity, e.t.c. ) [Sorry, typo, corrected.] If the prepared light was not the same, it's very possible and measurable to a significance for them to disagree with the unit length of $1c$ in practice. $\endgroup$ – ShoutOutAndCalculate May 31 '19 at 5:05
  • $\begingroup$ “speed of light was exact ... only for plane wave in vaccume” The BIPM’s definition of the meter (bipm.org/metrology/length/units.html) says nothing about plane waves. $\endgroup$ – G. Smith May 31 '19 at 6:05

I believe that in your first point, what you are trying to get at is that $h$, as a fundamental basis for the system, the unit of action, is subject to uncertainty in its measurement, and thus how that uncertainty relates to its use as a definition for units. The answer to that is quite simple: uncertainty in measuring $h$ becomes uncertainty in being able to realize an object with unit property, i.e. here, uncertainty/inability as to how well you can create an object with a mass as close to exactly 1 kg as possible. It's changing "uncertainty from how many kg are needed to make something" to "uncertainty as to what a kg is".

For the second point, it seems what you're wondering is whether or not there could be some sort of spatial variation in constants like $h$ or $c$ (which is what is used to define the meter, which is the unit that was originally built upon a "stick") and whether or not this is taken into account. The thing is, we don't know, but we can say that if there is, it's much smaller than any experiment of ours can measure, or we'd have found it out by now with different labs at different locations systematically and consistently reporting different values and moreover, our best-tested theories don't posit such variations. Thus, for all work done so far, using $h$ and $c$ as constants is the best thing we've got.

Incidentally, that last point brings up an important philosophical/meta-scientific point that should be mentioned and that is that all measurements are fundamentally built on a theoretical basis, and thus, in a way, are "not better than the theory on which they're built". That said, if that basis were wrong, it would show up as the measurements start doing things not expected from the theoretical basis on which they're built. However, the other philosophical point that then comes up is whether we should account for that by revising the theory of measurement, or by holding the measurements as consistent and transferring the variability to the theory of what is being measured. Both are, actually, empirically equivalent: thus, why I say, it's a fundamentally philosophical point. You can't escape philosophy!!! GRR.

| cite | improve this answer | |

Not the answer you're looking for? Browse other questions tagged or ask your own question.