A new dual system for the fundamental units including and going beyond the newly revised SI

Publication date: Available online 6 May 2019Source: Comptes Rendus PhysiqueAuthor(s): Pierre FayetAbstractWe propose a new system for the fundamental units, which includes and goes beyond the present redefinition of the SI, by choosing also c=ħ=1. By fixing c=c∘ m/s=1, ħ=ħ∘ J s = 1 and μ∘_=μ∘ N/A=21, it allows us to define the metre, the joule, and the ampere as equal to (1/ 299 792 458) s, (1/ħ∘=.948...×1034)s−1 and μ∘N=μ∘c∘/ħ∘s−1=1.890...×1018s−1. It presents at the same time the advantages and elegance of a system with ħ=c=μ∘_=ϵ∘_=k=NA=1, where the vacuum magnetic permeability, electric permittivity, and impedance are all equal to 1. All units are rescaled from the natural ones and proportional to the s, s−1, s−2, ... or just 1, as for the coulomb, ohm and weber, now dimensionless.  The coulomb is equal to μ∘c∘/ħ∘=1.890...×1018, and the elementary charge to e=1.602...×10−19C=4πα=.3028....  The ohm is equal to 1/μ∘c∘ so that the impedance of the vacuum is Z∘=376.730...Ω=1.  The volt is 1/μ∘c∘ħ∘s−1=5.017...×1015s−1, and the tesla c∘V/m=c∘3/μ∘ħ∘s−2=4.509...×1032s−2.  The weber is 1/μ∘c∘ħ∘=5.017...×1015.  The flux quantum is Φ∘=h/2e=2.0678...×10−15 Wb =π/e=10.374..., with KJ=483597....GHz/V=e/π=.09639..., and RK=25812....Ω=1/2α≃68.518.  One can also fix e=1.602176634 C, at the price of adjusting the coulom...

Source: Comptes Rendus Physique - May 7, 2019 Category: Physics Source Type: research