My idea for unitsystem:
for first I set unmultiplied units so that
##h=1## Planck constant
##c=1## speed of light
##k_b=1## bolzmann constant
##k_E=\frac{1}{2*2\pi}## Coulomb constant
##k_G=\frac{1}{2*2\pi}## Newtons gravitational constant.
In this unitsystem many formulas have simpler form than in unitsystem, where ##k_E=1## and ##k_G=1##.
conversion of unmultiplied units to SI:
##t_b=c_{SI}^{-5/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2pi)^{1/2}*2^{1/2} \approx 4.79042770714*10^{-43}*s## time unit
##l_b=c_{SI}^{-3/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2pi)^{1/2}*2^{1/2}\approx 1.436134097196*10^{-34}*m## length unit
##m_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*(2pi)^{-1/2}*2^{-1/2}\approx 1.539006070965*10^{-8}*kg## mass unit
##q_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{E\ SI}^{-1/2}*(2pi)^{-1/2}*2^{-1/2}\approx 1.326211321739*10^{-18}*C## electriccharge unit
##T_b=c_{SI}^{5/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*k_{b\ SI}^{-1}*(2pi)^{-1/2}*2^{-1/2}\approx 1.001840552719*10^{32}*K## temperature unit
Now to make units that are more similar to values in everydaylife I multiply unmultiplied units with ##2^n## (n is arbitrarily chosen for every unit). Name of new unit will be name of unmultiplied unit, but n added to lower index of its name.
conversion of multiplied to SI:
##t_{b144}=t_b*2^{144}\approx 10.683010768898102*s## time unit
##l_{b110}=l_b*2^{110} \approx 0.18642086403260658*m## length unit
##m_{b28}=m_b*2^{28} \approx 4.131237964462824*kg## mass unit
##q_{b40}=q_b*2^{40} \approx 1.4581847691398792*10^{-6}*C## electriccharge unit
##T_{b-104}=T_b*2^{-104} \approx 4.9394552831557474*K## temperature unit
##F_{b-150}=F_b*2^{-150} \approx 0.0067481914578038016*N## force unit
physical constants are very easily derivable in this system:
- take dimension of constant in units that you want to use this constant with ##[k_G]=\frac{F_{b-150}*l_{b110}}{m_{b28}^2}## (solve defining formula ##F=\frac{k_G*m_1*m_2}{l^2}## for constant ##k_G=\frac{F*l^2}{m_1*m_2}## to get it)
- replace every unit in dimension of constant with ##2^{-n}##, where n is n of unit in this unitsystem that you are using(for example n of ##q_{b43}## is 43). ##\frac{2^{150}*(2^{-110})^2}{(2^{-28})^2}=2^{-14}=6.103515625*10^{-5}##
- multiply the value with constants value in unmultiplied system. ##2^{-14}*\frac{1}{2*2\pi}=\frac{2^{-15}}{2\pi}##
- and the value of physical constant has been found ##k_G=\frac{2^{-15}}{2\pi}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2} \approx 4.857023409786845*10^{-6}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2}##.
n of force unit or any other unit can be changed independently from n's of other units, but it might create physical constants to formulas, that do not have physical consants in SI system. For example if you used ##F_{b-140}## instead of ##F_{b-150}## , then there would be physical constant in formula ##a=2^{10}*\frac{F}{m}## (Newon's 2. law)good properties of this unitsystem:
- units are defined purely by physical constants without using quantities, that can not mathematically expressed, but only be measured (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom is used to define second in SI unitsystem.)
- very easy to convert to natural units
- units are approximately in same size as things in everyday life are
- using this unitsystem gives people more intuition of what dimensional physical constants are
- easy to derive numerical values of physical constants in this unitsystem
What do you think of this?
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bob012345 said:
Does setting ##h=1## and ##c=1## give people more or less physical insight to the way the universe works? To me, that is the metric.