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Banaticus

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## Homework Statement

This isn't homework, it's just something that I've been thinking about, but I thought that this was the best forum to ask this.

The meter was first attempted to be defined as 1/10 millionth of the distance from the North Pole to the Equator through Paris. This seems so... egocentric? Not only for one country, but for our world. True, math is a universal language, but were we to meet with aliens at a higher technological level, would our meter, kilogram, etc., seem as parochial as the Roman Empire mandating that a mile be exactly equivalent to one thousand paces, but then shifting to be equal to pretty much equal to eight furlongs?

Were a meter, kilogram, etc., to all be defined somewhat differently, how would this affect different standard constants? For instance...

Gravitational potential energy is given as: [tex]G\frac{M*m}{r^2}[/tex]

Electrical potential energy is given as: [tex]k\frac{Q*q}{r^2}[/tex]

Those formulas are pretty darn close. Is it possible to recalculate SI units and base them on some sort of "universal constant" so that those two formulas would use the same constant? Sure, charges only attract between opposite "types" (positive and negative) and all mass attracts (mass is only positive), but on the surface of the formulas, the way it looks, the major difference is pretty much G and k.

If we were to redo basic SI units so that G and k were equal to one another, so that we could have one equation of the form [tex]x\frac{Thing_1*Thing_2}{r^2}[/tex] with r again measured in meters, but with the ability to either plug in two charge values or two mass values and use the same constant x, how should we go about redoing SI units?

## Homework Equations

Gravitational potential energy is given as: [tex]G\frac{M*m}{r^2}[/tex]

Electrical potential energy is given as: [tex]k\frac{Q*q}{r^2}[/tex]

## The Attempt at a Solution

We could redefine the length of the meter. The platinum-iridium bar is sort of hokey, since it's short by 1/5 of a mm from what it was purported to be.

We could redefine the kilogram, based on either the regular meter or a redefined meter. Should [tex]H_2O[/tex], although common and absolutely necessary for life as we know it, be the basis for our weights? Why not carbon? Or hydrogen, the most common element in the universe. 1.0008, it's almost 1, can't we find some way to redefine SI units so that it is exactly 1, just like 1 liter is exactly 1000 deciliters?