Homework Help: Redefining the meter, kilogram, etc.

1. Feb 18, 2009

Banaticus

1. The problem statement, all variables and given/known data
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: $$G\frac{M*m}{r^2}$$
Electrical potential energy is given as: $$k\frac{Q*q}{r^2}$$

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 $$x\frac{Thing_1*Thing_2}{r^2}$$ 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?

2. Relevant equations
Gravitational potential energy is given as: $$G\frac{M*m}{r^2}$$
Electrical potential energy is given as: $$k\frac{Q*q}{r^2}$$

3. 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 $$H_2O$$, 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?

2. Feb 18, 2009

Staff: Mentor

Actual definition of meter is distance travelled by light in vaccum in 1⁄299,792,458 sec, before it was 1,650,763.73 wavelengths of the orange-red emission line of the krypton-86 atom. Definitions of other constants changed as well.

You are not the first one to think about such a universal system. Question is - does it make sense? We have enough problems converteing between feets and meters already.

3. Feb 18, 2009

Banaticus

But that definition of a meter, with its crazy value in seconds (why not something simple like exactly 1/3.0x10^8) was developed to match the length of the platinum-iridium bar, which (despite all their best efforts) is ever so slightly changing. Just like citizens of the United States don't want to have to reconfigure everything to switch over to some new measuring system, citizens of other countries don't want to reconfigure everything to switch over to some new meter. Witnes the Dutch pond, how it was officially switched over to be 1 kilogram, even though everyone still uses it as equal to only half a kilogram.

Those of us on this forum aren't anyone official. We don't have the power to switch even the smallest of countries over to some different system, nor would it likely be in anyone's economic best interest to switch to some new system. But, as long as we're talking hypothetically, what do you think would need to be changed? Is there something that seems more "natural"?

4. Feb 18, 2009

mgb_phys

The metre was intended NOT to be egocentric. Rather than being the length of some official bar somewhere the idea was that anyone anywhere in the world could make their own standard metre by simply observing a star at two places North-South of each other. Really you are jsut measuring the length of some latitude angle difference on the earth. The 10,000,000 was chosen to be a nice round number and give a result that was a convenient size for everyday use (and similair to the Yard).

Unfortunately in making the measurements to determine this distance they discovered that the earth wasn't round and so their technique couldn't be used anywhere else and had to be defined in terms of a real object again.
Switching to the wavelength and then the time definition is just a better technological solution to their original intention.

The reason for the odd number is due to the definition of the second - which is similairly arbitrary. You could define the speed of light as 1m/s and create a new 'second' but it would be a little confusing.
In lots of areas of physics you do make up convenient local units like solar masses or eV or set the speed of light to be 1.