In Search of GUS (God's Unit System)

[dicerandom]

OK, so this is spawning off from a discussion between myself and some of my physics inclined friends. We were talking about E&M and electrostatic units (i.e. statcoulombs) and how it results in nice things like $$\epsilon_0$$ being 1. If we then go further and define length and time appropriately (i.e. centimeters and light-centimeters), we can get c=1 and simplify Maxwell's equations even further.

In this light I'd like to ask the following question: What unit system does God use? How can we define our units in such a way as to make as many physical constants as possible either equal to 1 or some geometrically derived identity?

 

[KingNothing]

What do you mean? We already have made all of our units very 'elegant' and simple to work with. It wasn't always that way though, that's why we have very outdated units such as Furlongs, Fathoms, and Chains, for example.

 

[dicerandom]

What do you mean? We already have made all of our units very 'elegant' and simple to work with. It wasn't always that way though, that's why we have very outdated units such as Furlongs, Fathoms, and Chains, for example.

Well in my example I started out with the slightly-ugly form of Maxwell's equations in the MKS system and noted how they can be significantly cleaned up by using a different unit system. There are all kinds of other physical constants that pop up all over the place, for instance $$\hbar$$ in quantum mechanics, and I'm wondering what other changes we can make to our unit systems so that we can eliminate as many of these constants as possible.

 

[Danger]

I hope that no one can answer your question because if they do, then I as an atheist would be left dimensionless.

 

[dicerandom]

I hope that no one can answer your question because if they do, then I as an atheist would be left dimensionless.

Just substitute "God" with "the universe" and I think it'll work out

 

[HallsofIvy]

This has been done (although, I don't think God has to measure anything!)

Do not take "length", "time", etc. as the fundamental measurements- instead look at universal constants.

Since c is a constant speed, take c= 1.
Since the G in "F= GMm/r²" is a universal constant, take G= 1.
Planck's constant, $\lambda$ is a univerasl constant of action so take that to be 1.

YOu can then calculate the corresponding sizes of other measurements.

For example, the unit of length works out to the (quantum) radius of an electron and the unit of time is the time it takes a photon to cross the radius of an electron. Not very convenient for everyday use!

 

[Ivan Seeking]

Planck units are called God's units.

...The Planck units are often semi-humorously referred to by physicists as "God's units". They eliminate anthropocentric arbitrariness from the system of units: some physicists believe that an extra-terrestrial intelligence might be expected to use the same system.

Natural units can help physicists reframe questions. Perhaps Frank Wilczek said it best :

...We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in Natural (Planck) Units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)]...(June 2001 Physics Today)...

http://en.wikipedia.org/wiki/Planck_units

 

[dicerandom]

Dang, beat to the punch by over a century!

 

[rbj]

Dang, beat to the punch by over a century!

this is also one of my pet topics in physics.
listen, i thought of the same thing in the seventies, had no idea they had a name until someone on my usual internet hangout (comp.dsp) told me. i think a generic name for this concept might be "Natural Units" rather than either Planck's or God's.
one thing where i think that Planck missed is that he should have normalized (by judicious choice of units) $4 \pi G$ instead of just $G$ because of how fundamental the concept of flux is to inverse-square laws. also Planck never defined a "Planck Charge" that i know of, but other physicists have essentially extended the concept of Planck Units to a unit charge by (after the natural units of length, time, and mass have been defined and then additional units for force, energy etc.) defining the natural unit of charge so that the Coulomb Force Constant ( $1 / 4 \pi \epsilon_0$ is also set to 1 like $G$ ) just as it is in the cgs unit system. but, we can see what happens to Maxwell's equations when you do that, extraneous factors of $4 \pi$ in 2 places. far better to normalize $\epsilon_0$ (to get rid of the $4 \pi$ ) and likewise better to normalize $4 \pi G$ (for the same reason in the so-called "Gravito-Electro-Magnetic" or GEM equations that look just like Maxwell's except that charge density is replaced by mass density and $1 / 4 \pi \epsilon_0$ is replaced by $G$).
so, to get to "God's Units", i don't think that Planck got it perfectly, but very close.

 

[dicerandom]

rbj: I was actually thinking of something simmilar, although the bits relating to G didn't occur to me. I was thinking that I'd rather have $\epsilon_0$ normalised since then you get a nice physical equation for the electric field of a point charge:

$$\frac{Q}{4 \pi r^2}$$

which, I think, nicely shows the spherical symmetry of the situation.

 

[rbj]

Since c is a constant speed, take c= 1.
Since the G in "F= GMm/r²" is a universal constant, take G= 1.
Planck's constant, $\hbar$ is a universal constant of action so take that to be 1.
You can then calculate the corresponding sizes of other measurements.
For example, the unit of length works out to the (quantum) radius of an electron and the unit of time is the time it takes a photon to cross the radius of an electron. Not very convenient for everyday use!

Hall's, are you sure about that? the Planck Length is about 10^-25 of the Bohr radius. i thought the radius of an electron is about 10^-5 times the Bohr radius.

BTW, the Planck units are defined in such a way that there is no special prototype (not even elementary particles) or substance or "thing" to base them on. they are defined purely from the properties of the vacuum. the interesting thing is that the Planck Charge happens to be in the ballpark of the Elementary Charge (related by the square root of the Fine-Structure Constant) $e = q_P/\sqrt{\alpha}$) even though its definition had nothing to do with the Elementary Charge. i like to think that the Fine-Structure Constant has taken on the value that it has, because of the amount of charge (measured in Natural Units) that Nature (or God, for the purpose of imagination) has assigned to electrons, protons, positrons (or the quarks that make them).

in the "Most Natural Units" i have alluded to in the post above, that dimensionless number, the amount of charge (in natural units of charge $q_N \equiv \sqrt{\hbar c \epsilon_0}$) that Nature has deigned to sprinkle onto the electron is

$$e = \sqrt{4 \pi \alpha} \ q_N = 0.30282212 \ q_N$$ .

That is the number physicists should be putting up on their walls and staring at instead of 137.03599911 . (IMO, anyway.)

 

[rbj]

rbj: I was actually thinking of something simmilar, although the bits relating to G didn't occur to me. I was thinking that I'd rather have $\epsilon_0$ normalised since then you get a nice physical equation for the electric field of a point charge:

$$\frac{Q}{4 \pi r^2}$$

which, I think, nicely shows the spherical symmetry of the situation.

well, there is spherical symmetry of the E field anyway, but the root to this concept of flux density does lie at the area of a sphere, $4 \pi r^2$. i wish that the cgs guys would have considered that and defined their unit of charge (the "Statcoulomb" or "esu of charge") so that $\epsilon_0$ was normalized instead of what they did (normalize $4 \pi \epsilon_0$).

it's the same mistake that Planck made in normalizing $G$ instead of normalizing $4 \pi G$.