Constantless equations

[Proton Head]

Okay so I've been trying to find units for physical formulas which would negate (as many as possible) constants from the equations as possible.

(Is this even possible, heck I don't know, I'm just bored.)

 

Like instead of F = G*mM/R^2

it would be F = mM/R^2

 

That means that the unit for mass and lenght would be defined so that [m]*[m]/[L]^2 = G

 

But I need to find multiple equations in order to solve this.

I've done some calculations but with no luck.

I'm having trouble finding usable equations.

 

Thus far I've used the above, F = k*qQ/R^2 and E = hf.

 

I've also tried to attack the universal gas constant and the permittability of free space, but I get no sense out of those equations, since in case of the gas constant, its equations tend to cancel each other out, and the magnetic force equation is only usable at infinitesimal distances.

 

So any ideas of an equation that could be used?

[Proton Head]

Hmm, wait should the units of Force come into that Equation too?

 

Blah looks like it doesn't work that way, oh well...

[Severian]

You might find this thread useful.

[Martin]

Severian, thanks for remembering that thread about Planck units---to which you and I both contributed.

 

that was a thread actually about a VARIANT version of the natural units in which instead of G we had 8 pi time G take the value unity.

 

Proton Head will not find that so nice. he wants to have the numerical value of G itself be unity. That is what he is doing here:

 

Okay so I've been trying to find units for physical formulas which would negate (as many as possible) constants from the equations as possible.

(Is this even possible' date=' heck I don't know, I'm just bored.)

 

Like instead of F = G*mM/R^2

it would be F = mM/R^2

...[/quote']

 

==============

Proton Head, it looks like what you are groping for is just the conventional Planck system of units that some theoretical physicists use.

 

In 1899 Max Planck proposed a system of units, now called Planck units, which are used some in theoretical physics, and which do have |G| = 1

 

And they go way beyond just that, because and the numerical value of the speed of light |c| = 1. So when you want to do E = mc² there is nothing to multiply. the amount of energy is same as the amount of mass.

 

and when it comes to temperature and gas law etc they also have the Boltzmann constant k value unity, that is |k| = 1

 

 

and also h-bar the Planck constant people largely prefer these days, has unit value too.

 

So the upshot is in this system of units a whole lot of equations and formulas for stuff dont involve any number except 1.

 

Equations have a nice clean look and a lot of trouble with arithmetic is avoided.

 

You can look up PLANCK UNITS and find out more.

 

The downside is that the sizes of the units tend to be extreme. The speed unit is the speed of light. So if you want to talk about the speed of sound it is around a MILLIONTH! And the speed cars go on the road is about\

10^-7

that is, a tenth of the speed of sound. which is 10^-6

 

metric prefixes like nano and pico might help

 

but most people cannot handle such extremely large or extremely small units

 

the Planck length unit is about 1.6 x 10^-33 centimeter

 

the speed of light is 1 length unit per time unit. So you can tell that the time unit is very small too---the time it takes light to travel one length unit.

 

that is just how it comes out when you want to give all these natural constants the value one

when you insist that |G|=|hbar|=|c|=|k|=1 it forces the sizes of the units to be Planck units.