Setting the Fundamental Constants of Physics

What would happen if we tried to make physics easier by setting all the fundamental constants to 1?" This would make the procedural math we must do in physics much easier. This proves to be possible, using basic algebra, because there are four fundamental constants (G, h, e, mu) and four units of measure (d, t, m, q). This exercise will turn out to have interesting implications regarding the structure of the universe.

Written 2000

Formatted 2010

  We can start by listing the fundamental physical constants:

Gravity

G

6.67x10-11 nt/m2

Electrical Permitivity

e

8.85 pF/m

Magnetic Permeability

mu

400pi nH/m

Speed of Light

c

3x108 m/s

c = (e*mu)-1/2

Uncertainty

h

6.63x10-34 erg*s

Through simple algebra we can define new units of measurement where each of these constants will be one. Showing only the final step of the algebra we get:

distance

d

=h1/2G1/2c-3/2

1.43x10-34 m

Our unit length is approximately equal to the planck length.

time

t

=h1/2G1/2c-5/2

4.78x10-43 s

Our unit time is approximately equal to the planck time.

mass

m

=h1/2G-1/2c1/2

1.54x10-8 kg

charge

q

=h1/2c1/2e1/2

1.33x10-18 c

Our unit charge is slightly larger than the charge of an electron or proton.

All we did was create new unit measures based on the desire to have our constants set to one, which is the easiest number to use. However, we have noticed some intriguing coincidences.

These coincidences suggest that we stumbled onto some basic properties of the physical universe itself. The pure mathematicians will argue that our values are not equal. But we did not start by looking for properties of the universe using methods of physics; all we did was attempt to be lazy using methods of algebra.

If we changed our approach from simple algebra, to integrating across physically significant spaces we will get answers that have the same magnitude but vary by our integration constants. This may produce answers that match the actual physical values. Feel free to suggest how this might be done. Here's a simple attempt.

 

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