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May19-03, 11:39 PM
Sci Advisor
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marcus's Avatar
P: 23,125
Natural units make a lot of things easier to calculate and the Casimir force formla simpliefies to

F = (pi2/240) A/L4

the constant in front is about 1/24, since pi-sqare is about ten.

With all these formulas if you want to work them in metric you have to put the hbars and cees and maybe some Gees back in first. In other words make them more messy before you can use them. Oh, and sometimes kays too.

However the cost of having radically clean formulas with c=G-hbar=k=1 is that the scale is unfamiliar.

For example E38 is a mile and E35 is a pace---a thousandth of a mile, around 1.6 meters---and E30 is 16 microns.

E-50 is about a micronewton of force---more exactly 1.2 micronewton.

So you could say "It is hopeless, I will never be able to learn this new scale----E44 is a million miles and E-50 is a micronewton---it's impossible" But it's actually OK and one does get used to the scale and the clean simplicity of the formulas is a big plus.

Anyway: think of two plates 1.6 meters on a side so E35 on a side, area is E70. And imagine the separation is 16 microns which is E30.

the force is easy to calculate, just the area (E70) divided by the fourth power of the sep(E120) which gives E-50 that micronewton thing, and you have to include the numerical constant which is about 1/24.
Maybe I should include that tiny force of 1.2 micronewtons in the dictionary:

E60-----1.7 billion years
E44-----a million miles
E38 ----a mile
E6 ------22 grams
E-50----1.2 micronewtons

Here's the list of constants etc, for review:

the proton compton wavelength----2.103E-14 meter---13E18
the CMB temperature-----2.725 kelvin----------1.93E-32
the Hubble time----4.35E17 seconds------------8.06E60
average sunlight photon----2E-19 joules----------E-28
the distance to the sun----150 million km---------93E44
earth orbit speed------30 kilometer/second--------E-4
solar constant----1380 watts/sq.meter------------E-119
2.701k----3.73E-23 joule/kelvin-------------------2.701
sigma-----5.67E-8 watt/sq.meter kelvin4--------pi2/60
a (the aT4 law)---7.565E-16 joule/cub. meter kelvin4---pi2/15

I see I havent yet used the proton compton. Maybe that should be next.