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Monday, December 29, 2003

GUTz – Essay n. 003 - Force unification - I 

Force unification - I

---------- Introduction

In this essay we are going to demonstrate that all the actual different forces, are all expressions of a fundamental and unified force.

This Essay as two parts. In the first one, we “work” at “Plank level”. At that level we are going to use for the different Dimension involve in the laws, the Plank limit values of each Dimension (in SI units).

In the second part we are going to see that the force unification is truth also in all others (conscience) levels (in the entire Universe, all the time,...). To accept this conclusion we must have an open mind, because some old fundamental ideas, upon which physics theory is built, must be improved.

--------- Force Unification – I

---1) Beginning by showing some universal constants that are going to be used for demonstration.

We have at “Plank level”:

Plank constant – hp = 6,626 068 76 * 10^-34 (J s)

Gravitational constant – Gp = 6,673 * 10^-11 (N m^2 Kg^-2)

Light speed in vacuum – vp = c = 2,997 924 580 * 10^8 (m/s)

Elementary Electric charge – Cep = e = 1,602 176 462 * 10^-19 (A s)

Plank Force – Fp = c^4/Gp = 1,210 491 340 * 10^44 (N)

Plank Area – dp^2 = (hp Gp)/c^3 = 1,641 024 082 * 10^-69 (m^2)

Plank Mass – mp = ((hp c)/Gp)^1/2 = 5,456 042 671 * 10^-8 (Kg)

Plank Energy – Ep = mp c^2 = 4,903 646 606 * 10^9 (J)

Plank Time – tp = (d^3/(Gp mp)) = 1,351 253 321 * 10^-43 (s)

Plank Acceleration – ap = c/tp =2,218 625 134 * 10^51 (m/s^2)

Plank Current – Ip = Cep/tp = 1,185 696 595 * 10^24 (A)

Plank Potential – Vp = Rp Ip = 3,060 615 807 * 10^28 (Volt)

PI Plank – PIp = 2Pi = 6,283 185 307 (rad)

Classic Permeability of vacuum – mu0
mu0 = 2PIp * 10^-7 = 1,256 637 061 * 10^6 (H/m)

Natural Permeability of vacuum – mup (see note 1)
mup = Rp/c = hp/(e^2 c) = 8,610 225 807 * 10^-5 = PIp/ALFA * 10^-7 (H/m)

Classic Permittivity of vacuum – epsilon0
epsilon0 = (2PIp c^2 * 10^-7 ) = 8,854 187 818 * 10^12 (F/m)

Natural Permittivity of vacuum – epsilonp
epsilonp = 1/(Rp c) = e^2/(hp c) = 1,292 242 697 * 10^-13 = (ALFA * 10^7)/(PIp c^2) (F/m)

Plank Resistance (or von Klintzing resistance) – Rp (or Rk)
Rp= hp/e^2 = Vp/Ip = (mup/epsilonp)^1/2 = 2,581 280 759 * 10^4 (ohm)

note 1. ALFA - Fine structure constant = 7,297 352 523 = 1/(137,035 999 834)

---2) The different laws for force (at “Plank level” in “positive side”):

Newton’s second law
Fp = mp ap (N)

Newton’s law of gravitation
FGp (Gravitic Plank force)
FGp = Gp (mp^2/dp^2) (N)

Coulomb’s law
FEp (Electric Plank force)
FEp = (1/(2PIp epsilon0)) (e^2/dp^2) = (ALFA/(PIp epsilonp)) (e^2/dp^2) ((N)

Magnetic Plank force
FMp (Magnetic Plank force)
FMp = 2 (mu0)/(2PIp) Ip^2 = ((2 ALFA mup)/PIp) Ip^2 (N)

---3) Relationship between mu0 and mup, and epsilon0 and epsilonp:

mup = mu0/(2 ALFA)
epsilonp = (2 ALFA) epsilon0

---4) Demonstration

Fp = FGp = Gp (mp^2/dp^2) = ((hp c)/mp^2) (mp^2/dp^2)
= (hp c)/dp^2 = Ep/dp = mp ap (N)

and

Fp = (PIp/ALFA) FEp = (PIp/ALFA) (ALFA/(PIp epsilonp)) (e^2/dp^2)
= (1/epsilonp) (e^2/dp^2) = ((hp c)/e^2) (e^2/dp^2) = (hp c)/dp^2
= Ep/dp = mp ap (N)

and

Fp = (PIp/(2 ALFA)) FMp = (PIp/(2 ALFA)) ((2 ALFA mup)/PIp) Ip^2
= mup Ip^2 = (hp/(e^2 c)) Ip^2 = (hp c)/(Ip^2 dp^2) Ip^2
= (hp c)/dp^2 = Ep/dp = mp ap (N)

so we have:

Fp = mp ap (N)
Fp = Ep/dp (N)
Fp = (hp c)/dp^2 (N)
Fp = Gp mp^2/dp^2 (N)
Fp = (PIp/ALFA) (1/(2 PIp epsilon0) (e^2/dp^2) (N)
Fp = (1/epsilonp) (e^2/dp^2) (N)
Fp = (PIp/(2 ALFA) (mu0/(2 PIp) Ip^2 (N)
Fp = mup Ip^2 (N)
Fp = c^4/Gp (N)
Fp = (Vp Ip)/c (N)

that is, we have only one Force (the Plank Force) at “Plank level”.

In GUTz – Essay n. 003a - Force unification – II, we are going to see the force unification at all levels and some of the implications in ours classic ideas about how the world works.


Thanks in advance, by yours comments

Yours sincerely
Viana Abreu

gutz_va@hotmail.com or ceo@neworldream.com
GUTz is a Global Unified Physic Theory where zero is the primary source and last destiny of all manifestation in Universe.

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