Science > Physics > Quantum Gravity 102.2: Unification and Electromagnetism and Gravitation
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
14 Mar 2007 05:18:06 PM |
| Object: |
Quantum Gravity 102.2: Unification and Electromagnetism and Gravitation |
From Osher Doctorow
In Nordstrom's first paper (1914), the electromagnetic state of what
we would now call space is represented by a vector, the Minkowski six-
vector f, while the gravitational field becomes a 4-vector, the first
with components:
1) fxy, fyz, fxu, fyu, fzu, u = ict
and the second (gravitation) has components:
2) fwx, fwy, fwz, fwu (with fxw = -fwx, etc.)
The components of the magnetic field strength H and electric field
strength are respectively:
3) Hx = fyz = -fzy, etc.
4) -iJx = fxu = -fux, etc. (x, y, u, z, are subscripts here)
Let me interrupt here to discuss the question of Unification of forces
around the time of the Big Bang, which Nordstrom doesn't discuss.
Suppose that we look at the two Coulomb-like g and electric "static"
laws:
5) F_g = Gm1m2/r^2 (G constant)
6) F_e = kq1q2/r^2 (k constant)
What if I told you that in the earliest Universe (at least, of "this
cycle" if there were more than one cycles), when F_g (the force of
gravitation) = F_e (the electrostatic force), then it can be proven
that m1 = q1, m2 = q2, and vice versa which is to say that mass =
charge? You might suspect that we're on the right track. Here's a
proof, with one slight physical assumption that is reasonable.
We consider the same distances r in both (5) and (6) and set F_g =
F_e, later reversing the reasoning to obtain the results. We get:
7) Gm1m2 = kq1q2
since r^2 drops out. However, (7) says:
8) m1/q1 = (k/G) (q2/m2) = (k/g)(1/(m2/q2)
This doesn't make physical sense unless m2 = q2 since the two masses
m1 and m2 (and similarly the two charges) are "undistinguished" from
each other except by labelling with the exception of the possibility
that m1 for example is much larger than m2 (but that wasn't even
assumed). In reversing this argument, we have to specify why m1 = m2
is a reasonable physical or mathematical assumption. Using Probable
Influence/Causation (PI), the analog of (7) is:
8) P' (q1q2 --> m1m2) = 1 + m1m2 - q1q2
which is optimized or maximized when P' = 1, in which case:
9) m1m2 = q1q2
and again m1/q1 = 1/(m2/q2), which is physically nonsensical unless m1
= q1, m2 = q2.
Osher Doctorow
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| User: "" |
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| Title: Re: Quantum Gravity 102.2: Unification and Electromagnetism and Gravitation |
14 Mar 2007 11:13:21 PM |
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You got it backwards so I fixed it;
.........................................................................
worotcoD rehsO
..2q = 2m ,1q =
1m sselnu lacisnesnon yllacisyhp si hcihw ,)2q/2m(/1 = 1q/1m niaga dna
2q1q = 2m1m )9
:esac hcihw ni ,1 = 'P nehw dezimixam ro dezimitpo si hcihw
2q1q - 2m1m + 1 = )2m1m >-- 2q1q( 'P )8
:si )7( fo golana eht ,)IP( noitasuaC/ecneulfnI
elbaborP gnisU .noitpmussa lacitamehtam ro lacisyhp elbanosaer a si
2m = 1m yhw yficeps ot evah ew ,tnemugra siht gnisrever nI .)demussa
neve t'nsaw taht tub( 2m naht regral hcum si elpmaxe rof 1m taht
ytilibissop eht fo noitpecxe eht htiw gnillebal yb tpecxe rehto hcae
morf "dehsiugnitsidnu" era )segrahc owt eht ylralimis dna( 2m dna 1m
sessam owt eht ecnis 2q = 2m sselnu esnes lacisyhp ekam t'nseod sihT
)2q/2m(/1()g/k( = )2m/2q( )G/k( = 1q/1m )8
:syas )7( ,revewoH .tuo spord 2^r ecnis
2q1qk = 2m1mG )7
:teg eW .stluser eht niatbo ot gninosaer eht gnisrever retal ,e_F
= g_F tes dna )6( dna )5( htob ni r secnatsid emas eht redisnoc eW
..elbanosaer si taht noitpmussa lacisyhp thgils eno htiw ,foorp
a s'ereH .kcart thgir eht no er'ew taht tcepsus thgim uoY ?egrahc
= ssam taht yas ot si hcihw asrev eciv dna ,2q = 2m ,1q = 1m taht
nevorp eb nac ti neht ,)ecrof citatsortcele eht( e_F = )noitativarg
fo ecrof eht( g_F nehw ,)selcyc eno naht erom erew ereht fi "elcyc
siht" fo ,tsael ta( esrevinU tseilrae eht ni taht uoy dlot I fi tahW
)tnatsnoc k( 2^r/2q1qk = e_F )6
)tnatsnoc G( 2^r/2m1mG = g_F )5
:swal
"citats" cirtcele dna g ekil-bmoluoC owt eht ta kool ew taht esoppuS
..ssucsid t'nseod mortsdroN hcihw ,gnaB giB eht fo emit eht dnuora
secrof fo noitacifinU fo noitseuq eht ssucsid ot ereh tpurretni em teL
)ereh stpircsbus era ,z ,u ,y ,x( .cte ,xuf- = uxf = xJi- )4
..cte ,yzf- = zyf = xH )3
:ylevitcepser era htgnerts
dleif cirtcele dna H htgnerts dleif citengam eht fo stnenopmoc ehT
).cte ,xwf- = wxf htiw( uwf ,zwf ,ywf ,xwf )2
:stnenopmoc sah )noitativarg( dnoces eht dna
tci = u ,uzf ,uyf ,uxf ,zyf ,yxf )1
:stnenopmoc htiw
tsrif eht ,rotcev-4 a semoceb dleif lanoitativarg eht elihw ,f rotcev
-xis ikswokniM eht ,rotcev a yb detneserper si ecaps llac won dluow ew
tahw fo etats citengamortcele eht ,)4191( repap tsrif s'mortsdroN nI
worotcoD rehsO morF>
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