Re: Newton's Rotating Bucket, Mach & NASA Gravity B Space Probe
xxein_at_bellsouth.net
Date: 03/30/05
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Date: 29 Mar 2005 16:20:09 -0800
Jack Sarfatti wrote:
> Wheeler's solution to my EEP question is also below.
>
> One of the first theorems of Newton's 17th century Principia is that
a
> test particle inside a uniform density hollow spherical mass shell
does
> not sense this outer shell. Not so when the shell rotates according
to
> Einstein's GR. Remember there are no Shipov torsion effects here in
this
> model. That is a larger theory than the 1916 GR considered here where
> only T4 is locally gauged to Diff(4) to get the
coordinate-independent
> objectively real LOCAL B compensating connection field 1-form whose
> self-covariant exterior derivative 2-form is
>
> B ~ Lp(Goldstone Phase),u of the post-inflation Higgs field from
ODLRO
> vacuum coherence ABSORBING most of the random ZPF of ALL fields
> explaining the small cosmological constant at large-scales.
>
> Lp^2 - hG/c^3
>
> ,u = ordinary partial derivative
>
> There are non-trivial winding number effects in the line integrals of
B
> from multiple-connectedness non-contractible loops. More on that
later.
>
> S = DB = dB + B/\B is an ANTISYMMETRIC Cartan 2-form
>
> S = A&P "torsion" =/= Shipov torsion from locally gauging O(1,3).
>
> DS = 0 is Bianchi identity for local current conservation of the
> "torsion" current
>
> D*S = *J is the source "field equation"
>
> *J is a 3-form source
>
> D*J = 0 is local conservation of the torsion source currents
>
> None of the above should be confused with the Einstein
geometrodynamic
> picture.
>
> To get from this gauge force picture to Einstein's 1916 traditional
> picture one MUST use the TETRAD EEP as the connecting bridge
>
> g(LNIF) = (I + B)(LIF)(I + B)
>
> Within this geometrodynamic picture:
>
> "Inside a hollow, static spherically symmetric distribution of
matter,
> in vacuum, we have the flat metric (Mink)uv. Therefore, in the weak
> field and slow motion limit,the metric INSIDE A SLOWLY ROTATING
MASSIVE
> SHELL may be written guv = (Mink)uv + huv.... Inside a thin shell of
> total mass M and radius R rotating with angular velocity dW/dt ... by
> substituting in the geodesic equation ... the acceleration of a test
> particle INSIDE the rotating shell: G = c = 1 rotation axis is z
>
> d^2x/dt^2 = -(8/3)(M/R)(dW/dt)(dy/dt) + (4/15)(M/R)(dW/dt)^2x
>
> d^2y/dt^2 = +(8/3)(M/R)(dW/dt)(dx/dt) + (4/15)(M/R)(dW/dt)^2y
>
> d^z/dt^2 = -(8/15)(M/R)(dW/dt)^2z "
>
> 6.1.38 p. 323
>
> Note that the equation for a simple 1D harmonic oscillator is
>
> V = (1/2)kz^2
>
> F = ma = -dV/dz = - kz
>
> dz^2/dt^2 + (k/m)z = 0
>
> k/m = f^2
>
> So that there is a natural frequency of oscillation here for the test
> particle along the axis of rotation direction of the vacuum cyclone
in
> the interior of the rotating shell
>
> f^2 = (8/15)(GM/c^2R)(dW/dt)^2
>
> The signs are wrong for the x & y degrees of freedom that are not
> oscillatory, but are "Coriolis" in the velocity dependent terms and
> "centrifugal" ~ f^2r
>
> EEP QUESTION
> AHA! on bottom of p. 323 Wheeler shows how to get h'0i = 0 by a
counter
> rotation
>
> phi' = phi - (4/3)(GM/c^2R)dW/dt
>
> about the axis "and by a suitable redefinition of t and r one gets
the
> FLAT MINKOWSI METRIC INSIDE THE SHELL". So this conforms to g = (I +
> B)(Flat)(I + B)
>
> Wheeler also cautions on p. 324 "despite the beautiful ... analogies
> between classical electrodynamics and classical geometrodynamics, the
> two theories are fundamentally different ... even for weak fields ...
> [because of] the equivalence principle." See 6.11 for more details.
>
> 6.2 discusses Mach's principle in the form that "centrifugal forces
are
> due to rotational motion of a system relative to other matter".
>
> However, one cannot deduce the rest masses of the lepto-quark as any
> kind of Mach Principle effect. Also the "matter" may be "VIRTUAL"
i.e.
> exotic vacua of both dark matter and dark energy that is 96% of the
> stuff of the world.
>
> On Mar 28, 2005, at 1:06 PM, Jack Sarfatti wrote:
>
> Earth's J = 5.861 10^40 cm^2gramsec^-1 = 145 cm^2 Planck units
>
> Earth's Mass M is 6x10^27 gm = 0.44 cm Planck units
>
> Therefore J/Mc ~ 145/0.44 ~ 3 meters
>
> For the Sun it's J/Mc ~ 1.6 x 10^48 gcm^2sec^-1 ~ 10^8 J(Earth)
>
> M(Sun) ~ 10^6M(Earth)
>
> So that only gives J/Mc ~ 300 meters for Sun - still too small.
>
> Note that J/Mc > GM/c^2 is a naked singularity for collapsed objects.
>
> So the macro-quantum BE degeneracy effect, if any, would have to be
done
> with black holes which are also identical for same mass & J if
no-hair
> theorem is correct.
>
> On Mar 28, 2005, at 10:21 AM, Jack Sarfatti wrote:
>
> Checking with Wheeler
>
> g0phi = - (4JG/c^3r^2)sin(theta)
>
> Should be
>
> g0phi = - (4JG/c^3r^2)sin^2(theta)
>
> The dipole pattern, i.e. the second factor of sintheta that I put in
the
> base vector rsin(theta)dphi should be in g0phi.
>
> This issue of the De-Broglie-Compton wavelength as J/Mc for giant
> objects is curious.
>
> V(Newton)rot = (J/Mc)(c^4/G)g0phi = (Macro-Quantum Compton
> Wavelength)(String Tension)(Kerr Gravimagnetic Field)
>
> is curious.
>
> Imagine several identical giant rotating masses M separated by a
> distance L << J/Mc anything weird happen like in a Bose-Einstein
atomic
> gas condensate? What about the Blackett effect here?
>
> George Chapline says that the vacuum OLDRO field, central to my
theory,
> can carry information like radio waves can. That is interesting also.
> Chapline also says that Zurek is wrong about the emergence of
classical
> physics from environmental decoherence super-selection, that it
really
> comes from the generalized phase rigidity of the vacuum OLDRO Higgs
> field. That basic idea is in PW Anderson's papers and I tend to agree
> with it.
>
> On Mar 27, 2005, at 6:32 PM, Jack Sarfatti wrote:
>
> Sufi Physics for Whirling Dervishes
>
> The Shipov torsion field is zero here. The Brazilian (Arcos-Pereira)
> "torsion" is simply the anti-symmetric Yang-Mills 2-form of the
> non-trivial part of the Einstein-Cartan tetrad field and is,
therefore,
> the "square root of the geometrodynamic tidal curvature". It's simply
a
> neat Cartan form way of doing plain-vanilla 1916 GR with its
symmetric
> metric g without the extensions to Shipov torsion from locally
gauging
> O(1,3) in addition to locally gauging T4 to get Diff(4)xO(1,3) in the
> tangent bundle.
>
> Problem 1
>
> Area = JG/c^3
>
> The weak-field slow motion Kerr solution for a swirling whirling
> gravimagnetic field vacuum tornado is
>
> ds^2 ~ - (1 - 2GM/c^2r)(cdt)^2 + (1 - 2GM/c^2r)^-1dr^2 + r^2(dtheta^2
+
> sin^2thetadphi^2)
>
> - (4JG/c^3r^2)(sin^2theta)rdphi(cdt)
>
> There there is only one dimensionless gravimagnetic field "dipole"
> component in the spherical polar basis of Cartan 1-forms in R^3,
i.e.,
> {dr, rdtheta, r(sintheta)dphi} with dimensions of length
>
> g0phi = - (4JG/c^3r^2)sin(theta)
>
> that is zero along the axis of rotation and maximum along the
equator.
>
> (Note that in classical Newtonian mechanics J^2/Mr^2 is the
centrifugal
> effective potential energy Vrot in the rotating non-inertial REST
frame
> of the rotating body. Therefore, (J/Mc)(c^4/G)g0phi)= Vrot, where
J/Mc
> is a kind of macro-quantum DeBroglie-Compton wavelength! )
>
>
>
> Compute explicitly the Einstein-Cartan tetrads
>
> eu^a = Iu^a + Bu^a
>
> That obey the EEP, i.e.
>
> (Weak Kerr Metric)uv = eu^a(Minkowski)abev^b
>
> Is there a vacuum ODLRO Goldstone Phase for this Bu^a?
>
>
> On Mar 27, 2005, at 5:16 PM, Jack Sarfatti wrote:
>
>
> In fact, I have shown exactly how the Brazilian Yang-Mills "torsion"
> connects the the geometrodynamic curvature and WHY exactly you cannot
write
>
> (LC) = Inertial + Gravity
>
> What you can do is write
>
> Einstein-Cartan tetrad = Inertial + Gravity = e = I + B
>
> You NEVER have e = 0 the way you have (LC) = 0 in the LIF!
>
> (LC) is BILINEAR in the tetrads
>
> In the simplest case of Minkowski space with Gravity B = 0 neglect
> Goldstone phase origin of gravity & inertia
>
> (LC) = Inertial
>
> end of story
>
> In the general case gravity B =/= 0
>
> (LC) = Inertial + Inertial-Gravity + Gravity
>
> There are always cross-terms when B =/= 0 in the Yang-Mills "torsion"
> picture.
>
> The EEP that (LC) = 0 locally in the LIF is not a simple cancellation
>
> Inertial + Gravity = 0
>
> Remember, I define these terms as pieces of tetrads and their is no
> conflict with Newtonian gravity
>
> i.e. B0^0 ~ V(Newton)/c^2 ~ (GM/c^2)(d/dr)log(r/Lp)
>
> Goldstone Phase ~ log(r/Lp) for the ODLRO vacuum coherence Higgs
field
> post-inflation.
>
> in Newtonian weak field limit neglecting "geon" B^2 PLASTIC terms.
>
> This is beautiful because it shows WHY the famous factor of 2 from
the
> ELASTIC Yang-Mills gauge potential CROSS-TERMS!
>
>
> On Mar 27, 2005, at 4:37 PM, iksnileiz@earthlink.net wrote:
>
> The idea is that the Einstein field and its energy-momentum can be
> locally decomposed into inertial
> and gravitational parts, in a frame-independent manner.
>
>
> J: This is meaningless since you have no math. If by Einstein field
you
> mean (LC) then you are wrong. The math says no!
>
> Z: It seems to because of the "cross terms" in (LC).
>
> J: I was doing the first non-trivial interesting problem in Minkowski
> space with B = 0, NO CROSS TERMS to simply show you that the INERTIAL
> ACCELERATION IN (LC) you asked about comes from the GCT Xu'^u
> independent of B. Now, when B =/= 0 then you get cross terms, but the
> extra g-force in (LC) you mentioned still comes from Xu'^u as before.
> There is NO PROBLEM with Newtonian limit either!
>
> When B =/= 0, in the Newtonian limit, with B << I
>
> g00 ~ (1 - 2V(Newton)/c^2) ~ (I0^a + B0^a)(Minkowski)ab(I0^b + B0^b)
>
> -2V(Newton)/c^2 ~ B0^a(Minkowski)abI0^b + I0^a(Minkowski)abB0^b
>
> = 2B0^0
>
> Note the FACTOR OF 2
>
> Ignore the PLASTIC term ~ B^2
>
> V(Newton) = c^2B0^0
>
> e.g. in Schwarzschild solution
>
> V(Newton) = GM/r
>
> B0^0 = GM/c^2r << 1
>
> Solves the Newtonian limit in terms of the non-trivial part of the
> tetrad and its Goldstone Phase log(r/Lp).
>
> Everything WORKS PERFECTLY!
>
> LNIF = (FLAT + CURVED)(LIF)(FLAT + CURVED) = EEP
>
> of course from this POV it's obvious there are g0i terms here in
general.
>
> The issue is whether we can invert this relation to
>
> (LIF) = (FLAT + CURVED)^-1(LIF)(FLAT + CURVED)^-1
>
> Probably there is a simple general proof we can do that when guv is
> non-singular?
xxein: Probably everything will fall into its simple place (wrt math
and symbology) when the nature of gravity is understood.
Think about E and B and how mysterious it was before the proper
relation of the em physical effects.
But gravity pervades and affects that realm. We guage with a guess
about the nature of gravity. An incorrect one; otherwise, there would
be absolutely no dissention, and formulas for prediction could follow a
simple scene to ~10^100 - except for our ability to 'compute' enough
amid the so-called 'chaos'.
If we fail to understand nature, we make chaos into chaos^3 or ^4
(depending upon which wrong understanding we use). And even 'that' can
exponentiate with the subsequent applications of belief.
In short form: I can't recall Wheeler's analogy of building a house
and what Einstein did, but he (AE) clearly used math to subvert the
proper foundation to fit the math rebuild upon it.
Don't fool with mother nature!!!
- Next message: Jim Greenfield: "Re: Light Speed Test versus Special Relativity"
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- In reply to: Jack Sarfatti: "Newton's Rotating Bucket, Mach & NASA Gravity B Space Probe"
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