On Oct 27, 2007, at 12:03 PM, Paul Zielinski wrote:
"OK, fine. But then how does your BEC model explain the relationship between the material sources and the the Higgs-Goldstone fields? Are not material sources sources of your Higgs-Goldstone fields?"
Very simple. I have written the equations a jillion times. BTW much simpler than George Chapline's vacuum ODLRO theory. I have a more direct motivation from superfluid helium and I don't need supersymmetry, extra dimensions and all the stuff for which there is no evidence - let's see what LHC drags in, if they ever can engineer the magnets properly - like the optics error in the Hubble Space Telescope - multi-million dollar FUBARs. It's hard to find good help these days - the Decline and Fall of Western Science & Civilization and the regression to 7th Century fundamentalist barbarism? ;-)
The pre-inflation unstable false vacuum is essentially the standard model of particle physics, but without the electro-weak Higgs. All quanta have zero rest mass. The moment of inflation creating our pocket universe on a landscape (when you localize GL(4,R) in effect you get additional control parameters that are like extra dimensions. The 4 dimensions of spacetime are from T4 translation group) is the zero temperature quantum phase transition to 8 macroquantum coherent vacuum ODLRO Goldstone phase Cartan 0-forms THETA^a & PHI^b connecting 9 real scalar Higgs fields. You need one "space dimension" for each real Higgs scalar field in order to have STABLE topological defects (i.e. non-trivial homotopy groups larger than the identity (simply connected manifolds). So we now have a physical picture of extra space-dimensions. Supersymmetry generators Q^iA is the "square root" of the translations, something roughly like
[Q^iA,Q^jA] = C^ijPA
PA generates translation group in 9+1 spacetime.
The 3 + 1 space-time emerges from the tetrad 1-forms
A^a = M^a^a
and the spin connection 1-forms
S^a^b = - S^b^a = M^[a,b]
where the Witten turned topsy turvy upside-down M-Matrix of non-closed 1-forms is
M^a^b = (dTHETA^a)(PHI^b) - (THETA^a)(dPHI^b)
The world hologram idea is in the use of non-closed 1-forms giving non-zero 2-forms that are essentially the quantized area operators of Loop Quantum Gravity (LQG) giving the Bekenstein BITS ~ Horizon Area/4Lp^2 of "volume without volume" since the 3-forms vanish.
Einstein's 1916 GR is regained from
e^a = I^a + @A^a = Einstein-Cartan tetrad 1-form
@ = dimensionless coupling
ds^2 = guvsx^udx^v = e^aea = I^aIa + @(I^aAa + A^aIa) + @^2A^aAa
in no sense are the 2nd & 3rd terms on RHS intrinsically "SMALL" although they can be.
The 1905 Special Relativity pre-inflation false vacuum has
ds^2 = I^aIa
I^a = I^audx^u
I^au = 4x4 identity matrix in GIFs as given by Rovelli Ch2
If you go to GNIFs extending 1905 SR only meant for GIFs (Global Inertial Frames)
then A^a =/= 0 but the curvature disclination GMD field 2-form R^a^b is identically zero, i.e.
R^a^b = dS^a^b + S^ac/\S^cb = 0
also the globally zero torsion gap dislocation GMD field 2-form T^a is identically zero, i.e.
T^a = de^a + S^ac/\e^c = 0
It's impossible to have a RIGID GNIF therefore Newton's idea of uniform static gravity field breaks down in passing from Galilean relativity (Gr) to 1905 SR (Special Relativity) before we even get to 1916 GR (General Relativity).
1916 GR is from localizing only T4 and imposing T^a = 0, which still allows a non-vanishing R^a^b as shown in Rovelli's torsion-free spin connection from the tetrads only in eq. (2.89). Localizing P10 gives an additional T^a =/= 0 and going further to GL(4,R) gives new conformal boost and dilation GMD fields - all relevant to dark energy and dark matter together 96% of our pocket universe in the multiverse of universes next door.
"You've indicated that when these fields collapse you are back in an unstable pre-inflation Minkowski vacuum. So I have to presume that there is a causal connection between your Goldstone phases and the presence and location of matter. What exactly is it?"
As above for the umpteenth time passing over your head. Look to the skies. The Truth is Out There.
"And exactly what is the connection between your Higgs-Goldstone fields and Einstein's frame acceleration fields?"
S^a^b = - S^b^a = M^[a,b]
with T^a = 0 in the 1916 GR limit.
Jack Sarfatti wrote:
even if you can do it, it's not important - nothing to be learned - it's futile
On Oct 27, 2007, at 10:57 AM, Paul Zielinski wrote:
Jack Sarfatti wrote:
These two Yahoo Groups now have ~ 600 members world wide.
On Oct 27, 2007, at 2:33 AM, Paul Zielinski wrote:
"I think we can still compare gravitationally deformed geodesics with corresponding flat space geodesics at each spacetime point, as you suggested."
Only in the weak field linearized huv approximation in a non-dynamical Minkowski background which throws away the new physics of GR. You cannot do it in a strong field, e.g. at the horizon of a small black hole where
r ~ rs = 2GM/c^2
"I think I'd prefer to avoid extreme pathological cases like black holes, at least for now. But you have a point that any such model must work for strong fields and not just for weak fields. If the comparison is point-by-point, then we are at most only dealing with infinitesimal neighborhoods and intrinsic curvature should therefore not prevent us from arriving at a covariant description of the gravitational deformation of geodesics resulting
from the presence of material sources. Geometrically, you could think of a flat tangent Minkowski spacetime intersecting with the curved object manifold at each point on the manifold, and local projection of a global Cartesian system projected onto both the curved manifold and the flat tangent manifold. Isn't that basically what happens in the tetrad model when we "solder" a Minkowski spacetime to the abstract tangent vector space at each point using the tetrad one-form? As the object manifold deforms from flat under the action of material sources, you can keep the Cartesian system fixed (fixed
homeomorphic map from the coordinate space R^4 to both the curved and intersecting flat manifolds) while only the metric relationships between the points on the curved manifold change under the deformation. That should zero out the coordinate artifacts that in Einstein's theories are interpreted as frame acceleration fields, leaving an objective residue that we can call the "actual" gravitational field."
No, curvature at horizon ~ rs/r^3 ~ 1/rs^2 -> infinity as rs -> 0
Now you may think this is a paradox - eh?
Because as rs -> 0 that should be flat Minkowski spacetime right?
Not quite because when M falls below 10^-5 gm (assuming G(Newton) at small scale) that's trans-Planckian where quantum gravity takes over.
I don't know about you, but I was talking about Einstein's 1916 theory of gravitation -- how it works, what it does, what it means. Note in my theory what happens is rather boring, when the post-inflation vacuum condensate Higgs-Goldstone fields vanish you are back to pre-inflation false vacuum unstable Minkowski spacetime.
"But how do you relate your Higgs-Goldstone fields to material sources? What is it about matter that its presence results in the appearance of those
BTW on George Chapline's precocious dark star paper - it's brilliant but physically unmotivated. Also his detailed arguments are not clear in their logic and he makes so many premises that one can prove anything. The point is that so far there is no evidence for these premises - same is true for most theoretical physics today of course.
"OK, fair point."
PS George's basic idea is that repulsive dark energy is behind the event horizon (where a phase transition happens) preventing collapse to the classical singularity.
I had this idea myself independently qualitatively. Also George working with Laughlin (Nobel fractional quantum Hall effect) has a kind of holography using a 3D analog to 2D anyons (Chern-Simons action), which I think is a fundamentally a correct idea.
"OK. Also, the standard covariant acceleration is fine, since only the sign changes when you use the flat space geodesics as references, as opposed to using the curved space geodesics. Again, the comparison has to be point-by-point, as you suggested."
My point here Paul is that there is no algorithm to implement your quest globally beyond the trite linearization of GR.
"Obviously it also has to work for strong fields -- but I don't think that curvature is a problem for the model I'm proposing. See above. You can intersect a virtual tangent Minkowski reference spacetime with the actual spacetime at each point x and use a fixed Cartesian coordinate chart from R^4 to both manifolds. That allows you to project the effect of the curved metric into a copy Minkowski space at each spacetime point, very much along the lines of the tetrad model ("soldering" one-form)."
Furthermore, even if you could do it, why bother? "Who ordered that?" It's a waste of time. It's not an interesting question. The ball is in your court to prove me wrong here, but I think you are wasting your time.
"It reduces the gravitational field of 1916 GR to an ordinary physical field that has a completely objective definition that can be described entirely in terms of generally covariant quantities, has no intrinsic dependence on any observer's world line, and is thus not fundamentally different, physically speaking, from the electromagnetic field. All that this really requires is dropping all the traditional hocus pocus about "general relativity", and being contented with objective geometrodynamics instead.
Jack Sarfatti wrote:
"accelerative deviation" makes sense only in linearized GR on a non-dynamical flat background - it's weak field and excludes all the "nonlinear" effects of GR that makes it qualitatively different from Newton's theory. Roger Penrose has discussed this at length. You are working on a trite problem.
On Oct 26, 2007, at 4:14 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Oct 26, 2007, at 3:34 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Oct 26, 2007, at 2:54 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
"the change in the trajectories of freely falling test particles *with respect to gravity-free inertial trajectories* that is predicted to be observed in the presence of gravitational sources." Zielinski
For a given set of initial conditions the 1916 theory predicts a gravity-free trajectory (sources removed), and a gravitational trajectory. Each trajectory is defined as a spacetime geodesic that is defined in a fully covariant manner according to the geodesic equation. These trajectories are clearly not the same . They are two different world lines in spacetime.
Trivially - so what? No way to compare them in general. Apples & Oranges - your idea is background dependent - hence no good in general beyond the trivial linear approximation
guv ~ (Minkowski)uv + huv
huv << (Minkowski)uv
Are you saying that the accelerative deviation of the gravitational geodesic from the corresponding gravity-free geodesic for a given test body has no meaning in Einstein's 1916 theory?
Yes it has no meaning. Show an effective procedure to calculate that.
If there is no precise mathematical description of the accelerative effect of a gravitational field on the trajectories of freely falling test objects in 1916 GR, relative to those in gravity-free spacetime, then I would say the theory must be useless.
Freely falling particles in GR are on timelike geodesics, which by definition, have zero 4D covariant acceleration! You could make a point-by-point comparison in the weak curvature limit, but so what? This is a trite issue. Paul, I have lost interest in reading further. Again you are beating a dead horse. The problem in my view is not at all interesting even giving you the benefit of doubt that there is a problem. I am much more interested in looking at Matt Visser's papers - Matt has a good sense of what the important problems are.
"OK. I've made my argument. It's fine with me if you want to set this aside -- at least for now. Without a precise measure of the relative accelerative deviation of gravitationally deformed and gravity-free test particle trajectories, how would you do that?"
All you can do is locally at a single P
(Minkowski LIF)ab = (Tetrad)a^u(Tetrad)b^v(Curvilinear LNIF)uv
this is the deeper meaning of the equivalence principle as the minimal coupling of all matter fields to the GMD field via the tetrads.
On Oct 26, 2007, at 11:39 AM, Paul Zielinski wrote:
"Your position as I understand it is that in 1916 GR, the choice of a "hovering" reference frame, non-accelerating with respect to the surface of the earth, in which the observed acceleration of test particles near the surface is equal to g (the traditional Newtonian "acceleration due to gravity") is "purely contingent" upon an arbitrary choice of the observer's frame of reference, and thus has no special physical significance in Einstein's 1916 theory. "
That's correct. It has psychological meaning only because we evolved on Earth's surface. It is the amount of non-gravity force we must apply to stand still on a timelike non-geodesic in curved spacetime. That's why we feel heavy. If we were space creatures like in Stapledon's "Star Maker" or Fred Hoyle's "Black Cloud" evolving in a weightless zero-g timelike geodesic environment such a provincial non-Copernican ego-centric requirement would never occur.
"I don't agree with this proposition."
Fine. In any case this is hardly an important question compared to questions about the true nature of the stuff of the world that is 96% something else (i.e. dark energy & dark matter).
I think dark energy/dark matter should lead any rational being to ask some hard question about 1916 GR -- what it means, and why it works within a certain domain of validity.
Yes, but I don't think you have asked a good question.
"Now experimentalists believe that theorists don’t know anything about tools, but that is not true. In my own case, I owned a British sports car for over 20 years (a 1965 Austin-Healey Sprite) and an Italian economy car (a 1974 Fiat 128) for more than 5 years. Anyone who has owned either of those marvels of engineering has had to use tools very often. In my experience, you only need two tools to fix anything: duct tape and WD-40. There are only two rules:
1. If something moves and it shouldn’t, use duct tape.
2. If something doesn’t move and it should, squirt it with WD-40.
The equivalent theoretical tools used for dark energy are the anthropic (or Landscape is you speak string) explanation, and scalar fields (known as quintessence for this purpose)." - Michael Turner