Tuesday, December 28, 2004

Metric Engineering Investigations 1.4

Limitations of the Galilean-Newtonian equivalence principle

"However, the fields to which noninertial reference systems are equivalent are not completely identical with 'actual' gravitational fields which occur also in inertial frames." L & L "Classical Theory of Fields"

Again there are no 'actual" gravitational "force" fields in the local inertial frames (LIFs) of Einstein's general relativity as there are in the GIFs of Newton's gravity theory. There are tidal stretch-squeeze curvature effects in both theories. The term "curvature" is not used in Newton's theory. "Inhomogeneous gravity field" is used instead. Einstein's theory is the better theory including phenomena like gravimagnetism not found in Newton's theory but now actually observed. Gravimagnetism is not in Hal Puthoff's PV over-simplified theory either.

Section 81 of L&L is only about Newton's theory and care must be taken not to import it unthinkingly into Einstein's theory. However, the following is also true in Einstein's GR, actual classical gravitational fields must come from localized sources and, therefore, must be asymptotically flat. This precludes, for example, an exact uniform constant gravitational field over the entire universe. One possible exception to this is the quantum zero point dark energy which at large scales > 10^26 cm has average energy density (10^19Gev/10^-33cm)10^-56 cm^-2 ~ 10^(19 + 33 - 56) Gev/cm^2 ~ 10^-4 Gev/cm^3 = 10^5ev/cm^3 ~ 10^-7 ergs/cm^3 ~ 10^-14 Joules/cm^3.

The equivalence principle is only a local metric principle not a global principle.

""However, the fields to which noninertial reference systems are equivalent are not completely identical with 'actual' gravitational fields which occur also in inertial frames. For there is a very essential difference with respect to their behavior at infinity. At infinite distances from the bodies producing the field, 'actual' gravitational fields always go to zero. Contrary to this, the fields to which noninertial frames are equivalent increase without limit at infinity, or, in any event, remain finite ... for example, the centrifugal force which appears in a rotating frame of reference increases without limit as we move away from the axis of rotation."

Let S' be rotating noninertial frame with angular velocity pseudovector W , S the non-rotating inertial frame whose z axis is the axis of rotation of S'. S & S' share common origin. Think of S roughly as a Foucault Pendulum at rotational North Pole with Earth as S' In Galilean relativity v/c << 1,

a = dv/dt

W,t = dW/dt

a' = a + 2Wxv + WxWxr + W,txr

2Wxv = Coriolis inertial force in the noninertial frame

WxWxr = centrifugal inertial force

W,txr = torque inertial force

dL/dt = torque = (applied force) x r

L = angular momentum

From rotation inertial forces to translational inertial forces

"the field to which a reference frame in accelerated linear motion is equivalent is the same over all space and also at infinity." p. 226

Remember this is only for Galilean relativity of Newton's gravity force theory and it is clearly only a unrealistic idealization not permitted in Einstein's theory.

Note that Einstein's gravity field with GCT comes from locally gauging the 4-parameter translational symmetry group. In addition, if we locally gauge the 6-parameter Lorentz group we get new torsion field dynamical degrees of freedom in addition to the 4 translational degrees of freedom.

Translational gravity field on a point test particle is locally equivalent to a translational inertial force.

Rotational torsion field on an extended gyroscope is locally equivalent to rotational inertial force. (G. Shipov)

This is in addition to the Lense-Thirring gravimagnetic frame drag with happen in zero torsion field.

Torsion means that infinitesimal parallelograms of parallel transport fail to close in second order rather than in third order as in zero torsion 1916 GR.

* Is there a natural split of the Einstein metric tensor field into purely curvilinear coordinate and intrinsic geometry pieces? Even if there is, it will not carry over to the connection field that is NONLINEAR quadratic in the metric tensor components and its first order partial derivatives.

That is even if we have the LOCAL METRIC property

(metric) = (metric)intrinsic + (metric)coordinate

(LC) = (LC)intrinsic + (LC)coordinate + (LC)intrinsic-coordinate

Note that (LC) is a 1-form

Curvature = d(LC) is a 2-form

Obviously if

(LC) = Exact 1-form + Non-Exact 1-form

The Exact 1-form does not contribute to the tidal curvature.

Exactness is a GLOBAL topological property (allowing Vilenken-Taub "curvature without curvature" for a thin unstable wall of dark energy) not to be garbled with the above LOCAL metric property.

Note that

ds^2 = guvdx^u/\dx^v

appears to be a 2-form.

its exterior Cartan derivative is then a 3-form, therefore the connection 1-form (LC) must be *DUAL to the 3-form in 4D spacetime.

guv = (Minkowski)uv + (1/2) Lp^2(Macro-Quantum Coherent Goldstone Phase)(,u ,v)

where ,u is the ordinary partial derivative in the holonomic coordinate basis.

Note that the separate terms on RHS are not GCT tensors individually only their sum is. Also there is no perturbation theory here. The second term on RHS is not "small" compared to first.

* The intrinsic curved spacetime geometry must obviously originate in the post-inflationary world hologram Macro-Quantum Coherent Goldstone Phase second order partial derivatives.

Note that there are 16 second-order partial derivatives. The mixed partials {01, 02, 03, 12, 13, 23} need not commute when there is a torsion field, but if they do, that leaves 10 independent parameters. There are 64 = 4^3 3rd-order partial derivatives for the connection non-tensor and torsion tensor fields and there are 4^4 = 256 4th-order partials for the tidal curvature subject to constraints that cut that down to 20 in the presence of matter and 10 in the classical /\zpf = 0 non-gravitating non-exotic vacuum with zero dark energy/matter density for the conformal curvature tensor. Also the partial derivatives of the macro-quantum Goldstone phase of the Higgs field may be minimally coupled gauge covariant relative to U(1)xSU(2)xSU(3). Note that the virtual electron-positron PV condensate has U(1)xSU(2) coupling even though the net charge is zero.

A GCT comes from the generating function of a canonical transformation overlap transition function, which is obviously the guv|coordinate piece that Z is looking for.

Chi(x^u,x^u') where x^u and x^u' are two local coordinate charts with common support in a neighborhood of physical event P.

The Jacobian matrix of the GCT at P is

Xu'^u(P) = Lp^2Chi,u'^u(P)

The mixed partials here, one from each chart, obviously DO NOT COMMUTE.


Xu^v'Xv'^w = Kronecker Deltau^w etc.

gu'v'(P) = Xu'^u(P)Xv'^v(P)guv(P)

= Xu'^u(P)Xv'^v(P)[(Minkowski)uv + (1/2) Lp^2(Coherent Goldstone Phase)(,u ,v)]

= (Minkowski)u'v' + (1/2) Lp^2(Coherent Goldstone Phase)(,u' ,v')]

(1/2) Lp^2(Coherent Goldstone Phase)(,u' ,v')

= Xu'^u(P)Xv'^v(P)(Minkowski)uv - (Minkowski)u'v'

+ Xu'^u(P)Xv'^v(P)(1/2) Lp^2(Coherent Goldstone Phase)(,u ,v)]


Coherent Goldstone Phase (x^u') = Coherent Goldstone Phase(x^u) + Chi(x^u,x^u')

Is this consistent?

That is

Xu'^u(P)Xv'^v(P)(Minkowski)uv = gu'v'|coordinate =/= (Minkowski)u'v'

Xu'^u(P)Xv'^v(P)(1/2) Lp^2(Coherent Goldstone Phase)(,u ,v) = gu'v'|intrinsic

Metric Engineering Investigations 1.3

On Dec 26, 2004, at 7:19 PM, Jack Sarfatti wrote:

Look at sections 84 & 97 in Landau & Lifshitz Classical Theory of Fields.
More anon.

BTW Landau & Lifshitz from the Soviet Era, in spite of Lysenko, is still probably the best course, even today in 2004, in "classical" theoretical physics including the earlier versions of quantum field theory. Better than Weinberg because it is closer to observation and even in the English translations the explanations are generally very clear. Better than MTW in some respects.

Also in 82:

"in the general theory of relativity it is impossible in general to have a system of bodies which are fixed relative to one another. This result essentially changes the very concept of a system of reference in the general theory of relativity, as compared to its meaning in the special theory. In the latter we meant by a reference system a set of bodies at rest relative to one another in unchanging relative positions. Such systems of bodies do not exist in the presence of a variable gravitational field, and for the exact determination of the position of a particle in space we must, strictly speaking, have an infinite number of bodies which fill all space like some sort of 'medium'. Such a system of bodies with arbitrarily running clocks fixed on them constitutes a reference system in the general theory of relativity."

Paul you cannot improve on Landau & Lifshitz, they have covered all the real ground on the classical foundations.

"In connection with the arbitrariness of the choice of reference system, the laws of nature must be written in the general theory of relativity in a form which is appropriate to any four dimensional system of coordinates (or, as one says, in 'covariant' form). This, of course, does not imply the physical equivalence of all these reference systems (like the physical equivalence of all inertial reference systems in the special theory)."

Now Hal Puthoff's PV is not generally covariant in this sense as Hal's coworker at IAS Austin, Michael Ibison, has written explicitly. This is basically why Hal's theory is almost universally rejected by all the Top Guns in spacetime physics down to almost the last man standing. Hal is basically using the fixed background of special relativity in his action principle with the variable "dielectric" whose controlled variation is much too small for the practical metric engineering of Warp, Wormhole and Weapon (from C^3 to W^3) anyway. That is not how to Make Star Trek real. PV is not the "Right Stuff" to reach for the stars and beyond.

Note BTW that Landau & Lifshitz explicitly say that non-Cartesian CS are only for "noninertial reference frames" on p. 228 "Thus, in a noninertial system of reference, the square of the interval appears as a quadratic form of a general type in the coordinate differentials, that is, it has the form

ds^2 = gikdx^idx^k

... Thus, when we use a noninertial system, the four-dimensional coordinate system ... is curvilinear."

Now there is no way to make such a non-inertial system of reference as an approximation to "an infinite number of bodies which fill all space like some sort of 'medium'. Such a system of bodies with arbitrarily running clocks fixed on them constitutes a reference system in the general theory of relativity" without non-gravity forces. That is, in a purely gravitational universe noninertial systems of reference do not exist! Actually gravity is not a fundamental field at all. It cannot exist without the electromagnetic field to give it its light cones. Indeed it also needs quantum theory to emerge as a macro-quantum coherence effect.

Metric Engineering Investigations 1.2

On Dec 27, 2004, at 2:45 PM, iksnileiz@earthlink.net wrote:

OK, then can you explain your understanding of their distinction between "physical equivalence of all these reference frames", on the one hand, and general covariance of the laws, on the other? In your own words?

I have many times now. The distributions of detectors connected by GCTs - different regions of extended phase space of the detector distributions connected by the GCTs in same region of configuration space (within a given neighborhood of event P)

A set of Alice detectors Ai (i = 1 to N) and a set of Bob Bj (j = 1 to N) detectors pepper a neighborhood of even P in the overlap region that is the domain of the GCT transition function. Each set of detectors is a point in extended phase space including the (LC) at the position of each detector. Although the A & B detectors occupy the same point in configuration space, they occupy different points in phase space. Indeed, let the physical event be P with coincident (Ai,Bi) detectors be located at common events Pi close to P. We want to plot (LCA)i and (LCB)i as degrees of freedom, we can also plot the "velocities" relative to the micro-wave background in principle. This gives an extended "phase space" for the two detector configurations in a small neighborhood of the event/process P that is being simultaneously measured. Note that N = 1 is good enough. The GCT connects physically distinct reference frames in this sense.

Obviously the two configurations of detectors measuring the same event P are physically distinct. The GCT connecting these different points in phase space that share a common point in configuration space enable the objective comparison of raw data taken independently by both of them. Of course, this does not extend to quantum measurements on the same micro-quantum system. One can work with ensembles of course.

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