Sunday, March 04, 2007

Paul Zielinski AKA Z has for almost a decade been fighting a hopeless rear-guard action to restore the Lorentzian physical length contraction "aether" interpretation not only for global special relativity without gravity but for general relativity. Similar attempts are seen in Hal Puthoff's PV model based on outmoded ideas of Dicke (1961) and Yilmaz. None of these models are consistent with Einstein's local equivalence principle with general covariance. I think James Woodward's Mach Principle model for propellantless propulsion is also subject to this same defect because his theory is based on a globally flat scalar wave equation that is not generally covariant if I am not mistaken?

Z tries to restore Newtonian "inertial compensation." Let's review how that works. In Newton's 17th Century classical mechanics if we look at a cannon ball shot out of a cannon

The Earth bound observer is approximated to be in a global inertial (non-accelerating) frame of reference in which there is a conservative gravity potential per unit test mass

V(Newton) = -GM/r

M = source mass

m = test particle mass

Newton's second law for the path-independent holonomic potential in the inertial frame

F/m = - dV(Newton)/dr = -GM/r^2

The result is a parabolic path, details depend on initial position, velocity etc.

This curved parabolic path is not a "geodesic" (AKA straightest path) in the flat Galilean spacetime.

Therefore, in Newton's physics there is a gravity force just like an electric force, no essential conceptual difference.

But Baron Munchausen is weightless (no g-force on him). No problem, the Baron is in an accelerating frame and the "fictitious inertial translational force" on the Baron exactly cancels, compensates, the gravity force on the Baron so that the net force on the Baron is zero. Another way to understand this is that the cannonball is not pushing back up on the Baron's rear end because they are both falling with the same acceleration. This later way of looking at it is simpler and more in line with Einstein's thinking based on the equivalence principle.

Now here is how Einstein explains the same above problem.

First of all the observer Bob on Earth feels "weight," i.e. g-force. Therefore, the Earth-bound observer is in the non-inertial accelerating non-geodesic frame relative to curved space-time. Two observers on Earth anti-podally placed on opposite sides on a line through the Earth's center are accelerating relative each other, but their separation does not change because this back-to-back mutual acceleration is in curved spacetime. Of course if the spacetime were flat the distance between them would change. See Hawking's "The Universe in a Nutshell" for a nice picture of this. Therefore, the weightless Baron Munchausen is on a geodesic non-accelerating local inertial frame. It's the Earth-bound observer Bob who is really accelerating. Bob feels weight because the electrical forces of the ground are pushing him off his natural weightless curved spacetime geodesic path. This g-force on Bob is created by the non-gravity electrical force of the ground (with quantum exchange effects of Pauli exclusion et-al).

In fact, in the math of Einstein's theory the curved spacetime non-geodesic Earth-bound observer has a non-vanishing covariant scalar invariant magnitude 4-acceleration "a" caused by the non-gravity force in the covariant generalization of Newton's second law F = ma. The Baron's geodesic invariant acceleration is zero.

Now, with that as background, to Creon Levit's gedankenexperiment. Creon and I met at Caffe Trieste last Fri nite and I have added some detail to his thought that night.

Alice is in a rocket ship stationary at fixed r a safe distance from a small rapidly evaporating black hole of mass M(t).

Her arrival in position is at t = 0. Her protocol is to fire her rocket at t = 0 at a thrust directed to the center of the black hole corresponding to

g = GM(0)/r^2 ~ c^2(Local Curvature at t = 0)r

She closes her ports and agrees not to look outside.

M(t) decreases rapidly to zero from the Hawking radiation.

What does Alice experience? She feels no local change. Her artificial gravity g is same because her rocket engine thrust is kept constant. However, Eve looking at the whole thing from the outside sees Alice's radial position r(t) relative to the shrinking black hole increasing. The local curvature field at Alice's position is evaporating away. But it makes no difference to Alice's local measurements of first-order g-force. Of course if she measured geodesic deviation of freely falling test particles inside her ship she could detect the evaporating curvature field, but that measurement is orthogonal to her g-force measurement. The corresponding operators commute, they are compatible measurements in the quantum sense.

Now Z says that the local g-force = tensor curvature piece + inertial force piece

Z then argues that

g = GM/r^2 is the tensor piece

However he never proves that this term is actually a GCT tensor. I am pretty sure it's not.

So in Z's view at t = 0 the complete g-force is a tensor with no inertial part, and at t -> infinity the complete g-force is inertial with no tensor part.

This is simply word play of course and there is no formal proof that

g = GM(0)/r^2

is a GCT tensor. What it really is, is an arbitrary choice of convenience. i.e. choosing a "static" constant r observer (assuming no evaporation of the source mass of course). If Alice looked outside she would have to lower her thrust to stay at fixed r.

PS. Z's appeal to the arcane math of Alex Poltorak and Waldyr Rodrigues, Jr on ineffable connections and non-metricities are clearly excess formal baggage muddying clear waters, red herrings designed to dazzle and snow experimental physicists. Fancy math is used when the write lacks a good physical idea. Most papers in theory on archive today are of that character. I would rather have "mathematical nonsense" like Feynman's diagrams than rigor mortis math that is "physical nonsense."

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