On Feb 8, 2014, at 1:23 AM, "This email address is being protected from spambots. You need JavaScript enabled to view it." wrote:

For those of you who are trying to figure out what Jack and Paul are arguing about, sometimes on this list again, the basic issue, put simply, is whether gravitational fields are present in spatially flat spacetimes.  Jack says no.  That non-vanishing spatial curvature must be present if gravity is present.

JS: Jim is muddling my position.

1) Real gravity fields must have curvature.

2) Artificial gravity fields exist without curvature.

3) Einstein's Equivalence Principle (EEP) is: imagine you are inside an elevator with no windows.

Situation A: Elevator is standing still on surface of Earth. The reaction force (radially inward) of your body down on the scale is your weight

W = (your inertia in kg)10 meters per sec^2

Your inertia is

m = E/c^2

E is your total energy in Joules

c = 3 x 10^8 meters/sec^2

In Einstein's GR you have an upward net non-zero off-geodesic proper tensor acceleration (radially outward) g = DV/dt = 10 meters per sec^2 in order to stand still (hovering static LNIF) in the Earth's curvature field. Your world line is not a geodesic of the Earth's curvature field.

V = 0 and dV/dt = 0 in the hovering static LNIF

g = - {LNIF}V0^2 = + GMEarthr/r^3 radially outward

The action-reaction pair of electrical contact forces of Newton's third law is LOCAL having no astrological magic influence from the distant stars. It is caused by local U1 electromagnetic gauge invariance + quantum field theory.


dP/dt = 0 P = total charge momentum + EM field momentum

= mV + (e/c)A

From quantum field theory, the local U1 gauge transformation is simply mostly the exchange of a near field spacelike virtual photon between the charge e of inertia m and the EM field A coincident with the charge.

The dominating Feynman diagram is >---|

> = electron world line

--- = virtual spacelike photon world line

| = Glauber macro-quantum coherent state of virtual photons order parameter describing the near field A

A is exactly like the Bose-Einstein condensate reservoir in superfluid helium it is also analogous to the Higgs vacuum field - these are all examples of spontaneous broken continuous symmetry groups of the dynamical action.

note subject of my PhD was "Local Gauge Invariance in the Theory of Superfluids" 1969 UCR

Formally the internal symmetry local U1 gauge transformation is

mV -> mV' = mV + hGradS

S = quantum phase of the charge's information BIT field.

A -> A' = A - (hc/e)GradS

Therefore, the total canonical momentum P of the Hamiltonian for minimal QED coupling is GAUGE INVARIANT

P -> P' = mV + hGradS + (e/c)A - hGradS = P

dP/dt = 0

The formal U1 internal symmetry local gauge transformation actually describes the transfer of a virtual photon from the classical near EM field to the charge and vice versa! It's a quantum field virtual dynamical process in space-time and it obviously implements Newton's 3rd Law that the total momentum of the system of interest is LOCALLY CONSERVED.

Change in momentum of charge + change in momentum of near field = 0

The radially outward real force pushing the charge off a timelike geodesic is

F = hGradS/&t

The radially inward real reaction force of the charge back on the source of the near field A is

- F = -hGradS/&t

this radially inward reaction force causes the pointer of the scale to show weight.

&E&t < h for virtual photon (Heisenberg uncertainty principle)

Situation B: the elevator is properly accelerating at 10 meters per sec^2 in any direction in flat empty spacetime.

The observer inside the elevator cannot tell whether he is out in empty space or sitting still on surface of Earth.

We assume of course that he has no windows and no tidal curvature measuring capability.

Therefore, subject to these conditions one cannot distinguish artificial non-tidal gravity defined as the Levi-Civita connection from the non-tidal gravity field associated with tidal curvature.

JW: Paul says yes.  That spatially flat spacetime does not preclude the presence of gravity.  That Paul is right should be obvious from the fact that general relativity is predicated on the assumption that in sufficiently small regions of spacetime, the Minkowski metric (spatially flat) applies.

JS: Jim, you have totally muddled two different meanings of the ambiguous term "gravitational field". Also you are dead wrong. You have made a very elementary error.

Your "the Minkowski metric (spatially flat) applies"

The Minkowski metric is flat in the 4D sense, not only in the 3D sense.

Your argument here is a non sequitur

"Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises.[1] In a non sequitur, the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. All invalid arguments are special cases of non sequitur. The term has special applicability in law, having a formal legal definition. Many types of known non sequitur argument forms have been classified into many different types of logical fallacies." wiki

JW: It is also the boundary condition in the Schwartschild solution of Einstein's equations.

JS: Schwarzschild, also it's another non sequitur red herring.

JW:  And in critical cosmic matter density cosmologies, spatial flatness obtains in the presence of black hole horizon strength gravity.  The problem for Jack (and other "modernists") is that if you allow that, the WMAP results give back Mach's principle as a simple prediction of general relativity.  

JS: I challenge you to give a mathematical model that WMAP proves Mach's Principle.
You do not need Mach to have k = 0 in the FRW metric.

JW: Do not expect closure on this any time soon.  :-)