On Nov 7, 2004, at 7:42 PM, iksnileiz@earthlink.net wrote:

Jack Sarfatti wrote:

This is much ado about trivia. What can you explain that is worth explaining? Nothing. You are clutching on to this one silly parody of an idea ignoring all the important stuff going on in modern relativity.

Jack, if this is so trivial, then why did you put so much effort into refuting it?

It's not trivial.

Why?

1. We are friends.

2. Your general quest was worthwhile.

3. As it developed your rhetoric got more and more sounding like cliche crackpot Einstein-bashing or should I say MTW bashing?

4. Your confusions are common and worth explicating.

Off the top of my head here is how I see them:

I. You are confused about the relation of "coordinate systems" to "reference frames". This also has to do with confusions about epistemological "map" vs ontological "territory" that leads to Magickal Thinking.

First consider linear coordinate transformations, Galilean for simplicity.

x -> x' = x - vt

t -> t' = t

This is a GLOBAL transformation.

It can be physically approximated by two fleets of rocket ships out in free space far from gravitating sources. Each fleet moving uniformly relative to the other and internally relatively at rest to each other. All rocket engines off in that case!

Similarly for a global constant acceleration transformation

x - > x' - vt + (1/2)gt^2

t --> t' = t

Note that this is nonlinear.

Again one fleet fires its rockets. The other fleet keeps its rockets off.

In this case we have a homogeneous inertial force in the S' global frame that is not asymptotically flat! This is not real gravity as Landau & Lifshitz point out in Ch 10. You have been disparaging of the asymptotic boundary condition BTW missing entirely its physical relevance to your problem.


GCT in GR, u = 0,1,2,3

x^u -> x^u'(x^u)

With Jacobian matrix X^u'u = x^u',u

,u is ordinary partial derivative - trivial flat zero connection field.

Tensors transform locally and multilinearly with products of coefficients X at a fixed local physical event P that is not same as a formal manifold point p.

This GCT can always be approximated by two fleets of rocket ships (exchanging EM signals understood) in arbitrary relative motion both intra-fleet and inter-fleet.

Therefore, the relation between the coordinate system and the reference system is same in GR as it is in Galilean relativity except now there is complete local "gauge freedom" on how each rocket ship will fire its engines! In Galilean relativity, the fleets must be internally in lock-step like troops marching in formation.

II. The {L-C} = GCT Tensor + Non-Tensor

pseudo-problem

This is like "ruler and compass constructions" leading to Galois finite group solvability and Godel undecidability.

The problem here is, using ONLY the concepts within Einstein's original 1916 theory i.e. using only the {L-C} connection itself, with covariant partial derivatives

;u = ,u + {L-C}

no second connection allowed, no torsion, no non-metricity etc.

Can the above split be constructed entirely within the original 1916 GR considered as an axiomatic formal system?

That's the FORMAL problem.

All the additional machinery Alex brought in with a second affine connection different from the {L-C} connection is a completely different problem and is not relevant to the actual problem you first raised years ago without any notion in your mind of affine connections with torsion and non-metricity.

Now it is obvious that you formulated this problem by confusing it with the following {L-C} transformation under GCT

{L-C}^uvw -> {L-C}^u'v'w' = Xu'^uX^vv'X^ww'{L-C}^uvw + X^u'lY^lv'w'

Y^lv'w' = x^l,v',w'

Since the RHS is a tensor transformation + non-tensor piece

This is obviously what gave you the idea but you garbled the categories mistaking a transformation for the object transformed.

Finally, your trying to separate the vanishing g-force in a Local Inertial Frame (the LIF) into an objective tensor force minus an inertial force is a gross violation of the equivalence principle (WEP to be precise).

Gravity is locally equivalent to an inertial force.

All inertial forces disappear in an inertial frame.

There is NO OBJECTIVE TENSOR gravity force! That is a complete confusion.

The weight W^i, i = 1,2,3 we feel in a rest LNIF (Local Non-Inertial-Frame) is the electrical reaction force to the inertial force ~ gravity force, i.e. on the timelike non-geodesic:

W^i = mc^2{^i00} = -F^i(EM reaction force)

Note that only the mixed space-time components of the connection field contribute to weight.