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On Feb 19, 2012, at 2:43 PM, Paul Murad wrote:

I have sat quietly over this for about a week regarding this conversation. I have two trivial questions.
First, Einstein did this about a century ago.

Jack: That's correct.

Murad: How come you all are still arguing about these issues?

Jack: Good question.

Murad: One would have assumed by now, we should know what is going on by now.  If not, then mankind is really dumb!

Jack: Excellent observation! ;-)
Murad: Second, you have a Coriolis force that works but other forces makes no sense?

Jack: That's not what I said. I don't know what Jim or Z said. Coriolis, centrifugal - all inertial fictitious forces are coded into the the symmetric torsion-free metric Levi-Civita-Christoffel connection that works in globally flat Minkowski space-time of 1905 SR as well as the curved space-time of 1916 GR. The former is a limiting case of the latter. "Fictitious" means there is no g-force on the observed test particle from them. However, there are real g-forces on accelerometers clamped to the detectors measuring the motion of the test particle.

Murad: That sounds like nonsense. Forces have to go into the stress-energy tensor unless you are pulling out the Coriolis force into the curvature tensor. The issue is how do you segregate it from the force balance to do this and still satisfy conservation or is this the crux of the issue?

Jack: Fictitious forces are at the level of the connection. Curvature is the covariant curl of the connection with itself in a self-referential way.

All the UNIVERSAL inertial fictitious forces are already there in Minkowski spacetime.  Therefore, curvature is independent from them. Fictitious forces are an optical illusion caused by the purely arbitrary contingent non-geodesic motion of the detector/observer.

The fault Dear Murad lies not with the test particles, but within ourselves. ;-)

pun on Shakespeare's Julius Caesar
Murad: Sorry for my ignorance...
Paul Murad
Morningstar Applied Physics, LLC


From: Paul Zielinski <iksnileiz@gmail.com>
To: "jfwoodward@juno.com" <jfwoodward@juno.com>

Sent: Sunday, February 19, 2012 3:18 PM
Subject: Re: Misner Thorne Wheeler p. 63 no centrifuge redshift & speed of light in accelerating frames

If you interpret this as meaning that centrifugal forces are not really forces, but only *look* like forces in rotating frames of reference. then it makes sense.

Jack: That's been my crystal clear position all along.

Z: The underlying inertial effects are real, but they are not really due to the operation of *forces*.

Jack: That's right if you mean the observed test particle. It's not right if you mean the CLAMPED observer-detector forced to move off a time-like geodesic in the objectively real local tetrad-spin connection fields that are general coordinate transformation invariant local scalar 0-rank tensors. The four tetrad Cartan 1-forms e^I transform as 4-vector under the local LIF --> LIF' Lorentz group, and the six spin connection Cartan 1-forms S^I^J are not an antisymmetric 2nd rank tensor under the local Lorentz group.

Z: Then it becomes clear that purely kinematical fictitious forces (such as Coriolis forces) are fictitious in the much deeper sense that  there is no underlying objective effect, that they are *purely* a matter of appearances.

Jack: Yes, for test particle. No, for the CLAMPED accelerometers on the detectors whose pointers move off zero when their twins CLAMPED on the test particle do not!

Z: As long as we clearly distinguish between these two different definitions of "fictitious", there should be no confusion.

Jack: Subject to the distinction above that you did not make.

On 2/19/2012 03:05, jfwoodward@juno.com wrote:

All of the confusion about inertial reaction forces, I think, can be traced back to elementary physics where we all learned that centrifugal forces were allegedly not "real".  Rather, they were allegedly fictive, and the only "real force" was the centrepital force causing the rock on the end of the string being swung around you to deviate from inertial motion in a straight line.

So Jim I am still in the dark about how you related the fictitious forces to Mach's Principle. I would not do so. I would related the "jerk" radiation reaction force to Mach's principle, but that is not an F = ma force at all.