On Feb 18, 2012, at 10:33 AM, JACK SARFATTI wrote:
PS I still haven't a clue of what
phi = c^2 means operationally in terms of possible local measurements to test its correctness.
I don't see its value added.
As I. Rabi said of Pauli's neutrino "Who ordered that?"
Of course there are neutrinos.
From what I do understand Sciama used
phi = c^2 in some toy model cosmological argument around the very obscure "Mach's Principle" with about 8 different meanings according to Rovelli.
Well cosmological metrics do not work locally without a lot of justification. A point in a cosmological metric is an entire galaxy so you can't use it in the lab in a local thrust measurement for example. The only way one could use it perhaps is to invoke some kind of fractal dilation scale invariance in the sense of the conformal de SItter group extension of the Poincare group?
Remember my argument, that seems to go over all the Pundit's heads so far that
If the Hawking temperature in a Planck thickness of our future cosmological event horizon is
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kT(horizon) = hc/Lp
where
g00(r) = 1 - r^2/RH^2
we are at r = 0
Then advanced Wheeler-Feynman Hawking radiation back from our future to us at r = 0 will be redshifted down to
kT(us) = hc/(LpRH )^1/2
Then Planck's et-al's black body law T^4 for real photons gives the observed dark energy density hc/Lp^2RH^2 that we see as zero point vacuum fluctuations (virtual photons).
On Feb 18, 2012, at 10:16 AM, JACK SARFATTI wrote:
On Feb 18, 2012, at 12:13 AM,
Date: Fri, 17 Feb 2012 17:05:32 -0800
Z: Glad to see you guys are coming around to my way of thinking re: GR. :-)
JW: I don't think Jack is coming around to your way of thinking. Neither really am I. :-) I was sloppy in lumping Coriolis forces in with inertial forces. I still think the standard interpretation of GR and the EEP are basically correct. Because it's the non-localization of gravitational potential energy aspect of the EEP that makes the identification of the scalar part of the gravitational potential [GM/R] as a locally measured invariant along with c. But I will say that the conversation has been very helpful in sharpening the issues for me, and I thank you and Jack for that. Seriously. I'm revising chapters 1 and 2 of the book accordingly. And the two of you will be acknowledged for the helpful exchange.
JS: I still fail to see the mathematics of what you mean Jim by inertial forces? Do you mean formally essentially the Levi-Civita connection { }? That's what I mean.
Formally Newton's 2nd Law on a test particle with coordinates x^u and REST MASS m, charge q is (neglecting special relativity, radiation reaction jerk, and rocket ejection effects)
D^2x^u/ds^2 = d^2x^u/ds^2 + {^uvw}(dx^v/ds)(dx^w/ds) = (q/m)F^uvdx^v/ds
This equation works in Special Relativity for an accelerating detector in Minkowski space - and it also works generally in curved spacetime in the limit when variations in test particle m are small.
More generally use
DP^u/ds = qF^uvdx^v/ds + radiation reaction
Pu = Mdx^u/ds
ds^2 = guv(LNIF)dx^udx^v = nIJ(LIF)e^Ie^J
M = 1905 SR total mass as in
E = Mc^2 for the localized test particle
The fictitious inertial forces are the term {^uvw}(dx^v/ds)(dx^w/ds)
The pointers of accelerometers measure the deviation of the object's motion off a local timelike geodesic in an arbitrary curvature field.
The reason that they are "fictitious" is that an accelerometer CLAMPED to the test particle does not register any g-force from them.
In contrast, (q/m)F^uvdx^v/ds will cause the pointer on the test particle's accelerometer to move off zero. So will the radiation reaction force.
{^uvw} indicates a real non-gravity force on the detector! An accelerometer's pointer CLAMPED to the detector will move off zero independent of the test particle.
Fictitious inertial forces on test particles correspond to real forces on their detectors.
The LOCAL FIELD equations of Einstein's GR always express a relationship between LOCALLY COINCIDENT observed test particle and detector.
Mathematicians never seem to grasp this.
When for example one writes
g00 = 1 - rs/r
That is only for static LNIF detectors held by real forces at fixed r.
On 2/17/2012 14:57,
OK, you are partly right. The "kinematical" part of rotation effects that show up in Minkowski spacetime are "Coriolis" type "fictional" forces. These are what should be called "fictional fictional" forces because the motion of the test objects observed is inertial and the "forces" they appear to experience are a consequence of the rotation of the observers frame of reference. This is what Paul challenged me on when I made a comment about "fictional" forces now seemingly a long time ago. He was right. There are two types of "fictional" forces.
But, and I think Paul agrees with me here, there are "real fictional" forces. They are inertial forces generally, and in the case of rotation, centrifugal forces. They get lumped in with gravity as "fictional" because, like gravity, with a suitable choice of geometry they can be made to disappear. Why, because with gravity, they are universal and satisfy the EEP. For gravity you have:
F = GMm/r^2 = ma
and the ms cancel as is universally acknowledged. For inertial forces Newton's third law applies and if
F = ma,
then
Finert = - ma
and just as for gravity, when these are equated, the ms cancel. That means that inertial forces are exactly like gravity forces and satisfy the EEP. Why? Because they are gravity forces too -- that arise from the g0i that correspond the the matter currents in Tuv (and generally currents that arise from everything that gravitates). That's what Einstein and Sciama were after with Mach's principle. Paul doesn't agree with the last part of this (yet). But he does agree with the reality of inertial forces (unless he's changed his mind since our last exchange).
As for inertial structure in Minkowski spacetime, a little explanation of my earlier comment is likely in order. In the era before Einstein, GRT, and his attempts to explicitly show that "Mach's principle" was a part of GRT, everyone looked around at local space and saw that the Pythagorean theorem applied to reality exactly, at the limit of observation of course. (In this era, gravity gets treated as a force, so those complications do not arise. And gravity is very weak anyway.) Inertial reaction forces, of course, are an obvious feature of Newtonian mechanics, and the generalization to SRT involves only treating energy as having inertia (via Einstein's second law (according to Wilczek) m = E/c^2. Since they are generally decades of orders of magnitude larger than Newtonian gravity forces, no one imagined that inertial forces might be caused by gravity.
Now from GRT cosmology and the WMAP results we know that at cosmic scale space is flat. We also know from Sciama's calculation (and Einstein's calculation of 1921 and Nordtvedt's of 1988 if we extend their time derivative of the vector potential term to include cosmic sources) that spatial flatness implies phi = c^2 (up to a numerical constant of order unity perhaps) which in turn means that as a matter of calculation, not assumption, that inertial reaction forces are due to gravity. But locally, because the cosmic effect of gravity is universal and the ms in EEP situations cancel, there seems to be no gravity effects present.
This explains why folks before Einstein (and a lot after too) could assume that Minkowski spacetime, assumed empty, has inertial structure, notwithstanding that in our reality the inertial structure of spatial flat spacetime is in FACT due to the gravitating stuff chiefly at cosmological distances from us.
I don't expect to convince anyone. But I hope to hear your criticisms -- and that you understand what it is that I am saying: This is all built in to standard 1915 GRT. There's no "new" physics involved in this.
---------- Original Message ----------
From: Jack Sarfatti<
To: Paul Zielinski<
Subject: Re: Misner Thorne Wheeler p. 53 no centrifuge redshift& speed of ligh t in accelerating frames
Date: Fri, 17 Feb 2012 14:00:47 -0800
The math is simple clear and in text books. Jim disputing that fact is not rational. Of course Tuv will also give a contribution to g0i in addition to the part from simply spinning the disk or accelerating a clock translationally.
Sent from my iPhone
On Feb 16, 2012, at 1:59 PM, Paul Zielinski<
Jack is saying you can get g_0i =/= 0 for some i even in Minkowski spacetime, in certain frames of reference.
That means you can have g_0i =/= 0 in the absence of all gravity.
You don't seem to agree with that.
On 2/16/2012 01:08,
only now you do not explicitly talk about the gravitational vector potential, though it is still there in your paper unidentified.