Z: OK.
Jack: My P.W. Bridgman approach may not be that obvious to many mathematicians working in relativity. It's basically Wheeler's ideas.
Z: Yes you do seem to follow Wheeler's approach pretty closely.
Jack:Yes, because it makes sense to my mind grounded in Einstein's use of gedankenexperiments. One can imagine fleets of little micro-drones in space with rocket propulsion and all the sensors and detectors needed to make measurements -- well there will be bandwidth limits for small detectors, but they can use the interferometer trick for long wavelengths. Rocket motor firing LNIF, rocket motor off LIF - all the measurements of space-time structure GMD fields in a finite region of 4D spacetime vacuum can pictured in terms of them:
Tetrad LIF <-> LNIF
GCT T4(x) LNIF <-> LNIF'
SO(1,3) LIF <-> LIF'
all explained clearly in operational terms.
On Dec 6, 2010, at 7:12 PM, Paul Zielinski wrote:
Yes I have to agree that while the spectral action/commutative geometry approach to GTR is mathematically
very sophisticated, unless it is capable of producing falsifiable predictions it is really nothing more than
applied mathematics.
On first glance it certainly looks like the kind of *post hoc* tailoring of an abstract formalism to already known
empirical content that I tend to associate with string theory.
As for being more "advanced" than what we've been talking about here, I'm not so sure. Mathematically, perhaps,
but what we have been debating has fundamental implications for the physical meaning of the GTR. I doubt that
the same can be said of this paper.
On Mon, Dec 6, 2010 at 2:54 PM, JACK SARFATTI
Hi Jonathan
Her work looks interesting, but much more advanced than what we are discussing - foundations of Einstein's GR and its physical/operational meaning what David Bohm called "GR's measurement theory" in analogy with "quantum measurement theory". I don't see off hand how her work can be Popper falsified and is relevant to the pressing anomalies today, i.e. dark energy, dark matter, Pioneer anomaly, matter-antimatter asymmetry etc.
On Dec 6, 2010, at 10:50 AM, Paul Zielinski wrote:
Do you feel this might be relevant to what we were talking about? Or are you just trying
to change the subject?
Sure the topologies of solutions of the E-H field equations can be physically significant.
On Mon, Dec 6, 2010 at 10:13 AM, Jonathan Post
Have you guys been following the exciting work of Matilde Marcolli,
currently on faculty at Caltech? You can download a PDF from:
http://arxiv.org/abs/1012.0780
Title: The coupling of topology and inflation in Noncommutative Cosmology
Authors: Matilde Marcolli, Elena Pierpaoli, Kevin Teh
Comments: 30 pages, LaTeX, 11 pdf figures
Subjects: High Energy Physics - Theory (hep-th); Cosmology and
Extragalactic Astrophysics (astro-ph.CO); Mathematical Physics
(math-ph)
We show that, in a model of modified gravity based on the spectral
action functional, there is a nontrivial coupling between cosmic
topology and inflation, in the sense that the shape of the possible
slow-roll inflation potentials obtained in the model from the
nonperturbative form of the spectral action are sensitive not only to
the geometry (flat or positively curved) of the universe, but also to
the different possible non-simply connected topologies. We show this
by explicitly computing the nonperturbative spectral action for some
candidate flat cosmic topologies given by Bieberbach manifolds and
showing that the resulting inflation potential differs from that of
the flat torus by a multiplicative factor, similarly to what happens
in the case of the spectral action of the spherical forms in relation
to the case of the 3-sphere. We then show that, while the slow-roll
parameters differ between the spherical and flat manifolds but do not
distinguish different topologies within each class, the power spectra
detect the different scalings of the slow-roll potential and therefore
distinguish between the various topologies, both in the spherical and
in the flat case.
On Mon, Dec 6, 2010 at 10:02 AM, Paul Zielinski
>
>
> On Sun, Dec 5, 2010 at 11:30 PM, JACK SARFATTI
>>
>> On Dec 5, 2010, at 9:47 PM, Paul Zielinski wrote:
>>
>> I meant,
>>
>> "And why should the concept of the true value of a metric derivative be
>> any different in a curved
>> spacetime?"
>>
>> Stupid question. Independent of curvature, there is no true value of the
>> ordinary partial derivatives of the metric.
>
> Well my "stupid question" is: Why not?
>>
>> The first order ordinary partials of the metric are artifacts of the
>> detector's non-geodesic motion.
>
> OK that's clear. This is a dynamical interpretation of g_uv, w =/= 0.
>
> So you fuse the dynamics of the detectors with the kinematics of the
> observer's reference frame in the concept on an "LNIF".
>>
>> In Minkowski spacetime you can still have LNIFs with induced LC
>> connections, but every time you calculate their self-referential covariant
>> curls you get zero.
>
> Shouldn't this be telling you something? You are constructing the covariant
> curl of the Minkowski metric and getting zero. In other words
> you are covariantly differentiating a constant covariant derivative, and
> naturally getting zero.
>
>>
>> Minkowski spacetime is simply a boundary in the space of solutions - that
>> subspace with vanishing curl of any PHYSICAL connection you choose on it.
>
> No question that Minkowski spacetime is globally Riemann-flat. But
> mathematically speaking this is a theorem, not a definition.
>>
>>
>>
>> On Sun, Dec 5, 2010 at 9:43 PM, Paul Zielinski
>> wrote:
>>>
>>>
>>> On Sun, Dec 5, 2010 at 9:31 PM, JACK SARFATTI
>>> wrote:
>>>
>>>> However, in the case of LNIF ---> LIF the true derivative is the
>>>> ordinary partial derivative with respect to the LIF coordinate chart since
>>>> the LC connection is zero via EEP
>>>
>>> Even in a flat spacetime? If the geometry is uniform, how can the true
>>> values of the metric derivatives not be zero?
>>>
>>> And why should this be any different in a curved spacetime?
>>>>
>>>>
>>
>
>