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Note added Dec 27, 2020 - Synopsis
The Cartan formalism is Spartan in the sense that Dirac liked as seen in his “bra - ket” QM formalism.
Cartan formalism is manifestly coordinate-independent - it is local objective classical field reality in the way Einstein liked.
However, it has profound physical significance, in that the Hodge dual * operator describes the transition from vacuum to matter as in electrodynamics
D = E + 4piP
B = H + 4piM
 
EM 2 Form F describes E and B in vacuum
*F describes H and D in matter connection to sources of the field.
In vacuum P = 0 and M = 0

The tetrads e are Cartan exterior 1 forms with dual co-forms w corresponding to dx in the usual coordinate representation.

The tetrad 1-forms as variable fields over spacetime are directly induced by locally gauging T4 translation Lie group.
The invariant 0-form metric field for curved spacetime is
ds^2 = *[e/\e/\w/\w]
* = Hodge dual
The Levi-Civita metric field connection is the 1-form
(LC) = *[e/\de]
The covariant exterior derivative is
D = d + *[e/\de]
The vacuum Weyl curvature 2-form is
R = D(LC) = {d + *[e/\de]}*[e/\de]
DR = 0 Bianchi identity in vacuum
The inside matter Ricci + Weyl curvature 2-form is given by Einstein’s modified gravity field equation
*R = - 8pi(G/c^4)|S||T|cos(s + t)  
S = |S| exp(is) Sarfatti-Wanser 0-form scalar field matter EM response function
T = source stress-energy 2-form
D(*R + 8pi(G/c^4)|S||T|cos(s + t)] = 0 
Local conservation of stress-energy current densities.
D*R =/= 0 inside matter
 
 
 
 
3rd Draft Typo Corrected
When I use “teleparallel space” I mean (and Shipov and others mean) a generalized Minkowski space in which the covariant curl of the general connection C with itself vanishes globally - in symbols of exterior forms
DC = 0
D = d + C
C = 1-form
d = exterior derivative
d^2 = 0
The “Curvature” F (generalized) is the 2-FORM
F = DC
This has nothing to do directly with comparing separated objects - that is done by “parallel transport” of the object V parallel to itself using the connection
DV = 0  like in the geodesic equation as a particular example where V is the timelike tangent vector 1 form e0 moved parallel to itself forming a timelike geodesic path.
Where in general DC =/= 0
Example 1 classical electrodynamics in vacuum with possibly elementary electric charge current densities J = 1-form.
A = 1 form connection from locally gauging U(1) internal fiber space global group in Minkowski flat space-time and for LIFs where C = 0.
dA = F = EM field 2-form includes E and B 3-vector fields.
d*F = J (Ampere’s law + Gauss’s law)
*F = Hodge dual of F includes EM susceptibilities of matter.
d^2*F = dJ = 0 local conservation of source electric current densities
dF = 0 (Bianchi identity) (Faraday induction, and no micro magnetic monopoles in classical vacuum).
Gauge transformations A —> A’ = A + kdPhi
F —> F’ = F U(1) gauge invariant
Phi = 0 form phase.
Example 2 Einstein GR
C = Levi-Civita metric connection
R = DC = Riemann Christoffel Curvature 2-form
DR = 0 Bianchi identity
*R = - 8pi(G/c^4)ST   Einstein’s field equation
T = source stress-energy 2 form
S = Sarfatti Wanser scalar field from EM response of meta-material Tic Tac fuselage to applied EM pump field inside meta-material.
DT = 0 local conservation of stress-energy source currents only if
D*R = 0
In most materials *R = R to a good approximation (SELF DUALITY)
But in pumped meta-material dissipative resonances
*R =/= R  SELF-DUALITY BREAKDOWN
D(*R + 8pi(G/c^4)ST) = 0
With direct current exchanges among *R inside metamateria, S scalar field and T input EM pump field)
i.e.
D*R + (8piG/c^4)[SDT + TdS] = 0
Also gauge transformation Q = GCT
C —> C’ = QCQ^-1 + QdQ  
QCQ^-1 is usual tensor transformation
e.g.
R —> R’ = QRQ^-1 = R gauge invariant as an exterior 2-form
But is tensor covariant in component tensor index formulation

Note added Dec 26, 2020
On Dec 26, 2020, at 12:25 PM, David Chester <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Chill out, words are imprecise.

Yes.
 
What’s important is some new physical insights gelled in this kerfuffle that Zielinski and I have periodically. ;-)
 
The exterior calculus is very elegant, sparse in sense of Dirac, yet very powerful.
 
I always had a problem formulating GR in terms of it, though Rovell does it in Ch II of Quantum Gravity.
 
In EM internal symmetry U(1) local gauge in Minkowski flat spacetime of global special relativity for now.
 
A —> A’ = A + kdphi
 
F = dA —> F’ = F because d^2phi = 0.
 
Bianchi identity is
 
dF = 0 works only for VACUUM!!!!!! (Faraday induction + no magnetic monopoles)
 
i.e. there is broken Hodge duality inside matter - this is key.
 
*F =/= F
 
d*F = J (Ampere’s and Gauss’s laws)
 
d^2F = dJ = 0 local current density conservation
 
EM in a gravity field Levi Civita metric connection (LC) from locally gauging T4 translations.
 
D = d + (LC)
 
F = DA = dA + (LC)/\A
 
DF = d^2A  + (LC)/\dA + d[(LC)/\A] + (LC)/\(LC)/\A =/= 0 in the LNIF
 
d^2A = 0
 
Note EEP is (LC) ~ 0 in locally coincident LIF
 
Also
 
D*F gets new terms inside matter.
 
Next Einstein’s 1916 GR
 
R = D(LC) = d(LC) + (LC)/\(LC) = Riemann-Christoffel curvature 2-form =/= 0
 
Einstein’s field eq is INSIDE MATTER MUST USE HODGE DUAL that depends on CONSTITUITIVE PARAMETERS from condensed matter quasi-particles and collective modes.
 
*R =- 8pi(G/c^4)ST
 
R =/= *R INSIDE METAMATERIAL
 
D*R + 8pi(G/c^4)D(ST) = 0
 
DS = dS
 
DT = dT + (LC)/\T
 
D(ST) = TdS + SDT
 
D*R = d*R + (LC)/\*R
 
S = Sarfatti Wanser spin 0 complex U(1) scalar EM susceptibility matter field
 
T = source stress-energy 2-form which is also a complex numbered function from dissipative imaginary susceptibilities causing relative phase shift between (ST) INPUT and *R OUTPUT 
 
Bianchi identity is
 
DR =0
 
But just like in EM where D*F =/= 0, here D*R =/=0
 
THIS CHANGES THE PHYSICS DRAMATICALLY WITH DIRECT STRESS-ENERGY CURRENT TRANSFERS BETWEEN THREE FIELDS
 
1) HODGE DUAL GRAVITY FIELD *R INSIDE MATTER
 
2) SARFATTI-WANSER SCALAR FIELD EMERGENT INSIDE MATTER, ESPECIALLY IN PUMPED META-MATERIAL RESONANCES.
 
3) APPLIED EM PUMP FIELD WHOSE STRESS-ENERGY TENSOR IS T IN Tic Tac Tech APPLICATION.
 

Jack is talking about teleparallel spaces, while Paul is focusing on a theory of teleparallelism. 
The term "teleparallel" by itself is a confusing name since there are very many teleparallel theories of gravity. Various people have tried different formulations with or without success.
Is "teleparallelism" a theory, multiple theories, or a general framework? Depending on the context, all 3 can be correct.
In 1928, Einstein worked on a teleparallel theory of gravity, but it didn't work. Probably many others have made different theories of teleparallelism. 
By 1976, it seems to have been formulated properly to become equivalent to GR in vacuum. 
Since 1998, using the term teleparallelism to refer to the consistent torsion-only theory also went out the window, as Nester and Yo formulated a symmetric teleparallelism with nonmetricity.
Therefore, the 1976 theory is called metric teleparallel equivalent to GR, as it is metric-compatible. The 1998 theory is called symmetric teleparallel equivalent to GR because it has vanishing torsion (the antisymmetric part of the connection). 
Referring to Einstein's 1928 work on teleparallelism in 2020 as "the teleparallelism" is certainly done, but this is not practical for researchers in the field of gravitation. I'm sure that a lot of physics professors at top universities who don't specifically research these topics would believe teleparallelism is just Einstein's failed theory from 1928, but the history is more subtle.
Would the most general subsector of metric-affine gravity with vanishing curvature still be a teleparallel space even though it is neither of these teleparallel theories mentioned above? If metric-affine gravity and it's higher-dimensional operator generalizations give the "most general theory of relativity", then perhaps there exists a "most general teleparallel theory" that has not been sufficiently explored in the literature.
If yes, then Paul suggesting that Jack focuses on metric-affine gravity still allows Jack to discuss teleparallel spaces, especially if we agree that there exists some "most general teleparallel theory of relativity", which is not really a term I've seen used.

See Kibble’s classic paper on this.
Utiyama first locally gauged Lorentz group SO(1,3) and had to put in GCT’s by hand and then set torsion to zero ad_hoc (as I recall) to get to 1916 GR.
Then, Kibble locally gauged entire 10 parameter Poincare group - set torsion to zero ad hoc to get 1916 GR.
 
If you think about the physics and forget the maths, you will see that the physical meaning of general coordinate transformations is to formulate physics in locally proper accelerating frames. This is the meaning of locally gauging global T4 to T4(x).
Physically, T4(x) describes Alice and Bob on nearly colliding arbitrary timelike world lines each measuring the same set of events using far field light signals. ds^2 = guv(Alice)dx^udx^v = gu’v’(Bob)dx^u’dx^v’ where Alice and Bob are separated by intervals small compared to radii of curvature.
 
guv(Alice) = Xu^u’Xv^v’gu’v’(Bob)
 
X’s are GCTs from T4(x) see Hagen Kleinert’s books on line for details
 
Global translations are
 
x^u —> x^u = x^u + a^u
 
Local gauging T4 means
 
x^u —> x’^u(x) =  x^u(x) + a^u(x)
 
dx^u =  x’^u(x) - x^u(x) = X^uu’dx^u’
 
a^u(x) = X^uu’dx^u’
 
X^uu’(x) are Einstein’s GCT’s obviously they are T4(x) transformations.
 
Quod Erat Demonstratum.

On Dec 26, 2020, at 2:32 PM, David Chester <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
"I may misunderstood you, but I don't think Levi-Civita is found from gauging translations. "


Jack: Sez who? I just gave you the simple physical picture to the contrary.

"GR isn't a gauge theory, even though there is a GL(4,R) diffeomorphism invariance. Metric teleparallelism gauges translations.

I think gauging translations can allow for contortion to cancel Levi-Civita's contribution to curvature (at least in metric teleparallelism).

But as we know, there are many different subtle theories of gravity, so maybe there's something I'm missing. It has been confusing to disentangle what theory of gravity you are studying with the recent discussions of torsion. For instance, there are now 3 notions of curvature, R(C), R(T), and R(C,T) = R(C) + R(T), where R(C) is from Levi-Civita and R(T) is from torsion.

As soon as torsion is introduced, talking about curvature tensors becomes more vague. 

I am guessing you are attempting to invoke translational gauge symmetry to get R(C) = -R(T), but then since you want to stick closer to GR, you are sticking to R(C) instead R(C,T)=0. The most sense I can make with your words is that you are finding R(T) by gauging translations, not R(C), but it ends up being related if R(C,T)=0.

I still haven't worked out precisely how Einstein's vacuum field equations come from metric teleparallel equivalent by gauging translations, but still, I don't see how gauging translations literally gives Levi-Civita."
I proved by explicit construction, that local gauging T4 —> T4(x) gives Einstein’s general coodinate transformations that physically correspond to local frame transformations between Alice and Bob each on arbitrary timelike world lines that momentarily are close to each other. My argument is complete contained explicit independent of any of the points you mention below. 
 
I said nothing about torsion et-al in that limited precise elementary physically transparent argument that I repeat here again for the record
 
If you think about the physics and forget the maths, you will see that the physical meaning of general coordinate transformations is to formulate physics in locally proper accelerating frames. This is the meaning of locally gauging global T4 to T4(x).
Physically, T4(x) describes Alice and Bob on nearly colliding arbitrary timelike world lines each measuring the same set of events using far field light signals. ds^2 = guv(Alice)dx^udx^v = gu’v’(Bob)dx^u’dx^v’ where Alice and Bob are separated by intervals small compared to radii of curvature.
 
guv(Alice) = Xu^u’Xv^v’gu’v’(Bob)
 
X’s are GCTs from T4(x) see Hagen Kleinert’s books on line for details
 
Global translations are
 
x^u —> x^u = x^u + a^u
 
Local gauging T4 means
 
x^u —> x’^u(x) =  x^u(x) + a^u(x)
 
dx^u =  x’^u(x) - x^u(x) = X^uu’dx^u’
 
a^u(x) = X^uu’dx^u’
 
X^uu’(x) are Einstein’s GCT’s obviously they are T4(x) transformations.
 
Quod Erat Demonstratum.
 

On Dec 26, 2020, at 6:05 PM, David Chester <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Subsectors of metric-affine gravity are not very simple. 

I only provided clarity to point out that GR + non-propagating torsion as found in Einstein-Cartan theory is not teleparallelism and it is not gauging translations. You implied it did and now, rather than being a big boy and correcting yourself, you are retreating back towards "it's just simple metric engineering".

Some days you are interested in dark energy, others in metric engineering. 

Both problems are important, the first for fundamental physics, the second for national security.
 
On Dec 26, 2020, at 5:54 PM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote to Tim Ventura:
The Physics explaining the whole bloody thing is quite elementary and well understood it’s only an engineering problem now 

of course there’s weapons implications and of course we should think of this as an imminent threat

Sent from my iPhone

On Dec 26, 2020, at 4:50 PM, Tim Ventura <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

This is something I'm playing with - maybe for a presentation or something. We have 70+ years of mythology to deal with, but even if only a tiny fraction of it is real, it would indicate that UAPs are not our friends & we should develop defenses to counter a potential threat.


Are UAPs Russian or Chinese?
- Capable of acceleration & maneuvers far beyond human vehicles
- UAP performance would kill a human pilot
- Flight & maneuverability without conventional engines, lifting or control surfaces
- Capable of transverse medium propulsion (air/water)
- Flight capabilities of UAPs date back decades, even if Russia/China could do this today, they couldn't 50 years ago.
- No record of markings or writing on UAPs in known languages
- Close encounter reports dating back 50+ years indicates non-human occupants

Jack: All explained conceptually elementary physics. Problem is the incompetence of the people involved. For example, watch Elizondo stumble here trying to explain what I have already explained precisely.
 

Assumptions:

- UAPs are not God (why does God need a starship?)
- They're not much more advanced than us.
- Appear to be physically weak & rely on technology.
- Tend to control interactions, presumably because they have vulnerabilities (and unexpected events do cause damage)
- UFOs may not be real (20th century manifestation of need for fairies, angels, etc...)
- even if they are real, the stories about them may not be (mass hysteria)
- it's dangerous to assign motive to unknown actions & judge aliens by human standards


Why are they here:

- To catalog & categorize our biosphere
- To understand human beings & social behavior
- They don't need our minerals (more easily mined in space)
- They don't need our technology (presumably less advanced than theirs)
- Probably not to colonize (unlikely good bio match, and lots of unpopulated explanets to start with)


UAPs are not our friends:

(they appear to recognize us as sentient, but don't ascribe us basic rights)
- Human Abductions (how many unsolved missing persons reports annually?)
- Human Implants & Experimentation (Violates International Law)
- Human Casualties to UFO Encounters (Encounter burns, PTSD, etc...)
- Cattle Mutilations
- Two Attempts To Launch ICBM's
- Attempts to break radar lock during intercepts
- Infringing on Sovereign Airspace
- Interfering with Military & Civilian Air Traffic
- They achieve goals through power, not consent
- They're untrustworthy (actions to do not UFO believer claims about love & peace, they're not transparent, etc...)
- UAP encounters indicate presence off East / West Coast for easy access to population centers
- Spying on data communications? https://www.submarinecablemap.com/
- Demonstrate zero regard for human life (Even if the majority of these claims are false, the remainder show a pattern)


UAPs should at least be held accountable:

- To uphold basic human rights as chartered by UN: https://www.un.org/en/sections/issues-depth/human-rights/
- To establish & abide by a publicly known standard of conduct (maybe they don't have to follow all of the laws, but we should know which ones & why)
- To abstain from actions that would interfere with duly appointed government or defense representatives
- Never in human history has "bowing before superior capabilities" led to a good outcome.
- To ensure they don't inadvertently bring disease or pathogens into our biosphere


Defense aspects of this:

- Need defense awareness of UAP presence - especially scope of activity, which is undocumented.
- Need public involvement to help report UAP activity.
- We need defense capabilities to deter, deny access, and repel unwanted UAP actions
- Missiles & bullets are likely not fast or manueverable enough to intercept UAPs
- Beam weapons (laser, maser, particle beam) are preferable because there is no advanced warning before damage begins
- Radar signals implicated in the Roswell crash, suggesting their electronics may be vulnerable
- Space-based weapons provide maximum horizon for engagement & deterrance entering/leaving atmosphere
- Any weapons effective against UAPs would have conventional defense applications, incentivizing development.
- Computer-controlled weapons might be preferable due to speed of response & decision-making (with manual override).


Sincerely;


Tim Ventura
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Social: Facebook | LinkedIn 


On Tue, Dec 22, 2020 at 7:02 AM JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
On Dec 21, 2020, at 6:09 PM, Kim Burrafato <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

🤣👍🏻😎
Sent from my iPhone
We knew that would happen.
Ill conceived.
Mellon, Elizondo, Justice not up to the real job.
Meaning well is not good enough.
It did bring PR however to the UFO issue.
We are the “Last Man Standing” ;-)
We have actually solved the essential physics problem behind the entire Phenomenon that stumped them.




I don't know what name to give "it" because we have been discussing many things.

Yes, the mainstream has missed the validity of Einstein-Cartan, which is related to why people can't make sense quantum gravity with matter.

But once again, what does torsion have to do with your metric engineering? Your answer seems to fluctuate.

I tried making the analogy between the antigravitic torsion of an electron and your metamaterials already and you ridiculed me. Now, you are essentially saying what I said a day or two ago. 

If you are "only" interested in metric engineering, make up your mind if torsion is relevant or not. It seems relevant only when you talk about it but not others. 

It's hilarious if you think you are the first to apply differential forms to GR. That doesn't mean you shouldn't do it. The geometric algebra community has, as well as Derek Wise under Baez, probably goes further back though.

Remember, I mentioned torsion being relevant for antigravity and you called me out. Now you are pointing it out that torsion inside matter changes things. It's hilarious how much you like to disagree while secretly agreeing.

On Sat, Dec 26, 2020, 3:52 PM JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

Both you guys are making something simple overly complicated.
I don’t care what name you give it.
Everything I had to say is now elegantly formulated neatly as Cartan exterior forms.
So far, the equations I wrote down do not apply to Shipov’s theory.
 
1) Classical EM in Minkowski space time (LIFs)
 
2) Classical EM in curved space-time (LNIFs)
 
3) Einstein 1916 GR - no torsion - but inside MATTER giving new physics that even Pundits like Kip Thorne and Sean Carroll have completely missed.
 
Specifically R =/= *R in matter therefore you cannot write Bianchi identity D*R = 0 inside MATTER generally - certainly not in pumped resonant metamaterials that explain Tic Tac Tech.
 
Remember my purpose is METRIC ENGINEERING PHYSICS of


& this


I will get back to Shipov particular model 4) soon using Cartan’s forms because it may be natural setting for both dark matter and dark energy as difference quantum vacuum phases at different scales, frequencies and wavelengths.


On Dec 26, 2020, at 9:09 PM, Paul Zielinski <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
No torsion, but what inside matter?

On 12/26/2020 3:51 PM, JACK SARFATTI wrote:
This email address is being protected from spambots. You need JavaScript enabled to view it." class="">
 
3) Einstein 1916 GR - no torsion - but inside MATTER giving new physics that even Pundits like Kip Thorne and Sean Carroll have completely missed.
 
Specifically R =/= *R in matter therefore you cannot write Bianchi identity D*R = 0 inside MATTER generally - certainly not in pumped resonant metamaterials that explain Tic Tac Tech.
 

In EM the Hodge Dual *F inside matter contains B = H + 4piM and D = E + 4piP
 
In vacuum M and P vanish and F = *F self-dual

Similarly in GR

R =/= *R inside matter

R = curvature 2-FORM

None of the GR text books take this into account because most people in GR are really mathematicians and have little knowledge of condensed matter physics.

Since

*R ~ - (G/c^4)ST

You cannot use Bianchi identity DR = 0 inside matter because R =/= *R inside matter.

Therefore, the assumption in GR textbooks Tuv^;v = 0 is WRONG INSIDE MATTER.

Now in ordinary matter R ~ *R to a sufficient approximation, but in Tic Tac meta-material that is not the case and that is the key to low power warp drive.


Locally gauging T4 takes us from global 1905 Einstein SR to allowing global IFs and global NIFs to Einstein 1916 GR with guv(x) metric tensor fields. Once you have locally variable guv(x) you get LC connection by first order partial differentiation.
 
http://stardrive.org/57ec7ddb-112f-409d-8de8-c27030d86f61" alt="Screen Shot 2020-12-26 at 9.46.42 PM.png" width="278" id="<FD08D796-C8C2-4B13-A622-9F5154B908EC>" class="Apple-web-attachment" style="opacity: 1;" apple-inline="yes" />
 
The point is until you locally gauge T4 you do not have a variable guv(x) symmetric tensor field to play with.
 
This involves physical intuition - pictures in your mind. If you are blind to pictures and can only think algorithmically step by step like a Turing machine you may not be able to grok this.

On Dec 26, 2020, at 9:15 PM, Paul Zielinski <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Gauging T4 coordinate transformations alone cannot give you either curvature or torsion.

So what do you and Kibble gain from gauging passive T4?

 Note added Dec 27, 2020
The Cartan formalism is Spartan in the sense that Dirac liked as seen in his “bra - ket” QM formalism.
Cartan formalism is manifestly coordinate-independent - it is local objective classical field reality in the way Einstein liked.
However, it has profound physical significance, in that the Hodge dual * operator describes the transition from vacuum to matter as in electrodynamics
D = E + 4piP
B = H + 4piM
 
EM 2 Form F describes E and B in vacuum
*F describes H and D in matter connection to sources of the field.
In vacuum P = 0 and M = 0
The tetrads e are Cartan exterior 1 forms with dual co-forms w corresponding to dx in the usual coordinate representation.
The tetrad 1-forms as variable fields over spacetime are directly induced by locally gauging T4 translation Lie group.
The invariant 0-form metric field for curved spacetime is
ds^2 = *[e/\e/\w/\w]
* = Hodge dual
The Levi-Civita metric field connection is the 1-form
(LC) = *[e/\de]
The covariant exterior derivative is
D = d + *[e/\de]
The vacuum Weyl curvature 2-form is
R = D(LC) = {d + *[e/\de]}*[e/\de]
DR = 0 Bianchi identity in vacuum
The inside matter Ricci + Weyl curvature 2-form is given by Einstein’s modified gravity field equation
*R = - 8pi(G/c^4)|S||T|cos(s + t)  
S = |S| exp(is) Sarfatti-Wanser 0-form scalar field matter EM response function
T = source stress-energy 2-form
D(*R + 8pi(G/c^4)|S||T|cos(s + t)] = 0 
Local conservation of stress-energy current densities.
D*R =/= 0 inside matter
On Dec 27, 2020, at 9:25 AM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.; wrote:
PS Lue Elizondo has recently been talking about my idea of Tic Tac Warp Drive without giving me credit. He never talked about it prior to the Franc Milburn BESA White Paper.
 
 
 
 
 
No David, you do not understand.
 
We do not need torsion to explain the antigravity warp drive of Tic Tac.
 
That is a dissipative (inelastic scattering photons off charges) phase shift effect in traditional 1916 metric GR with only Levi Civita connection.
 
*R = - 8pi(G/c^4)|ST| cos(s + t)
Positive cosine is induced gravity red shift, negative cosine is induced anti-gravity blue shift.
S = |S|exp[is] 
 
is the metamaterial EM response complex scalar field 0-Cartan form
 
T = |T| exp[it]
is the applied EM pump field’s stress-energy Cartan 2-form also complex from dissipation in the permittivity and permeabilities of the anisotropic time change metamaterial fuselage of Tic Tac
 
*R is the Hodge dual of the curvature Cartan 2-form R.
 
*R = R in vacuum, but not in matter in the same way that F =/= *F in matter because of M and P response fields of real charges.
 
Bianchi identity DR = 0 FAILS INSIDE MATTER, though in many cases the degree of violation is negligible, but not in pumped metamaterial resonances as shown in Tic Tac flight.
 
D*R + 8pi(G/c^4)[TdS + SDT] = 0 local conservation of stress-energy current densities.
 
DT = dT + (LC)/\T
 
*R = *[d(LC) + (LC)/\(LC)]
 
D*R =/= 0 i.e. direct coupling of gravity field to the S and T matter fields.
Yes, there may be quantum spin induced torsion inside artificial metamaterial that may make an additional anti-gravity effect.
 
You and Zielinsky continually confuse necessary conditions for sufficient conditions and vice versa.
 
To review:
 
Local gauging T4 translations directly induces tetrad coefficients from physically real Alice LIF <—> Bob LNIF when Alice and Bob are locally coincident measuring same external events with far field light signal propagating in vacuum not inside matter.
 
Alice’s LIF has ds^2 = (cdt)^2 - dx^2 - dy^2 - dz^2 = nIJdx^Idx^J
 
Bob’s LOCALLY COINCIDENT LNF has ds’^2 = guv(x)dx^udx^v
 
ds^2 = ds’^2 for Alice and Bob measuring same external events with light signals.
 
This is physics independent of coordinate representations.
 
The tetrad coefficient fields eu^I(x) are the direct result of the local T4 gauging. The LNIF metric tensor guv(x) and (LC)^luv connection fields are indirectly induced from the tetrad fields.
 
For example, LOCAL GAUGING T4 MEANS THIS
 
dx^I(ALICE LIF) = e^Iu(x)dx^u(BOB LNIF)
 
The symbol small x = Einstein local coincidence not a coordinate - all this is coordinate independent.
 
Zielinski et-al confuse coordinate shadows for Platonic light (forms).
 
Local gauging T4 describe coordinate-independent physically real local frame transformations that have GCT formal representations.
 
guv(x) = eu^I(x)ev^J(x)dx^Idx^J
 
THE POINT IS WITHOUT LOCALLY GAUGING T4 THERE ARE NO VARIABLE TETRAD FIELDS TO FORMULATE GR WITH - AS A MATTER OF LOGIC AND META-THEORETICAL CONCEPTUAL UNDERSTANDING.
 
Note also (LC)^muv ~ eu^I(x)(d/dx^v)eI^m
 
Einstein’s TENSOR GCTs are quadratic in tetrad coefficients i.e. X(x)u^u’ = e^uI(x)e^Iu’(x)

On Dec 26, 2020, at 6:05 PM, David Chester <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Subsectors of metric-affine gravity are not very simple. 
I only provided clarity to point out that GR + non-propagating torsion as found in Einstein-Cartan theory is not teleparallelism and it is not gauging translations. You implied it did and now, rather than being a big boy and correcting yourself, you are retreating back towards "it's just simple metric engineering".
Some days you are interested in dark energy, others in metric engineering. 
I don't know what name to give "it" because we have been discussing many things.
Yes, the mainstream has missed the validity of Einstein-Cartan, which is related to why people can't make sense quantum gravity with matter.
But once again, what does torsion have to do with your metric engineering? Your answer seems to fluctuate.
I tried making the analogy between the antigravitic torsion of an electron and your metamaterials already and you ridiculed me. Now, you are essentially saying what I said a day or two ago. 
If you are "only" interested in metric engineering, make up your mind if torsion is relevant or not. It seems relevant only when you talk about it but not others. 
It's hilarious if you think you are the first to apply differential forms to GR. That doesn't mean you shouldn't do it. The geometric algebra community has, as well as Derek Wise under Baez, probably goes further back though.
Remember, I mentioned torsion being relevant for antigravity and you called me out. Now you are pointing it out that torsion inside matter changes things. It's hilarious how much you like to disagree while secretly agreeing.

On Sat, Dec 26, 2020, 3:52 PM JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Both you guys are making something simple overly complicated.
I don’t care what name you give it.
Everything I had to say is now elegantly formulated neatly as Cartan exterior forms.
So far, the equations I wrote down do not apply to Shipov’s theory.
 
1) Classical EM in Minkowski space time (LIFs)
 
2) Classical EM in curved space-time (LNIFs)
 
3) Einstein 1916 GR - no torsion - but inside MATTER giving new physics that even Pundits like Kip Thorne and Sean Carroll have completely missed.
 
Specifically R =/= *R in matter therefore you cannot write Bianchi identity D*R = 0 inside MATTER generally - certainly not in pumped resonant metamaterials that explain Tic Tac Tech.
 
Remember my purpose is METRIC ENGINEERING PHYSICS of
& this
I will get back to Shipov particular model 4) soon using Cartan’s forms because it may be natural setting for both dark matter and dark energy as difference quantum vacuum phases at different scales, frequencies and wavelengths.

On Dec 26, 2020, at 3:28 PM, David Chester <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

Jack, I think you are confusing Einstein-Cartan(-Kibble-Sciama) theory with metric teleparallel equivalent to GR (TEGR).
Einstein-Cartan has vanishing torsion outside matter, yet TEGR has vanishing curvature with propagating torsion in a manner that is equivalent to GR's curvature.
I don't think Einstein-Cartan is a theory of teleparallelism. Similarly, it is not in Weitzenbock geometry, as it uses Riemann-Cartan geometry. This combines Riemannian geometry with Weitzenbock geometry, in some sense.
Poincare gauge gravity has propagating curvature and torsion in the vacuum according to Hehl. Lorentz gauge gravity has curvature, Translations have torsion.
Einstein-Cartan has benign torsion, as it is not propagating. Going to Poincare gauge gravity then includes 1915 GR, Einstein-Cartan, and TEGR as subsectors. In a sense, Einstein-Cartan contains GR, but TEGR is orthogonal.
STEGR has vanishing curvature and torsion, yet it still has a curvature contribution from Levi-Civita. However, the disformation (from nonmetricity) leads to a cancellation, similar to how contortion (from torsion) cancels with Levi-Civita in TEGR.
GR from 1915 is second-order with dynamical metric. However, first order formulations lead to an affine theory via an affine connection, which is more sophisticated, as the connection is geometrically different than the metric. 
Sean Carroll has nice discussions in his online textbook about how an affine connection that is metric-compatible and torsion less uniquely leads to Levi-Civita. So mathematically, starting with Levi-Civita may not be rigorous, but it is effectively okay.
Metric-affine gravity refers to an independent metric and affine connection. It is also meant to be very general, although the original paper only discussed a simple subsector with 2 terms in the Lagrangian. The most general metric-affine gravity has I believe 28 terms in the Lagrangian.
It includes Einstein-Hilbert, all possible second-order curvature terms with loss of symmetry of standard Riemann tensor in GR, as well as 3 terms from TEGR, 5 terms from STEGR, and mixed terms that combine torsion and nonmetricity.
It's still not clear to me what precisely Jack is discussing, but I don't think we should assume it is Weitzenbock space, as he keeps latching onto GR and Einstein-Hilbert with torsion in a manner that seems more similar to Einstein-Cartan. It's unclear, I think he is still confusing EC and TEGR.


On Sat, Dec 26, 2020, 3:09 PM Paul Zielinski <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Please disregard this version. 

On 12/26/2020 3:06 PM, Paul Zielinski wrote:
Words are imprecise if you're sloppy.

The standard term for what Jack appears to be talking about is a "Weitzenbock space". 

That terminology neatly avoids any possible confusions about implied claims of teleparallelism.

On 12/26/2020 1:16 PM, JACK SARFATTI wrote:


On Dec 26, 2020, at 12:25 PM, David Chester <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

Chill out, words are imprecise.

I have to straighten Jack out from time to time. It's a dirty job, but someone has to do it. :-)

 
Jack is talking about teleparallel spaces, while Paul is focusing on a theory of teleparallelism. 

I think he's talking about a Weitzenbock spacetime -- characterized by a metric derived from the Weitzenbock connection.

Strictly speaking, there is no such thing as a "teleparallel space"; but at least now I think I understand what Jack and Shipov mean by this.
[CD] The term "teleparallel" by itself is a confusing name since there are very many teleparallel theories of gravity. Various people have tried different formulations with or without success.

Exactly -- confusing.

Is "teleparallelism" a theory, multiple theories, or a general framework? Depending on the context, all 3 can be correct.

It's a property that defines a class of geometric models for gravity.

The property is the ability to directly compare the angles of field vectors in different tangent spaces at
arbitrary separation.

In 1928, Einstein worked on a teleparallel theory of gravity, but it didn't work. 

It didn't work for other reasons, but it did deliver teleparallelism. In that respect it did work.


Probably many others have made different theories of teleparallelism. 

Right.


By 1976, it seems to have been formulated properly to become equivalent to GR in vacuum. 

In these kinds of theories, torsion is only present inside matter. In the vacuum region torsion vanishes and the theories are equivalent.

Since 1998, using the term teleparallelism to refer to the consistent torsion-only theory also went out the window, as Nester and Yo formulated a symmetric teleparallelism with nonmetricity.

Why isn't that
 a metric-affine theory?

Therefore, the 1976 theory is called metric teleparallel equivalent to GR, as it is metric-compatible. 

Non-metricity is set to zero?

Is this theory really a teleparallel theory?
 Or is it just called that for historical reasons?


The 1998 theory is called symmetric teleparallel equivalent to GR because it has vanishing torsion (the antisymmetric part of the connection). 

But it has curvature? Or at least a curvature connection with degrees of non-metricity? 

If so, how can it qualify as teleparallel?


This has been confusing me since you originally mentioned it.

How is this different from a matric-affine theory with zero torsion?


Referring to Einstein's 1928 work on teleparallelism in 2020 as "the teleparallelism" is certainly done, but this is not practical for researchers in the field of gravitation. I'm sure that a lot of physics professors at top universities who don't                       specifically research these topics would believe teleparallelism is just Einstein's failed theory from 1928, but the history is more subtle.

But as I said, there is -- strictly speaking -- no such thing as a "teleparallel spacetime".

But if by this you only mean a Weitzenbock spacetime, then fine. as long as that is clear.

Would the most general subsector of metric-affine gravity with vanishing curvature still be a teleparallel space even though it is neither of these teleparallel theories mentioned above? If metric-affine gravity and it's higher-dimensional operator generalizations give the "most general theory of relativity", then perhaps there exists a "most general teleparallel theory" that has not been sufficiently explored in the literature.

It's just a question of avoiding confusion resulting from ambiguous terminology, that's all.

Why not call it a "Weitzenbock space", which is the standard term?

If yes, then Paul suggesting that Jack focuses on metric-affine gravity still allows Jack to discuss teleparallel spaces, especially if we agree that there exists some "most general teleparallel theory of relativity", which is not really a term I've seen used.

I have no problem with Jack using a Weitzenbock space, as I've defined it here. I'm just trying separate that from any implied claims of teleparallelism -which at this point I don't think Jack intended to make.

Paul you simply do not understand the physical picture of Alice and Bob in local coincidence measuring the same external events with light signals.
 
Allowing Alice and Bob to be on arbitrary timelike world lines is described by local T4 gauging that directly induces tetrad coefficients from which metric tensor and Levi-Civita connection are derived.

Local gauging T4 is represented formally by this equation
 
dx^I(ALICE LIF) = e^Iu(x)dx^u(BOB LNIF)
 
“x" = local coincidence =/= coordinate


Where
 
x^u —> x’^u = x^u + a^u(x) = LOCAL GAUGING T4
 
a^u(x) = e^uI(x)dx^I = X^uu'(x)dx^u
X^uu’(x) = e^uI(x)eu’^I(x) = EINSTEIN GCT
I = LIF tensor index
u,u’ = LNIF tensor indices