Text Size

 

On Apr 3, 2014, at 2:09 PM, Paul Zelinsky  wrote:

"Also, what do you think the Minkowski fiber bundle represents in modern formulations of GR? It represents a local mapping of the curved base space inner products determine by g_uv onto the Minkowski fibers defined by the globally flat Minkowski metric n_uv."
To which I replied:
 
That’s precisely what I mean by LNIF <—> LIF (both local frames COINCIDENT)
 
frame field for LNIF is eu(LNIF) with curvilinear metric guv(LNIF).
 
One can always find LNIFs where in Taylor series about origin 
 
g^u^v(LNIF) ~ n^u^v(Minkowski) + {Levi-Civita Connection}^u^vw&x^w + {Riemann Curvature Tensor}^u^vwl&x^w&x^l + ….
 
ds^2 = guv(LNIF)e^u(LNIF)e^v(LNIF)
 
frame field for LIF (Cartesian coordinates a must as Einstein stipulates in his papers) eI(LIF)  tangent bundle fiber metric Taylor expansion is
 
n^I^J(LIF) = n^I^J(Minkowsk) + {Riemann Curvature Tensor}^I^JKL&x^K&x^L + ….
 
ds^2 = nIJ(LIF)e^I(LIF)e^J(LIF)
 
Small font indices u,v ... are in the LNIF base space
 
Caps I,J are in the LIF fiber
 
The tetrad transformation is
 
e^u(LNIF) = e^uIe^I(LIF) etc.
 
EEP means that
 
{Levi-Civita Connection}^I^JK = 0
 
though in general
 
{Riemann Curvature Tensor}^I^JK =/= 0
 
ARTIFICAL (FIRST ORDER NON-TIDAL) GRAVITY FIELDS IN SENSE OF EINSTEIN AND NEWTON CORRESPOND TO
 
{Levi-Civita Connection}^u^vw =/= 0
 
Riemann Curvature Tensor}^I^JKL = 0
 
REAL GRAVITY FIELDS IN THE SENSE OF MISNER, THORNE AND WHEELER (SECOND ORDER WEYL TIDAL VACUUM + RICCI MATTER COMPRESSION) CORRESPOND TO
 
Riemann Curvature Tensor}^I^JKL =/= 0
 
Note that e^I(LIF) is a set of 4-vectors with components e^Iu
 
e^u(LNIF) is a set of 4-vectors with components e^uI
 
e^uIe^Iv = kronecker delta uv etc. ORTHOGONAL GROUP O(1,3)
 
ds^2 = nIJ(LIF)e^Ie^J = guv(LNIF)e^ue^v
 
LIF Alice and LNIF Bob are COINCIDENT
 
LIF Alice has zero proper acceleration
 
LNIF Bob has non-zero proper acceleration
 
ds is invariant space interval between 2 neighboring events measured simultaneously by both Alice and Bob.
 
Since we impose COINCIDENCE no problem with simultaneity.
 
Also clock postulate that proper acceleration of clocks in LNIF can be synchronized to clocks in LIF if they are coincident.

 

Category: MyBlog

Categories ...

't Hooft 100 Year Star Ship Abner Shimony accelerometers action-reaction principle Aephraim Sternberg Alan Turing Albert Einstein Alpha Magnetic Spectrometer American Institute of Physics Andrija Puharich Anthony Valentin Anton Zeilinger Antony Valentini anyon Apple Computer Artificial Intelligence Asher Peres Back From The Future Basil Hiley Bell's theorem Ben Affleck Ben Libet Bernard Carr Bill Clinton black body radiation Black Hole black hole firewall black hole information paradox black holes Bohm brain waves Brian Josephson Broadwell Cambridge University Carnot Heat Engine Central Intelligence Agency CIA Clive Prince closed time like curves coherent quantum state Consciousness conservation laws Cosmic Landscape Cosmological Constant cosmology CTC cyber-bullying Dancing Wu Li Masters Dark Energy Dark Matter DARPA Daryl Bem David Bohm David Deutsch David Gross David Kaiser David Neyland David Tong de Sitter horizon Dean Radin Deepak Chopra delayed choice Demetrios A. Kalamidas Demetrios Kalamidas Dennis Sciama Destiny Matrix Dick Bierman Doppler radars E8 group Einstein's curved spacetime gravity Einstein's happiest thought electromagnetism Eli Cartan EMP Nuclear Attack entanglement signals ER=EPR Eric Davis Ernst Mach ET Eternal Chaotic Inflation evaporating black holes Facebook Faster-Than-Light Signals? fictitious force firewall paradox flying saucers FQXi Frank Tipler Frank Wilczek Fred Alan Wolf Free Will G.'t Hooft Garrett Moddel Gary Zukav gauge theory general relativity Geometrodynamics Gerard 't Hooft Giancarlo Ghirardi God Goldstone theorem gravimagnetism gravity Gravity - the movie gravity gradiometers gravity tetrads Gravity Waves Gregory Corso gyroscopes hacking quantum cryptographs Hagen Kleinert Hal Puthoff Hawking radiation Heisenberg Henry Stapp Herbert Gold Higgs boson Higgs field hologram universe Horizon How the Hippies Saved Physics I.J. Good ICBMs Igor Novikov inertial forces inertial navigation Inquisition Internet Iphone Iran Isaac Newton Israel Jack Sarfatti Jacques Vallee James F. Woodward James Woodward JASON Dept of Defense Jeffrey Bub Jesse Ventura Jim Woodward John Archibald Wheeler John Baez John Cramer John S. Bell Ken Peacock Kip Thorne Kornel Lanczos La Boheme Laputa Large Hadron Collider Lenny Susskind Leonard Susskind Levi-Civita connection LHC CERN libel Louis de Broglie Lubos Motl LUX Lynn Picknett M-Theory Mach's Principle Mae Jemison Making Starships and Star Gates Martin Rees Mathematical Mind MATRIX Matter-AntiMatter Asymmetry Max Tegmark Menas Kafatos Michael Persinger Michael Towler microtubules Milky way MIT MOSSAD multiverse NASA Nick Bostrum Nick Herbert Nobel Prize nonlocality Obama organized-stalking Origin of Inertia P. A. M. Dirac P.K.Dick P.W. Anderson Paranormal parapsychology Paul Werbos Perimeter Institute Petraeus Physical Review Letters Physics Today Post-Quantum Physics pre-Big Bang precognition presponse PSI WARS Psychic Repression qualia Quantum Chromodynamics quantum computers quantum entanglement quantum field theory quantum gravity Quantum Information Theory Quantum Theory RAF Spitfires Ray Chiao Red Chinese Remote Viewing retrocausality Reviews of Modern Physics Richard Feynman Richard P. Feynman Rindler effect Robert Anton Wilson Robert Bigelow Roger Penrose rotating black holes Roy Glauber Rupert Sheldrake Russell Targ Ruth Elinor Kastner S-Matrix Sagnac effect Sam Ting Sanford Underground Research Facility Sarfatti Lectures in Physics Scientific American Second Law of Thermodynamics Seth Lloyd signal nonlocality Skinwalker Ranch social networks space drive space-time crystal SPECTRA - UFO COMPUTER spontaneous broken symmetry SRI Remote Viewing Experiments Stanford Physics Stanford Research Institute Star Gate Star Ship Star Trek Q Stargate Starship Stephen Hawking Steven Weinberg stretched membrane string theory strong force gluons Stuart Hameroff superconducting meta-material supersymmetry symmetries telepathy Templeton The Guardian Thought Police time crystal time travel topological computers Topological Computing torsion UFO Unitarity unitary S-Matrix false? Unruh effect Uri Geller VALIS virtual particle Virtual Reality Warp Drive weak force Wheeler-Feynman WIMP WMAP WMD world crystal lattice wormhole Yakir Aharonov Yuri Milner