Mordred

No I am describing a rank two tensor under GR ( though just the starting steps to understand a rank two tensor). I hadn't gotten into components of a vector. (A special rank two tensor would be the Dyad.. The reason you need a rank two tensor describe gravity is that you a gradient to describe gravity.

Well that would certainly involve a lot of antisymmetry relations. Acceleration caused a rotation due to rapidity. Torsion would give antisymmetry to the metric tensor. Ie to describe torsion using the metric tensor you would have to specify a direction of rotation. What you actually need is a covector vector and a vector. The covariant vector is the column vectors while the vector is the row vectors. Using the two vectors above will preserve invatiance under coordinate transformations. Gravity itself is a form of flux of the energy momentum stress tensor. With the Minkowskii tensor you have already made a coordinate choice (cartesian) so you can use the inner product of two vectors. Which will return a scalar value [math]\mu\cdot\nu=s[/math] the Minkowskii tensor is orthogonal all orthogonal groups are symmetric and commute. [math]\mu\cdot\nu=\nu\cdot\mu[/math] However this would not be invariant under coordinate transformation so the column vector would use a covector.

Somehow I don't want to know. 😖

Every physics theory has competitive theories this is true of inflation. The CMB itself is supportive evidence through big bang nucleosynthesis of the BB. One of the difficult things to explain is how the supercooling due to rapid expansion and reheating due to the inflation slow roll leads to the metalicity values measured at z=1090. When you get right down to it the percentages match those predicted by inflation and quite frankly limit the range of viable inflation models. So it really doesn't matter what one believes. The only thing that matters is what observational evidence tells us. If you want a listing of viable inflation models that match observational evidence (though the last update was 2013.) See here https://arxiv.org/abs/1303.3787 The opening section explains the criteria. Personally I'm a fan of a single scalar field with a low kinetic term Higgs inflation. However my opinion doesn't mean it's factual. Lol at least that one is still viable according to Planck datasets.

It describes the probability wavefunctions. An oscillator isn't restricted to object motion but can also be used to describe any repeating varying value. A sinusoidal waveform in electronics is a good example.

With the uncertainty principle one cannot accurately measure the position and momentum of a particle at the same time. Measuring one observable P or Q will interfere with the other. Also the more accurately you measure one the less accurate you can determine the other. Both observable's will have a probability amplitude.

I like your reference four paper, there is several Langrangians in that paper I will latex later on to have a handy copy of them. I also like what you did with the overbrace and underbrace. I don't see any problems thus far

Looks good thus far the reference 7 page 11 equation 47 has the covariant derivative of the graviton propogator, as your employing the same tensors you should be be good.

See here for further detail you will also find the one loop vacuum polarization propogator handy https://arxiv.org/abs/1504.00894 Lol this article does mention the k term

Here is one of the better papers for the graviton spin 2. Note equation [math]g_{\mu\nu}\rightarrow \eta_{\mu\nu}+k h_{\mu\nu}[/math] https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/gr-qc/0607045&ved=2ahUKEwjCzqGC1PXmAhW1oFsKHT-HAs4QFjAAegQIBBAB&usg=AOvVaw30-hmokcbjp_amGXWvZtet The article provides the general spin Compton scattering for the other spin statistics as well as spin 2. My recommendation is to start with the linearized Einstein Hilbert action. See the following Doctorate thesis. (It's a common methodology for modelling the graviton) https://www.google.com/url?sa=t&source=web&rct=j&url=https://academiccommons.columbia.edu/download/fedora_content/download/ac:201929/content/GarciaSaenz_columbia_0054D_13501.pdf&ved=2ahUKEwi90_f23vXmAhX6JTQIHd0cCU8QFjACegQIAhAB&usg=AOvVaw22sjBJZaLwriZmm2fuX0wt By using the Einstein Hilbert action your already working in quanta Ie quanta of action and thus can make the correlations to the creation and annihilation operators for the Feymann path integrals. Though the difficulty will be avoiding infinite one loop corrections. Divergence that ruins renormalization Edit almost forgot in the above equation [math]k^2=16\pi G [/math] I'm not sure any of the above articles mention that. The above formula is a fairly standard equation in numerous papers for massless spin 2 propogators.

Much better for the Jacobian in spherical weak field limit. However It looks to me your graviton application is spin 1 dipolar. You need quaternion relations spin 2 (quadrupolar). To match up to gravity wave data. ( Though I will have to study your equations for reference 6 further) Let dig up some good graviton modelling and the relevant GR spin 2 application. Keep in mind in order to properly model the gravitons you will need it's wavefunction for transerve and longitudinal component. (In gauge treatments you must be renormalizable. )

Lol I always seem to get caught by spell check lol. Correction made thanks for the catch

Here is one example Schwartzchild metric Vacuum solution [latex]T_{ab}=0[/latex] which corresponds to an unaccelerated freefall frame [latex]G_{ab}=dx^adx^b[/latex] if [latex]ds^2> 0[/latex] =spacelike propertime= [latex]\sqrt{ds^2}[/latex] [latex]ds^2<0[/latex] timelike =[latex]\sqrt{-ds^2}[/latex] [latex] ds^2=0[/latex] null=lightcone spherical polar coordinates [latex](x^0,x^1,x^2,x^3)=(\tau,r,\theta,\phi)[/latex] [latex] G_{\alpha\beta} =\begin{pmatrix}-1+\frac{2M}{r}& 0 & 0& 0 \\ 0 &1+\frac{2M}{r}^{-1}& 0 & 0 \\0 & 0& r^2 & 0 \\0 & 0 &0& r^2sin^2\theta\end{pmatrix}[/latex] line element [latex]ds^2=-(1-\frac{2M}{r}dt)^2+(1-\frac{2M}{r})^{-1}+dr^2+r^2(d \phi^2 sin^2\phi d\theta^2)[/latex]

Lol correction applied

[math]g_{\alpha\beta}[/math] is the metric tensor the indices run (0,1,2,3). The form will vary according to the spacetime being modelled it can have either or both the covariant and contravariant terms accordingly to the Einstein summation convention. In the above its specifying covariant.

[math]\mu\cdot\nu=\nu\cdot\mu=\eta [/math] is the inner product symmetry relations for the Minkowskii metric tensor. You identified it as the GR symmetry matrix expression. You need the first order partials for the Jacobian matrix while I don't have polar coordinate form handy you can look here for the Minkowskii form though you will have to switch the signature. https://en.m.wikipedia.org/wiki/Four-gradient The one forms mentioned are invariant under coordinate change

Lol considering I am only 5 foot seven and 155 lbs my legs can press 250 kg for ten reps on a Universal machine. 60 kg is nothing.

You would deal with the position and momentum uncertainty with quantum particles however relativity itself is a classical theory which it's mathematics doesn't incorporate probabilities or harmonic oscillators for the uncertainty principle. Those get incorporated when you deal with theories such as QFT. However freefall paths via principle of least action (Langrangian) does involve uncertainty in the chosen path that the particle will take at each infinisimal. (GR itself doesn't get too much into the Langrangian) so when studying GR I wouldn't worry about uncertainty in freefall paths. That's would be far too distracting until you get really comfortable with GR

Welcome back and excellent post as always. I particularly agree with your caveat that spacetime is a mathematical model.

Higgs field with above [math]\mathcal{L}=(D_\mu H)^\dagger D^\mu H-\lambda(H^\dagger H-\frac{v^2}{2})^2[/math] v=246 GeV Quartic coupling [math]\lambda=m_h^2/2v^2=0.13[/math] [math]\langle H^\dagger H\rangle =v^2/2[/math] Fermions (matter content) (goal tie in CKMS and Pmns mixing angles (latter for leptons)) will require unity triangle... [math]\displaystyle{\not}D=\gamma D^\mu[/math] self reminder Feymann slash contraction of the gamma matrix with a four vector [math]\displaystyle{\not}a=\gamma a^\mu a_\nu=\gamma_\mu a^\nu[/math] a is any four vector.

Pulling this post back to where I can find it to add Yukawa couplings details this weekend [math]\mathcal{G}=SU(3)_c\otimes SU(2)_L\otimes U(1)_Y[/math] Color, weak isospin, abelion Hypercharge groups. Couplings in sequence [math]g_s, g, \acute{g}[/math] [math]\mathcal{L}_{gauge}=-\frac{1}{2}Tr{G^{\mu\nu}G_{\mu\nu}}-\frac{1}{2}Tr {W^{\mu\nu}W_{\mu\nu}}-\frac{1}{4}B^{\mu\nu}B_{\mu\nu}[/math] Field strengths in sequence in last G W B tensors for SU(3),SU(2) and U(1) Leads to covariant derivative [math]D_\mu=\partial_\mu+ig_s\frac{\lambda_i}{2}G^i_\mu+ig\frac{\sigma_i}{2}W^i_\mu+igQ_YB_\mu[/math] Corresponds to [math]G_{\mu\nu}=-\frac{i}{g_s}[D_\mu,D_\nu][/math] [math]W_-\frac{I}{g}[D_{\mu}D_{\nu}][/math] [math]B_{\mu\nu}-\frac{I}{\acute{g}}[D_\mu,D_\nu][/math]

[math]\acute{D1}=\frac{D1 c}{(c-V)}[/math] do you think this statement is correct ? Sorry but this just doesn't make any sense. Why didn't you just use Galilean relativity to start with ? [math]\acute{x}=x-vt [/math] [math]\acute{t}=t [/math] [math]\acute{y}=y [/math] [math]\acute{z}=z [/math]

From what I can tell he is rambling. Particularly since he also stated Ie no seperation distance ???? Tell me OP when are you ever going to address direct questions correctly ? Every response you give leads to more confusion. Sounds like you don't know how to describe your theory. Your now invoking virtual phase and group velocity but still haven't shown how your keeping the phase velocity equal to c for all observers... This asked of you by several posters.... Now here is another question for you you specifically stated a wave requires a medium to propogate. So why does both you phase and group velocities have wave equations ? Perhaps you should start with the basics [math]v=\lambda f [/math] [math]k=\frac{2\pi}{\lambda}[/math] [math]f=\frac{2\pi}{\omega}[/math] At least you can start with the basic electromagnetic wave equations. You should at least realize in a vacuum you can have any frequency or wavelength as long as [math]\lambda f=c [/math] Though if you want the modern method use https://en.m.wikipedia.org/wiki/Electromagnetic_wave_equation Though you would have to admit your phase and group velocity usage is completely wrong in modern terminology usage.

I have read your papers and the biggest lack I can see is that you haven't understood that physicists in the early years do not understand basic wave mechanics. You are quite wrong on that aspect. Please define absolute motion including the vector transformation rules required to keep phase velocity equal to c for all observers. Unless you can do that I don't see any validity in your theory. pS mathematics not words. From what I have read your theory requires you definition of phase velocity being equal to c for all observers. So provide the necessary vector transformation rules required under 3d treatment to produce that requirement.

One of the problems ppl have when they present ether based theories is the assumption that the tests have stopped at the more commonly known tests. There have been dozens of different tests looking for an ether that all show null results the latest that I am familiar with was done in 2009. This test looked for Ether at the quantum level with its extreme precision. [math]\Delta c/c=1*10^{-17}[/math] for the precision level. Still absolutely no indication of an ether. @Op your going to need some incredibly strong evidence well beyond any mathematics your papers indicate to account for how these null results can occur with your theory. Quite frankly without extremely accurate precision tests you really don't have much hope in competing with the overwhelming evidence against you. Here is the relevent arxiv to the result above https://arxiv.org/abs/1002.1284