Mordred

In essence what you have described thus far is feasibly sound. The article will provide much of the critical details. There are plenty of references on how a graviton would relate to gravitational potential of a field so having a higher number density as a result of gravitational waves is easily formulated with the above. As a vector gauge boson those gravitons would be off shell in essence the internal lines on a Feymann diagram. The article above also covers this. I should add Maxwell Boltmann uses phase space this article isn't bad on it https://ps.uci.edu/~cyu/p115A/LectureNotes/Lecture13/lecture13.pdf

Ok so the critical aspects to examine are as follows. First you require the geometry of the metric. No need to create one as there is plenty of available examples for a minimally coupled scalar field involving gravity. The graviton would be required to be a spin 2 boson. ( this is a direct consequence of GR spacetime metric ) any good GR textbook also covers this.. You will require a canonical perturbation method using integrals for decay rates. Which is compatible with QFT, as this is also a Lorentz invariant metric using the Klien Gordon equations of QFT. So far so good there is previous work for the majority of the above. The decay rates for a for a graviton however will be tricky to find good examples. Any examples will also be speculative as we only have theoretical possible rates including any other properties such as mass etc. For particle number density one can use the Bose-Einstein statistics for a spin 2 particle or alternately the creation/annihilation operators of QFT. So although numerous steps much of the work has existing formulas that can be employed to develop a proper model. As your toy modelling and not claiming to have a working model lets add some mathematics behind your theory. I will save you some time and post some of the relevant formulas to get you started. Also helps a majority of the ones I feel will work for you I already have latexed on this site so I can copy/paste the ones I feel will be useful to you. GR section GR line element in weak field limit \[ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] FLRW metric \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] Minimal gravitational couplings \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] Maxwell Boltmann and Bose Einstein statistics the method is compatible with the QFT equivalent using creation/annihilation operators for particle number density to blackbody temperature relations. Although in QFT its more specifically related to the Fourier transformations via the wave equations involved in the creation/annihilation operators. \[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\] \[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\] \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3\] decay rates related mathematics This part applies to a generalized quick guide to what is involved in decay rate calculations Fermi's Golden Rule \[\Gamma=\frac{2\pi}{\hbar}|V_{fi}|^2\frac{dN}{DE_f}\] density of states \[\langle x|\psi\rangle\propto exp(ik\cdot x)\] with periodic boundary condition as "a"\[k_x=2\pi n/a\] number of momentum states \[dN=\frac{d^3p}{(2\pi)^2}V\] decay rate \[\Gamma\] Hamilton coupling matrix element between initial and final state \[V_{fi}\] density of final state \[\frac{dN}{dE_f}\] number of particles remaining at time t (decay law) \[\frac{dN}{dt}=-\Gamma N\] average proper lifetime probability \[p(t)\delta t=-\frac{1}{N}\frac{dN}{dt}\delta t=\Gamma\exp-(\Gamma t)\delta t\] mean lifetime \[\tau=<t>=\frac{\int_0^\infty tp (t) dt}{\int_0^\infty p (t) dt}=\frac{1}{\Gamma}\] relativistic decay rate set \[L_o=\beta\gamma c\tau\] average number after some distance x \[N=N_0\exp(-x/l_0)\] spin statistics spin 2 graviton. you can look through this as a vast majority of the formulas are mentioned here in modelling the graviton couplings to the spacetime field https://arxiv.org/pdf/1812.07571.pdf Hope that helps

You wish to prove me wrong then post how you performed the mathematical operations to invert your 11 dimensional tensor to the Kronecker delta tensor by posting the actual mathematical steps here. Do not verbally claim you have done so without being able to directly show your mathematical work here. Your the one that has 11 dimsions you describe as a metric not I. Or you can invert the following Ie the Minkowskii tensor [latex]dx^2=(dx^0)^2+(dx^1)^2+(dx^3)^2[/latex] [latex]G_{\mu\nu}=\begin{pmatrix}g_{0,0}&g_{0,1}&g_{0,2}&g_{0,3}\\g_{1,0}&g_{1,1}&g_{1,2}&g_{1,3}\\g_{2,0}&g_{2,1}&g_{2,2}&g_{2,3}\\g_{3,0}&g_{3,1}&g_{3,2}&g_{3,3}\end{pmatrix}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] Which corresponds to [latex]\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}[/latex]

Really ? If the first equation you start with is incorrect then any derivative from that equation would subsequently be incorrect. This is one of the reasons I asked the questions I did concerning gravity itself. Specifying you examine your understanding of gravity via Newtons laws under Newtons Shell theorem. You cannot invert a tensor with 11 dimensions and end up with a rank 2 tensor. That's not how the inverse of a tensor works. A tensor is simply a representation of an equation. In essence an organizational tool. It is a means of keeping track of vectors or one forms which involve vectors.

Just an FYI Schrodingers equation doesn't work well in field theories. Hence QFT uses the Klein Gordon equation where the operators of QM position and momentum have been replaced with field and momentum by using the potential energy of the field and the kinetic energy of the particles momentum. In essence it works well for Lorentz invariance of SR.

No the difference is they are professional peer reviewed theories developed by other physicist and are not personal models or theories. You can find professionally written literature as a reference supporting those theories that have been reviewed by other professionals as being mathematically viable possibilities. If research prove them to no longer be viable. Those theories will either adapt or be dropped all together.

Assuming the existence of a graviton, which isn't a new idea. You can find examples including string theory and SO(10) MSSM. In both cases you would have a unified field oft termed supergravity. That part of your post is viable. However even with the unified force the spacetime curvature will globally be zero with the stress energy momentum term being zero. Under QM and QFT you will still have the quantum harmonic oscillator. Now curvature actually refers to the geodesic paths that particles will follow so in this case all particle paths are not undergoing any form of acceleration.in essence a freefall state where there is no force acting upon their paths. Once you get anistropy due to the previous harmonic oscillations then things get interesting in so far as that unified force could potentially act upon particle paths. However I should note the other do exist at all times but are in a condition called thermal equilibrium which is a symmetric state. Electroweak symmetry breaking occurs a little later once the universe due to inflation/expansion allows the other forces as well as Higgs to drop out of thermal equilibrium. ! Moderator Note Any member can remind another member of a site forum rule. Personal pet theories is a rules violation when replying to other forum members posts. Any member may also also report a rules violation to the moderator staff as a corrective action

You will never be able to get funding unless you can prove mathematical feasibility. You can trust me on that. They are not something handed out without extensive mathematical proofs. Not on any physics related topic or application.

No I cannot because your not applying correctly known physics. Nor could you provide a mathematical proof to show your compatible with known physics. This included statements from you that you are not applying the term dimensions in accordance with how a physicist would apply that term. Your descriptive involving gravity isn't accurate to the model of GR. I can only guess your description of open and closed systems are a thermodynamic definition as opposed to an open and closed group. Your descriptive of primes in an 11 dimension application makes zero practical sense. Even one of the images has the fine structure constant which is only one of the primary constants used in physics. The majority of which has nothing to do with prime numbers. The Rheiman zeta function itself is a complex variable that is extremely useful by physicists we employ it often in various theories but you were never clear on how you apply it on say an actual graph. However according to you all of physics is simply old school so I cannot trust your correctly applying any mentioned theory without personal modification and claims.

so you claim but have not supplied the required details. I have a bridge to sell you in Brooklynn enough said this statement alone counters any claims that you model is compatible with GR it also counters your claim of General Covariance. Einstein also provided a mathematical proof of every one of his theories no one took his word of honor that his mathematics works. He had to mathematically prove they would work with known physics at the time.

Every single inflationary related theory will have its own variations on the equations of state. The w=-1 is an approximation that essentially states its constant. However it also doesn't require to start out prior to electroweak symmetry breaking as precisely w=-1. The primary goal however is to include the Mexican hat potential of the metastability conditions. Predict the correct number of e=folds and have the correct slow roll to match observational data. The minimum required e-folds needed is 55 anything lower will not match however higher values still have the potential to match depending on slow roll rates. Anyways the real reason I posted those equations was to give an example of what steps are required to develop a proper theory. Yet they never ever take the time to provide the details on how they precisely derived their equations. EVER> If you cannot provide the mathematical steps to derive a given formula then the formula is absolutely useless to anyone else. Every formula has a mathematical Proof, that mathematical proof gives all the required steps on how that formula was mathematically derived. No formula is ever randomly created by intuitive imagination....It simply doesn't work that way. spacetime itself is not gravity. Spacetime is the geometric field, You can have spacetime without gravity. That is the point I was making. Gravity results form spacetime curvature itself not from a uniform distribution. Or more accurately spacetime curvature aka what we consider gravity is a result of a non zero stress energy momentum tensor. If every particle is non accelerating ie in the freefall equivalent state you can motion without gravity. Google Einstein's equivalence principle for further details on that That is not the Limblad master equation. here is the mathematical proofs related to the Limblad master equation. https://arxiv.org/pdf/1906.04478.pdf see the required steps to arrive at equation 92 of said article. If you wish to counter me on that last statment feel free to provide a peer reviewed article showing the equation you provided as the Limblad master equation.

I agree, I too feel that's likely the most possible method at least as far as I have come across.

accretion disks can have numerous variations its not nearly straightforward as one might think. One of the better references regarding accretion disks I hve come across is this lengthy article http://arxiv.org/abs/1104.5499 :''Black hole Accretion Disk' the merging of two blackholes would likely diffuse the accretion disks over a wider area thus reducing its overall density and subsequently reducing the gamma rays emitting from them over a wider area. Anyways hope you enjoy the article it is rather lengthy but highly informative on many of the BH related processes. Anyways as you can see due to numerous factors many involving hydrodynamics, disk types BH spin, available material etc. The answers to your questions above can range in answers due to those various factors.

Well technically every equation I just posted is the simplified form. With the exception of the SM Langrangian the remaining equations are in the Newtonian limit. The first equation would take roughly 30 pages of partial derivatives. Lol yet the highest dimension involved is 4. So I wouldn't hate to see the chain rules applied to 11 dimensions. By the way +1 on your last post. It is a daunting task but an essential step to validate any formula or model. There is mathematical proof behind every equation even simple ones like f=ma. Edit I should also point out having a large number of dimensions isn't desirable. You always want to reduce any formula to the lowest number of dimensions possible to describe a system or state. The fewer dimensions the better.

Ok this is getting to be a waste of time. Its obvious you have far more claims than the mathematical proof to substantiate your claims. So lets start with something simple. gravity itself forget everything else. Lets toy model a system where you have a stress energy momentum tensor where \[T^{\mu\nu}=0\] you have zero spacetime curvature setting k=0. Whatever mass/energy value you like doesn't matter as this defines the T_^00 component. In essence you have a uniform mass/energy distribution. Now apply Newtons shell theorem which shows in this case g=0. aka no gravity. Why would this situation cause the creation of our universe as you claim when you have in essence a condition of zero gravity ? Mathematically prove this is possible and arrive at the covariant derivative for the standard model \[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\]. Don't worry I honestly don't expect you to be able to do so but lets see if you can which amounts to what your claims and boasts have been gearing towards in regards to a GUT theory. lets examine a professional example done properly to simply examine the possibility of the cosmological constant (dark energy as the result of the Higgs field and subsequently connecting it to inflation.. (not my work credit will be included.) Higgs Inflation Single scalar field Modelling. \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] set spin zero inflaton as \[\varphi\] minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term) \[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\] where \[V(\varphi)\] is the potential term integrate the two actions of the previous two equations for minimal scalar field gravitational couplings \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] variations yield the Euler_Langrene \[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\] using Euclidean commoving metric \[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\] this becomes \[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\] \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] and \[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\] with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as \[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\] \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] \[w=\frac{p}{\rho}\] \[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\] ***method by Fernando A. Bracho Blok Thesis paper.*** https://helda.helsinki.fi/bitstream/handle/10138/322422/Brachoblok_fernando_thesis_2020.pdf?sequence=2&isAllowed=y that is what I am looking for. This example tells me how the author arrived at the equation of state where w=-1 using the Higgs field. This is what is meant by a mathematical Proof... The author provides all the pertinant mathematical detail required for a thesis paper.

No problem with what you have specifically on the Kronecker delta with the notations involving the raising and lowering the indices. That part is correct. Do you also have the Rheimann permutation tensor (Levi-Cevita) psuodo tensor in your derivatives ? Yes further detail as to how you went from the formula you posted as well as the elements in your GEM 11 dimensions would be helpful. I look forward to the further details you mentioned. It's hard to examine a theory with essential details missing lol. I assume your applying the Kronecker delta in coordinate basis ?

One quantum field theory I keep an eye in the hopes of a gravitational quantum field theory is quantum geometrodynamics. I find many of the methods of the theory promising but much like LQG has the same issues with gravity to address. Granted it also has some of the same methodologies to LQG. It's also likely one of the reasons I enjoy studying it is its a canonical field theory which I typically prefer over the conformal methods

I went through what you had on that website. I sincerely hope you have better detail beyond a bunch of claims that you haven't included the mathematical proofs behind them. By mathematical proofs I am not talking formulas one can readily find from other authors or textbooks. I am specifically talking about mathematical proofs that you can truly account for observational evidence for claims in regards to dark matter, dark energy etc. Not flim flam verbal claims that A results in B but your specifically derived mathematical derivatives. For example inverting an 11 dimensional tensor is not a straightforward procedure it is a very process. How you arrived at \[g^{ij}\] by doing so is something your going to have to demonstrate. I can't even imagine what steps you missed..... You mentioned above the Rheimann zeta function but I have yet to see any mathematical detail directly related to it. Yes it is oft used in numerous physics applications. That doesn't tell me how you applied it specifically. Once again not the verbal description or a bunch of pictures but how you specifically mathematically apply it to your theory. A little golden rule a true physics theorist does everything in his ability to prove his own theories wrong. It is one of the best ways to develop a robust theory. All physics theories must make testable predictions. That inherently requires the relevant mathematics. Without that it is nothing more than personal belief. If you are willing to honestly develop a proper working theory then the direction I would recommend is to apply the Lanqrangians via the covariant derivatives of each field in the standard model including the minimally coupled Langrangian to spacetime. Include any relevant manifold connections to preserve invariant between transformations. Needless to say your claim of dark matter and dark energy in regards to gravity is extremely outlandish and I have yet to see anything from what you posted here on that site to convince me otherwise

Finally some of the related mathematics. Now just to get it into a more readable form hallelujah. At least it's a start.... Overall you have standardized common knowledge stuff until you deviate to your own model. Since when is a 2 dimensional tensor the inverse from an 11 dimensional tensor yes I'm back at \[g^{ij}\] How did you arrive at a 2 dimensional tensor by inverting an 11 dimensional tensor ?

Sigh I don't need to know what GR states. I'm very well versed in GR, nor do I need prime numbers to describe that bump. I can describe it using differential calculus. Hence my comment above on Kronecker delta and Levi- Cevita connections. I can further describe every single particle interaction utilizing the same geometry. The very purpose of mathematics in physics is to describe physical objects and physical processes . Hence the very name of the science. (Physics). Do you honestly expect me to interpret images and words ? Where is the mathematical proofs behind your statements?

Ok the very statement open and closed system alone tells me you are not using correct mathematical terminology but are throwing buzzwords without understanding the mathematical implications of those terms. All systems or states in any and every physics theory is mathematically defined. Yet you still have avoided the essential question. How does one employ prime numbers to define a geometric object ? Every theory you mentioned above applies geometry so this is of essential importance

If it's not the physics application of dimensions then how can I trust it to define define a manifold ? Keep in mind verbal descriptive are never sufficient for me. This includes professional peer reviewed literature. I never accept claims that cannot be shown mathematically. Mathematically one rarely ever needs more than 4 dimensions to describe spacetime paths that result from spacetime curvature. So why do you require 11 ? You claim to be 100 percent compatible with GR then you should have no problem addressing the fundamental aspects I have mentioned involving GR and geometry in the above questions.

No I will not download your book nor join the site it is on. However from what I have thus far your theory smacks of numerology. I do not see any importance or practicality in designating any significance on prime numbers with regards to spacetime. Nor do I see any practicality behind needing 11 dimensions or effective degrees of freedom in describing spacetime. Unfortunately none of the math you have posted answers the latter part. \[g_{ij}\] at best describes a geometry with a Kronecker delta function that one would find in a Euclidean geometry. You do not so any Levi-Cevita connection that would find relevant for curved spacetime. So obviously you are not using any standard forms. By the way welcome to the forum just a forwarning the first day of new membership you will be limited to 5 posts the first day. After that it's unlimited. How does prime numbers handle the vectors of spacetime. You might want to start there

I agree negative I've found simpler for others to relate to than potential vs kinetic energy or vacuum. As vacuum is rather misleading with all the different fields that use the vacuum term. Good example being Higgs metastability vacuum

I always found Guths method for inflationary E-fold related calculations one of the easier methods. Another method can be found here. Both methods incorporate the equation of state for the scalar field. https://cds.cern.ch/record/1420368/files/207.pdf