Mordred

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

In a sense but that is too simple a picture. The number of E folds is a consequence of the kinetic vs the potential energy terms within the equation of state for the scalar field. As simple as possible for an explanation the high kinetic energy of the particles involves greatly exceeded any binding potential energy of the fields at that time. Which prior to electroweak symmetry breaking were in essence one field as you have no effective weak, strong Em or Higgs field. You wouldn't even have an effective gravitational field. In essence without a mass term you effectively don't have any real binding energy. It is the binding energy of field interactions that lead to the mass terms. Any high energy density will trend to a lower energy density unless binding energy prevents it from doing so. Once the volume increases sufficiently to allow temperatures to drop (temperature is the average kinetic energy in a volume) to allow symmetry breaking resulting in the mass terms the rate of expansion begins the slow roll phase in inflation. A useful analogy might help think of a very high positive pressure zone. That high pressure zone will want to disperse to a lower pressure state. Much like a balloon when you pop it. Though in the case of the universe there isn't a lower surrounding pressure region like the balloon. There is no outside the universe. However the similarity is there.

Nah in this case it brought up an interesting thought experiment.

Well you will certainly get gravitational wave chirps as well as variations in any EM signals emitting from the accretion disks including the accretion jets. If you want further detail on gravitational wave chirps the commonly used formulas are provided here. https://en.m.wikipedia.org/wiki/Chirp_mass.

Glad you found a workable solution. That solution works well for me. Lol you had me really thinking on that one. It's definitely a scenario I really hadn't thought of before tbh.

Ask yourself is any object in the universe today or then truly at rest. Under GR all observers are inertial. Under SR the observer is always considered at rest even if they are in actuality in motion. The fundamental problem with that is velocity c isn't considered a valid inertial reference frame. It's a very good question that may be a point where relativity breaks down to not being useful.

One of the QFT tricks to handle renormalization to handle divergences in a field theory is to employ a regulator operator. The main divergences being IR and UV divergence. Using Planck units provide a lower and upper bound (upper being Planch temp as one example) were all familiar with the lower lol. One of the problems is that we do not know of any upper boundary to mass density.

In the FLRW metric they use what's called a fundamental observer. That is in essence an observer situated on the global mean average Mass potential. This link has a half decent explanation https://people.ast.cam.ac.uk/~pettini/Intro Cosmology/Lecture01.pdf

The small size made prior to inflation made any anistropy trivial even any plausible curvature would be trivial. Your time frames above for symmetry break are within estimated values. I had a copy of his original paper on inflation. Might still have it in my archives he did at one time utilize the inflaton. May have changed it when he published his book. Prior to thr symmetry breaking one can accurately describe the universe via its temperature exclusively with the volume as all particles were in thermal equilibrium. So would only need the Bose Einstein statistics to calculate the number density of photons. This doesn't mean photons were the only particle but rather one couldn't distinguish any particular particle species at this point in time.

I too had issues with the inflaton or using any of the quasi particles such as the curvaton (Coleman) etc. However the Higgs inflation models produce the same scalar equation of state as the inflaton so as such has been gaining a wide spread popularity including Inflationary Encyclopedadia which examines the most likely Inflationary models for best fit. I also found a couple of papers from Alen Guth who has also switched to Higgs inflation from the inflaton. . I decided to examine how the equation of state for Higgs was derived as well as its Breit Weigner cross sections, Saha equation and Bose Einstein statistics to further examine the feasibility. The formulas I have posted on the thread I have in the BB nucleosynthesis thread in Speculations. As I rarely take any papers on verbatim. I couldn't find any reason to doubt the feasibility not yet anyways lol. The Higgs inflation model can produce a number of E-folds in the required range to satisfy observation data. When one considers the kinetic energy terms vs the potential energy terms via the scalar field equations of state along with the critical density associations it becomes readily apparent that the initial conditions are ripe for an Inflationary expansion. However despite my personal research that is still just my opinion on the topic lmao. Regardless the Higgs inflation model has become my personal choice as to the most likely of the inflation models.

On the contrary the majority of our members enjoy well thought out and well presented debates on a wide variety of topics. Simply pulling ideas out of one's imagination typically doesn't qualify. For example humming itself would be extremely unlikely to affect anything with regards to the food being cooked. If the food tastes better due to humming then the likely argument is that the humming affects the mental susceptibility to enjoying the food that has been cooked. Taste is highly subjective to mental states and personal opinions. We all have those relatives that no matter how good a meal is prepared or how well it tastes they will find disgusting

You need to understand the process producing the light to get a handle on the initial frequencies of light that should be produced. Hydrogen for example has extremely well understood spectral lines. Standard candles as StringJunky mentioned are also used. Any well understood process can serve as a standard candle. Secondly we don't rely strictly on redshift alone to determine distance or motion. Other methods include parallax, in several forms as well as luminosity distance. Though the latter is also subjective to redshift. The luminosity of a star depends primarily on its composition and mass.

Yes the speed limit also results in a maximum speed limit to causality.

Unfortunately the common descriptive of c is the speed of light in a vacuum. That likely is what Geordief is referencing.