Mordred

Been a bit busy with work will look through this when I can give it the proper attention. At first glance it's not bad but I will have to look at it closer

Both Ajb and I regularly discussed lie algebra. It's a very useful tool to understand physics in particular the standard model. However it's used in every major physics theory in general. I'm a little tied up atm but I will add more detail later on with regards to isospin and hypercharge.

Lol I get the offer to be a co author quite often. My reply is always the same. In that I have no issue with assisting someone with their models by pointing out better methods, supplying corrections etc I have no interest in receiving credits for doing so. The real reward is helping someone improve in their understanding. However thanks for the offer. You and I look at physics as a hobby a bit differently each week I try to find a new challenge or model to study as a good hobby to my way of thinking is something that has the goal of continual improvement. Yes I recognize that in regards to physics its not an easy task. Anyways I look forward to see how you handle the vacuum catastrophe.

The Klein Gordon equation is Lorentz invariant. So it's a useful choice where relativistic effects become involved. It modifies from the Schrodinger equation. QfT itself employs the Klein Gordon for this reason. However the Dirac equations are also Lorentz invariant. You can also use the Dirac equations for quarks though you would need the Gell Mann matrices rather than the gamma matrices. Both QED SU(2) and QCD SU(3) incorporate the Pauli matrices which are Hermitean and via the Pauli four momentum Lorentz invariant.

Ok so your article already includes zero point energy. Keep in mind I am only going off what is shown here on this forum so its good to know. So my question still remains are you looking to improve your articles ? the other question is how are you accounting for the vacuum catastrophe that results from zero point energy ?

The reason I asked about the use of Euler coordinates is that it is the most common method to describe Euclidean spacetime and subsequently it also is used for the basis vectors of GR for the infinitesimal invariant manifolds of a Riemannian curvature. The major element you haven't got in your mathematics is geometry nor any vectors. ( or more accurately no directional vector components) You also have no equations describing multiparticle systems. I have no issue with trying to describe a universe from nothing model. However mathematically you truly are going about it the wrong way. That's understandable if your not very familiar with GR but in all honesty there is a far more versatile method under GR to develop your model. You also can factor in much of your equations and subsequently greatly simplify the calculations using geometric units. Commonly referred to as normalized units. https://en.wikipedia.org/wiki/Geometrized_unit_system you can readily set c=g=h=K=1 under geometry you can then apply the FLRW metric. However for the universe beginning or as close as possible without singularity issues at \(10^{-43}\) seconds one would need to have a scalar field in which all particles are in thermal equilibrium this field has no invariant mass as it is prior to electroweak symmetry breaking. This is something your theory runs counter to. As there is no invariant mass (rest mass) at this time. Then there is also no gravity. Yes gravity can self interfere example gravity waves however if the stress energy momentum term at this time is has only one entry. typically \(T^{00}\) for a scalar field however one can substitute the scalar field equation of state. One example being a method used by Guth in one his papers. \(\rho=T^{00}=\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\nabla_i\phi)^2+V\phi\) where \(V\phi)\) is the potential energy density. negative pressure in this is when the potential energy dominates a scalar field leading to what is commonly described as repulsive gravity. Its a bit of a misnomer as it involves pressure. \(p=\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\nabla_i\phi)^2-V\phi\) this is valid when you have a system with no rest mass or invariant mass such as that prior to electroweak symmetry breaking for the volume at that same time. I am very familiar with Allen Guth's modelling methods. I have studied his works for years. in spacetime tensor form for the stress energy momentum tensor you fill the energy density term at T_{00} the pressure terms on the diagonal. \[T=\begin{pmatrix}\rho&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{pmatrix}\] If you truly want assistance helping you to properly toy model your universe proposal and are willing to revamp your article using the higher mathematics (in particular those more applicable to multiparticle systems). Then I have no issue in helping you lean how to go about it. Let me know if you want to learn how to properly model a universe spacetime. For example Guth applies what is known as the scalar field equation of state to describe the potential energy and the kinetic energy terms. Under this method vacuum energy is a result of the kinetic energy terms exceeding the potential energy terms. https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) see the scalar field equation of state here. Anyways let me know if your interested in significantly improving your understanding as well as your papers here is an older post I have done detailing Higgs inflation I didn't bother adding more to is as it didn't generate any discussion or interest lol However the mathematical formulas used here are largely applicable to what you are attempting to do further equations can be found here where I have been setting myself reminder notes of key equations I will need. LOL it may look grandiose but the truth is all of these equations are covered in the first and second years of cosmology and particle physics. Every equation can be readily found in introductory level textbooks. This should give you a better understanding of the type of mathematical weight you will need to send a good impression of your articles in the academic circles. Using the formulas you have so far ( not trying to be offensive) screams that you are lacking in understanding the more suitable mathematical methods. Key aspects you will need being geometry and under that geometry a setting for invariance which includes the conservation laws. You also need to incorporate thermodynamics, this is essential. hence the equations of state methodology

I had done these calculations before for another post awhile back. However don't particularly have time atm. However this site performs the same relevant calculations https://www.forbes.com/sites/chadorzel/2016/04/12/how-hard-does-the-sun-push-on-the-earth/ The numbers are roughly in the same orders of magnitude that I recall when I did them.

What's wrong with QFT itself which uses canonical mathematics via perturbations with integrals. String theory is a conformal theory it uses a different methodology ie spinors. The two methods have distinct mathematical methods in how the describe a waveform or wavefunction.

I see your struggling to figure out which latex system this site uses. Here is a guide https://www.scienceforums.net/topic/108127-typesetting-equations-with-latex-updated/ As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own. In one of your equations you use the subscript \[i<j\] I assume i,j,k are Euler coordinates with index 1 to 3 please confirm your usage . Gravity results from the curvature term or more accurately via the stress energy momentum tensor, If I have a homogeneous and isotropic mass/energy distribution I wouldn't have a system with gravity when k=0. (zero curvature) (apply Newtons shell theorem) \[ {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} \] I have no idea what your using for i and j here the standard notation for i and j involve Euler coordinates judging from this equation your not using Euler coordinates please confirm. I should also not \(e=mc^2\) is not the full equation. This only involves massive particles not massless particles. You want the full energy momentum relation detials here https://en.wikipedia.org/wiki/Energy–momentum_relation

I'd say it's a visually pleasing representation so for me it's "art" lol

That's the general idea behind the scholastic background. It would give details much like we get with the CMB but closer to the inflationary and electroweak time periods. ( in theory). Yes I have read that one before it's a pretty decent article.

The next several decades with all the equipment proposals to measure the GW wave schotastic should prove interesting. It may likely provide insights beyond the cosmological dark ages including frozen in signals due to inflationary process

They look like back up folders of some kind though I could be wrong

It certainly makes it a lot easier same rule applies with sanding wood for vanishing.

One detail I should add stick to the same direction while grinding or polishing.