Mordred

Don't pay to much attention to the pop media coverage of findings from the James Webb telescope for starters. No result from the James Webb telescope tells us that the universe isn't expanding. lets look at your scenario for a second, Expansion is roughly 70 km/Mpc/sec. That is extremely slow relative to the speed of light, especially considering that a single Mpc has roughly \[ 3.262*10^6\] light years. It is only at extreme distance that expansion becomes measurable, also it only occurs in regions that is not gravitationally bound. The evidence of an expanding universe occurs in a great deal of observational evidence. For example the CMB wouldn't even exist if expansion didn't occur. The temperature history which shows the universe cooling down as a direct result of expansion and how it applies to the ideal gas laws is another key piece of evidence. Cosmological redshift is another but certainly not the only piece of evidence

So mathematic were supplied by him yet even knowing that the mathematics were required in that scenario. You still can't see that you may require the mathematics for your theory ? In order to be a theory mathematics are required its a simple fact.

Under GR every observer and event is inertial. There is no at rest frame. All frames of reference are also equally correct, there is no preferred frame of reference. Yes everything we see or measure is relative to the observer. However that was even true prior to GR/SR under Galilean relativity. That in and of itself is nothing new and has been understood for centuries. They key difference is time is absolute Under Galilean relativity.

pray tell how do you program a traveling wave without applying some form of mathematics ? I've done enough programming to know unlikelyhood of programming a travelling wave without some mathematics. Considering I've written programs in well over 30 different languages over the years. Yet another claim, here is the think Unless you can make testable predictions which requires mathematics. Any claim is worthless. That's the simple reality in Physics the very fundamental purpose is to be able to make testable predictions of cause and effect. That's precisely why The Pilot wave, Including its guiding wave has relevant formulas where the interpretations can potentially be testable. Aka EPR, vs Copenhagen vs Pilot wave etc tests constantly being conducted with each of the aforementioned having its own variations of mathematical treatments. The mathematics are readily available for each of the mentioned theories. Any interpretation of any given theory should always involve the mathematics of that theory otherwise what's the point.

This is oft something poorly understood. Geodesic paths are never truly straight nor smoothly curved. You learn to understand this via the Principle of least action which further applies calculus of variations. Take for example a thrown ball. At each infinitesimal of its flight, there will be variations in its direction. Those variations will result from the principle of least action. The geodesic path is the extremum of those variations. A common misunderstanding also includes trying to think in terms of 3d space which under graph vs a 4d spacetime graph can have rather surprising results. For example that thrown ball lets say you throw it a height of 20 meters and a distance of 10 meters on a 3d graph it would be a curved arced path. However lets say it took 1 second to travel there and 1 second back. Under a Minkowskii spacetime diagram using the interval (ct) you will find that the path is incredibly straight. Now further apply Interval (ct) to your different observers under the Minkowskii spacetime diagrams

A geometry requires a metric. I have yet to see any relevant metric. Please describe your theory under the mathematical holonomic restraints. this is a holonomic test equation see link https://en.wikipedia.org/wiki/Holonomic_constraints as the link shows the term holonomic has precise mathematical implications, including the time dimension. perhaps you can demonstrate your understanding of Bohmian nonlocality including holonomy under your metric. keep in mind Bohm was an excellent mathematician, he would also describe nonlocality under mathematical definition. Good example of how he goes about this is his pilot wave theory. So at least you will have a source of the relevant equations.

Probably easiest to simply examine what each means under the metric. One of the better ways has been how Barbera Ryden teaches each in her Introductory to cosmology. A key feature I haven't mentioned is how Pythagorus theorem applies in each case. Without trying to go too far astray one of my webpages uses her method and the paths descriptive. http://cosmology101.wikidot.com/universe-geometry this page just describes the critical density relations the next page has the needed images http://cosmology101.wikidot.com/geometry-flrw-metric/ note the following section Consider a two-dimensional surface of constant negative curvature, with radius of curvature R. If a triangle is constructed on this surface by connecting three points with geodesics, the angles at its vertices α β,γ obey the relation α+β+γ=π−AR2. a key detail to recall or understand is a negative curvature is a hyperboloid example the saddle image in the second link

That example doesn't particularly apply. The reason being that two falling objects as they approach either CoM of either BH would converge. They would also converge as they approached the barycenter. The most commonly known example is Anti-Desitter spacetime. This is used in the FLRW metric as one of the viable solutions historically it applied to an open as opposed to a closed universe. Which is another topic lol as explaining the two can get tricky. https://en.wikipedia.org/wiki/Anti-de_Sitter_space

While analogies can be useful, I've always found they tend to mislead. In this instance I have always found the method of describing spacetime curvature using geodesics paths of two parallel light beams far more useful. If the two beams remain parallel then you have flat spacetime. If the beams converge the positive curvature. If they diverge then you have negative curvature. It's a simple descriptive provided you include the details that mass is resistance to inertia change as well as ensuring that the reader further understands that the (ct) interval is what provides time with dimensionality of length.

Bump going to continue with this project

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.