Mordred

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.

My wife is a member of our local Pagan society. I will day I personally like their views. The members I have met tend to be more open minded to the beliefs of others. As for myself I don't particularly follow any form of faith, however that's just me. I do know the local membership has been steadily growing in my locality.

Yes provided you use Maxwell Boltzmann statistics for mixed states or its QFT equivalent. http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis you can find further details in these two Introductory level articles. Both articles will provide an excellent overview of the major equations used in modern Cosmology.

The answer to that will depend on if the conservation laws of thermodynamics applies to the Universe. Under the LCDM (BB) model the universe is treated as conserved and expansion under thermodynamics is treated as an isentropic and adiabatic expansion. In essence a closed system. So under the LCDM model of the BB the photons become redshifted the density decreases but the total number of photons remain constant. A neat trick results from this mathematically. One can estimate the blackbody temperature at any given value of Z by using the inverse of the scale factor

Interesting thought experiment, I would like to think about this scenario a bit in terms of the stress energy momentum tensor and how it will correlate to the permutation tensor \(H_{ij}\). I will also have to dig into just how symmetric a supernova would be. The answer is yes regardless of how symmetric the core collapse occurs one other factor is that acceleration can also generate GW waves. Though a supernova collapse is never likely to stay symmetric. One simple reason being the typical bulge at the equator of rotation. That's not getting into details such temperature anistropies of the plasma etc. The Shockwaves themselves are sources of GW waves

Not really considering the temperature at the same time is roughly 10^19 GeV which when you convert to Kelvin isn't far off Planck temperature. Using the Bose Einstein statistics that equates to roughly the equivalent to 10^90 photons squeezed into a single Planckian volume. Good luck finding anistropy distribution under those conditions. (Also a symmetric state as all particles are in thermal equilibrium).

If it is its a good one, as a physical wavelength doesn't involve any probability so it's handy being able to readily distinguish between the two types of waveforms. (Physical vs probability). That honestly depends on the system being described for example the Earth due to rotation and Mountains (non uniform mass distribution) can generate GW waves. However the effect is incredibly miniscule. Any non symmetric spinning object can do so. However a symmetric sphere won't regardless of how fast it spins. In the case of inflation you get regions where the expansion rate may vary from other local regions. Though on a global average its roughly uniform. It is those local regions of non uniform expansion rates that can generate GW waves. At \(10^{-43}\) the universe would incredibly uniform in mass/energy density that no GW waves could result. Likely the earliest feasible GW waves would generate via electroweak symmetry breaking and inflation.

One trend I have noticed is the term wavefunction tends to indicate probability functions but the term wavelength tends to refer to physical waves such as Compton and DeBroglie. Do not know if this has become a convention but as an avid reader of numerous physics theories its a trend I have noticed.

We only examine our Observable universe. We can only conjecture based on what we learned from our Observable portion. However that Observable portion also equates to all forms of causality. That is a fundamental distinction. You agree that GR works great for describing what we can observe but that also applies to causality. In cosmology this defines the Cosmic event horizon aka our observable universe. GW waves have wavelengths that far exceed the size of our universe at the earliest stages ie inflation and prior. This has been calculated I recall Bardeen presented a solution for inflation giving the resulting wavelengths at \(10^3\) km for the quarterly wavelengths (needed detector length). Note that's well beyond the volume of the Observable universe at that time. We look for the frozen in effects (that is the literal descriptive oft given ) with regards to traces of relic dynamics due to inflation etc. However those traces are incredibly difficult to detect (relevant wavelengths including redshift due to expansion). I should add gravity waves only result from anisotropic conditions. That list includes mass/energy distribution. The EFE shows this. As you agreed it works well with observational evidence

Not accepting my challenge? Proof yourself mathematically. This is physics derive a QW wave with its wavelength using the mass of the universe. Then run expansion backwards to \(10^{-43} \) seconds. Let me know if you can fit the wavelength inside the observable universe at that time. Go ahead prove me wrong. In order to have a wave you must have a measurable wavelength

There is no assumption it is trivial to perform the calculations something you likely will not have for any of your declarations. You likely don't even know how spacetime via the Einstein field equations pertain mathematically to the GW wave. You cannot have GW waves without sufficient spacetime volume. Go ahead I challenge you to mathematically prove me wrong. Those mathematics is part of our rules and regulations when it comes to rigor and testability. Lol truth be told with your declarations above you likely have never bothered looking at the relevant mathematics of a QW wave. Those same mathematics involving Einsten field equations which you believe are wrong allowed us to predict the existence of GW waves long before we ever measured them.

All particles have pointlike characteristics as well as wavelike that is what specifically is described by wave particle duality. In thermal equilibrium however all particles are indistinct from one another. In essence they all would have identical wavefunctions as well as pointlike properties. So you could have gravitons as well as the SM particles however you wouldn't be able to tell them apart. Keep in mind though it's feasible we still have no evidence of a graviton. Gravity is well described without it however via spacetime curvature.

Might help to understand the BB theory starts at \(10^{-43} \) seconds. The theory describes how the Universe expands from that time forward. The theory does not state what created the universe. That is a common misconception. Expansion itself simply follows the thermodynamic laws. So there is nothing unusual there.

Not even close. Not possible,the BB singularity if you run expansion backwards you would hit a volume roughly one Planck length at 10^-43 seconds. At this volume even curvature has no meaning nor does a GW wave. For that matter as there is no curvature term due to the miniscule volume you wouldn't even have gravity.

with water droplets the light enters and leaves the droplet so refraction does apply https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_1e_(OpenStax)/25%3A_Geometric_Optics/25.05%3A_Dispersion_-_Rainbows_and_Prisms here obviously some light will simply reflect but you get refraction due to light entering and exiting the water droplets. Seriously if a water droplet were a perfect mirror then you would have 100 percent reflection. However a water droplet is semi transparent so naturally refraction will be involved. Anytime light enters a medium you apply refraction. With reflection its simply the surface or internal reflections in both cases Snell's law covers both. Angle of incident= outgoing angle for the reflected case \[\theta_i=\theta_O\] . with refraction obviously you have a much wider range. Quite frankly I can't think of any reason for color separation via reflection as opposed to refraction. I'm fairly positive your well aware of this though Studiot lol. Its still good info for other readers