Mordred

Why would I think that when I'm referring to the first equation on your article. Where you have total energy but only included potential energy terms That's where the error lies your total energy formula is wrong. If the first formula is wrong any later formulas are likely incorrect as well.

Of course it is its the rest mass\invariant mass The momentum is p \[E=p+m^2\] using normalized units where c=1. The kinetic energy term isn't mc^2 its the momentum given by p If your using just PE your system is static with no particle motion.

Yes I know the first equation is just the potential energy. However under mainstream physics so is the invariant rest mass given by E=mc^2. So my argument still stands your subtracting potential energy from potential energy giving the result of zero. However in your article you claim that it is total energy and not potential energy and are ignoring kinetic energy terms for an expanding volume. Just because your model isn't mainstream doesn't mean it shouldn't match mainstream physics when it comes to the rudimentary physics under Newton treatment. (For the record stating someone's conjecture isn't mainstream is one of the most common excuses used on this forum) it's a very common and lame argument. Potential and kinetic energy relations has been mainstream since Newton if it can stand that test of time applicability then obviously it's a very robust and accurate methodology. You most certainly will not solve the cosmological constant nor any equation of state without including kinetic energy terms it's literally impossible as those terms involve kinetic energy for its momentum equivalence. If your theory has any motion or expansion of a matter field you need PE and KE. Hopefully you dropped negative mass as that has numerous ramifications you haven't considered.

We already run very complex simulations example testing our mathematics involved for Cosmology. https://www.illustris-project.org/ Mathematica is also a very useful tool commonly used by physicists such a the Feycalc extension Even for the Saha equations one requires coded simulations thankfully this one doesn't have huge computing power requirements. None of these require AI.

Don't worry I fully expect you to search through internet looking for every possible instance of negative mass treatments they always boil down to not understanding how that negative mass is applied to a global vs local field treatment. What you are describing is a global treatment not local to a non zero global baseline. Example a solid state lattice network with negative and positive holes. Global energy value with negative local energy compared to the global energy value. If you had a non- zero baseline that would run counter to a Universe from nothing.... I will state this once again Energy is the ability to perform work a property... it does not exist on its own. Mass is resistance to inertia change hence the momentum terms.... As we are describing a Universe any theory must work as a field treatment such as GR. (Good luck on this point). For Newtonian case try it as a momentum vector field not simply scalar lol it would get trickier when you apply contravariant terms and anti- commutations... Lol after all I should be able to throw any SM particle into this universe and its subsequent equations of motion will work under multi particle field treatment. Hence all the above statements

I should have added "Where is this negative mass you claim exists ? No standard model particle has negative mass and even DM doesn't match the characteristics of negative mass. DE matches the characteristics of negative pressure but not a matter field. Just a side note \(E^2=(pc)^2+(m_o c^2)^2\) is the energy momentum relation if you place a minus sign in front of the RHS your not stating negative mass your stating negative momentum. Not even antiparticles has negative mass nor momentum. So the questions still remains name any particle with negative mass or momentum ? Good luck on that question I certainly know I can't think of any particle with negative coupling strength can you ? You may want to rethink your other article as well as this one. That's just a strong suggestion though Particularly since in your E- and E+ momentum that would be the equivalent to two seperate fields one collapsing while the other is expanding. If you don't believe that statement try using the stress energy momentum tensor with negative momentum with the Einstein field equations. Would not the result be two opposite curvature terms? Or did you even consider that problem ? When you apply thermodynamics to that, one field would be cooling down while the other is heating up. Not what we see is it ? What is obvious to me is that you never considered your proposals beyond Rudimentary Newtonian treatment nor considered the ramifications under a field treatment such as under GR. Let alone the absolute lack of any standard model particle to meet your criteria. If only negative mass was that easy we would already have an Alcubierre warp drive

That's clearly not shown in your mathematics The article I linked shows precisely how \[\frac{3}{5}\frac{GM}{R}\] is derived using an expanding volume. So your expression gives a balance of precisely zero at all times. If that is not your intent then that expression is wrong for your purposes. The relation above is specifically a derivative of the mass density evolution for an expanding volume clearly shown in the article I linked. specifically \[E_t=MC^2-\frac{3}{5}\frac{GM}{R}=0\] Now your telling us that your applying negative mass which under GR itself is considered impossible. If you ever applied a force to a negative mass and Newtons laws to negative mass you have inverse relations Specifically the more force applied the less displacement you get. All you need to get expansion is to have a kinetic energy term to exceed the positive energy term as per the scale field equation of state used in Cosmology. In essence pressure the energy density relations. That is how the FLRW metric works Is this paper not suppose to show how a universe from NOTHING is possible ? Is that not the claim of the paper ? the term mass energy if garbage by the way. mass is resistance to inertia change if an object has mass it has resistance to inertia change or acceleration. its already been mentioned energy DOES NOT exist on its own. It is a property just as mass is a property Your attempt to treat mass energy as something seperate from mass is simply wrong by any definition of mass. The definition for mass should make the inverse relations to force obvious had you considered the definition of mass with regards to negative mass. And please don't tell me your going to disagree with the very definition of mass or energy (ability to perform work) that has been around since the 16th century and how they apply to Newtons laws of inertia If you do then you better get busy rewriting the entirety of every physics theory since then.

Here is how total energy can be calculated it took me a bit to find a methodology that matches your \[\frac{3}{5}\frac{GM^2}{R}\] relation The author also has that same relation but for the potential energy here is a dissertation paper where the author has the identical term for potential energy. The kinetic energy term is derived under Newtonian treatment "Total Energy of the Freidmann-Robertson_Walker Universes " by Maria Mouland https://core.ac.uk/download/pdf/30798226.pdf specifically arriving at \[\frac{3}{10}MH^2R^2\] The inclusion of both terms is what you need for total energy She shows further down how the two terms arrive at equation 1.28 \[H^2+\frac{kc^2}{R^2}=\frac{8\pi G}{3}\rho\] which is a well known relation used in the critical density formula. (proof of methodology ) it is a matter only treatment which is fine w=0 as the critical density formula is also a matter only treatment. If I recall correctly Peebles also had a similar treatment in one of his Introductory to cosmology textbooks. I do know he had the 3/5 relation in his density contrast term of his Large scale structure of the Universe article. Anyways hopefully you find the above article useful

A mediator is an offshell boson or field of bosons for EM field its virtual as opposed to real photons. For strong force it's gluons, for Higgs its Higgs boson for the weak force is W+ W- and Z bosons. https://en.m.wikipedia.org/wiki/Force_carrier

Don't be concerned with Hubble tension, I've been following the Research but the gist of the problem isn't a need for new physics. Its a problem more in terms of fine tuning of luminosity to distance relations. Holicow used near field measurements while Planck is far field ie CMB. Both require fine tuning but more so with the Holicow dataset for using standard candles. We will get into the FLRW metric later on (its a good stepping stone to cosmology and GR) This is one of the more recent papers on the Tension https://arxiv.org/abs/2408.06153 On Leavitt Law calibrations https://arxiv.org/pdf/2205.06280 this stuff is too advanced for you but suffice it to say its being researched

found a fundamental flaw with your total energy equation You have only calculated the Potential energy term and didn't include any term for the kinetic energy. The primary mistake results from just using e=mc^2 instead of the full energy momentum relation. You should be using this as your basis equation for the field \[E=\sqrt{(pc)^2+(m_o c^2)^2}\] the \(\frac{3}{5}\frac{GM^2}{R}\) is just potential energy it doesn't include any momentum its just from the mass term. This equation is accurate for the potential energy but not as the total energy your subtracting two equivalent terms by the operation \[E_t=mc^2-\frac{3}{5}\frac{GM^2}{R}=0\] would be the result it can only give zero the second term is a derivative of the first term. So the result can ONLY be zero. Under sphere treatment as the sphere expands via Hubble constant you do not have the equations of motion just the mass term Is that your intent ? if so what gives rise to any later energy content ? If not and if you like I can provide the kinetic energy term as a Newtonian treatment which you seemingly prefer for an expanding Universe. however if it is your intent then it would the equivalent of zero particles for any kinetic energy term as the result would always be zero nor would you have a mass to begin with and no remaining kinetic energy term to drive expansion which does not make any sense whatsoever. A total energy balance of zero is an empty universe with no component to drive expansion. Doesn't work You need to incorporate the kinetic energy side of the gravitational field as a result of expansion as well for total energy (hint the kinetic term can be derived using Hubble constant) if you want I will post how upon request. I know a Newtonian treatment for that. The essence however is that as the universe expands driven by the equations of state the kinetic term becomes involved as required to maintain a homogeneous and isotropic mass distribution. It is that term that is missing.

have you ever thought to look into zero energy universe ? https://arxiv.org/abs/gr-qc/0605063 you may find this helpful still looking if I still have a copy of one of the earlier Universe from nothing papers I once had a copy of

Khan University Simple harmonic motion pendulum case. https://www.khanacademy.org/science/physics/mechanical-waves-and-sound/harmonic-motion/v/pendulum lectures from Unit 8 Oscillations and mechanical waves main page https://www.khanacademy.org/science/physics/mechanical-waves-and-sound Feymann lectures are also useful https://www.feynmanlectures.caltech.edu/ tons of study material just click on the links to turce e volume and get the volume table of contents then click the section of interest. example https://www.feynmanlectures.caltech.edu/I_09.html for momentum and force this open source textbook on basic physics also contains numerous hyperlinks to various video lectures so should prove useful https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/Physics-WEB_Sab7RrQ.pdf you will notice it will contain links to khan university for support lectures example Newtons first law of motion https://www.khanacademy.org/embed_video?v=5-ZFOhHQS68 current discussion is covered in chapters 1 to 5

Sure I will dig up some good lectures this evening for you

Square root symbol encompasses the RHS of the equal sign.

start with f=ma then recognize pressure is force per unit volume

no problem try to think of it this way any complex problem is composed of little problems. In a sense its similar to programming you break the program into smaller simpler steps to get the final form. Its no different in physics you start with classical physics then you build it up to your complex systems. Every physics theory is comprised of kinematics (equations of motion) even when those equations of motion are waveforms they have vector equivalence.

F is force given in Newtons which is the amount of force to accelerate a 1 kg mass 1 meter per second squared. \[f=ma\] https://www.lehman.edu/faculty/anchordoqui/chapter07.pdf it becomes easier to learn complex physics by first mastering basic classical physics

Here is a handy article showing how phase and amplitude has similarities and equivalence in mathematics to the pendulum simple harmonic motion. https://www.lehman.edu/faculty/anchordoqui/chapter23.pdf as mentioned its an invaluable lesson

energy for E yes its a box with lots of particles hence its a total summation of hitting each box edge ie a probability function of number density striking the surface. \[E=\sqrt{(pc)^2+(m_o c^2)^2}\] start with 1 particle first to learn the math then determine the number density after then do your summation is the steps to learn this ( hint I already provided the formulas for number density above) Edit correction applied to above formula

no problem its why we have a Speculation forum is to help others learn as well as assist in how to properly model a new theory.

take a hypothetical box and place an ensemble of particles in the box. the box boundaries is the boundary conditions equivalence in the mathematics. Calculate how much force is delivered by the momentum term of the particle on the box boundaries. That's how the equations of state are determined ie the pressure term. matter has low momentum so exerts no pressure radiation has high momentum so it exerts pressure

All particle fields in Cosmology have an equation of state association this is analogous to thermodynamic hydrostatic fluid equations that includes DM even though we don't know the cause of DM we can model and determine its equation of state. w=0 meaning it has no pressure term.

Yes that's what I wrote try adding your own statements and I don't need you to rewrite my statements. I know quite well the mathematics for both gravity and the Higgs field. The Higgs field does not account for all the mass terms of the Standard model which means it does not account for all mass involved in gravity only roughly 1 percent of the mass of a single proton for example. So regardless of dimensionality it cannot account for all elements involved in gravity as it does not account for all the mass For example equation 1 will not work with the three primary Higgs field cross sections Higgs cross sections partial width's \[\Gamma(H\rightarrow f\bar{f})=\frac{G_Fm_f^2m_HN_c}{4\pi \sqrt{2}}(1-4m^2_f/m^2_H)^{3/2}\] \[\Gamma(H\rightarrow W^+ W^-)=\frac{GF M^3_H\beta_W}{32\pi\sqrt{2}}(4-4a_w+3a_W^2)\] \[\Gamma(H\rightarrow ZZ)=\frac{GF M^3_H\beta_z}{64\pi\sqrt{2}}(4-4a_Z+3a_Z^2)\] These cross sections above describe all the Higgs field interactions The first term is the interaction between Higgs and other fermions such as leptons. the next two are the bosons W+,W- and Z This should be a strong indication that your math is insufficient for the task as an assist here is the Higgs electroweak couplings. \[(\frac{g}{2}\vec{\tau}\cdot\vec{W}+\frac{\acute{g}}{2} B)\phi_0\] this equation involves wavefunctions and Fourier transformations so include tensors for the associated fields

For starters Higgs is a quartic field the mass couplings differ for W+, W- and Z bosons leaving one field uncoupled. This is confirmed via experiments so equation 1 is incorrect. Your equation for higher dimensions doesn't include any higher dimensions. In physics a dimension is not an alternate reality or other such item but refers to effective degrees of freedom Example {ct, x,y,z) has 5 values that can alter without any dependency on the other variables. I do not know what ChatGPT is placing in for the right right statements I can only assume Dirac Bra-ket notation. For latex on this site use \[latex\*] just remove the * I placed there to prevent activation. As mentioned DO NOT rely on ChatzGPT it's nothing more than a glorified search engine You will not be able to show higher dimensions using the definition for dimension I provided using Newtonian mathematics all your equations would fall under scalar field treatment and do not have the vector and spinor relations for particle field interactions. The closest statement you have to a vector is the inner product in equation 1 but that equation is still wrong