Mordred

No that is absolutely wrong. I gave you this information in this thread previously. Did I waste my time here? What about the Pauli exclusion principle? does your formula calculate the number of electrons per the principle quantum numbers to determine the allowable number of electrons in an orbit? Can it calculate the mean lifetetime of a particle? which applies to the first question? ie part of the answer

You will never get the big equation with the method your using. Lets demonstrate calculate the range of each force for starters If you can't do that your program isn't accurate

A bundle is a manifold of a principle vector field thats the power of group theory. Ie how do you calculate the projection map without using the M and N tensors under G https://en.m.wikipedia.org/wiki/Fiber_bundle every term on that page is detailed via group theory which uses scalar and vector quantities at its core for the tensor group symmetries via vector calculus. Start with understanding the Natural units I posted previously because your Langrene and Hamiltons use them specifically. every QFT treatment use Natural units....

No they are functions that include scattering diagrams Feyman that takes all these equations and works with the elenents that are common among them. Something you have never bothered to look for. Ie my continous hints to study the mathematical proofs of each equation your using. To find the variables that are common to 2 or more seperate equations. Specifically the scalar and vector quantities thrmselves. ie What tensors are about organizing

Do where is the problem? every particle interaction and dynamic is defined by the above groups with the Hamilton. Do you need specific equations when all you require is the displacement from coordinate a to b in your scatterings etc as per S-Matrix ie Feyman diagrams for particle intersctions? Every interaction and interference is defined by action under those groups. Why would you need E rest, relativistic, nuclear binding etc when its all detailed under lie algebra?

so [latex] SU(3)\otimes SU(2)\otimes U(1) [/latex] includes all the above electrodynamics, Higgs,color, flavor It is all the SM particles under symmetry. You don't need other groups SO(5) and above unless your going supersymmetric. I even linked ghost fields specific to those groups under g instead of G. The Hamiltons all correspond under these groups, The Special orthogonal groups are double cover under the above.

I've never come across any model that does. Though keep in mind some metrics can reflect changes to the boundary of the EH which is specifically an apparent singularity and not a true singularity. https://en.m.wikipedia.org/wiki/Eddington–Finkelstein_coordinates A true singularity breaks down regardless of whatever choice of metric you apply such as the singularity condition at the theoretical centre of the BH.

Have you ever considered that piece mealing random equations might just be the wrong approach all along and that it might just be better to step back and study the proofs of those equations ? I realize your only interested in simulation development but honestly the best tools is the symmetry groups.

So explain why DE doesn't follow the normal thermodynamic rules on regards to change in volume as per the FRW metric equations of state for an adiabatic and isentropic fluid which equates to no net inflow or outflow of energy without invoking alternative universe? I suggest reading the preposterous universe link by Sean Caroll before replying. See post above by Strange. Not to say there isn't viable solutions, the one I'm thinking of doesn't require alternative universes. Simply curious if you happen to have some viable solution in mind. Considering the conservation laws in regards to the universe is still an open question. See post by Swansont after reading the preposterous universe link. Edit actually considering another article once posted by Strange make that two.

Ooh boy another limit to what I would really prefer to describe when discussing physics lol. No thanks I have enough struggle keeping things as simple as possible lol

The key fundamental difference between the two which Strange is pointing out is how the two singularity conditions may or may not behave under the sheer conpression due to gravity itself. Keep in mind the observable universe singularaty of our Universe past only represents the lightcone of our Observable universe, the distribution of shared causality differs significantly than the mass distribution of a BH singularity. We have absolutely no means of testing either limit, it is well beyond any capability we have. Either from any form of observation or lab test. These are theoretical limits based upon a huge body of evidence of numerous incredibly accurate mathematical models. It also forms a primary aspect on the quantzation of gravity itself. We can speculate on this till the cows come, we have absolutely no means of validation. The other aspect is the irreversible aspects of entropy. Some processes are considered irreversible. Here is a question even I don't know the answer to. Is the electroweak symmetry break via the Higg's field reversible? Trust me I've looked for that answer for several years now and still cannot answer that question. Is there any involvement of the Higgs field inside the EH of a BH. (absolutely no clue) can't answer that one either.

The two temperatures have a point where they reach where the math breaks down to giving rise to nonsense answers. There is a theoretical upper bound to temperature. Planck temperature, which connects to the minimal Planck length via its wavelength. https://en.m.wikipedia.org/wiki/Planck_temperature

This is actually tricky to answer, as it really depends largely on the system being measured as to whether or not a local system probe is a sufficient test. Its not unknown that localized dynamics can wash out global dynamics. Personally The upper bounds and studies of the CMB provided a far stronger test between Cartan and GR. This is something I tried without much success in pointing out to the OP in his speculation thread. The gravity probe B test itself was by design a low orbit test, so it was viable a global intrinsic torsion as per say a rotating universe could be washed out. PS the CMB studies also favor GR.

While I agree that equality of your proposal isn't definitive. I think you may not be grasping the usages of the dimensionless constants for the scale factor nor the w term. These two constants by themselves are simply dimensionless ratios only. They have no units unto themselves. The units of measure of those formulas cancel under dimensional analysis.

Well done your getting a good grasp of it.

OK lets try an example everyone can relate to. Start with an oscilloscope and assume were measuring an electrical circuit. We start with some baseline voltage reading that is approximately zero but the closer you look at that signal the more interference you start seeing. We call this static from other signals and the harmonics of the baseline signal. This is the fluctuations were talking about. There is no distinctive signal that we can see, its random static or fluctuations. Now you get a signal that comes in a sharp "Excited" state. This is the excitations were talking about distinctive signals that we can readily trigger our oscilloscope onto and take measurements upon. Now keep in mind this is a macro world descriptive, when dealing with the quantum level the analogy does apply but under much greater resolution. \now I have been trying to get this to work with latex so bear with me. The representation will not be exact. Let us look at a Feyman diagram which is a representation in and unto itself specifically thee amplitudes of particle reactions. [math]\array{e^+ \searrow &&\nearrow u^-\\&\\ &\leadsto^\gamma &\\ e^-\nearrow &&\searrow u^+}[/math] Not pretty but close enough. The inbound legs on the diagonal arrows is the particles we typically define as real ie not virtual. Same as the outbound diagonal lines. In th actual diagrams the lines are all connected but haven't mastered that trick under latex yet roflmao the squiggly horizontal line is the non measurable VP interactions ie field fluctuations between the inbound and outbound legs. (excitations) Does that help?

Not everything is quantum fluctuations your taking those two terms a little out of context. Space is simply volume itself, you haven't indicated you haven't understood that part. Now onto the fluctuation portion. A fluctuation is distinctive from an excitation. This may sound trivial but it isn't. Probably would be a good idea to add the term Fields to your Mantra. A field fluctuation is in essence the harmonic oscillator vibrations from the field ground state. This is where the the HUP is described and defined. These fluctuations can give rise to the field excitations that we associate as particles. Now don't start thinking everything is fields either. A field is an abstract device that we can assign a value or function to every coordinate. The trick to understand is that physics is about modelling relations. This includes relations between various coordinates/events of a field. We are measuring the properties we come to associate at each coordinate an describing their relations to other coordinate properties. Physics doesn't concern itself too much with "What is". We leave that philosophers. This is one of the reasons why it would be nice to express things in the mathematical detail as sometimes its easy to make statements too heuristic.If I try to get too mathy (new word lol) very few people will understand it and no one learns. So its a real struggle to keep explanations as simple as possible and at the same time avoid confusion.

LOL I was just about to type that in when you posted. Saves me the time lol

You have essentially identified the main aspect of boson's having integer spin. All boson's can share the same quantum state and space. While fermions essentially take up space if in the same quantum state. The fermion family is what comprises what is referred to as matter while the boson's are attributed as force guage bosons. The details of why this works with the Pauli exclusion principle gets rather technical and requires an understanding of the principle quantum numbers and how they affect the probability amplitude functions.

Yes that is a very good paper and quite detailed on the process of mass. In greater detail the process in the paper can also help understand particle generations of the SM model via the symmetry breaking process and the Higg's field interactions. Though keep in mind the paper is rather out of date on the Higg's research itself since the paper was published we have identified the Higg's boson and the mass term of the Higg's so many of the numbers the paper provides will change as a result.

Another excellent question and one deserving an equivalent answer. What is mass? well the correct way to thinking of mass is resistance to inertia change. Which is the definition of mass under physics. Under particle physics treatments the mass term arises from the coupling constant [math]\alpha=\frac{e^2}{4\pi \epsilon_0 \hbar c}[/math] https://en.wikipedia.org/wiki/Coupling_constant

you might want to read this http://backreaction.blogspot.ca/2017/11/astrophysicist-discovers-yet-another.html In essence their is numerous errors in his paper

[math]\array{ \mathfrak{g} \times X && \overset{R}{\longrightarrow} && T X \\ & {\llap{pr_2}}\searrow && \swarrow_{\rlap{p}} \\ && X }[/math] [math]\array{e^+ \searrow &&\nearrow P^-\\&\leadsto &\\ e^-\nearrow &&\searrow P^+}[/math] [math]\tanh [/math] [math]pc[/math] [math]\wedge^\bullet_{C^\infty(X)} (\mathfrak{g}^\ast \otimes C^\infty(X)) \;=\; \underset{ deg = 0 }{ \underbrace{ C^\infty(X) }} \oplus \underset{ deg = 1 }{ \underbrace{ C^\infty(X) \otimes \mathfrak{g}^\ast }} \oplus \underset{ def = 2 }{ \underbrace{ C^\infty(X) \otimes \mathfrak{g}^\ast \wedge \mathfrak{g}^\ast }} \oplus \cdots[/math] [math]\array{ J^\infty_\Sigma(E)/T\Sigma \\ \downarrow \\ \Sigma/T\Sigma }[/math]

Your welcome and excellent valid question. The details is the first section of the article I linked where all the constituents of the sodium atoms become describable under a single wavefunction via equation 2.2 De-Broglie wavelength. LOL if you look at that article the visual aid also has the squiggly lines in figure 2.1. That's what that image is trying to describe

watch what happens to the images of the atom in transition to the Bose condensate state from this video Notice how the atoms appear to deform as it undergoes the phase transitions to the Bose condensate state? a lot of pop media articles mislead this loss of information phase transition under the descriptive squiggly lines. Keep in mind this is a graphic animation of the process including the images of the atoms etc in the first place. Not actual images of the atom in the first place lol. The mere act of trying to measure a condensate state heats up that state thus causing further phase transitions. In condensate state one cannot identify individual particles as per the article I attached above.