Mordred

The graph here gives the rough idea the rudimentary idea of freefall the constant velocity where no force acts upon the falling object on the paths toward the center. It's gives the basics of the weak equivalence principle if you were to place a person inside an elevator and drop the elevator. The seperstion distance representing tidal force is where your acceleration term (tidal force) would reside though it gets more complicated than a graph in reality. https://webs.um.es/bussons/EP_lecture.pdf See local inertial frames in above link (The acceleration term is handled through the spacetime geometry in the mathematics) Above link gives some visual examples The overall method is the rudimentary idea of parallel transport. However the mathematics have a method that you do necessarily require two falling objects to accomplish parallel transport. For example if you were to simply draw a wavy line across a piece of paper (curved line doesn't matter the actual curves you can make it a varying as you like) Now take a point on the curved line and draw a tangent line connecting tp that point. From the point where the tangent vector connects to the curve draw another line 90 degrees perpendicular to the tangent with a new vector. Let's just call this vector ( B) You now have a representation of a covector dual vector as the tangent vector follows the curved path the angle B will change in relation to the x or y axis itself. Now if you do the same procedure to another point on that curved line you will notice that as you move both points along the curve the angle (B) of point 1 and point 2 will vary from one another as they follow the curve (geodesic) The last representation I described gives the rudimentary method of the Reimannian dual vectors. The link above gives a more rigorous example ( under bending of light Rigorous example). Now what I have been showing you is the rudimentary basics behind geodesic paths and how one can apply parallel transport with those geodesic paths using dual vectors See figure 1.1 of this article https://amslaurea.unibo.it/18755/1/Raychaudhuri.pdf For the last example above. (PS the point of the tangent to the curve is where the affine connection is made ) It is this basis where I recommend you place your bi-directional vectors. Figure 1.1 Little hint the last article also details how acceleration is handled using figure 1.1. For acceleration under the equations the increase in velocity ( is the boost magnitude only) for the directional component of the vector ( this is the rotation operations ) of the lorentz transformation matrices.

That's not an uncommon approach so lets stick to visual representations Newtonian scale. For this reply I strictly describe a freefall gravitational visual representation. Take a sphere the Earth for example. In freefall if you were to take two object or more and place them freefall they will fall toward a common center of mass. The simplistic a circle towards the center. So from that center draw at every angle a vector (line) with the motion towrd the center. Now notice a very very important detail. In the freefall condition all the objects fall towards the center at the same rate. However the distance between the two decreases as they fall. (Converges) That's positive spacetime curvature. Now if the freefall paths of any two objects remain parallel ( non divergent ) the spacetime is flat. If the freefall paths of any two objects increases (diverges) spacetime has negative curvature. The mathematics places gravity as the tidal (pseudoforce) by using the distance of separation ratio of change between between two or more freefall paths. GR describes gravity as the tidal force for the above methodology. So the equations will follow from the above. Under vector field treatment. It's also how physics measures curvature by the seperation distance between any two or more freefall paths.

How would that help in regards to understanding or representing any equations involving gravity ? Even Newtonian physics wouldn't be able to apply your representations as they place freefall and force lines to a common center of mass

That is actually a very good article I did enjoy reading it you might find that the stochastic treatment in this paper falls in line with another current thread and could be useful in comparison Both papers are looking at stochastic treatments for GR. Which is quite different from conformal treatments of ADS/CFT and canonical treatments of QFT. This is one those terms oft missed terms but has distinctive differences @joigus also mentioned that term vacuum that term can have significantly distinctive differences in what a vacuum is in different theories. The FLRW metric describes vacuum in a more classical format being a pressure relation. However QM/QFT looks at vacuum via potential/kinetic energy relations and GR can oft apply the Einstein vacuum which is devoid of all particles Condensed matter physics depending on the specific theory has own distinctive vacuums. In essence it's rather misleading term and one must examine the mathematics to understand how that term is being applied. Stochastic calculus https://www.math.uchicago.edu/~lawler/finbook.pdf Notes on conformal theory https://nbi.ku.dk/bibliotek/noter-og-undervisningsmateriale-i-fysik/notes-on-conformal-field-theory/Notes_on_Conformal_Field_Theory.pdf Canonical forms https://cseweb.ucsd.edu/~gill/CILASite/Resources/12Chap8.pdf Anyways I for one think we may have hashed this thread to death I will of course help answer anyone's questions as I usually do so will still pay attention to it but I really don't have anything more to add the the actual OP paper As far as to answering specifically to the graviton that discussion per site rules would amount to thread hijacking regardless. Anyone that wants a good discussion of the main stream physics views on the graviton is more than welcome to open a thread asking specific questions on the topic. If it's not personal theories can be discussed in one the main steam forums. Theory building of course belongs in Speculation

Here is a good article on Supersymmetric BCS. I will be adding articles of different treatments under methodologies as I locate what I see as decent ones. Readers will also note it also includes Kaluzu-Klein https://arxiv.org/abs/1204.4157 However one critical detail is that these mathematics are being applied to condensates Bose-Einstein and Fermi-Dirac condensates. This article is quite a bit simpler to relate to but the holographic treatments can get just as tense as above. https://phas.ubc.ca/~berciu/TEACHING/PHYS502/PROJECTS/20-HolSC-SB2.pdf Here is decent more classical article on condensed matter physics. Treat it more as a starting point a more textbook format if you will. https://www.eng.uc.edu/~beaucag/Classes/AdvancedMaterialsThermodynamics/Books/PhysicsofCondensedMatter.pdf This will definitely draw interest the last article includes something many people have rarely heard about. The Einstein frequency though the name Bose-Einstein condensate should be a obvious clue. https://en.m.wikipedia.org/wiki/Einstein_solid Hope that helps you will note these treatments do use terms such as vacuum ( the vacuum in these cases is NOT the same as an quantum or spacetime vacuum.) They are vacuums due to lattice spacing. Hope that helps. https://arxiv.org/abs/2303.14741 Above is a decent coverage of condensed matter gauge groups. I'm going to add another suggestion to all readers attempting to teach themselves physics. Anytime you are studying an article and see a reference to terminology, theory etc stop reading the original article and familiarize yourself with the theory or terminology before continuing to read the original article. The more you do that the easier it becomes to understand professional level articles. Lol I lost count the number of times I started reading articles that I thought were related to Cosmology applications then suddenly hit some theory I had never heard of and when I examined that theory or term realized I'm reading the wrong treatment for what I was looking for. Lol though if the article is particularly good I do read the full article with the methodology above. A good personal example is this (Fields) https://arxiv.org/abs/hep-th/9912205 I've been studying this for several years and only halfway through when I get time. However that's just a suggestion. Another useful technique if you can't afford textbooks then search for dissertation papers and lecture notes

Sure but I would prefer to take the time to find half decent literature examples in this case. A large part of it is different methodologies to handle the nonrenormalization of the findings of the Nambu-Jona-Lasinio model mentioned here. This is a huge part of the reason for all the SU(3) lattice gauge articles you guys are finding. This all is also part of BCS theory mentioned in below link https://en.m.wikipedia.org/wiki/Nambu–Jona-Lasinio_model But in this case I'm only loosely familiar with some of the research as it's not one of my specialty areas in so far over the years I've read numerous articles on the topic and some of the research but don't particularly follow it closely or rather not as much as I do in early universe processes as I'm a Cosmologist with formal training in Cosmology and particle physics. One detail to recognize is that a gauge theory such as SU(3) isn't necessarily identical in every treatment that's one of the things recognize when it comes to gauge theories. A good example is the distinctions between QM and QFT they both use SU(3) but the operators themselves in each case are different. So it's essential to look specifically how any given theory applies a given gauge group.

A little hint on the Holographic principle in regards to SU(3) lattice networks treatments you can also find String theory treatments as well as MSSM super symmetric.

The more physics one studies the more interconnected one realizes different theories get +1

Correct where for the ZPE it's proportional not inverse.

Switch that around the the coupling strength gets stronger at low temperatures due to asymptotic freedom weakest as temp increases. See second graph coupling strength on Y axis conversion from GeV to Kelvin 11606 Kelvin per eV for x axis The article has zero mathematics for SU(3) so it's claims on that regard That really amounts to trying to build a workable model for the Author as none of those mathematics are inclusive.

Let's give an assist of the first 5 pages or so looking specifically at the two primary treatments. 1) The harmonic oscillator equations. (That's not spacetime) 2) the SU(3) relations specifically the strong force. Now here is a trick in Lattice networks the mathematics do have a \(\Lambda\) term but its a different application than that of cosmological Lambda. It also has a scale factor (a) for the lattice spacing. So let's keep the above in mind. Now let's try a simplified mathematical overview of how each scenario evolves as you go from high energy physics to low energy physics. In the equation for the harmonic oscillator you have the \(\hbar\) which tells you that as the energy increases this value also increases ie the kinetic energy in the equations example the 1/2 is specifically describing the action of a spring. So one this case as the temperature increases so does the energy produced by the Zero point energy formula. Sounds good makes sense so the energy calculated with be proportional to the temperature as one increases so does the other. I believe everyone will agree on that. However now look at the SU(3) example. Apply that for the strong force obviously you need something for that strong force to act upon so lets simply use two quarks. Great we can now calculate the strong between them. Sounds good. However there is a little detail called asymptotic freedom/quark confinement. Why is the important well as you raise the temperature or how from high low energy to high energy the coupling strength is inversely proportional to the energy/temperature not proportional As you raise the energy/temperature the strong between the two gluons decreases and it increases as you approach zero Kelvin which is the exact opposite of the zero point energy formula given in the article.. I will everyone think about that. Why is there so much research on SU(3) lattice gauge has to do specifically on fine tuning the couplings and group parameters not solving the vacuum catastrophe believe me this isn't the article I've seen attempts to solve the cosmolgicsl problem using SU(3) lattice networks in the 30 years of reading articles. There is nothing new for me on these attempts they follow very similar patterns in the way they are written but they rarely ever look at the temperature range vs each and what results at different temperature/energy levels..... It's not the first time I've seen this conjecture on forums lol for that matter this paper is an excellent example of look at the mathematics involved and not the verbal descriptives. Verbal descriptions can oft be an excellent tool to mislead the reader. One of the more common warning signal is the defenders stating " ignore the mathematics this is new physics the mathematics don't apply" Or " it's the concept that's important not the math this is new physics" Those statements sound literal alarms with my experience on forums.

Lmao I had to share that with my wife who is trying to learn French she just laughed her head off with the response " it's true" between gasping for breath and running for the bathroom. Thought I would share that response lol.

G is a residual virtual gluon field rest is correct. They are the free particles not part of the nucleus. No particle ever exceeds c virtual particles are off shell meaning they typically be bosons hence massless except W and Z bosons after Higgs coupling so their momentum depends on mass and kinetic energy as it has mass it cannot travel at c must be less than c

Spacetime itself has nothing to do with SU(3) Spacetime is SO(3.1) and you cannot measure anything in spacetime without having something to measure it's just volume without other particle fields. With time given dimensionality of length via the Interval without other fields you can literally treat it as just space devoid of any mass energy term. In essence the Einstein vacuum devoid of any other particles including virtual which under QM is considered an impossibility. Yeah that operator zero being ground state zero not true zero.

There has certainly been similar ideas around the concept of eliminating quantum noise from other fields to focus on a specific field interaction is a fully valid idea. Obviously one of the better ways to accomplish this is through cooling to reduce quantum vibrational interference so there is nothing unheard of there. It was never the conceptual ideas I ever had an issue with. It's literally how it was handled and described by the authors paper. It's also why I consider this thread worthwhile to examine and spend a considerable amount of my personal time suggesting better treatments to shoot ideas on how to make it a fully usable professional peer review quality. Truthfully I wish I could directly talk to the author himself.

That was a point I was trying to get across but I prefer your overall descriptive to the manner I presented the problem which obviously went over everyone's heads +1

Lol back when I was first learning particle physics I recall how ugly all the different variations and equations were. So many different takes and different treatments that I often threw my hands up in absolute despair. One example was the sheer number of different virtual particles papers most of which you never hear about nowadays. Modern methods with its standardization are far more elegant. So I fully relate to your comment above. +1 I have read numerous papers where it's been questioned as to whether or not there was any real need to renormalize gravity or even treat it as a quantum field so that aspect has has been around for awhile however as you described what's new is keeping it stochastic in a full well connected treatment. For those not familiar with Sturm Liouville one of the better books/articles I've come across on it was Mathematical methods for Physicists by Arftken However this article is also pretty decent. https://jahandideh.iut.ac.ir/sites/jahandideh.iut.ac.ir/files/files_course/sturm-liouville_theory_and_its_applications.pdf

Detail I forgot above one of the reasons I chose two quarks was to see if you would make the connection to meson condensates. However apparently that was missed. Those Cooper Pairs previously mentioned by @studiot for example. https://www.mdpi.com/2571-712X/2/3/25 Ie BCS theory ring any bells ?

Nothing to out of the reasonable it will of course depend on those mathematics given the dimension definition I provided above. It does have familiarity with Roveilli"s Planck stars from your descriptive.

The article should be more clear on that as it applies its theory on a cosmological scale (global) particularly with the manner it tried relate volume to its SU(3) atoms and its Higgs references. If you ever examined Higgs as Cosmological constant papers you would understand where I'm coming from there. example here https://helda.helsinki.fi/server/api/core/bitstreams/eda33736-53b7-4db8-a1de-4fbe3871e4fa/content the equation of state it gives provides the same equation of state for Lambda w=-1 In that regards the VeV itself isn't actually the vacuum energy density The VeV is an expectation operator. Thsi is where I myself rather disagree with the method of calculating the Higgs energy density its typically done through the critical density formula hence I spent a good part of 10 years trying to narrow down a better method. have you read my comments about breaking gauge invariance and Lorentz invariance in this regard ? lets put it simply what is mediating the superconducting fields ? under EM its the mediator offshell photons. Now what occurs if you were to give mass to those photons upon mediation ? do You not see the problem with regards to Lorentz invariance ? The Higgs field doesn't give mass to the photons its excluded nor does it give mass to gluons its not in the known Higgs cross sections. A little FYI those cross sections also determines the VeV vacuum expectation OPERATOR. Given by for example the cross section with the W boson. Any particle it interacts with would do though. \[v=\sqrt{\sqrt{2}G^0_F}\] Higgs cross sections partial width's first one is the cross section with applicable fermions \[\Gamma(H\rightarrow f\bar{f})=\frac{G_Fm_f^2m_HN_c}{4\pi \sqrt{2}}(1-4m^2_f/m^2_H)^{3/2}\] \[\Gamma(H\rightarrow W^+ W^-)=\frac{GF M^3_H\beta_W}{32\pi\sqrt{2}}(4-4a_w+3a_W^2)\] \[\Gamma(H\rightarrow ZZ)=\frac{GF M^3_H\beta_z}{64\pi\sqrt{2}}(4-4a_Z+3a_Z^2)\] I have never encountered any cross section for Higgs and photons Meissner effect treatment or otherwise. So if you happen to have a professional peer review article showing one I would love to see it. As that would be useful in my personal line of research. The above cross sections are what's applied in electroweak symmetry breaking agreed on this detail I understood that from the start. I have no problem with being some Localized and strictly condensed matter physics treatment its how its applying on the cosmological scale that needs addressing or rather what the paper implies.... It still needs work though so I'm honestly hoping there is some improvements made there was some improvements particularly with renormalization which can be applied hence the QM/QFT above via creation/annihilation operators method above as its particularly useful.

Ooh I really like that paper still studying it. That paper is very well thought out thanks for sharing. +1 https://journals.aps.org/prx/abstract/10.1103/PhysRevX.13.041040

Here is a simpler breakdown using operators ie QM or QFT which would have been far easier to apply symmetry breaking with regards to the paper https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://faculty.pku.edu.cn/_resources/group1/M00/00/0D/cxv0BF5mDfKAOPDbACEBbOQBol4139.pdf&ved=2ahUKEwj-jdiwhaaJAxWvJTQIHZQ3C58QFnoECDYQAQ&usg=AOvVaw0bF6zGAJhSK_UcqzuzVZ4o There is a reason why the vacuum catastrophe is also called the EM field ultraviolet catastrophe the problem is directly related to how it was renormalized... Here is a quick breakdown of the method I would have liked the author to have applied . Bose Einstein QFT format. \[|\vec{k_1}\vec{k_2}\rangle\hat{a}^\dagger(\vec{k_1})\hat{a}^\dagger(\vec{k_2})|0\rangle\] \[\Rightarrow |\vec{k_1}\vec{k_2}\rangle= |\vec{k_2}\vec{k_1}\rangle\] number operator \[\hat{N}=\hat{a}^\dagger(\vec{k})\hat{a}\vec{k})\] Hamilton operator \[\hat{H}=\int d^3k\omega_k[\hat{N}(\vec{k})+\frac{1}{2}]\] momentum of field \[\hat{P}=\int d^3k\vec{k}[\hat{N}(\vec{k})+\frac{1}{2}]\] renormlized Hamilton \[\hat{H_r}=\int d^3 k\omega_k\hat{a}^\dagger(\vec{k})\hat{a}(\vec{k})\] Now for the full SU(3) Langrangian \[\mathcal{L}=\bar{\psi}^fi\gamma^\mu \partial_\mu \psi^f_0\bar{\psi}^f\psi^f+g_o\bar{\psi}^f\gamma^\mu t_a\psi^f-\frac{1}{4}Fa_{\mu\nu}F^{\mu\nu}_a\] where \[F^{\mu\nu}_a=\partial^\nu A^\nu_a-\partial^\nu A^\nu_a+g_oF_{abc} A^\mu_bA\nu_c\] where a=(1,2.....8) for the gluon fields =26 fields=6 flavors+3 colors+8 gauge bosons gives 7 parameters+1 coupling There is \(SU(3)_c\) notice that this also applies to the weak force with 6 flavors and the 8 gauge bosons for the strong force ? that's the full QCD langrangian the SU(3) langrangian but that still doesn't include the Higgs couplings? So once again I ask what the bugger is an SU(3) atom as the only Langragian the author included was the QED langrangian.

SU(3) is the color and flavor group \(SU(2)+\otimes U(1) is the EM gauge U(1) doesn't fully describe the EM field Try a little better than that I pointed out that very problem with regards to those gauge groups and not atoms A long time ago in this very thread. That's one of the very reasons the articles SU(3) atoms makes absolutely no sense. That's been pointed out too many times to bother counting Why do you think my example for quarks was used go ahead do those calculations using gluons mediating the strong force between those same two quarks. Though I recommend you use Feycalc to sum the amplitudes What is an Su(3) atom is it just a gluon field field which one of the 8 possible 8 fields interacting the color combinations? A gauge group does not exist on its own its a flipping mathematical treatment There isn't any single reader that can answer the question What is an SU(3) atom... Both gluons and photons have the identical degrees of freedom so the calculation under Bose-Einstein is identical. It is the degrees of freedom used for the chemical reaction term under field treatment application when you apply that formula.... I already mentioned that the calculations above you could apply to strictly massless particles including gluons and you will still have an issue. It's the momentum terms that's the issue..the paper preserves the momentum terms for the SU(3) interaction which is quite distinct from the harmonic oscillator. It has greater degrees of freedom in its polarities the harmonic oscillator is an application of Hookes equations for a spring at each coordinate that is why if you don't renormalize the integrals will give infinite energy if applied at every infinitisimal. That is the very reason why we have a renormalized Hamilton in the first place. You don't sum it at every infinitisimal Do you want a decent methodology for harmonic oscillators see section 3.4.5 Advanced Quantum theory. https://uwaterloo.ca/physics-of-information-lab/sites/default/files/uploads/documents/aqm_lecture_notes_79.pdf That should make it clear that how modern physics handles harmonic oscillators Have gone beyond the formula used in the article The equation of motion in the article Is the harmonic oscillator for a diatomic molecule. Had the author applied those in superconductivity in regards to the harmonic oscillator and applied those equations it would have made a whole lot more sense in terms of condensed matter physics Then it would be more likely useful. I already mentioned Anderson Higgs treatments which applies to Higgs field superconductivity relations... There are decent articles on that topic But as I stated I cannot see any methodology contained in the authors paper that makes it useful as it is written too many ommisions and in some cases wrong methodology.

Yes I am fully aware of that however he is leaving the SU(3) gauge untouched. That calculation is a two quark to quark interaction which applies to the SU(3) gauge. How do you maintain 1 kelvin and leave the momentum terms untouched for the SU(3) gauge you can literally remove every single other interaction and run those calculations without any other Field or gauge including Higgs you can keep the particles completely massless and you would still be above 1 kelvin with preserving the SU(3) gauge interactions momentum terms. He literally specifies that in his opening paragraphs NO particles without mass. except SU(3) so tell me how do you maintain less than 1 kelvin and preserve SU(3) momentum terms ? particularly since his calculated number of SU(3) atoms exceed to particle count estimation for the Observable universe using the corresponding CMB temperature to number of photons relation via Bose-Einstein statistics. Which over the volume of the Observable universe would correspond to 10^90 photons. That calculation is prior to electroweak symmetry breaking where every particle is massless and in thermal equilibrium so indistinct from one another. let me know when you can answer that and tell me again how the model has validity. lmao for the record if you take the critical density formula and calculate the energy mass density the value will equate to roughly 5 protons per cubic meter. That's at 2.73 Kelvin Does that make it clear precisely why I stated the article is unusable in its present form ? I would certainly hope so

When a physicist looks at a paper he wants to be able to employ the mathematics to apply testability with known physics.. I literally in 100 percent all honesty could never ever use this paper as a reference or in any practical application it's as simple as that. If one has to sit there and make random guesses as to what the author is describing that doesn't help. A reader should never have to that to begin with I could take for example the simple equation for ZPE and upon integration get infinite energy in return and that is the same equation used in the article. There is no renormalization term included. The paper does not even mention the renormalized Hamilton let alone use the formula with the Pauli Villars regularization any calculation performed using gluon fields will give higher energy density for the volume given. It must with no choice as that region contains other fields. There is no getting around that. Furthermore There is a HUGE difference between a local condescend matter state than a global vacuum. So any comparison requires far better examination than what the paper offers. It is literally provable that the conditions required by the article HAS NOT OCCURED I cannot stress that enough the paper requires photons to have mass and that same paper just threw in the particle data group constraint on photon mass without doing a single calculation. TRY actually studying the difficulties in achieving a Bose-Einstein or Fermi-Dirac condensate state then compare what happens in a nucleon nucleon interaction As well as do the conversions from eV to Kelvin go ahead try and figure out how the model works when any individual particle has a corresponding temperature conversion greater than close to absolute zero The author never specified how close so lets say 1 kelvin or less. go ahead prove me wrong but don't forget to include the particles momentum term pick any including its momentum example formula for quark quark interaction ground state of a bound system. \[E(r)=2m-\frac{\alpha_s}{r^2_o}+br+\frac{p^2}{m}\] where m is the mass p the momentum the radius of the ground state is \[\frac{2}{mr^3_o}=\frac{\alpha_s}{r^2_o}+b\] here is a table for you http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/quark.html apply any quark combination in that table then do the conversion with the eV to kelvin conversion 11606 Kelvin per eV. now tell me how the model works ?