Mordred

Indeed it would have made more sense to use something along the lines as multiple of squares of the Planck length Example \[ L^2_p=\frac{G\hbar}{c^3}= 2.75*10^{-66} cm^3\] Assuming that back of the envelope calculation I did is correct. Though the articles SU(3) is too poorly defined.

As a member of numerous forums including physicsforums.com heated discussions can occur on any forum. I Don't always use the same callsign on other forums. This site is simply my chosen favorite but I can attest heated discussions can occur on any forum. For the reasons I mentioned above we both simply felt strongly in our understanding. It's as simple as that and yes we both learned a few things in this discussion I hope others have as well. In my case I learned a bit more on how useful rapidity is in deriving a logarithmic function as one example but not the only lesson... Example treatment here https://www.hep.shef.ac.uk/edaw/PHY206/Site/2012_course_files/phy206rlec7.pdf Keep in mind there are some slight distinctions between how particle physics applies rapidity to how SR will apply it ( primarily frame of reference the particle physics frame of reference being the center of beam or amplitude) ie c.m frame as one case

Sometimes this occurs when both parties feel strongly about their current understanding so the debate can sometimes get rather heated. Lol often end up expressing the same thing but differently. I never treat it as personal and in the case of this thread never considered md65536 as delivering any personal attack. It may oft seem that way but it's not the case. For the record I'm equally to blame for how heated the discussion had gotten and fully admit that. I also never hold grudges and have nothing against md65536

We didn't cover quantum tunneling I was about to make a correction spell check interference when I saw the cross post notification it should have read didn't cover. The earlier DE models uses quantum tunneling just an FYI so did Allen Guth's False vacuum inflation which is the first inflationary models. So quantum tunneling is workable for DE but not DM

Try a term we haven't covered. You have system one with its boundary conditions system 2 also has a boundary condition. The two boundary conditions form a potential barrier. The leakage replace with quantum tunneling. We cross posted see above

Excellent video I didn't see any mathematical errors throughout and it detailed the primary relevant equations for the cosmological constant problem Hopefully everyone picks up on a very important detail ( momentum terms) aka the velocity relations being precisely what is being used. Then think back to the OPs article and what would occur if you suppress velocity ie near absolute zero. The opposite end of the temperature scale to the Planck energy at 10^-43 seconds after BB. This is what I have been trying to get across for several pages of discussion. Condensed matter physics is the low end of the temperature scale and is looking at a different set of relations the coupling strength vs the temperature scale is inverse. The energy density scale increases as the volume decreases so does the temperature so if the SU(3) coupling strength at the high end of the scale is at its weakest. Two very different graphs. One graph proportional the other inverse. Thank you for sharing that Migl may I suggest that video gets a separate thread or added to one of the Astronomy and Cosmology pinned threads that one is a keeper. ( lol the only calc in that video I didn't think of doing was to place the vacuum catastrophe term to determine the resulting expansion rate. ) The rest is Introductory level. The video applied the equations for the lambda dominant era ( which is why the radiation equations of state was not included.) Critical density formula that wasn't included in the article but still well described. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] Anyone can simply plug in the Hubble value and determine the energy density of Lambda via that formula. Anyone that wishes to do that calculation for any time in the past use the following \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] To determine the Hubble value at a given redshift Z. As that is tricky the cosmocalc in my signature can perform that last calculation. For FYI the cmb temperature at a given Z using above will correspond to the inverse of the scale factor. Treatment below equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

A question to ask " is science to blame for those weapons?" Science itself is what increases our understanding its purpose is not to determine how governments or the military or engineers apply the understandings that science provides Seems to me all too often ppl place the blame in the wrong court.

Little hint on photon photon scatterings. photons being their own antiparticle ( through whats called charge conjugation). The above article is specifically photon photon so doesn't need to apply charge conjugation just thought I would add that note. The photon doesn't have charge but does have charge conjugation -1 See here for relevant details. Note the charge conjugation usage for particle vs antiparticles in link http://www.personal.soton.ac.uk/ab1u06/teaching/phys3002/course/20_PCCP.pdf

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