Mordred

That may very well be true but its not included in the article under discussion. I noted that numerous times on page one. The discussion is the OP paper itself we shouldn't have to piece meal it together through dozens of other literature. His later or earlier articles may very well be excellent but the discussion is the OP paper. I'm not about to go scrounching and searching however many papers the author wrote or didn't write to justify the OP paper.

Snyders spacetime can be applied to the quantum oscillator certainly but it doesn't do anything for number density of particles. Here is the treatment https://arxiv.org/abs/1308.0673 For the harmonic oscillator under Snyder. How familiar are you with the terms Abelion vs non abelion ? In terms of symmetry groups as that is relevant to the opening paragraph of the above article.

Have you ever really studied quantum field theory the four momentum is applied everyone in this discussion is well aware of the spatial and time components. Doesn't make that 10^123 atoms correct by any stretch of the imagination. The holographic principle itself for SU(3) is separating SU(3) left handedness and SU(3) rightedness through z/2. Now what that means is matter and antimatter which the author doesn't even discuss So I'm really curious as to where your drawing your conclusions ? I'm quite familiar with Snyders metric it is not more fundamental than bose einsteins or Fermi dirac I'm quite familiar with Snyders metric it is not more fundamental than bose einsteins or Fermi dirac. It's not even describing the same thing

Lol part of the difficulties with the holographic principle is that Hoof't the originator intended its usage for cosmological horizons such as the BH event horizon. Ads/cft (anti Desitter/conformal field theory makes use of this. Nowadays it seems everyone is trying to somehow invoke the holographic principle it's largely becoming unrecognizable. Example holographic principle of consciousness or mind articles truthfully I have little to no interest in those. However that's just me as my time is spent on cosmological applications which obviously must include particle physics. In that regard they holographic principle is actually useful in dimensional reduction. A technique to help minimize calculations to something manageable. However pop media and metaphysics love to blow that simple aspect out of proportion. Example the universe as a hologram etc etc. Yet most of these conjectures cannot supply anything testable. Beyond its applications under Ads/cft or string theory I gave up trying to follow all these alternative theories simply don't have enough time to keep up with them

This article though doesn't fully describe the running of the coupling constant gives the formula for doing so see top 3 formulas https://people.frib.msu.edu/~witek/Classes/PHY802/QCD2.pdf The full treatments tend to be far far complex. Should give the idea that coupling strength will vary over a temperature range third formula down gives the resulting spacing between quarks. Now apply those relations to the condensed matter lattice network spacing and then you would be far more accurate than the OP article. Those are the formulas for SU(3) color gauge spacing in Lattice network treatment. However you wouldn't want that spacing throughout the observable universe itself too high a density.

One of the articles I posted earlier has the relevant mathematics of how temperature effects the effective range of the strong force. It's not as constant as one not a physicist would assume from common literature. I'm currently occupied but will detail it later when I get the time but the essence is that the range of the force is mediated by in the case of the strong force by two primary factors. The stability of the mediator particle and its momentum. So the range used in the article 10^{-15} meters is not constant at all temperature ranges. A large volume of literature will give the range based of the mediators momentum term but that's more an approximation This is the more common classical treatment using mass of pion 140 MeV/c^2 \[\rho= \frac{\hbar}{m c^2}\] This is the commonly known formula for getting the \( 10^{-15}\) meters range Now if you think about it temperature will influence momentum so near absolute zero ? The other factor is that the observable universe volume density to temperature relations would also vary as the mean average density changes with its volume. This is why I mentioned numerous times one should apply Bose-Einstein and Fermi-Dirac statistics for thr number density of particles

Lol yeah that's been hashed to death this thread lmao

Verbal explanations isn't sufficient the 10^123 atoms don't involve the holographic principle

So develop the model for the Author to make it workable instead of that being the authors responsibility is that what your stating ?

I totally disagree with this statement in physics any achievement should still be compatible with other known physics. Achievement isn't accomplished through hand wavy statements that one cannot apply known physics to describe

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.