Mordred

My first take on the article may or may not be off, going to study it in greater detail If this is your paper can you show the orthogonal group correlations, in particular the O(3.1) orthogonal group, ( Lorentz group) I would also like to see your gauge symmetry breaking . Those details are missing in your paper, so I cannot see how your running The coupling constants. This papers purpose is to unify gravitons to photons. Gravity vs electromagnetism. I'm surprised you didn't include those details, where is your symmetry breaking? How do you correlate the Lorentz group to the Su(2)*U(1) group? The O(3.1)group is the Lorentz group. Your paper refers to relativity. So this should be detailed. (Feel free to go as technical math or other wise. I most likely can follow) ( I am probably one of the hardest to convince audiences. So I will need the full mathematics.) Key details conservation of charge, isospin and parity Feel free to include QED and quantum geometrodynamics. I studied both fields. ( keep in mind, numerous posters on this site have various levels levels of degrees. We may or may not choose to divulge our particulars) myself included

If you actually study the FLRW metrics, the Einstein field equations or even LQC. Then look at the term Homogeneous and isotropic expansion, as it is measured to apply to how large scale structures are separating with uniformity you would realize that LSS, are not being pushed. Take a uniform and even interaction every where in equal measure at every point in space. Let's use pressure. Which is force per volume aka vacuum energy density. Then apply Newtons laws of motion. Lets use any object say a galaxy, Now as that pressure is homogeneous and isotropic there is no preferred direction or location. The pressure is uniformly distributed. As this uniform distribution surrounds the galaxies, there is no net direction in the sum of forces. The galaxies can therefore gain zero momentum. This is in extremely strong agreement with observational evidence. Your electromagnetic whatever force cannot cause a homogeneous and isotropic expansion. Polarity has preferred directions. The cosmological constant (dark energy is a possibility) is a homogeneous and isotropic term, with the properties that can be described accurately as a vacuum ( pressure) influence. The only thing that changes between LSS, and galaxies is the volume between those structures. The structures do not gain any momentum or inertia. You cannot have a homogeneous and isotropic expansion using any of the 4 forces as they all have preferred directions and locations. According to the best of observable evidence, the cosmological constant (dark energy, possibly a contributor) Has a scalar uniform distribution. The four forces are vectoral

No your understanding is incorrect. Take the Earth itself for example. It's a spherical mass Is the force of gravity zero beneath the surface? Come on use some math not just descriptions. The key is NET force and vector sum. Dark matter distribution is NOT a hollow sphere its treatment is the same mathematically as the SOLID example. Yeesh The only difference is density. Do you not understand that term????: Density, every formula related to rotation curves uses this term learn it. I even gave you a galaxy modelling article. Did you bother reading it? Why do I even bother trying to teach you the real science involved I post you references supporting EVERY statement and example I provide. You still refuse to accept it. http://www.google.ca/url?sa=t&source=web&cd=5&ved=0CCwQFjAE&url=https%3A%2F%2Fwikis.uit.tufts.edu%2Fconfluence%2Fdownload%2Fattachments%2F9440479%2Fchemouni_bach_GE_dec07.pdf%3Fversion%3D1&rct=j&q=singular%20isothermal%20sphere%20profile%20of%20spiral%20arms&ei=xNQDVaDFLsfwoATsxoCACQ&usg=AFQjCNGm931PDgYo5WOdtIksZVMLKqwVSQ&sig2=fa628v9sgDG0sloyufaLVg&bvm=bv.88198703,d.eXY Here is the galaxy modelling article again. Read it There is no such thing as anti gravity. Gravity affects dark matter the EXACT same as baryonic matter. It does obey the shell theorem, you don't understand how the shell theorem Is correctly applied. Reason you don't apply it correctly is your not applying the vector sums. In shell theorem when the vector sum of mass =0 is the center of mass. It's also used in barycenter orbits. and Keplers laws. (The saving grace with all the effort I put into these answers is even if you don't study the material other readers will. )

In point there is a spherical symmetric treatment of the dark matter halo. The trick is defining the radius boundary. A common methodology is to set the boundary at [latex]R_{200}[/latex] The 200 value is 200* the critical density. This is the method used in the older universal rotation curve. Ned Wright has a good coverage. http://ned.ipac.caltech.edu/level5/March01/Battaner/node7.html I had almost forgotten that method as its more common to use NFW (Don't ask me why 200 was chosen, I honestly do not recall why. In regards to the question of the Op The spherical symmetric DM shell has net force zero within the shell, if and only if you have uniform density, which we don't. But even if we did the net force is only zero at the center of mass. This line is the one you overlooked on the wiki page. "A corollary is that inside a solid sphere of constant density the gravitational force varies linearly with distance from the centre, becoming zero by symmetry at the centre of mass" The main difference between a solid and a gas is density in terms of gravity.so assuming a perfect ball of uniform density the net force is only zero at the center of mass, not throughout the inner sphere. Now here is the next problem, the assumption of a ball like spherical DM halo. The halo being defined by R_ 200 will be elliptical. Remember gravity affects dark matter the same as baryonic matter. Now lets look at the singular Isothermal sphere. You have a sphere defined by velocity rotation. This causes a flattening, much like an asteroid belt or the the rings of Saturn. The galaxy rotation affects the dark element in a similar manner defined by R_200. We have to set the radius boundary somewhere. This is where the formula [latex]\rho_r=\frac{\sigma^2_v}{2\pi Gr^2}[/latex] comes into play, this is part of the NFW profile. [latex]\sigma^2_v[/latex] is the velocity dispersion Note [latex]R_{200}[/latex] is also used as the radius boundary of the dark sector in the NFW profile. I would also suggest you look at how the virial theorem is involved. Read this wiki carefully. In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, [latex]\left\langle T \right\rangle[/latex], of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy,[latex] \left\langle V_\text{TOT} \right\rangle[/latex], where angle brackets represent the average over time of the enclosed quantity http://en.m.wikipedia.org/wiki/Virial_theorem

The detail your having trouble with is the distribution of DM is everywhere within and outside the galaxy . The difference is in the density at different locations. This is detailed in the NFW profile note the NFW uses the virial theory. Shell theory is great but it's not practical when your distribution is everywhere at varying densities

We already know it's not. Dark matter is influenced by gravity, it falls into gravity wells just as normal matter does. We account for this in the BAO (baryon accoustic oscillations) in the CMB measurements. As anisotropies form DM falls into the localized anistropies. This provides a major aid in early large scale structure formation. Around galaxies (spiral) your distribution profile is the Navarro Frank White NFW profile http://en.m.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile

The Feynman lectures are excellent for teaching the math as well as basic physics, anyone here can help. We also have some very capable mathematicians on this site. The handy part is you can reference the page your stuck on in the lectures.

Usually at Planck Epoch 10-43 seconds forward. This is the region of our shared causality or worldline Though this can be set different ie CMB forward. CMB being an ideal reference frame in Cosmology.

No problem it's never a waste of time when someone learns. A good site that provides some textbooks to read online is http://www.feynmanlectures.caltech.edu/ My signature also has numerous textbook style articles

This description is similar enough to the Eather theory, this theory has been proven wrong. Space itself has no substance, it's not in and of itself made up of particles Or some phantom medium Space is geometric volume, that volume has the particles were all familiar with residing within that volume. In terms of forces, virtual gauge bosons transfer the momentum, charge etc from one particle to the other in an exchange. Or more correctly interaction. This is true even in field theories. One thing to note QM uses a mathematical representation called phase space. http://en.m.wikipedia.org/wiki/Phase_space http://en.m.wikipedia.org/wiki/Phase_space_formulation Sometimes called the Wigner distribution functions WDF. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0CCAQFjAA&url=http%3A%2F%2Fcds.cern.ch%2Frecord%2F709576%2Ffiles%2F0402021.pdf&rct=j&q=phase%20space%20formulation%20pdf&ei=xBgFVaX3BcKrgwT4toGICA&usg=AFQjCNGEs3lCFu3-O9xA9uSIwJEajgJiVg&sig2=3W-ujG3_AamjWAWXigBuuw This article has a good coverage. Though technical in the mathematics This article discusses several formulations used in QM, and does a quick comparison review of each "Nine formulations of quantum mechanics" http://www.google.ca/url?sa=t&source=web&cd=6&ved=0CDYQFjAF&url=http%3A%2F%2Fmath.bu.edu%2Fpeople%2Fmak%2FStyer%2520Am%2520J%2520Phys%25202002.pdf&rct=j&q=phase%20space%20formulation%20pdf&ei=oR0FVeSHE8rmoATa1IKAAw&usg=AFQjCNHdWWBw7bMzkO-_n0EeW40pT0R2Jw&sig2=lANnuT-YaLUdkjUFnm79tA

As near as our ability to determine we can only go back as far as 10-43 seconds. Prior to that our known physics breaks down. Singularity condition. (Not the same as the point like BH singularity.) The actual time scale depends on the Gut model used. The most common albeit one of the first is the Georgie Glashow model based on SO(5) standard model of particles. This is the chronology wiki presents. The break down here is pretty much the same http://www.physicsoftheuniverse.com/topics_bigbang_timeline.html Here is wikis graphical timeline. http://en.m.wikipedia.org/wiki/Graphical_timeline_of_the_Big_Bang http://en.m.wikipedia.org/wiki/Chronology_of_the_universe The above is well presented in Weinbergs "First three minutes" http://www.amazon.com/The-First-Three-Minutes-Universe/dp/0465024378 Here is a good review of GUT theories. http://pdg.lbl.gov/2011/reviews/rpp2011-rev-guts.pdfGRAND UNIFIED THEORIES it delves into a few variations including super symmetric SO(5) and SO(10) GUT.

If you can supply us with a particular field of interest to study. Let us know I have a huge database of useful training guides to help.

I posted a detailed articles in your other thread http://www.google.ca/url?sa=t&source=web&cd=5&ved=0CCwQFjAE&url=https%3A%2F%2Fwikis.uit.tufts.edu%2Fconfluence%2Fdownload%2Fattachments%2F9440479%2Fchemouni_bach_GE_dec07.pdf%3Fversion%3D1&rct=j&q=singular%20isothermal%20sphere%20profile%20of%20spiral%20arms&ei=xNQDVaDFLsfwoATsxoCACQ&usg=AFQjCNGm931PDgYo5WOdtIksZVMLKqwVSQ&sig2=fa628v9sgDG0sloyufaLVg&bvm=bv.88198703,d.eXY "Constructing basic galactic models" This should show you the complexity of the various factors. Keep in mind the title specified Basic

I really don't get you at all, I already provided all that information in 6 pages of posts. In all those posts you continously missed the terms Energy density profile. This term is where the Navarro Frank White this is the thread where we continously told you rotation curves follow density profiles. Not point mass from stars only. http://www.scienceforums.net/topic/87496-newton-gravity-for-spiral-galaxy/ Those energy density profiles use in part the NFW profile. The bulge itself has a different energy density profile than the disk. In some ways its the closest you get to modelling in terms of rigid body. The disk is modelled as either thin or thick disk, some of those papers in the first link uses both methods, this is done as an isotherm The halo is more uniform in distribution, the dark matter halo itself is usually considered a uniform develop and collionless. This is the specific section covered by The NFW profile that's why that link states Dark matter profile. http://en.m.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile The regions were separately modelled on this link here http://en.m.wikipedia.org/wiki/Galaxy_rotation_problem note different formula for the bulge, disk and halo. All this information was provided to you already. Jeans instability and the virial theorem correlates the interstellar medium You can honestly Google each term yourself. I'm positive that if you Google the terms and terminology in all those links, you will come across hundreds of related papers. pretty much all of them use Energy density/mass density distributions this is your mass distributions. The power law formula is an approximation of those other formulas A short hand if you prefer instead of having to continuously recalculate The separate density profiles in each region then combine them. Or go through the extensive NFW profile. You keep looking for easy answers, news flash there isn't any... We have formulas that help simplify things but how those formulas get developed involves dozens of formulas, Power law formulas are always an approximation, they are typically used to save steps. You have been provided the information, we have continously told you galaxy rotation curves are treated as a medium. The Interstellar medium, which is modelled as a Plasma/gas. Here http://www.google.ca/url?sa=t&source=web&cd=8&ved=0CDUQFjAH&url=http%3A%2F%2Fwww.ioa.s.u-tokyo.ac.jp%2F~sofue%2Fhtdocs%2F2013psss%2Fsofue2013psss.pdf&rct=j&q=galaxy%20rotation%20curve%20profiles%20pdf&ei=S8wDVb_sIsOdgwS4uIPgBw&usg=AFQjCNHOQ8f9k5pSmpGu5eSYpAQX4isv0Q&sig2=nxEIWgq67Gn664YkAVojpA&bvm=bv.88198703,d.eXY this is a 54 page article. It has the density profiles. That is the key term you kept missing, every article we posted uses that term. For a reason. This symbol is vital to understand. [latex]\rho[/latex]=energy|mass density This symbol is vital to understand. Some papers may use the below for spiral disk regions and NFW profiles http://en.m.wikipedia.org/wiki/Singular_isothermal_sphere_profile Here is a paper that discusses Jeans,NFW,virial theorem,density wave etc http://www.google.ca/url?sa=t&source=web&cd=5&ved=0CCwQFjAE&url=https%3A%2F%2Fwikis.uit.tufts.edu%2Fconfluence%2Fdownload%2Fattachments%2F9440479%2Fchemouni_bach_GE_dec07.pdf%3Fversion%3D1&rct=j&q=singular%20isothermal%20sphere%20profile%20of%20spiral%20arms&ei=xNQDVaDFLsfwoATsxoCACQ&usg=AFQjCNGm931PDgYo5WOdtIksZVMLKqwVSQ&sig2=fa628v9sgDG0sloyufaLVg&bvm=bv.88198703,d.eXY "Constructing basic galactic models" That last article is similar to what you would find in astronomy and astrophysics textbooks on the subject

The other details you need to include is the vector aspects of spin and how spin-spin interactions interfere with one another. Yeah that formula looks easy, it's a good approximation only, the reality is far far from simple. As it's a decent aspect here is Jeans instability and Jeans mass http://en.m.wikipedia.org/wiki/Jeans_instability http://m.iopscience.iop.org/0004-637X/507/1/226/fulltext/?providedHtml=38384.text.html

Not all particles behave the same, charged particles behave different than uncharged, DM behaves different than baryonic. Then you have collisionless vs collission hydrodynamics, relaxation times etc. Hydrodynamics is a complex field, so is thermodynamic temperature influences. These can be appropriated using the power laws.

That's why I provided the other links in your other thread. Keep in mind I'm trying to keep the explanations simple and straight forward. To account for every aspect is usually several chapters in textbooks. In " Essence of Astrophysics" they go through close to 30 related formulas. The majority players being Jeans equations, Poisson, Euler, NFW, Einstein field equations, etc, these are simplified to the power law equation I posted. I'm certainly not going to post dozens of equations and relations when I can supply you references and links that show the details.

That's not the truth, that is one of numerous models one without supporting evidence. We have zero zip evidence of a multiverse. We have zero zip evidence of a rotating universe which is one of the consequences of that model. No matter how slow a rotation you cannot maintain a homogeneous and isotropic universe. So observation evidence doesn't support the above model. This forum is specifically for mainstream questions and answers. What one would find in a textbook for example. The model you presented has been considered before it is not a unique idea. However no study has been able to support it. A universe forming from a wormhole has a preferred direction. Black holes rotate that rotation will impart its rotation upon ours. Measurements show no rotation. Poplowskii tried this model for years its still has not gained mainstream acceptance. Last I checked he is now trying an ADS/CFT approach.

Ajb's mention of fields is what I also see you explaining. Instead of interconnected, think of it as a field of baseline particles. well use the electromagnetic field as an example. Fill every point in space with photons (photon is the force carrying gauge boson. Add a particle to this field then describe the range of influence in that field. The key thing to note the forces are mediated by particle to particle interactions. Called gauge bosons, electromagnetic is photons strong force is qluons weak force is w and z bosons gravity would be gravitons but we have no proof of gravitons

Here is the problem I already did that in the other thread, I already explained if you have a force that has a rotation, it will affect different mass particles at different acceleration. Force =mass*acceleration. So Smaller dust will move faster than stars. How simple can you get? Eventually the faster dust will catch up to the previous formed stars. Wow is that hard for you? The above formula is simple it is the mass at each radius, it doesn't use a point center of mass. Rather it uses the accumulated mass as you go from the center of the galaxy outward. Get a Newton scale, hook it up to different mass weights measure the amount of Newtons it takes to move different mass objects. Spiral arms is not Rigid body. Each particle is influenced separately. They all have different mass, therefore they have different velocities. Here follow this N Body simulation, and explanation. http://articles.beltoforion.de/article.php?a=spiral_galaxy_renderer&hl=en&s=idTheory#idTheory That's really the crux of this thread, your upset your thread got locked, as you couldn't offer any supportive evidence or proper math. You also refused to accept anything that disagrees with your model. Despite the numerous professional papers we showed you. Well just too bad, You can either learn why the mainstream science supports the current models and theories and learn. Or you can keep deluding yourself. The subject of this topic is not rotation curves your thread on that subject was locked. Science follows the theory or model that best fits the data. Take this formula [latex] v^2=\frac{GM_r}{r}[/latex] Which is your velocity of TEST particles (test particles have zero mass) The numerator term is total mass of the enclosed radius. So this is basically a radius evolving mass calc of [latex]f=\frac{Gm}{r}[/latex] Now if f=say 10^5 Newtons how much acceleration will it give a one solar mass as opposed to a 2 solar mass? Will they have the same acceleration? Will hydrogen move faster or slower than helium? Use atomic weights now apply that to all the gas types in the interstellar medium. Apply that to the different mass stars. Get the picture ? Then look at what elements make up what classifications of stars. There is your regions aka hydrogen vs helium lines etc. Why do younger stars burn hotter than older stars. They are made up of heavier elements. Plus they burn up faster. That extra brightness illuminates the gas in the spiral arms making them highly visible. That provides your power law to luminosity functions on rotation curves.

Also the flat/curved is a density profile its a comparison of the Universes actual density to its critical density. (Calculated density at which the universe will expand, slow down then start collapsing) The first two articles I linked cover the above questions. Expansion only affects the regions not gravitationally bound. Galaxies are not dragged, the volume of space between large scale structures simply increases.

You can believe whatever you choose professional astrophysicists around the world use the rotation curve power law profile This is due in part, to density wave but only in part. [latex] v^2=\frac{GM_r}{r}[/latex] The thing is you do not apply f=ma or Newton properly, you also have no understanding on the hydrodynamic equations. if you want a good book read Elements of Astrophysics. The detail you refuse to accept Is galaxy rotation curves is based on gas laws. Every particle not just stars. Star formation is due to gas.... where the highest density is located is where new stars form. This is no different than Saturn which is dust that forms larger rocks. I think your biggest problem is you don't think at all scales of partulates. Saturn's rings has particulates of dust that dust makes larger rocks as they combine. Same as galaxies, plasma hydrogen, lithium etc etc, form to make stars so where the plasma is located is your star formation region. What I find fustrating is that I posted professional papers for you to study, yet you keep missing the important details which I repeatably explain I even show you an example such as the whirlpool (density wave) when you pull the plug in your sink full of water. Same principles, difference in the influence strengths due to different particulates and medium

Density wave works for both Saturn's rings as well as galaxy rotation curves. In principle the influence and nature of how particles of various mass move are the same. Just different size scales. I posted you dozens of articles and explainations on this topic before. Yes there are always alternative explanations no theory however solid is without a competing theory. No matter how effective a theory is. In density waves the majority of the competition is primarily fine tuning the metrics involved. Galaxy rotation curves have a huge variety of influences over an extremely long period of time so this is a natural consequence. On something as complex as detailing the average movement of every particle from gas to stars over its entire history of development, it would be foolish to think a few formulas cover every possibility. Wiki is not a final authority on any subject. If one wants a clear picture on what models or theories are considered " concordance". Ie the more effective and well recognized theories are. It's best to study the textbooks and dissertations written by professional physicists. Every textbook on astronomy I own or ever read covers density wave, this includes the vast majority of any related papers I read on galaxy rotation curves, this is over a course of the last 20 years. (Though I myself am not an astronomer I've had plenty of experience helping other forum posters understand this topic on numerous forums). Whenever I have seen rotation curves come up in questions on those forums, the professional astronomers on those forums answer with the density wave metrics. No theory is 100% every theory has a margin of error regardless of how accurate. Every theory has room for improvement. No theory is considered proved, so your proved,unproven classification is pointless. The correct classification is which theory is considered the most accurate to observational evidence. Currently this is density wave theory in regards to both Saturn's rings as well as spiral galaxy rotation curves. Here is a direct quote from one of the Astronomy textbooks I own. I'll have to free hand copy it in as its a hardcopy text. (Try not to make any mistakes) This is from page 294 Ian Morrison's "Introductory to astronomy and Cosmology" "In its life, our Sun has circled the galactic centre about 20 times so why have the spiral arms not wound up? The solution is hinted at by a visual clue. Spiral arms seen in other galaxies stand out because they contain many bright blue stars remember a single very hot star can outshine 50 000 suns like ours! However, very hot bright stars must be young as they have very short lives, so the spiral structure we see now is not that which would have been observed in the past. As Bertil Lindblad first suggested, it appears that the spiral arms are transitory and caused by a spiral density wave rotating round the galactic centre a ripple that sweeps around the galaxy moving through the dust and gas. This compresses the gas as it passes and can trigger the collapse of gas clouds so forming the massive blue stars that delineate the spiral arms. The young blue stars show us where the density wave has just passed through" I own 6 Astronomy textbooks, they all include similar statements and refer to the density wave theory. PS I have a huge collection of textbooks. I just bought Quarks and Leptons. Good book for entry level particle physics very informative. My current collection is approaching 50 textbooks.

Density wave is currently considered the best fit to observation theory, no theory is ever 100%

The figures on wiki pages will usually be referenced, for the source, look under the page reference. The Gut models today ie SO(10) break down the epocks differently, and at different temperature values