Mordred

Feyman has excellent lectures. I would ask any further questions not directly related to "what is space" please start another thread I'll be more than happy to reply there. I don't want this thread to describe the body of physics 😉

Spin is a property but one that is quantized. A VP being "off shell" may or may not exhibit spin. The minimum measurable quantizable value is [latex] E=\hbar w [/latex]. In QFT this defines the creation/annihilation operators (math term). The reason a VP isn't measurable is that they have insufficient energy to cause action to affect even the most ideal detection instrument.

Ok good images I can distinquish the problem using these. The external lines are your excitations (particles) these are termed your real particles. The internal ziggly lines on the right image is your fluctuations (virtual particles) it is those internal lines that is the issue. The external lines are renormalizable the internal lines are not. The external lines can induce effective action. While the internal lines has insufficient energy to do so. This is all described under S-matrix theory. Lattice QCD shows that an external line is really a boundary confined collection of fluctuations(VP) that sum up under confinement to an excitation. (particle) Spots in your eyes are more a biology discussion. I don't know the proper terminology but in essence your receptors are still sending delayed signals

Not at this point the problem with quantum gravity lies within a term called "renormalization" which is a very complex topic. Part of the problem with renormalization lies within the Heisenburg uncertainty principle itself. Just to be clearer there, when you hear the term "the problem is quantization" A quanta is the nimimum energy to cause "observable action". Action is a term to describe kinematic motion. Whats often described as a virtual particle for example cannot perform action as it is less than a quanta. The term particle itself is a classical misnomer as all particles are a field excitation. A field being a collection of excitations in this case. A field deviod of excitations being what is termed your zero point energy in QM. Under Cosmology true vacuum. However the Heisenburg uncertainty principle causes difficulty even after all excitations are removed. An excitation being a quanta, a fluctuation being VP of energies less than a quanta. I'm being a bit heuristic but this is where the problem lies between quantum gravity and relativity for a full blown TOE.

yes mass is resistance to inertia change so your common relation is momentum and factors that affect change in momentum. The stress tensor doesn't identify the cause but describes the influence to momemtum. Energy is "the ability to perform work." This all relates back to your Newton laws of inertia under a collective organization in your stress tensor. Spacetime curvature itself is a geodesic map of freefall motion. Described as the particles worldline. The stress tensor gives us the momentum based components of that map. So literrally any dynamic/interferance or interaction that can induce a resistance to inertia change is a form of mass. These are described under the stress tensor.

Not purely mathematical they are in essence fluid dynamic terms. flux is particles/unit area/unit time) across surfaces of constant x, y and z. Vorticity is a type of motion of those particles often described as the curl component. In essence describing rotational fluids. Classical examples being whirlpools etc. The curl component of the Maxwell equations being another example of vorticity. In essence vorticity is your angular momentum terms. Angular momentum being skew-symmetric

There is three main components to the stress tensor. Momentum, flux and vorticity.

I've always preferred stating the stress tensor instead of mass. Far more accurate but then many wouldn't know what the stress tensor is. @Tom one can apply a numeric description to anything in nature. That does not mean numbers are intrinsic to anything. Numbers are simply another form of language. A method of descriptive. Strange and Stingyjunky already covered the important details to Brownsfan77 post but I will add Any form of field can influence spacetime whether its electromagnetic, a matter field, the strong force etc. Using electromagnetic field to bend light is just one example but not the only one. While its great you showed that an electromagnetic field can bend light. So can other forms of either force or matter fields. With or without the presence of an electromagnetic field such as two asteroids far removed from any magnetic field. Another key distinction between gravity and any other force field is that gravity matches spin 2 statistics (which includes its thermodynamic character via Bose-Einstein statistics) No other known field does. Electromagnetic follows spin 1. So a GW wave is significantly different from an electromagnetic wave. We have now detected GW waves and confirmed the spin 2. Keep in mind a field is a mathematical abstract device to describe any collection of objects/events etc. Then again mass is also an abstract device to describe resistance to inertia change. Mathematics and physics simply describes what we understand as reality or aspects of it. Spacetime curvature is a mathematical geometric description of relations. Space is a description of volume, too often posters seek what it is fundamentally made up of due to trying to understand how it can curve. What curves includes additional relations causing resistance to inertia change.

nice reference and example Studiot. I don't want to add anything just yet. Might add confusion. My explanations often do lol.

Yes I'm familiar with some of Wolframs work. Though certainly not in great detail. Ok so you are simulating Newton gravity along x axis distance. Judging from above. This shows x axis, but what about the y and z axis? I look through your links I'm unclear which is your work or others. you may find these articles helpful. Cell Automata and Physics. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0ahUKEwi0js7IrpzPAhUGy2MKHefsA-8QFggbMAA&url=https%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F9907013&usg=AFQjCNHja_3J6NFDSGI3PzKbHvDALS-3mQ&sig2=ymSvYw3QO-umfbRFt5yLKA And "What are the hidden Quantum laws behind Newtons laws" http://www.google.ca/url?sa=t&source=web&cd=2&ved=0ahUKEwi0js7IrpzPAhUGy2MKHefsA-8QFgggMAE&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F9904036&usg=AFQjCNGiDpIcBEmWePTYr-qmDmD_O8qx-g&sig2=n2oIRg0Qj90JeDaINLgbKw both articles gives some excellent examples in Newton gravity. particularly in the 3d regime with CA having 26 neighbors. 2D only 8 ( see second article)

Ok mathematically I have no problem with using math to describe reality. This is essentially done with physics. Without having to search your links is there specific formulas you want to look at? The Newton limit we can already derive using math. So without having to search your links. Can you post the math in your solution? The extension of the Bohr model should also be looked at.

Good point on particles and fields. I was considering a rewrite on that post. Unpinning this thread and replacing the article. It had initially hoped for a more collaborative on its initial writing. A couple of details I wish to add is a decent example of many particle distribution and how it correlates to the metric tensor and geodesics. The problem isn't that I can't derive the necessary equations. It's finding a series of derivitaves that can be readily followed. Specifically thinking the Newtonian limit where [latex]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex] I'm certainly open to other suggestions. However I feel this may be a good way of showing the field aspects of mass only. In a way I've been posting numerous derivitaves along these lines in Speculations and relativity forum to test how well they are understood by others.

I believe the statement" space is filled with the standard model particles and fields" is a better statement than space being some form of ether is more accurate. It is those fields and SM particles that determines the topography. The point being space itself does not have its own unique particles, which would be required for an ether. Unless you accept the graviton neither does gravity... Even twistor theory doesn't state space itself has its own particles. Though I had to confirm that with a PH.d that specialized in string/twistor theory. The metric tensor is determined via SM particle distribution. Thanks for the spelling corrections. I'm curious though why you would post a 1922 translation. The details of that paper is outdated by later research.

Thanks for the catch, gotta love auto corrects. Correction applied.

No you shouldn't think of particle spin as meaning spinning on its axis. I rarely use YouTube vids to answer questions but in this case it will make it easier. http://m.youtube.com/watch?v=v1_-LsQLwkA

To give an example of where classical motion fails to describe the spin of a particle. Even though it's convenient to model a particles spin as a rotation this cannot be confused with a classical rotation. Take an electron for example it being a fermion has a non integar spin of -1\2. Mathematically though this means a 720 degree rotation to return to the same quantum state. see the problem? Normally a spherical object like say a planet returns to its orginal state in 360 degrees. Visualizing particles as little bullets instead of excitations will lead one astray. Yes they have poinlike characteristics, but at the same time wavelike. To Google how particle spin works Google spin statistics. "quantum mechanical spin is not described by a vector as in classical angular momentum. It is described by a complex-valued vector with two components called a spinor." https://en.m.wikipedia.org/wiki/Spin-%C2%BD PS glad to see your studying.

Lol good catch I'm surprised I, and everyone else missed that. Title error fixed. +1

I don't have too many tensor books however one I enjoyed is Bishop, R. L. and Goldberg Tensor Analysis on Manifolds Sean Carroll has a decent article on GR. " Lecture Notes on General Relativity" http://arxiv.org/abs/gr-qc/9712019 I found it well written, Another online resource being the Feyman lectures. http://www.feynmanlectures.caltech.edu/ You May find "Elements on Astrophysics" handy. It's not a textbook, however it has a huge coverage of numerous metrics used in Cosmology and astrophysics. I use this as a handy look up resource. http://www.ifa.hawaii.edu/~kaiser/lectures/elements.pdf (Lol that should give you a few months of study at least) With your software background, you might want to study N Body codes. I bought the tools and algorithm book sometime back, however never got around to actually developing N Body codes. ( note,The book is rather tricky to follow through) http://www.amazon.in/gp/aw/s//ref=mw_dp_a_s?ie=UTF8&i=stripbooks&k=Sverre+J.+Aarseth Refers primarily to Fortran. Though doesn't have any complete codes Off topic but I highly interesting. Here is a brief simulation of our universe. ( an excellent test of current models.) http://www.cfa.harvard.edu/news/2014-10 http://www.illustris-project.org/ Here is the peer review on the simulation. http://arxiv.org/ftp...5/1405.1418.pdf So this begs the question? Although you admit your model has flaws... does the dark matter distribution reflect on your model compared to the simulation you just saw? The video does an excellent job of approximating observational evidence. This is something any good model eventually needs to do. PS numerous models were tested in that simulation. You might want to Google the Navarro Frenk White profile. https://en.m.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile PS.. it's covered in Elements of astrophysics and no I don't expect your practice model to cover the details in the simulation. However it does show an example of needing to expand upon and incorporate various aspects outside of SR. ( on the textbooks I mentioned, Matt Roose does a good job on filament and large structure formation) It is fun, but you need more than SR for dark matter lol.Up to a challenge, write a FAQ on time. Don't include DM or DE Start it as a new topic, this forum could use a good SR descriptive on time. Some of your descriptives are to the point and accurate. I would be curious to see what you come up with. If your up to it you might want to read. Particularly if you want to cover multiverses in regards to time. "Time before time" http://arxiv.org/pdf/physics/0408111 ( PS overall, albeit a few side points your time descriptives are reasonably accurate. Hence I would like to see you help us out with a FAQ.) Hint... define time as a measure of rate of change or duration Not all change involves momentum.

No problem, I understood that you didn't have the background details in Cosmology applications and I treated your model as a "toy universe". While providing you the tools to increase your knowledge on Cosmology. Little hint, you will find the FLRW metric surprisingly easy to understand compared to GR. Even though The FLRW metric can be derived via the field equations. Out of the numerous textbooks in terms of the FLRW metric, that I've read. Probably the best one specifically covering the FLRW is Barbera Rydens "Introductory to Cosmology" In terms of GR, I like General relativity by Wald. Good intro texts into QM and particle physics are the Introductory books by Griffith. Physical Foundations of Cosmology by Muchanov does one of the better jobs covering nucleosynthesis. Modern Cosmology by Scott Dodelson does a good job on inflation. Introductory to Cosmology by Matt Roose I found good in taking each aspect and simplifying it. I mention the above as outside of formal training the best way to learn is to invest in the right textbooks. If you can't afford textbooks, I always liked dissertations and pedagonal review papers ( lol I'm a bit of a physics textbook collector. I never have enough) Forgot to add Quarks and Leptons is also excellent for modern day particle physics intro, including the Higgs field. As far as inflation goes I've learned a ton in discussions with Brian Powell.

Sure there may or may not be a CMB dipole dark flow. This is a subject still under considerable debate. Dark flow does not imply a center of the universe. Perhaps you should read up on dark flow. http://arxiv.org/pdf/1411.4180 Keep in mind there is numerous models that use dark flow as evidence of a multi universe evidence. Until the results are conclusive I will continue to answer questions and post what textbooks describe. If one gets too distracted by all the counter models to every theory, well lets just say you can easily be led astray. I've always felt its better to answer questions according to the concordance models. The links I choose to post reflect the textbooks. Currently in Cosmology the concordance models is the FLRW metric. Though LQC is a good competitor. That model also follows the cosmological principle. I've long ago lost track of how many models that never competed significantly to LCDM due to not following the cosmological principle. Are those models still around? In many cases yes. Are they largely considered by the majority of cosmologists as being good models of our universe to observational evidence. No. (Side note, our own peculiar velocity causes a large portion of the CMB dipole.) How much of The detected signal is due to calibration errors to compensate for redshift effects due to our peculiar velocity? The second set of Planck underwent considerable calibration refinements and does not support dark flow according to Planck. Yes I posted a counter argument paper. ( most forums follow the policy, of all answers to posts must be in accordance to the mainstream). Ie textbooks. Here is a quote from Matt Roose "Introduction to Cosmology" on the CMB dipole. "The interpretation today is that not only does the Earth move around the Sun, and the Solar System participates in the rotation of the Galaxy, but also the Galaxy moves relative to our Local Galaxy Group, which in turn is falling towards a centre behind the HydraCentaurus supercluster in the constellation Virgo. From the observation that our motion relative to the CMB is about 365 km s−1, these velocity vectors add up to a peculiar motion of the Galaxy of about 550 km s−1, and a peculiar motion of the Local Group of about 630 km s−1 [5]. Thus the dipole anisotropy seen by the Earth-based observer A in Figure 8.2 tells us that we and the Local Group are part of a larger, gravitationally bound system." Page 216 In further defense of the links I post. "Please note that all posts that are baseless in scientific fact or that are outside of mainstream physics can and will be moved to the Speculations forum. " So I ask you why would I incur infractions, by posting non mainstream answers and articles? Just a side note the above paper discusses Sunyaev-Zeldovich effect which involves the Kompaneets equation http://www.weizmann.ac.il/home/kblum/IPC/tutorial%20notes/TutKfirSZ.pdf

As promised I looked over your model proposal. Aside from the DE, extra dimensions, and dark matter conjectures which you will need to rethink. More on those points later on. There is one key detail that runs counter to observational evidence. " The Big Bang FoR has its origin located at the center of a four dimensional sphere that is expanding." The Cosmological principle states the universe homogeneous and isotropic. The model you presented defines a preferred location. (Big bang origin point ). To see why this is wrong read these two articles. http://www.phinds.com/balloonanalogy/: A thorough write up on the balloon analogy used to describe expansion http://tangentspace.info/docs/horizon.pdf:Inflation and the Cosmological Horizon by Brian Powell. Cosmological measurements agree that there is no center of expansion. A center has a preferred location and direction. Homogeneous means no preferred location, isotropy means no preferred direction. Together they define a uniform energy/mass distribution which is what the formulas of the FLRW metric also defines.

With your strong interest in mathematics here is two articles covering the mathematics involved in particle physics and how it ties into GR in the second article. First article is primarily differential geometry coverage. http://arxiv.org/abs/0810.3328A Simple Introduction to Particle Physics http://arxiv.org/abs/0908.1395part 2

Noted the textbook I was referring to is the particle physics by Liddle. It's primarily based on SO(5) rather than SO(10). The author took the time to cover the now improved physics understanding in the opening notes. It still has tons of useful information provided one remembers our understanding has improved since its writing.

Well I for one give you props for recognizing this example of model building has flaws, and not pushing " This is how it is". As such it's an excellent example of model building the right way albeit improvements to conform to the physics and ideal gas laws are needed. Wish other posters had the same diligence. If you take the time to look over the materials I provided above you will notice one of the links is a full (but older textbook). The Mathius Blau article is roughly 990 pages covering GR, with the last chapters covering Cosmology. Later when I get a chance I'll post more training material for you, with GR and thermodynamic applications. In particular the Einstein field equations. If you can afford and isn't adverse to buying textbooks. For GR I would recommend buying General relativity by Wald http://www.amazon.ca/General-Relativity-Robert-M-Wald/dp/0226870332 +1

Well this being my first time looking at this thread thus far I'm impressed by your rigor. Unlike most speculation models your backing up yours with mathematics. I still have to look over what you have thus far in greater detail however I see a couple of points and potentially counter arguments against your model. Looking over this this far it looks like your using primarily SR as opposed to GR. I can see some inherent problems with this but not in something previously mentioned throughout this thread. A common mistake in many speculations is that there is a belief that expansion is based primarily upon distance measurements as its primary source of evidence. This is far from the truth. In fact an even larger body of evidence is thermodynamics. Rather than go through an entire course in Cosmology applications of thermodynamic laws I'll jump to some primary relations. [latex]E=(\rho c^2+p)R^3[/latex] Expansion is adiabatic if there is no net flow or outflow of energy. So that [latex]\frac{de}{dt}=\frac{d}{dt}(\rho c^2+p)R^3=0[/latex] Let p be proportional to [latex]\rho c^2[/latex] This leads to the relation [latex]p=w\rho c^2[/latex] https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) This link gives the appropriate equations of state Without going through all the steps expansion is accurately described via the FLRW metric acceleration equation which can correlate energy density/pressure and temperature relations. The acceleration equation is [latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex] This leads to [latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex] where k is the curvature constant. now the curvature constant can have three main configurations 1,0-1. You've probably know about the stress energy tensor but this set of relation is handy to know. [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex] Which correlate the stress energy tensor to energy density/pressure in Minkowskii metric form. If you look through the universe geometry formula below I go into basics on the FLRW metric and how the curvature constant affects light paths. The FLRW metric to distance formula is. [latex]d{s^2}=-{c^2}d{t^2}+a{t^2}d{r^2}+{S,k}{r^2}d\Omega^2[/latex] [latex]S\kappa r= \begin{cases} R sin r/R & k=+1\\ r &k=0\\ R sin r/R &k=-1 \end {cases}[/latex] For example when k=0 light rays remain parallel, they Will either converge or defract depending if the curvature constant is positive or negative. http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry http://tangentspace.info/docs/horizon.pdf:Inflation and the Cosmological Horizon by Brian Powell http://arxiv.org/abs/1304.4446:"What we have leaned from Observational Cosmology." -A handy write up on observational cosmology in accordance with the LambdaCDM model. http://arxiv.org/abs/astro-ph/0310808:"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf:"Misconceptions about the Big bang" also Lineweaver and Davies The above links are basic articles on common misconceptions. These three will get you started on the ideal gas laws applications involved. The last will help you with your GR, and incorporates GR to the FLRW metric via the Einstein field equations and thermodynamic laws. http://arxiv.org/pdf/hep-ph/0004188v1.pdf:"ASTROPHYSICS AND COSMOLOGY"- A compilation of cosmology by Juan Garcıa-Bellido http://arxiv.org/abs/astro-ph/0409426An overview of Cosmology Julien Lesgourgues http://arxiv.org/pdf/hep-th/0503203.pdf"Particle Physics and Inflationary Cosmology" by Andrei Linde http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis http://www.blau.itp.unibe.ch/newlecturesGR.pdf"Lecture Notes on General Relativity" Matthias Blau the main concern is if you want your model seriously considered you will have to correlate the ideal gas law aspects to the EFE and FLRW metric to explain the thermodynamic history of our universe via your model Including Big bang nucleosynthesis and the corresponding particle species % found in the CMB. Anyways it's late at my locale, I will provide some arguments on galaxy rotation curves in terms of an ideal gas isothermal sphere and the NFW profile. As well as touch on the Integrated and non integrated Sachs Wolfe effect. For dark matter I will probably add some details on gravitational lensing which Will correlate its gravitational influence. Dark flow itself is a locale group interaction its not applied the the entire observable universe. Our local group is moving to a sulercluster called the great attractor. Accronym name. The main point is as far as I can tell your model is based mainly upon SR and how light can cause influence upon observable influences. Unfortunately Cosmology doesn't based its model strictly upon light. It's intensely includes particle physics and thermodynamic laws as well. For example the temperature of the universe at any time by the inverse of the scale factor a(t). I would also look into cosmological redshift and luminosity relations