Mordred

How to become a good researcher ? Good question. While the type of research I've done differs. Some of the criteria is the same.1) understand the goal of the research project 2) Understand which methodologies and experimental practices reduces various types of error 3) Understand how the experiments are appropriate to the experiment including any possible errors.( ie equipment error etc) 4) establishing good control points to help improve accuracy 5) Look for possible alternatives both for and against your line of research. (counter models etc) 6) Look for supportive research both supportive and against. 7) Self study always 8) Understand the limitations of the equipment and how to optimize their versatility and flexibility. 9) Look for ways to increase accuracy and consistency (error reduction/repeatability) 10) Consistency, consistency consistency in all the above. I'm positive others can name more One hint a good self researcher can often find his own answers. Via studying other research They are the ones that tend to supply the answers more than asking others for the answers. Most importantly if he doesn't know the answer. He knows where he can find the answer. Nobody remembers every formula. Develop a database and reliable sources for answers. Lets take a simple example spinning blood in a centrifuge. With the list above "What are the steps to properly test the blood sample in the most consistent and accurate manner? (including sources of error and means of addressing those errors) List them in order. (break it down to each individual step)

Oh really I think not. This is a complete garbage statement. What changes in how the observer measures light due to expansion? Don't make the mistake of confusing apparent or peculiar velocity with actual velocity. I think you better study these two articles. http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell http://arxiv.org/abs/astro-ph/0310808 :"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies Don't let the title of the first one confuse you. Its a simplified version of the second article. Written by a professor that has years of forum experience.

repeating these assertions isn't addressing our questions. x posted with Strange lol

Yes however lookback time requires those additional parameters to stay accurate. As well as flexible in particular to k values. lets try a key detail. 1) Is the rate of expansion constant over time? 2) What is the importance of those density values in regards to the rate of expansion today as opposed to the rate of expansion then? 3) How does the deceleration equation get involved? (hint number two can be answered from one of the equations I posted) your wondering where your deviations are coming from the above questions will provide your clues. While the formulas above are reasonable approximations. The parameters you mentioned can greatly increase their accuracy. There is a particular variation of the lookback time formula by Hogg's that is far more accurate than the standard look back time formulas. I will post it later when You've had time to consider the above. (Don't forget to look at the z corrections as well) (same hint as per above for question 2) the Hogg's version applies the same equation as per question 1 and 2)

Well this definetely grasping at straws on developing connections without understanding the material. Perhaps instead of posting numerous links on gyroscopes etc. You will show the actual math. Rather than expect us to connect your imaginary dots. I would recommend you start with the stress tensor for both electromagnetic and EFE. Then study the different spin statistics. Followed by showing 3+1 spacetime with 1 dimension for electromagnetism in the Kalazu Klien. Are you even familiar with the math I suggested ? If not Rindlers "General Relativity" has some excellent coverage. Granted it is an old thread, but its still considered thread hijacking when you present a personal speculation as an answer to someone else's thread. I recommend starting a new one under Speculations. Perhaps you might consider the detail that not all gravitational bodies have a electromagnetic field. Then again if you understood GR we already consider spinning bodies lol

Not everything is expanding. Only between the voids, away from LSS does expansion occur. So I'm having trouble making sense of your proposal. http://arxiv.org/abs/gr-qc/0508052 "In an expanding universe, what doesn't expand? Richard H. Price, Joseph D. Romano

As it is after work now atm, I can add some details. In particular on Cosmological redshift. There is some handy relations to be familiar with. first start with commoving coordinates [latex]r_1,\theta, \phi[/latex] photons follow null geodesics [latex]ds^2=0[/latex] thus [latex]cdt=\pm\frac{Rdr}{\sqrt{1-kr^2}}[/latex] key note k in flat geometry =0. The - sign is appropriate as the radius decreases as light approaches us. this essentially means [latex]\int^{t_0}_{t_1}\frac{cdt}{T(t)}=\int^{r_1}_0\frac{dr}{\sqrt{1-kr^2}}[/latex] For R(t) roughly constant over [latex]\Delta T_0[/latex] [latex]\frac{c\Delta t_0}{R(t_0)}-\frac{c\Delta t_1}{R(t_1)}=0[/latex] with c as a constant [latex]\frac{c\Delta t_0}{c\Delta(t_1)}=\frac{v_0}{v_1}=\frac{\lambda_0}{\lambda_1}=\frac{R(t_0)}{R(t_1}=1+z[/latex] So compare this series of equations with thee one you derived. Further details on the above can be found in "Modern Cosmology" by Max Camenzind page 205 (though I changed the commoving coordinates symbols to match those used by wiki and common textbooks)

Hubble horizon is at roughly 4400 Mpc. You can convert that to Gly to get a rough z. I will have to look later but one of the column options should give the Hubble horizon. Glad you like the calc, I find it incredibly handy. I should mention not all formulas in Cosmology are complex. The FLRW metric is fairly straightforward compared to GR. The advantages a formula has is more than simplicity. Its also its flexibility to define other formulas. For example this formula is extremely simple and flexible to correlate to more complex formulas. [latex]1+z=\frac {R (t_0)}{R (t_1)}[/latex] Whats of greater use though is the formulas involving scale factor. [latex] H(t)=\frac{\dot{a}(t)}{a(t)}[/latex] for example is further used to calculate proper distance and also temperature thermodynamic relations. There is simple correlations to the scale factor vs temperature evolution. You can see the flexibility in these two articles. 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/0409426 An overview of Cosmology Julien Lesgourgues [latex](\frac{\dot{a}}{a})^2[/latex][latex]=\frac{8\pi G}{3}\frac{\epsilon(t)}{c^2}[/latex][latex]-\frac{kc^2}{R_0^2}\frac{1}{a^2(t)}[/latex] Another handy article http://arxiv.org/abs/1302.1498 " The Waters I am Entering No One yet Has Crossed: Alexander Friedman and the Origins of Modern Cosmology" written by Ari Belenkiy This particular formula is incredibly handy [latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex]

Well sounds like you may find this resource handy. Particularly if your math skills is up to it. http://arxiv.org/abs/hepth/9912205 : "Fields" - A free lengthy technical training manual on classical and quantum fields. Another handy online resource is http://www.damtp.cam.ac.uk/user/tong/qft.html You will numerous lecture notes here. The subject is immense I would also recommend studying feyman diagrams, [latex]\phi^4 [/latex] theory, Hamiltons and Langrange's The first article has an excellent listing of different field theories. Should come in handy. You will need a good understanding of particle physics, relativity and obviously strong math skills. For the particle physics side. These two articles are handy. http://arxiv.org/abs/0810.3328 A Simple Introduction to Particle Physics http://arxiv.org/abs/0908.1395 part 2 Though if you can buy textbooks Quarks and Leptons is an intro to Particle physics. Also any books by David Griffith are handy. In particular his Introductory to particle physics.

Yeah if I recall we ran into that when we compared to Ned's calc. We opted to compare to Davies. On the top right is your dataset options Stretch equals 1.00 is present age. If you want to contact the developer himself you can find him here. This is the thread that we ran to develop the calculator. Unfortunately the trainer that taught ppl how to use it passed away (Marcus) but the Jorrie still frequents that forum. https://www.physicsforums.com/threads/steps-on-the-way-to-lightcone-cosmological-calculator.634757/ Ordinarily I don't like referring to other forums but in this case, the details on the calc usage is best described on this thread. Here is the formulas used in the calculator including reference paper. http://cosmocalc.wikidot.com/advanced-user You can fine tune the calculator by playing with the lower/upper stretch values keeping the number of steps at however many rows you want. This is handy for example in finding the inflection point where we switch from matter dominant to Lambda dominant at roughly 7.3 Gyrs. That thread has an example of doing so. ( my involvement was mainly writing the user manual)

Generate a graph then use the lightcone on my signature. Set your number of steps to 100. You will notice that there is further options such as graphing. The lightcone is done in proper distance. I suspect you may or may not see a deviation after Hubble Horizon but thats just from a glance on your last equation. Unfortunately the latex the lightcone generates doesn't post here on this forum. There is something that generates an error specific to the latex format here. The reason I suspect deviations beyond Hubble horizon is that z requires corrections beyond this point. Oh side note the lightcone has a couple of data options. Planck WMAP and combined from the 2012 Planck dataset. It will be closer than the calcs you have been using as it involves those data set parameters. Here is a correction workup I posted in another thread. ets look at the corrections to the redshift formula. First we define a commoving field. This formula though it includes curvature (global) you can set for flat spacetime. A static universe is perfectly flat. [latex]ds^2=c^2dt^2 [\frac {dr^2}{1-kr^2}+r^2 (d\theta^2+sin^2\theta d\phi^2)][/latex] we write [latex](x^0,x^1,x^2,x^3)=(ct,r,\theta,\phi)[/latex] we set the above as [latex]g_{00}=1,g_{11}=-\frac{R^2(t)}{(1-kr^2)},g_{22}=-R^2 (t)r^2, g_{33}=-R^2 (t)r^2sin^2\theta [/latex] the geodesic equation of the above is [latex]\frac {du^\mu}{d\lambda}+\Gamma^\mu_{\alpha\beta}\mu^\alpha\mu^\beta=0 [/latex] if the particle is massive [latex]\lambda[/latex] can be taken as the proper time s. If it is a photon lambda becomes an affine parameter. So lets look at k=0. we set [latex]d\theta=d\phi=0 [/latex] this leads to [latex]ds^2=c^2t^2-R^2 (t)dr^2=c^2dt^2-dl^2=dt^2 (c^2-v^2)[/latex] where dl is the spatial distance and v=dl/dt is the particle velocity in this commoving frame. Assuming it to be a massive particle of mass "m" [latex]q=m (\frac {dl}{ds})c=(1-\frac {v^2}{c^2})^{\frac{1}{2}}[/latex] from the above a photon emitted at time [latex]t_1[/latex] with frequency [latex]v_1 [/latex] which is observed at point P at time [latex]t_0 [/latex] with frequency [latex]v_0[/latex] with the above equation we get [latex]1+z=\frac {R (t_0)}{R (t_1)}[/latex] Please note were still in commoving coordinates with a static background metric. [latex]z=\frac {v}{c}[/latex] is only true if v is small compared to c. from this we get the Linear portion of Hubbles law [latex]v=cz=c\frac{(t_0-t_1)\dot{R}t_1}{R(t_1)}[/latex] now the above correlation only holds true if v is small. When v is high we depart from the linear relation to Hubbles law. We start hitting the concave curved portion. The departures from the linear relation requires a taylor series expansion of R (t) with the present epoch for this we will also need H_0. note the above line element in the first equation does not use the cosmological constant aka dark energy. This above worked prior to the cosmological constant Now for the departure from the linear portion of Hubbles law. [latex] v=H_Od, v=cz [/latex] when v is small. To this end we expand R (t) about the present epoch t_0. [latex]R (t)=R[(t_0-t)]=R(t_0)-(t_0)-(t_0)\dot {R}(t_0)+\frac {1}{2}(t_0-t)^2\ddot{R}(t_0)...=R (t_0)[1-(t_0-t)H_o-\frac {1}{2}(t_0-t)q_0H^2_0...[/latex] with [latex]q_0=-\frac{\ddot{R}(t_0)R(t_0)}{\dot{R}^2(t_0)}[/latex] q_0 is the deceleration parameter. Sometimes called the acceleration parameter. now in the first circumstances when v is small. A light ray follows [latex]\int_{t_1}^{t^0} c (dt/R (t)=\int_0^{r_1}dr=r_1 [/latex] with the use of this equation and the previous equation we get [latex]r=\int^{t_0}_t=\int^{t_0}_t cdt/{(1-R (t_0)[1-(t_0-t)H_0-...]}[/latex] [latex]=cR^{-1}(t_0)[t_0-t+1/2 (t_0-t)^2H_0+...][/latex] here r is the coordinate radius of the galaxy under consideration. Solving the above gives.. [latex]t_0-t=\frac {1}{c}-\frac {1}{2}H_0l^2/c^2 [/latex] which leads to the new redshift equation [latex]z=\frac {H_0l^2}{c+\frac {1}{2}(1+q_0)H^2_0l^2/c^2+O (H^3_0l^3)}[/latex] The last equation is the corrected redshift formula when recessive velocity exceeds c.. My suspicion is that you will match the linear portion from Hubbles law fairly close, but you will start deviating past Hubble horizon. PS most online calculators don't apply the corrections past Hubble horizon. Though the lightcone calculator is still to good approximation beyond Hubble horizon. It was compared graphically to the lightcones from Lineweaver and Davies. However it isn't 100% accurate either. Good luck and good job in requesting a comparison rather than stating your formulas is correct. Your showing proper methodology.+1 Oh I forgot to mention, it took me several years to find the corrections (last equation). Its not something included in the textbooks. Though they all state the cosmological redshift formula is only accurate when recessive velocity is small. I just wish I remember where I found those corrections. It was too long ago and I wrote them down in my notes but forgot to write down the source. (I saved the original paper I got it from on an old phone that died on me and haven't been able to relocate the original paper.) The source is somewhere on arxiv though. I only use peer reviewed sources I trust. Here is the paper we used for developing the lightcone calculator in my signature. http://www.google.ca/url?sa=t&source=web&cd=5&ved=0ahUKEwjG-_D-zJTQAhUC5mMKHcpMCOMQFggpMAQ&url=http%3A%2F%2Fwww.dark-cosmology.dk%2F~tamarad%2Fpapers%2Fthesis_complete.pdf&usg=AFQjCNHLzxKUp15sqgaDF2B8NU6i4xnBdg TM Davies. If you can match up with these lightcones your formulas are reasonably accurate.

Its a slightly different form in the first equation. However you will probably find this link helpful. http://web.mit.edu/~emin/www.old/writings/quantum/quantum.html If I'm not mistaken this relates to the first equation. I believe the first equation relates to the Heisenburg uncertanty. However my higher QM is rusty lol

that makes no sense, I think you better understand what a waveform means in physics. Might try starting with an electromagnetic wave.

incorrect this can happen in both the finite or infinite case.

Too close to flat, that it could be either negative or positive. Its that close that an exact determination is tricky. Though the datasets at present indicate a leanings towards the positive side. The best indicator is CMB distortions which is tricky to exactly determine

One day you will show how you derived the equations your posting. One doesn't just willy nilly new equations by simple replacement. Every equation you have posted for several months now is useless without showing how you derived them. In other words its been useless to merely post new equations. They have no meaning until you perform the taylor series expansion using kinematics and freefall motion. You have not shown a single corresponding geodesic equation of motion to even define your geodesic path. Which is of fundamental importance to relativity of simultaneaty. So how can you possibly conclude the above as being accurate? This has already been pointed out by Bignose. Try listening to what is being told to you. Do you even understand what |v| means ? it has specific meanings which you obviously ignored. As I cannot determine which usage your using. Choices are 1) absolute value: the magnitude of a real number without regard to its sign. Speed is the absolute value of velocity. If you have |v| as an absolute value then it has no direction. no longer a vector.. 2)determinant: determinant of matrix V 3)parallel: self explanatory 4)cardinality: the number of elements of set V none of these makes sense in your equation above Which is it? as your definetely not using the inner/outer Minkowskii dot product. Which you should be using.

Well there is alternate models where BB is a cyclic process of expand/collapse of our universe. In this scenario one can nearly remove the BB in a sense. It depends on how you define the BB in this case. LQC has a mathematical method to handle the singularity problem via "bounce" which is essentially the above. However as we cannot measure far enough back in time due to the mean free path of light prior to CMB. The mean free path was too short due to too much interferance from other particles (surface of last scattering). Hopefully if we can develop a reliable method of detecting neutrinos. We may be able to see much closer to the BB but not quite all the way as neutrinos dropped out of thermal equilibrium slightly later. Between this and LHC studies we can hopefully garnish a solution to BB

Absolutely, by the way I don't see anything outside of a common mainstream question so far in this thread. If you like I can move it to Astronomy forum but I'll let you decide

We can only conclusively confirm our observable portion. Due to lack of net flow either towards or inward flow, indicates via thermodynamic flow that the portion outside our Observable portion should be in roughly the same thermodynamic state. However we can't conclusively determine that. So yes the universe can be finite or infinite. The only viable means that I know of to determine one or the other is to solve the BB itself. We simply cannot measure the entire universe. Universe geometry isn't conclusive enough

light beams only return to origin on positive curvature. Fairly cut and dry, your back of the head scenario is only viable on that scenario.

It would never return in a perfectly flat scenario. Just continue a straight line path. A return path is only viable under positive curvature.

I believe there are others though less active lol. I'm still not positive on my interpretation of that paper. The spin statistics aspect is covered in numerous "Introductory to GR" textbooks. It is one of the lessons to learning GR. The chapter that covers this is usually under GR waves. What would really help on that paper is someone who better understands some of the gauge group symbology in that paper. Although I understand gauge groups to a certain extent. There is numerous relations symbols used on that paper that I don't recognize. More precisely two specific symbols. I'm not even sure I can latex them lol. Ah found them. [latex]\Upsilon, \Xi [/latex] they appear to be unique to this paper, collectively he has a group [latex]\begin{pmatrix}-\Upsilon&0&0&0\\0&-\Xi&0&0\\0&0&-\Xi&0\\0&0&0&-\Xi\end{pmatrix}[/latex] The majority of the rest is standard Euler-Langrange and Hamilton equations so those parts I'm familiar with. For your benefict "Introductory to Langrange mechanics" http://www.google.ca/url?sa=t&source=web&cd=1&ved=0ahUKEwifs6zvno7QAhVL6WMKHSogDIoQFggaMAA&url=http%3A%2F%2Fwww.macs.hw.ac.uk%2F~simonm%2Fmechanics.pdf&usg=AFQjCNHZnAntVnyYJnhX0bQrDFbA6n46QA as Dirac was mentioned some of the Dirac notation is used. http://www.google.ca/url?sa=t&source=web&cd=13&ved=0ahUKEwjH1PGnoI7QAhUK0WMKHX1mCeoQFghAMAw&url=http%3A%2F%2Fwww.users.csbsju.edu%2F~frioux%2Fdirac%2Fdirac.pdf&usg=AFQjCNEv9MysNDmO-XWbIhz6QftvngBTWA Another required study to understand paper is Hamilton. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0ahUKEwihgu--oY7QAhUDxGMKHXwLCLoQFggaMAA&url=http%3A%2F%2Fwww.damtp.cam.ac.uk%2Fuser%2Ftong%2Fdynamics%2Ffour.pdf&usg=AFQjCNE1AIMv-gse0hNgko8_XvYxW2RXHA Naturally you need a good understanding of tensors. The majority of that paper is fairly decent. The problem I'm having on full comprehensive understanding of it is the group above. Though those details are likely within the paper itself but I would have to study it in greater detail to know for sure.

Well I will be the first to admit that philosophy isn't my strong suit. I'm not sure what you mean by cover up. Anyways I spent some time studying numerous block style arguments. There is numerous key aspects shrouded by those articles. For example determinism and reversible processes. Yet when I mention those aspects, they were either ignored or split off... Much like presentism isn't compatible with relativity. Block itself doesn't work well with "probalistic observers". This is a specific observer used in evolving block. Which isn't identical to growing block. All of this put aside, as an off and on assistant instructor. I found my students "light bulb go on" when you detail the thermodynamic aspects of GR. Proper understanding of the ideal gas laws in GR removes the majority of the mystery behind spacetime curvature. Its too bad many forum members ignore this truth. Not just this forum, for some mysterious reason thermodynamics is too mundane a topic. They rather have the mystery. Little hint, if you truly want a comprehensive knowledge of block arguments, study the terminology including those relating to key thermodynamics. Quite literally when I read terms such as deterministic, reversible and irreversible processes etc. I literally see the related formulas. Lol what I find truly amusing, is that I posted some mathematics showing how Lorentz Ether could viably work under. Yet it 100% ignored. Imagine that.....so much for properly examining the two models... Lorentz ether vs SR ah well. You once mentioned that the mathematician in me interferes with understanding block. Quite the opposite, it allows me to better comrehend block and discern the quality of various papers on the subject.

If the universe has a slight positive curvature. Two parallel light beams will gradually converge. The light path will not be straight but slightly curved. A perfect flat universe, the light beams will stay parallel. In a negative curvature the light beams will diverge. Now assuming expansion stopped, with the current miniscule deviation from a flat universe in the Planck dataset. If you fire an ideal laser beam. It would take roughly 880 Billion light years for the laser beam to return to its original point. Of course we know its highly unlikely expansion will stop lol. Key note, at one time it was once thought that if you have a positive universe, the universe would be bounded. This however isn't true due to the cosmological constant. The universe can be bounded or unbounded.

I like the form you use of that equation, there is another form from Ryden that I find more useful. For other readers I will detail the equations with some explanation. First thing to understand is that the critical density formula and the one posted by Imatsfaal is the GR aspects of the FLRW metric, Other key aspects is the acceleration equation and the ds^2 line element of the metric. However for this post I'm just going to focus on the two equations posted above. Essentially those two equations are derived by inserting the Einstein field equations into the FLRW metric. This is for all contributors (photons, matter, radiation etc). So first we replace [latex]\rho(t)[/latex] mass density with energy density in the form [latex]\epsilon(t)/c^2[/latex] the GR form of the Freidmann equations is in the Newton limit in GR, this is low gravity such as stars, galaxies, LSS etc. It is a specific class solution in GR. This gives the form of [latex](\frac{\dot{a}}{a})^2[/latex][latex]=\frac{8\pi G}{3}\frac{\epsilon(t)}{c^2}[/latex][latex]-\frac{kc^2}{R_0^2}\frac{1}{a^2(t)}[/latex] If [latex]k\le0[/latex] and the energy density is positive, then the R.H.S of the last equation is always positive. This is an expanding universe that will expand forever. If matter is the dominant form of energy, as opposed to radiation this implies [latex]\epsilon\propto \frac{1}{a^2(t)}[/latex]. If k=+1 then the R.H.S must eventually reach 0, after which the universe will contract. To get to the density parameter we can substitute [latex]H(t)=(\frac{\dot{a}}{a})^2[/latex] and we can rewrite the above equation into the Hubble parameter. (note I hate calling it constant, as its only constant at a particular moment in time) [latex]H(t)=\frac{8\pi G}{3}\frac{\epsilon(t)}{c^2}[/latex][latex]-\frac{kc^2}{R_0^2}\frac{1}{a^2(t)}[/latex] if k=0 then [latex]\rho_c(t)=\frac{e_c(t)}{c^2}=\frac{3H^2(t)}{8\pi G}[/latex] with the following density parameter relations [latex]\Omega=\frac{\epsilon}{\epsilon_c}=\frac{\epsilon}{c^2}*\frac{8\pi G}{3H^3}[/latex] note how we correlate the constant c in the the above. The cosmological constant isn't included in the above, essentially the Cosmological constant leads to an increase rate of expansion from the above relations. Also as it is constant as far as we can tell, this universe will continue to expand. This is what I should have taken the proper time to post. Again thanks Imatsfaal for catching the above. Busy work week lol The thermodynamic details take a bit to explain but from the above and using the equations of state for each contributor one can determine the deceleration equation. Wiki has a decent enough coverage. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) https://en.m.wikipedia.org/wiki/Friedmann_equations