Mordred

Still waiting for you to show a homogeneous and isotropic expansion along with the fluid equations. That little equation is virtually meaningless and doesn't even describe gravitational redshift let alone any redshift.

Maybe you should read "time before time" https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/physics/0408111&ved=0ahUKEwiiuY_G4avQAhUKyWMKHXWwBbUQFggaMAA&usg=AFQjCNEAMlxtQFxQLl2b3S42gYPjn7fezw But in point of detail the BB model only starts at 10^-43 seconds. It only speculates before that.

Leading order. https://en.m.wikipedia.org/wiki/Leading-order_term follows from [latex]z=v/c+O (r/R)^2)[/latex] Your better off using the Hogg's equation that one was an older variation. https://en.m.wikipedia.org/wiki/Order_of_approximation here is further information on order of approximation. Here is a simplified papers discussing orders of approximation on redshift. http://www.google.ca/url?sa=t&source=web&cd=5&ved=0ahUKEwi3qZ7wx6vQAhUS2mMKHVA0CwgQFggpMAQ&url=https%3A%2F%2Farxiv.org%2Fpdf%2F1405.0105&usg=AFQjCNHtf3P8I-w61jkgeLzwoEwP-S6-bg By the way not a dumb question its very pertinant to the discussion +1

those degrees of freedom correspond the the fermi-dirac and Bose-Einstein statistics which involve the Boltzmann constant. They are not unimportant bugs, but of extreme importance. Don't base your arguments simply on trying to justify your simplified equations. Those equations at best have limited use. Those limits can be greatly increased by the additional details your choosing to ignore. For example earlier I posted the corrections to the redshift formula beyond Hubble horizon. I could not do that without those degrees of freedom. I showed you those corrections do you recall this? 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] Its amusing though, you posted the equation I hinting at on the other thread that I stated I would show later as I wanted you to think about it. This is the Hogg's equation I was referring to [math]t_l=\frac{1}{H_0}\int_{0}^{z}\frac{dz'}{(1+z)\sqrt{\Omega(1+z')^3+\Omega_k(1+z')^2+\Omega\Lambda}}[/math] Bunn and Hogg's are two of the leading experts in the kinematics of redshift. They find these details important. That should be a strong indicator that they may just be important after all. In point of detail the statistical mechanics of thermodynamics require those details to calculate the rate of expansion at a given redshift. Little off topic but you can also calculate the number density of each particle with those two statistics at top of page. Though it's far easier to apply Gibb's law. Those bugs are used to determine How much influence each particle has on Omega. Its simplified under your FLRW fluid equations. However those equations were calculated using the statistics mentioned above.

Specifically when expansion becomes Lambda dominant from matter dominant and we entered the Lambda dominant era.

Yes but this is under seperation distance treatment not expansion per Mpc

You have to study the deceleration equation itself to see the difference. For example at the time of CMB. For every Mpc the rate of expansion given by H was over a 1000 times the Hubble value today. Please read those articles particulatly the one done by Brian Powell. It clearly shows the distinction.

In QM an equation isn't complete until you apply relativity corrections lol. Quantum your making a lot of baseless assertions. Honestly bud you should really sit back and study the basics first. Ask questions but don't make assertions. This thread will be more productive if your asking instead of falsely asserting

First off throw away thinking of space as anything other than volume change. Secondly the acceleration of space is something of a misnomer. In point of detail the rate of expansion per Mpc is slowing down not accelerating. The acceleration portion is the seperation distance based on one formula for recessive velocity (which is not a true velocity but an apparent velocity) v=Hd. There is no centre of expansion, there is no inside or outside of the balloon, those analogies were never intended to define expansion. Its only intention is to show a homogeneous and isotropic geometry change of the dots on the surface of the balloon. (all points expanding equally without change of angle) please read these two papers on the above. 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

Even with years of study, one still makes mistakes. Which is something I discovered reviewing the Higgs field last night. Still kicking myself on that lol. Strange earlier posted one of the better sites to understand wave particle duality. However it takes reading each individual article on that site. As he has taken key lessons and seperated them. This particular page included. https://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/7-particles-are-quanta/ Read the entire site but this article is of particular importance.

The terminology in block is "presentism" and eternalism or on evolving block probalistic observer. Ask the ppl that developed block why there is no "relativistic presentism". Perhaps there is something your missing in their arguments. Maybe just maybe the purpose of block is to discuss absolute time vs relativistic time and not preferred observers. Which is what it seems you've coined under relativistic block. After all block specifically discusses the philosophy of time. There is only two possibilities in regards to time. Galiliean and relativity. So why introduce an ad-hoc self made up term such as relativistic presentism? Point being if your going to discuss a philisophical or mathematical theory. USE THE PROPER terminology those theories use. Not made up garbage. The two terms side by side is contradictory. Presentism and relativistic. Presentism doesn't acknowledge another time other than the observers present. Eternalism does. That is plain and clear in block papers, Hence we come full circle back to this. Presentism states only here-now is real which is contradictory to relativity as per above. Placing relativity with presentism is a conflict in terminology. Hence relativistic presentism is a contradiction on the two terminologies. Presentism is like saying "my present" sitting at 1530 ft above sea level is more real than your present where ever you are. Under Galilean both locations are equal under time. Not so in relativity which tells us each location is equally real even if we have different coordinate times. Lorentz ether tries to place the Ether as the only true here-now present. As the only true proper time. Presentism in this case, the here-now observer is the ether frame. (Priveleged observer). So how can you accurately state "relativistic presentism" ?

We even have a satellite dedicated to testing that curvature. However freefall under GR doesn't involve a force. The equivalence principle is inertial mass is the same as gravitational mass. Which isn't the same as saying gravity and acceleration is the same thing. An accerating frame is not an inertial frame. Acceleration causes rapidity under GR.

Its amazing that people that quote famous people. Don't follow in their footsteps. Where is your math? these famous people knew and used math. Including Galileo. He also looked for evidence long before he made known his discoveries. Not make his claims first then looked for evidence.

yes but this equation is usable regardless of the curvature constant and regardless of era. Ie matter dominant vs Lambda dominant which has two distinct expansion rates. [math]t_l=\frac{1}{67.9}\int_{0}^{z}\frac{dz'}{\sqrt{{(1+z'){0.307(1+z')^3}+0.0013(z+1')^2+0.693}}}[/math] The detail your missing is that those extras your complaining about gives us greater flexibility. Instead your shrugging it off as ad-hoc fitting. The equation above accounts for the evolution of matter, radiation and the cosmological constant. Which the other equations do not. PS don't flip the sequence under the sqrt. The third term is in the wrong order. Doesn't make much difference on this case, but its a bad habit that can confuse when you run a lot equations in one sitting. [math]t_l=\frac{1}{H_0}\int_{0}^{z}\frac{dz'}{(1+z)\sqrt{\Omega(1+z')^3+\Omega_k(1+z')^2+\Omega\Lambda}}[/math] The key point is this equation works for any value of H_0 or % of influence matter,radiation or Lambda has at any time

yes the Lorentz transforms only affect the x axis (assumed direction of motion) and the time axis ct. So we graph the x and axis and use trig for the rotations. For example on the last diagram. It shows the turnaround stage on the hyperbola. For calibrating two observers S and S' we shift the axis themselves. Axis rotation You can find the procedure here. Notice the shift in the ct' axis on the figure 3. http://www.google.ca/url?sa=t&source=web&cd=2&ved=0ahUKEwjby5jS36jQAhXC0FQKHaZKBQ0QFggcMAE&url=https%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F0703002&usg=AFQjCNH0WYF7gsM-vW-D0_w7iNx2VXyj3A This is probably closer to what your after with two inertial observers. The link above will show how to use two observers in the spacetime diagram on calibrating the two observers to the type of daigram above. See the "calibration Hyperbola" figure 3 here. from this site. http://www.scholarpedia.org/article/Special_relativity%3a_kinematics#Graphic_representation_of_the_standard_Lorentz_transformation

This will help save some time while I look for better coverage. http://www.as.utexas.edu/astronomy/education/spring06/komatsu/secure/lecture10.pdf essentially light-cone causality as per the images here http://plato.stanford.edu/entries/spacetime-singularities/lightcone.html This one might be a little too advanced. http://www.rpi.edu/dept/phys/Courses/Astronomy/CurvedSpacetimeAJP.pdf Try Kruskal diagrams If what I understand your after is accurate. Each event coordinate has its own causal connection. This is represented by seperate lightcones at each coordinate. In flat space the lightcones has an even distribution and same orientation. In curved space the lightcone distribution becomes more dense as per the individual event coordinates and will change alignment. The first image would be improved by showing the proper alignments. However think of tilted hourglasses. One can find decent coverage of this typically in Schwartzchild metric articles that go into the more advanced coordinate systems. Though I find the Penrose diagrams rather tricky to explain. By the equivalence principle these diagrams are equivalent for inertial observers and gravitational observers. The image here on this site shows a better representation of the lightcone orientation. https://en.m.wikipedia.org/wiki/Light_cone

point taken on the philosophy discussion.

Is that not the same thing as "something you made up ?. How am I confused on that detail? The point being you pick up any "block paper" you won't see that terminology used in any paper.

Well At least your font choice is getting a little easier on the eyes lol. I'm also getting a better handle on the aspects your getting at. The problem it appears your having is not really understanding gravitomagnetism which is a valid field of study. It provides key lessons into understanding GR itself. For example the lesson I posted in my last post itself. Did you understand what I meant by gravity isn't "coupled" to electromagnetism? Please elaberate on what you understand on that statement.

I read the thread that led to this question. Give me a bit to find a decent example with an explanatory. Most of the examples I have are in textbooks. http://www.scienceforums.net/topic/100658-simultaneity-split-from-is-time-real/#entry955873 Just to clarify your looking for one that specifically shows the following ?

I agree +1

I'm glad I read this before answering the other thread. I'll dig up a good example diagram for the other thread as it pertains to this one.

exactly. Excellent elaberation. Thank you for the above commentary. Those philosophy threads I enjoyed. Its nice getting into a well rounded debate. It also served to remind me of the issues others have in understanding spacetime. So in that regard I too found those threads useful.

Not really confident on that, not enough to move this thread. I'll let one of the more experienced Moderators make that choice lol. I'm only a sort of Mod with limited powers lol. Resident experts can move threads when appropriate.

! Moderator Note moved your thread as per request. above to the correct forum