Mordred

if you have zero expansion and nothing travels faster than c. The observable universe would be the Hubble horizon. Which is c×age of universe. However we have expansion so the observable universe is larger.

I'm not too sure. You might try Sloan sky survey

Ok first off you need to look at how v_rec is defined. [latex]v_rec=H_od [/latex] so if you have no expansion H becomes zero and so does the recessive velocity. Now in a static universe with no recessive velocity. The observable universe would be defined as c*age of the universe. This is the Hubble horizon where the recessive velocity equals the speed of light. (keep in mind this depends on seperation distance from the observer to horizon). Now recessive velocity does not state the speed of light is greater than c. The speed of light stays constant. The peculiar velocity of the object being measured decreases the closer the observer gets to the object. See formula above. Light beyond Hubble radius where recessive velocity 》c doesn't go faster than c to reach us. It still travels at c. So how does it reach us? This is where you have to recognize that peculiar velocity depends on the distance of separation from the emitter and observer. If you change the observer to one that is beside the light ray. There is no recessive velocity. Locally to the leading edge of the light path the rate of expansion is a measly 70 km/sec/Mpc. Light has no problem transversing this change in distance. Now due to expansion both the path ahead and behind the leading lightray edge increases. This leads to the Cosmological redshift. Its unfortunate Hubble used the term recessive velocity. The terminology leads to confusion. Would have been better to call it Hubble recession.

Recessive velocity in Hubbles law is an apparent velocity. Its a consequence of the formula used and the seperation distance to the observer. Locally though a galaxy gains no momentum due to expansion. Though the distances between two galaxies does increase which gives the illusion of inertia if you look at how Newtons laws of inertia work and consider a uniform fluid with a uniform pressure surrounding a galaxy. Then realize a body in space requires a difference in force upon a facing, we can't apply Newtons laws of inertia to galaxies. For that matter we can't even state expansion is due to pressure. This requires a difference in pressure from one region to another. A good paper covering the seperation distance details is http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell Dr Powell is a professor in Philosophies of Cosmology. His specialty is inflation, though he used to visit forums and wrote the above article with forum members in mind.

Here is the paper. http://www.google.ca/url?q=http://ciencias.bogota.unal.edu.co/fileadmin/content/oan/documentos/maestria/documentos/Cosmologia.pdf&sa=U&ved=0ahUKEwi6he_E-f_NAhVS82MKHYbhDh4QFggbMAM&sig2=iydAcDLIS7F_DZDWkLB2ew&usg=AFQjCNFVBsrWlemsOxVudLQqjXhJTbuSrw here is a counter paper... http://www.google.ca/url?q=http://arxiv.org/pdf/0911.3536&sa=U&ved=0ahUKEwi6he_E-f_NAhVS82MKHYbhDh4QFggSMAA&sig2=mBEbBM8SOGCcLnwoqkmypg&usg=AFQjCNH9F3gn0P4YiZ_m0R0A3HxQklldGg I wouldn't let the fate of the universe bother you. The heat death fate is based on the assumption that the present dynamics will always hold true into the extremely far future. Science uses all forms of light not just visible light. However you can look at the wavelength range for visible light. Then calculate the redshift to find when visible light will no longer be visible.

the CMB surface of last scattering is z=1100. However thats roughly 3 times the length of Hubbles radius. Its also referred to the cosmological event horizon (Observable universe which requires expansion in the commoving frame above). However to get an accurate distance you need the last formula I posted. this makes no sense sorry. Particularly since new space means new volume. Which means expansion. Remember your coordinates I really don't think you want to get into particle spin statistics. The terminology in the last quoted section is sheer gibberish. I strongly suggest studying how the equations of state of various particles influence expansion. Rather than make a fool of yourself that is... Oh by the way just so You can read a Peer review showing the first redshift equation as only accurate at close distances where v is much less than c. http://arxiv.org/abs/astro-ph/?9905116 "Distance measures in cosmology" David W. Hogg keep in mind Hogg's skipped numerous steps. He is also highly cited for other redshift works. One is trying to show cosmological redshift as gravitational redshift. (the method requires endless microsteps) the cosmological redshift with corrections is far more flexible and simpler. As I mentioned equations of state... here is another workup I did on another thread. What the above correlates to is particle degrees of freedom. One can calculate how much influence any particle with known properties influence the temperature... pressure... expansion relations. Provided one knows the correct correlations to the Einstein field equations. (the above can and does affect geodesic equations. Which in turn can and does affect redshift to distance calculations) So to that end a sample of how to define a geodesic may be handy. For that Im going to cheat again and use a previous post... Starting to see how I mean when I say your 90 page paper lacks the required mathematical weight?????? 😉

Weins Displacement law has more to do with the original emitter frequency. Which correlates back to hotter temperatures in the past. Anyways lets look at your questions above in more detail after. lets 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]

very good now were moving forward. You can't assume a static measurement or a non static. example if 32 Gly is wrong. Then the age value of 400 years after BB is also wrong. This could very well mean the value 13.4 Gly is also wrong.... It would mean that all Lyman alpha forest data for that sector is also wrong. see where Im going on the dangers of assumptions? another common method is luminosity to distance measurements. You will eventually need to adress these as well as they involve redshift. To assist you. Historically speaking Scientist once assumed no signal can go farther than Hubble distance. Yet when we first dicovered objects lying outside Hubble distance the scientific community went up in an uproar. What tests were involved that changed their minds. (redshift error was first called into question) What tests did they need to perform to confirm it wasnt a redshift error? Edit there is another hickup I forgot to mention. For Gn-z11 is 32 Gly the commoving distance or the proper distance? piece of advise start with learning how this equation which includes GR and thermodynamics influence the light rays worldline. (All redshifted lightrays follow worldlines) In the FLRW metric the worldline is the line element ds^2 [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] Note a redshift worldline is a null geodesic. Which is different from the normal infalling matter geodesics. I also recommend you graph your model vs the Standard model redshift. Distance vs redshift up to z= 1100. In proper distance not commoving distance. Which means you will need to convert the line element above to proper distance... THIS EQUATION CANNOT be used beyond Hubble sphere. [latex]1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}[/latex] I will post the correct equation beyond Hubble sphere. (When I work up how the first equation is derived. In Order to explain the new redshift equation beyond Hubble sphere.....) When I work up the two redshift equations. I hope you see your paper has the wrong equation being examined

You need to find a way to show how your model can account for the redshift values beyond Hubble sphere. There have been dozens of Galactoeccentric models that have used similar arguments that you have used. those models also stopped when v is less than c. Those even when peer reviewed didn't go anywhere. The scientific community essentially ignores them. They dont show what is needed. The math in them is more advanced than what you have. So if their papers didnt cut it..... The other problem is even photometric evidence shows an expanding universe without doing a single redshift calculation. For example did science stop at merely calculating the distance to Gn-z11 just using redshift? What other tests did they do? Why is it such a luminescence galaxy? What type of stars populate that galaxy? Most importantly what is the average plasma temperature. (this affects redshift wavelength). Hence posting Weins Displacement law earlier.

no you haven't lost us. Your not doing the necessary steps that are required to properly test your theory with observational data. Sorry but your not. For reasons Ive already given. You seem to feel science states a certain distance based strictly upon redshift beyond Hubble sphere. Yet redshift is merely one rung on the cosmic distance scale. Other rungs include Tully-Fisher, Extragalactic parallax, Luminosity-distance D-q function angular diameter distance etc. You assume a static universe. Fine but the rest of the scientific community disagees with you. You need to prove them wrong. With the correct math. You dont have the correct math unless you can prove Hubbles law is wrong. distances beyond Hubbles sphere for greater than c recessive velocity has been confirmed by more than method. Other than just redshift. All you have to do is look for redshift calibration papers to see this. Yet you assume your static universe and wont show how greater than c recessive velocities are solved via your model other than assumption of a distance based on a static universe assumption

you still miss the point. You need to mathematically prove the 32 Gly as wrong. why do we measure that distance using both redshift and angular diameter distance? Show us in the math.

your model isnt particularly testable for observation reality. Take for example GN z11. You believe your answer of 13.4 Gly is correct. Yet the professional community finds the distance as 32 Gly. So I asked you to show how your model accounts for this. You still haven't shown how your model accounts for this Hubble illusion. This is the part you keep denying. Quite frankly if you want to convince anyone we have a static vs an expanding universe. You need to mathematically show greater than c recessive velocity and explain why temperatures drop in a static universe. Until you do so Your model won't work After all the whole point of your model is to prove a static universe. You don't do this by assuming static distances ie 13.4 Gly is correct. When we measure 32 Gly and you ignore the observational evidence and use an assumed 13.4 Gly as being correct. Not without showing how the 32 Gly is wrong. Via the mathematics Quite frankly not accounting for mrasurement data beyond Hubble sphere isn't going to work.

you need to prove Hubbles law and recessive velocity in excess of c is invalid. Not just ignore it like you did the thermodynamic data. You gave 13.4 Gly in your paper. Not 32 Gly which science states. Unless I'm mistaken the title of this thread is. "Is the Hubble shift an illusion" I would state my question applies. (rather convenient to ignore counter arguments and data then claim you have a valid solution) lets see. You ignored thermodynamic. You didn't account for curvature. You werent aware that both observer a and b measure a slowing of each others clocks. Your now ignoring Hubbles law and recessive velocity greater than c. What are you going to ignore next?

you still cant show recessive velocity which is an occurance of Hubbles law in excess of c. Not without expansion which correlates to conformal time. Yet we see objects beyond Hubble horizon which c*age of the universe. This is what you need to show. How does your model account for greater than c recessive velocity measurements. Ok lets put into perpective. Your an observer sitting on Earth. You measure the recessive velocity of galaxies in the following relation. (You dont care what mass those galaxies are.) [latex]v=Hd [/latex]. regardless of mass of each galaxy this same relation holds. Yet your gravitational potential on Earth is unchanged. So how do you get recessive velocity greater than c using SR and without expansion? thats your challenge to show

no your trying to replace Cosmological redshift with gravitational redshift illusion. YOUR TRYING TO MODEL A STATIC UNIVERSE. So show recessive velocity greater than c without having expansion

repeating these assertions isnt going to help. Were all aware how spacetime works. The problem is your trying to equate all forms of redshift with an illusion of expansion. I gave you specific examples where this is not the case. Go ahead mathematically take two galaxies of equal mass seperated at a distance greater than 4400 Mpc. Where recessive velocity is greater than c. Try and use the Lorentz time dilation formula to show a recessive velocity in excess of c. Gn-z11 for example. Ill provide its recessive velocity for you. Works out using redshift 11.04 to be approximately 2.11 c. How do you explain that (math required) under your static model?

the reasons above is precisely why scientists don't rely strictly upon redshift. Take a galaxy moving toward us. With an unknown mass. which portion of the redshift is gravitational, Doppler or Cosmological? without further data you can't isolate the individual influences. the problem with your paper is your trying to describe all 3 at once. Which isn't correct. key example Andromeda. Its moving towards us. It has no cosmological redshift as its gravitationally bound into the same large scale system as the Milky way. yet inside Earths gravity well we measure a blueshift. Not a redshift. Believe me Ive done this one in a lab with the right equipment. The university I went to has a telescope and the necessary equipment attachments. What makes it worse is Amdromeda isn't headed straight for us. So you need the transverse doppler. Filtering out the dipole anistrophy for the Milky way and Earths movement is also an incredibly painful process.

no problem thats a reasonable request. take two systems of equal mass. Label them system a and system b. light redshifts as it climbs out of a gravity well then blue shifts as it falls into gravity well b. In a static non expanding universe this means both system a and b are in the same reference frame. (equal mass systems). no time dilation is involved no resulting redshift total. change in blueshift=change in redshift. now add expansion measured from those same systems. the wordline is stretched because the actual distance between a and b changes. Though neither a or b gain inertia. Recessive velocity isn't inertia. As the gravitational potential of neither a nor b has changed we should measure no gravitational redshift. Yet we measure cosmological redshift

of course you are. where do you think length contraction occurs? yeah so am I. which has nothing to do with cosmological redshift

lol most of the paradoxes in Relativity comes from SR limit. To stress Ajbs comment

man talk about denial go ahead believe whatever illusions you want. However if you want serious consideration of your paper. Then you will need the Scwartzchild metric and GR. Not SR

the problem is SR doesn't show the geodesic worldline paths. You need GR for that. The formulas in your paper is SR limit. The other problem is Hubbles law "the greater the distance the greater the recessive velocity." [latex]v_{recessive}=H_oD [/latex] isn't a true velocity.

thats one of those funny aspects of Relativity between Alice and Bob. Just comparing clocks between Alice and Bob isnt enough to define which observer is inertial. Which is a limit of SR as well. The SR equation places either the primed or unprimed observer at rest. This is where GR takes over for a moving observer. Or observer in a gravity well. For that you need curvature to describe the differences in geometry. SR works with Eucludean flat geometry. Newtonian weak field limit. It doesnt work to describe different wordlines. This is where you can use the Schwartzchild metric. or if you want rotation of the gravitational body. The Kerr uncharged metric

see my last example. You keep working with the mistaken assumption that Cosmological redshift means time dilation. my last example on cross edit will show this error. The problem is you keep trying to deny counter arguments based on your intuition rather than the science. I already proved we have expansion by thermodynamic evidence. Now Im showing you your errors on redshift itself

You dont describe relativity from a gravity well without curvature. That claim alone calls into question your math. The Einstein field equations work extremely well for global as well as local influences. Once you understand it. There isn't any significant time dilation for Andromeda from an observer on Earth. I all honesty I wonder if you fully understand when and where time dilation will occur. Sure there is some near Earth or near Andromeda. However its like worrying about the time dilation between your head and feet. Yes its there but it would take a thousand years to measure a significant change. The other problem is no observer will measure another clock going faster. alice and bob. each has his own clock. Bob is moving near c. Alice is static. if both Bob and Alice compare clocks. Both Bob and Alice will measure the same time dilation. Alice will see Bobs clock slow down. Bob will see Alice clock slow down. This also applies to length contraction of the worldline. Your paper claims one observer will measure greater distance while the other a shorter. Thats not how relativity works here. you can check yourself. "How it can be that both observers measure slower rates on the other's clock" https://www.google.ca/url?sa=t&source=web&rct=j&url=http://cosmo.nyu.edu/hogg/sr/sr.pdf&ved=0ahUKEwj-mfSrqPjNAhUY_WMKHS13C2MQFggbMAA&usg=AFQjCNG0nnnDOp0GWpXQnmUs_m3TcbUF8w&sig2=hHPb0pygO6NKrDfqkwdpPQ Now next scenario a light ray emits from a star of the same mass as our sun. lets assume a static universe. the light is redshifted as it climbs out of the stars gravity well and blueshifted the same amount at our sun. No time dilation. there is no difference in gravitational potential. Now add expansion. We don't need to change gravitational potential of either star. Yet we measure a Cosmological redshift. Not a gravitational redshift.