kawiusz Posted November 7 Posted November 7 (edited) Programmer is running a simulation of expansion with almost arbitrary scale factor function. The only constraint is its monotonical increase, so there is no collapse. The simulation has a variable time step with the changing length of the increasing period of the expanding wave of a single photon. Its period is proportional to its wavelength. In each step, the photon moves by the length of its own wave expanded in this step, and its distance from the source is expanded by the same factor. The simulation consists of N steps. For the programmer who started the simulation, it lasted for a time equal to the sum of N various time steps. How much time has passed for an observer living in the simulation, who fired our photon with an initial wavelength of L0 at the start, and what is the distance separating the observer from the photon in his reference frame after N steps, if the final wavelength is LN−1 ? I came to conclusion, that time that has passed for the simulated observer and the distance from the photon in his frame are independent of the history of expansion. To calculate how much time has passed for the simulated observer in each time step, its length must be multiplied by the value of the cosmological time dilation of this step equal to the reciprocal of the extension of the photon wave period, i.e. the reciprocal of the extension of the same time step. The result is always a unit of time, because the extension of the time step equal to the extension of the wave period cancels out with its own reciprocal. This means that N equal units of time have passed for our observer regardless of the history of changes of the time step. During the simulation, the photon has moved away from the observer by a distance of N extended lengths LN−1 of its final wave regardless of the history of changes in this length. That's why the observer's time and the distance from the photon will always be identical regardless of the history of the expansion. Where is my error? I don't need an answer from anyone who denies cosmological time dilation. Edited November 7 by kawiusz
Mordred Posted November 7 Posted November 7 (edited) The error is not looking at the equations for time dilation nor looking at the distinction when the recessive velocity exceeds c. In cosmology cosmic time (proper time for commoving observers) follows the scale factor via an affine connection to the scale factor. Try looking at the equations of the FLRW metric which uses GR not some home brewed calculation. For starters you didn't mention to which Observer nor did you even mention the Lorentz transformations with the gamma factor nor the FLRW metric. Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 (edited) [math]L_{N-1}/L_0=z+1=1/a(t_{emit})[/math] Please, try not to ask "so what?". I don't see the limitation for the expansion rate nor the limit for the relative velocity in this simulation. Superluminal velocity is the effect of the expansion of space between the photon and the emitter. What's your formula for the cosmological time dilation? Haven't you noticed the one I've used? You've added this after my reply: "For starters you didn't mention to which Observer nor did you even mention the Lorentz transformations with the gamma factor nor the FLRW metric." How many observers do you have in this simulation? Lorentz transformation and the temporal and spatial changes of metric are expressed by the redshift, the change in wave's period and the time dilation. Edited November 7 by kawiusz
Mordred Posted November 7 Posted November 7 (edited) Won't have range using the above you will hit infinity at the Hubble horizon where recessive velocity exceeds c. This has been examined numerous times. One of the easier to understand examinations https://arxiv.org/abs/astro-ph/0310808 Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 I will hit infinity when the double type exceeds its range. Please, don't answer if you don't understand the question. -2
Mordred Posted November 7 Posted November 7 (edited) No offense but I have degrees in Cosmology it is my profession please listen to what is being described to you and read that link for starters. Secondly any member can participate regardless if whether you like the response or not. Your equation does not take into consideration the equations of state nor the acceleration equation of the FLRW metric. Your simulation doesn't match how our universe expands nor calculates it's expansion rate so comparison is incorrect. 20 minutes ago, kawiusz said: I will hit infinity when the double type exceeds its range. Please, don't answer if you don't understand the question. Still not enough range and the fact your twice the range tells me your doing SR in a non mainstream fashion ie not following the Lorentz transformations. Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 (edited) I suggest you read it first, find the formula for the cosmological time dilation and paste it. Don't edit your answers after you were replied. "Still not enough range and the fact your twice the range tells me your doing SR in a non mainstream fashion ie not following the Lorentz transformations." Check what is double precision data type. "Your equation does not take into consideration the equations of state nor the acceleration equation of the FLRW metric." Which equation? Edited November 7 by kawiusz -1
Mordred Posted November 7 Posted November 7 No your not using msinstream physics nor mainstream SR so its pointless. Tell me what velocity are you using obviously your not applying recessive velocity \[v_{R}=H_oD\] in order to apply the lorentz transform so your not using SR let alone GR.
Mordred Posted November 7 Posted November 7 Your wasting ours if your here to state mainstream treatments are wrong and refuse to take the time to understand where your error lies when members show you the mainstream examinations. As you hit your 5 day limit I won't expect a reply till tomorrow. Take the time to read the article. Otherwise it's pointless for this thread to continue. If you cannot accept main stream physics responses then this thread If anything belongs in our Speculation forum and if you prefer attitude over learning will likely end up being locked.
kawiusz Posted November 7 Author Posted November 7 I repeat: you read it first, find the formula for the cosmological time dilation and paste it. -1
Mordred Posted November 7 Posted November 7 (edited) There is no formula for cosmological time dilation not any SR based formula pure and simple. Cosmological time affinely connected to the scale factor under GR Newtonian weak field limit. If you read the article those formulas are contained within it. It clearly shows where precisely SR breaks down and also shows GR alone doesn't fully describe the FLRW metric. So don't ask for a formula that doesn't exist. \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] proper time for commoving observers for cosmological time in the FLRW metric is this term \[-{c^2}d{t^2}\] Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 Read it again. You'll find it eventually. Read it 100 times more if you have to. Don't edit your answers after you were replied. -1
Mordred Posted November 7 Posted November 7 (edited) try answering direct questions. what velocity are you using to apply the Lorentz transformation ? how are you factoring in length contraction ? or did you forget about length contraction ? which is part of the Lorentz transformations Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 (edited) Velocity of what? Lenght contraction of what? Edited November 7 by kawiusz
Mordred Posted November 7 Posted November 7 (edited) 6 minutes ago, kawiusz said: Velocity of what? Lenght contraction of what? Do you not know SR to even ask that ? Are you serious ? \[\acute{t}=\gamma(t-\frac{vc}{c^2})\] \[\acute{x}=\gamma(x-vt)\] Are you not familiar with this ? what velocity are you using to supply v to those equations? Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 How many observers do you have in my simulation to apply the Lorentz transformation between them? One! Think! Don't edit your answers after you were replied. -1
Mordred Posted November 7 Posted November 7 if you ever do latex you need to edit to fix the latex. If your only applying simply one observer your examination is automatically wrong as any metric must be applicable for all observers.
kawiusz Posted November 7 Author Posted November 7 Think about what you wrote. If it's applicable for a million observers it's also applicable for one.
Mordred Posted November 7 Posted November 7 this is pointless quite frankly I'm reporting this thread for moderation. I'm done listening to garbage responses when its clear you cannot answer direct questions. What velocity are you applying to use the Lorentz transformations and where is your Length contraction which will reduce the separation distance to zero when v=c
kawiusz Posted November 7 Author Posted November 7 What is contracting if there is only one observer in the expanding universe? How do you want me to apply Lorentz transformation to a single observer? My responses are not the only garbage in this thread, mister. -1
Mordred Posted November 7 Posted November 7 (edited) oh my so your telling me your lecturing me on how SR works with velocity which follows Galilean Relativity taught in high schools with the sole exception to the γ c and do not understand it applies to any NUMBER of observers INCLUDING 1 observer ? Your observer for example is at coordinate (ctx,y,z) apply those formulas I supplied above with velocity Use the distance to the horizon your length or radius of the Observable universe which is accelerating according to the Hubble's law formula I provided. The reason for the acceleration is due to the equations of state I mentioned. However it is also due to the length changing by an Natural logarithmic scale. All of those details are IN THE ARTICLE I posted. \[\acute{t}=\gamma(t-\frac{vc}{c^2})\] \[\acute{x}=\gamma(x-vt)\] then apply \[v_r=H_O d\] when you hit recessive velocity v=c the separation distance between observer to cosmological horizon will be zero \[ds^2=0\] That is true for all Observers who observe the recessive velocity when it reaches v=c using Hubble's law. Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 So you're basically saying that the cosmological horizon is like the other material observer moving with the relative velocity v<c with respect to my only observer, yes?
Mordred Posted November 7 Posted November 7 (edited) How else do you think the scale factor is determined ? \[a(t)=\frac{R_{Then}}{R_{now}}\] so set radius of observable universe today as seen from Earth to 1 then determine what the scale factor is at a given Z using the equations of state. https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) so if the Universe is half the volume at say z=1100 its not its just an example. then determine the scale factor using above relation. so here it is on a chart from z=1100 till today. \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&T (Gyr)&R (Gly)&D_{now} (Gly)&D_{par}(Gly) \\ \hline 1.09e+3&9.17e-4&3.71e-4&6.25e-4&4.53e+1&8.38e-4\\ \hline 5.41e+2&1.84e-3&1.18e-3&1.91e-3&4.47e+1&2.78e-3\\ \hline 2.68e+2&3.71e-3&3.59e-3&5.64e-3&4.38e+1&8.88e-3\\ \hline 1.33e+2&7.47e-3&1.07e-2&1.64e-2&4.25e+1&2.75e-2\\ \hline 6.55e+1&1.50e-2&3.11e-2&4.73e-2&4.07e+1&8.32e-2\\ \hline 3.20e+1&3.03e-2&8.98e-2&1.36e-1&3.80e+1&2.47e-1\\ \hline 1.54e+1&6.09e-2&2.58e-1&3.89e-1&3.43e+1&7.27e-1\\ \hline 7.15e+0&1.23e-1&7.39e-1&1.11e+0&2.89e+1&2.12e+0\\ \hline 3.05e+0&2.47e-1&2.10e+0&3.12e+0&2.14e+1&6.13e+0\\ \hline 1.01e+0&4.97e-1&5.80e+0&8.05e+0&1.12e+1&1.74e+1\\ \hline 0.00e+0&1.00e+0&1.38e+1&1.45e+1&0.00e+0&4.62e+1\\ \hline \end{array}}\] Edited November 7 by Mordred
kawiusz Posted November 7 Author Posted November 7 Mister, what exactly is moving with the relative velocity v<c in my universe with a single observer and a single photon that he emitted?
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