Mordred

So you claim yet have only shown a single equation. Prove it mathematically here go ahead I challenge you to put your mathematics where your mouth is. Instead of claiming mathematically prove your claims. Start by proving it will work under SR first After all we still have to prove it will work in curved spacetime. Come on pit your mathematics skills and your single equation under examination that it will work under GR. I would love to see that but I already know you can't

Not a chance mate your equations are essentially useless as they do not describe how our universe evolves over time. Nor have you really anything particularly useful for physics scale factors are a dime a dozen in numerous theories Every major theory will have some form of scale factor. If your scale factor doesn't include any other related metrics specifically under a geometry treatment applicable to the system its describing then its essentially of little use as a replacement. Generating scale factor simulations is nothing new to physics and they can be widely varied. If your equations don't conform to observational evidence it's insufficient as proof.

Then you better show your equations if it deviates from GR you have your work cut out for you and believe me I'll be able to tell. If you don't understand the EFE and how it applies to the FLRW metric then you really don't understand its true flexibility. Every equation I posted you can be the observer. Even the only one why is the recessive velocity important is simple, velocity as shown by the Lorentz transformations directly apply to how we measure time so using recessive velocity is how we factor in the time time component vs the space space components. Using GR relations I will show how the FLRW metric fits with GR. but first here is an interesting trick simply take \[v_{recessive}=H_oD\] and to get an accurate recessive velocity all the way out to the cosmological event horizon do this substitution \[v_{recessive}=(H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}D\] Now this shows that the rate of change in distance to the Cosmological event horizon is accelerating and that the Hubble value for expansion is also not constant over time. The above substitution calculates how H changes as a function of cosmological redshift. That applies the equations of state and includes both equations of the FLRW metric its geometry previously shown. The second term is the acceleration equation for how radiation and matter energy densities evolve over time expansion relations. That's the portion under the square root including cosmological term. now under GR the above relations would give the following including all others I have already posted such as the FLRW metric. take the EFE (Einstein field equation) which is needed for its field treatments of multipoint coordinates. Any coordinate can be an observer including yourself \[G_{\alpha\beta}=\frac{8\pi G}{c^4}T_{\alpha\beta}\] \(T_{\alpha\beta}\) being the stress energy momentum tensor. \[ds^2=g_{\alpha}{\beta}dx^\alpha dx^\beta\] where \(g_{\alpha\beta}\) is the metric tensor as this is an orthogonal matrix above the non vanishing elements can be given in matrix form for the FLRW metric as below for the metric \[g_{\alpha\beta}=\begin{pmatrix}1&0&0&0\\0&-\frac{a^2}{1-kr^2}&0&0\\0&0&-a^2r^2&0\\0&0&0&a^2r^2\sin^2\theta\end{pmatrix}\] for the stress energy momentum tensor \(T_{00}=\rho c^2,,,T_{11}=\frac{Pa^2}{1-kr^2}\) the left hand side of the Einstein field equation becomes \[G_{00}=3(a)^{-2}(\dot{a}^2+kc^2)\] \[G_{11}=-c^{-2}(a \ddot{a}+\dot{a}^2+k)(1-kr^2)-1\] using above the time evolution of the cosmic scale factor then becomes \[\frac{a}{a}^2+\frac{kc^2}{a^2}=\frac{8\pi G}{3}G\rho\] \[2\frac{\ddot{a}}{a}+\frac{\dot{a}}{a}^2+\frac{kc^2}{a^2}=\frac{8\pi}{3}P\] where \(\rho\) is the energy density and P is the pressure. The overdot 's above the scale factor terms are the velocity for single dot with two dots its the acceleration term. This is shows why we use velocity and acceleration the choice of observer is irrelevant its obviously practical to more often than not treat yourself as the observer. The above also shows that the FLRW metric is a GR solution and its generalized relations. They already include any SR application but under GR field treatment which is better suited for spacetime curvature. Spacetime under GR always include the equations of momentum given by \[E^2=\sqrt{(pc)^2+(m_oc^2)^2}\] which is the full equation for \(e=m_oc^2\) called the energy momentum relation for previous. the above shows a mathematical proof that the substitution below is valid and how its applied. SR works for the first term but only at very close range and it degrades in accuracy due to equation 2 below. Equation two is a product of those relations above including how radiation, matter and the cosmological constant evolve over time in energy density and pressure relations \[v_{recessive}=H_oD\] \[v_{recessive}=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}D\] That should give you a good overview of why commoving coordinates are an essential aspect to an expanding universe. Its the influence of our matter/energy content and how they affect expansion. Yes the above is complex but once you understand it. It is absolutely remarkable how flexible the above is in describing how the scale factor evolves over time and why the affine connection for proper time or cosmic time is tied to the scale factor as given as \(a(t)\).

As I stated that Observer could be you but you are a commoving observer under the equations I posted. Those work just as well expressing you but invariance requires any observer for proper velocity relations for the four momentum. All part of GR requirements also required for SO(3.1) Poincare group = spacetime metric. Simply arguing your the observer so it shouldn't matter doesn't work when the very coordinates your located at are commoving with the universe. hence you would need a different geometry with a different flow of any measurements you take of any particles or objects around you unless you are moving with the coordinates ie fixed coordinate.

THEN define your reference frame mathematically and post the relevant details for discussion as you are required to have a geometry that should be a cinch. observer is measured by you it is commoving as everything in our universe is a commoving coordinate. So you better get to work on your observer. As it doesn't fall under SR nor GR unless your in some absolute frame of reference in which case this thread will belong under Eather based and isn't main stream physics.

I'm describing as measured from the Commoving observer using recessive velocity MISTER.

I already answered that read back prior to Hubble radius v<c after Hubble radius v>c Hubble radius The Observable universe if bigger than the Hubble radius by a significant amount. Hubble radius is defined as the radius where the age of the universe times c. So if our universe is 13.8 Gly the Hubble radius is only 13.8 Gly our observable universe is however 46.3 Gly in radius https://en.wikipedia.org/wiki/Hubble_volume equation from above link \[R_H=\frac{c}{H_0}\] the SR transformations will give ds^=0 at the above Hubble radius our universe is larger precisely what I described in my first couple of posts https://en.wikipedia.org/wiki/Observable_universe The reason why the universe exceeds the Hubble horizon is the following \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] \(H_0\) is not constant that is todays value but in the past its higher and at its highest at BB. Those equations of state I mentioned

The universe is smaller in the past when the photon gets emitted during its travel the universe expands how are you missing that detail ? the Universe is at its largest today and smaller in the past. Do you understand that part ? that is literally what expanding means

The blooming radius of the Observable universe pick any object or galaxy at the furthest you can examine and measure it how else do you think physics measures expansion pick any three or more galaxies and measure how they change distance from each other. I'm honestly beginning to feel your just trolling as no one an be that blind either that or you really need to study basic cosmology either that or I'm talking to some kid between ages 10 to 15. That has no prior knowledge of physics if thats true on the last part then we can help teach you the basics

the geometry is changing your photons must travel through spacetime. as the universe expands the distance your photons must travel increases. This leads to gravitational redshift which is Z. https://en.wikipedia.org/wiki/Gravitational_redshift That was the FLRW metric above the scale factor changes as your photons are trying to reach the observer. Here is the geometry again assume the flat case as its the easiest case \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] if you want the line integral for flat the total interval along the Worldline (null geodesic photon path is) \[\delta S=\int^b_a=\sqrt{ds}=\int^b_a\sqrt{-cdt)^2+(dx)^2+(dy)^2+(dz)^2}\] so using the Radius of the universe and how it changes the distance becomes \[(dL)^2=(\frac{dr}{\sqrt{1-r^2}{/R^2}})^2+(r d\phi)^2\] so your photons must travel further the last 2 equations do not include scale factor changes but include the same relation to determine scale factor by \[a(t)\frac{r}{R}\]

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. \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&T (Gyr)&R (Gly)&D_{now} (Gly)&D_{par}(Gly) \\ \hline 1.09e+3&9.17e-4&3.71e-4&6.25e-4&4.53e+1&8.38e-4\\ \hline 5.41e+2&1.84e-3&1.18e-3&1.91e-3&4.47e+1&2.78e-3\\ \hline 2.68e+2&3.71e-3&3.59e-3&5.64e-3&4.38e+1&8.88e-3\\ \hline 1.33e+2&7.47e-3&1.07e-2&1.64e-2&4.25e+1&2.75e-2\\ \hline 6.55e+1&1.50e-2&3.11e-2&4.73e-2&4.07e+1&8.32e-2\\ \hline 3.20e+1&3.03e-2&8.98e-2&1.36e-1&3.80e+1&2.47e-1\\ \hline 1.54e+1&6.09e-2&2.58e-1&3.89e-1&3.43e+1&7.27e-1\\ \hline 7.15e+0&1.23e-1&7.39e-1&1.11e+0&2.89e+1&2.12e+0\\ \hline 3.05e+0&2.47e-1&2.10e+0&3.12e+0&2.14e+1&6.13e+0\\ \hline 1.01e+0&4.97e-1&5.80e+0&8.05e+0&1.12e+1&1.74e+1\\ \hline 0.00e+0&1.00e+0&1.38e+1&1.45e+1&0.00e+0&4.62e+1\\ \hline \end{array}}\]

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.

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

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.

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?

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

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 \[-{c^2}d{t^2}\]

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.

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.

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. 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.

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

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.

Vibration means any oscillating state. For example a spring in motion is a form of vibration. Sound waves generate vibrations. Fusion in Cosmology occurs during stsr formation but on a cosmological scale doesn't occur. The early atoms such as deuterium, hydrogen and lithium will form once temperatures cool down sufficiently. Now that Studiot went through the chemistry aspects let's try an example of why you need cooling. Take a proton it wants to have an electron in orbit due to charge. However the universe at high temperatures has tons of other particles moving about. So say the proton captures an electron. Now another particle comes along and knocks that electron out of orbit. The particle that does this is irrelevant. The only requirement is that it delivers enough force ( in energy equivalence 13.5 ev.) The above is an example of ionization. Cosmic rays can for example ionize neutral hydrogen in the same manner. If the Cosmic rays produce 13.5 ev the electron in the outer shell can get removed from the atom. In terms of fusion you require pressure and temperature. To reach ignition you must meet the Lawson criteria which will vary depending on the composition. https://en.m.wikipedia.org/wiki/Lawson_criterion Unfortunately most decent articles on nucleosythesis gets rather high level mathematics for example https://astro.uni-bonn.de/~nlanger/siu_web/nucscript/Nucleo.pdf But you will notice the article describes different binding energies for several different atoms.

I'm trying to get you to make the connection between the photon to E or B field. For example photons have no electric charge but has charge conjugation. So ask your self how do photons mediate electric charge ? If the photon never carries electric charge? It is the same direction Studiot is getting you to see and where the mathematics Swansont pointed out becomes essential

Every particle in the SM model has polarizations but those polarizations are not physical twists in space. Your adding effects not seen in any study of photons for example the known polarizations have physical effects when photons pass through a polarization filter yet yours do not. So why are your twists not seen in any experiment ? Also your mathematics do not include any wave vectors