kawiusz

Because I have a total number equal zero of my own equations to prove. You can't prove the arbitrary scale factor function and the Friedmann's a(t) is already perfectly proved. You totally can't read with comprehension. What institute gave you your degrees?

I'm not your mate, pal. I can get the most accurate, explicit form of the equation for a(t) calculated from the Friedmann eq. in Lambda CDM with the most accurate density parameters and I will have the same result for my simulated observer, but you simply don't get it. Don't edit your answers after you were replied.

You probably forgot to throw in the multiplication table. "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." Every possible and arbitrary but monotonically increasing function of the scale factor function will have the same result for my simulated observer and I gave the explanation. That's why my explicit form of [math]a(t)[/math] is meaningless and makes no difference.

And these comoving coordinates manifest themeselves in the expanding distance between the observer and the photon that he emitted. "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." My geometry is expressed by the same expanding distance and the expanding wavelenght of the photon.

Can't you seriously imagine a universe with a single observer with his own reference frame, that is also the only reference frame in this universe?

There is no other comoving observer in my simulation, mister. There must be at least two to be comoving.

Your answer to my question should be: No, the observable universe radius has never increased with the velocity v<c. So I repeat my previous question: 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?

Do you understand the definition of the radius of the observable universe? Has it ever increased with the velocity v<c? Don't edit your answers after you were replied.

Is the blooming radius of the observable universe shorter than the distance traveled by my only photon emitted by my only observer? If it's not, then it's relative velocity can't be less than c. Is it? Don't edit your answers after you were replied.

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?

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?

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?

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.

Think about what you wrote. If it's applicable for a million observers it's also applicable for one.

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.

Velocity of what? Lenght contraction of what?

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.

I repeat: you read it first, find the formula for the cosmological time dilation and paste it.

Sorry, you're wasting my time.

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?

I will hit infinity when the double type exceeds its range. Please, don't answer if you don't understand the question.

[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.

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.

Can you help verify this theory?Continuous Gravitational Influence Theory.pdf