On Universal Acceleration and Lorentz transformation comprehension

Disclaimers:
No degree, just a sprouting armchair physicist.
I'd like to ask that unless you are willing to use numbers in any references equations you not post, as I will be doing a decent amount of math through this thread and responding to mathless inquiries would be tiresome.
Please just skip the mudslinging, I don't care what you guys think of each other I just wanna see how well I can debate.
Okay, so for this I'd like to start with the FES wiki and move to any questions and proof afterwards.

In relation to the Universal Acceleration model:

To quote the wiki:
Differential Equation for velocity on earth
"dv/dt = g/γ^3"

Integrating for velocity:
Image
Limit as t -> infinity
"c"

As you can see, it is impossible for dark energy to accelerate the earth past the speed of light.

While I know you have split off here is the other (possibly more readable) version of the same concept from a sister site:

Due to special relativity, this is not the case. At this point, many readers will question the validity of any answer which uses advanced, intimidating-sounding physics terms to explain a position. However, it is true. The relevant equation is v/c = tanh (at/c). One will find that in this equation, tanh(at/c) can never exceed or equal 1. This means that velocity can never reach the speed of light, regardless of how long one accelerates for and the rate of the acceleration.

http://shorturl.at/ekxF4
This is... kinda true. Yes acceleration won't magically halt at a certain point, but that isn't to say it won't slow down.

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To my knowledge the only explanation for Universal Acceleration in the FE model is the invocation of the term Dark Energy (Which in modern traditional physics is just as vague as in FE so I can't really rant about that) so we will ignore where the energy is coming from and focus on how much is being pumped in. The energy of a moving object is γmc2, where γ is the much-misused and fairly complex Lorentz factor. I'll try to simplify it so no one can think I'm pulling the wool over their eyes, we are going to take the simple approach, then use numbers. (depending on how much you really want to read in this post :/)
Simple:
γmc2 is really a simple way of saying:

(E = energy of moving object)
E = 1/sqrt(1-(v²/c²))mc²

now what this means for us, is that as the velocity of an object (Earth) goes up, the amount of energy required goes up too. As that number approaches light, this portion of the equation gets closer to 1:  v2/c2

That number coming close to 1 exponentially increases the value of γ, adding more energy into the total equation.

Moving to complex:

If I am 100 kilograms and am going 0.25c then the equation would work something like this:

E = 1/sqrt(1-(v²/c²))mc²
E = 1/sqrt(1-(74948114.52²/299792458²/))100kg * 299792458²
That is around 2.57841766×1012 Kilowatt hours, in context the entire United States of America used about 3.723356×1012 in 2017 (most recent stat I could find, http://www.ipsr.ku.edu/ksdata/ksah/energy/, Electricity Consumption by State, 2017).

I could run the same numbers for the Earth but in reality that doesn't help anyone, we see big numbers and just assume they are equivalent or comparable. I can show in a thought experiment (I lied I'ma use a graph cause I don't care about words) why it would be impossible to continue accelerating once you reach a near-light-speed:

https://www.desmos.com/calculator/io3tgqxlw9

The bottom equation has values divided by 100 for ease, note it does not give valid answers. What we care about here is the top equation's graph, it shows better than I the impressive growth of numbers. So, now that I've shown it two ways, I can get into the breakdown. As V approaches c E approaches infinity faster and faster and faster, because we know there is a finite amount of energy in the universe and the second law of thermodynamics states that energy in a system (universe counts) can't just disappear (i'm paraphrasing) we know that this couldn't happen.

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We can move on to v/c = tanh later, first a logic game:
Light cannot be accelerated, because light has wave-like properties however it CAN store energy independent of speed... so what happens when you shoot a photon from mach 4? Well the photon will actually "compress" (in reality the wavelength is what compresses) the energy stays in the system (as nature requires) just not in the form of speed. So, if we had the earth moving at insane speeds, (and this part also proves my last point of reasoning) A. how long would it take for us to notice, and B. What would happen?
Well A is interesting, this helps to prove my last paragraphs because those can be ignored by saying "we haven't hit that point yet".

The speed of light is about 299,792,458 meters per second
The acceleration of gravity, or acceleration of the earth in the UC model we are looking through, is about 9.8 meters per second per second.
So it would take only 30591067.14 seconds to reach the speed of light
That is only 509851.11 minutes
Which is 8497.51 hours
Which is 354.06 days, less than a year.

So it doesn't actually matter how fast we would START to see results, we would STOP seeing them just a few days later. Even if you ignore my last proof this states that sometime in that year (I could do the math here but its actually futile, light can only compress so much from Doppler shift (oh yeah the name for this is Doppler shift, this is how we know the universe is slowly drifting apart)) the Earth would be bombarded with increasingly powerful radiation. Even if you say the sun moves as the same rate and this equalizes it, photons from OTHER STARS would eventually be enough to shred our entire planet's vegetation and animal life.

Oh yeah and because spacetime is relative the universe would look like it is standing still and we would be zooming to the heat death of the universe.
Okay, back to math that you guys can actually use if you still want to try and make this model work.

v/c = tanh is an equation used in reference to "proper velocity" it can describe the relationship between the hyperbolic velocity angle (fancy phrase for the angle that uses similar relationships to trig... kinda) and the proper velocity of an object very well. What it cannot do is attempt to prove or disprove anything relating to acceleration to the speed of light (unless you use it to validate data in an experiment) or explain where the phantom acceleration would go.

If you feel I got something wrong, feel free to tell me. Once

To clarify, because of the way HTML and copying equations works on this site. There are some major typos, Fixed equations here in order:

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The energy of a moving object is γmc²

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As that number approaches light, this portion of the equation gets closer to 1: v²/c²

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That is around 2.57841766×10¹² Kilowatt hours, in context the entire United States of America used about 3.723356×10¹² in 2017

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Light cannot be accelerated

No, light can be accelerated, as direction is part of velocity. An example of this is gravitational lensing.

The speed of light is about 299,792,458 meters per second
The acceleration of gravity, or acceleration of the earth in the UC model we are looking through, is about 9.8 meters per second per second.
So it would take only 30591067.14 seconds to reach the speed of light

That is if you take the acceleration to be constant relative to an outside observer.
But if that was the case, the acceleration relative to us would be increasing.

UA speculates a constant proper acceleration which functions vastly differently.
And you have already indicated you know this, so why ignore it?
Instead of v=a*t, you need v=c*tanh(a*t/c) (if I understand correctly).
So putting in some numbers, with a constant proper acceleration of 9.8 m s^-2 and a time of your 354.06 days, relative to the outside observer we would only be travelling at 0.76 c.
After a year, it would be 0.77 c.
After 100 years it would be very close to, but still not quite the speed of light.

However, the important part is that the proper acceleration remains constant.
The other key part is that the entire universe is also accelerating, or at least all the objects in the universe.
This means after any amount of time we would still see the same result.

E = gamma mc² is rest mass energy. Find the full equation.

. . . I will be doing a decent amount of math through this thread:

"dv/dt = g/γ^3"

t -> infinity "c"

As you can see, it is impossible for dark energy to accelerate the earth past the speed of light.

Nobody thinks anything travels faster than light.

Quote from: Here for friendly debates on August 22, 2019, 11:23:47 AM

The speed of light is about 299,792,458 meters per second
The acceleration of gravity, or acceleration of the earth in the UC model we are looking through, is about 9.8 meters per second per second.
So it would take only 30591067.14 seconds to reach the speed of light

That is if you take the acceleration to be constant relative to an outside observer.
But if that was the case, the acceleration relative to us would be increasing.

UA speculates a constant proper acceleration which functions vastly differently.
And you have already indicated you know this, so why ignore it?
Instead of v=a*t, you need v=c*tanh(a*t/c) (if I understand correctly).
So putting in some numbers, with a constant proper acceleration of 9.8 m s^-2 and a time of your 354.06 days, relative to the outside observer we would only be travelling at 0.76 c.
After a year, it would be 0.77 c.
After 100 years it would be very close to, but still not quite the speed of light.

However, the important part is that the proper acceleration remains constant.
The other key part is that the entire universe is also accelerating, or at least all the objects in the universe.
This means after any amount of time we would still see the same result.

This is correct. The OP is misunderstanding that speeds are not added linearly when dealing with relativistic physics. Its a speed Limit, not a Speed Limit.

Why do you accept that speeds don’t add linearly but don’t accept everything that comes with this idea?

This is correct. The OP is misunderstanding that speeds are not added linearly when dealing with relativistic physics. Its a speed Limit, not a Speed Limit.

So you'll accept Einstein's Theory of Special Relativity where it supports UA.
And you'll accept Einstein's Equivalence Principle insofar as it equates gravitation with acceleration and indicates that gravitation might be an inertial force.

But, at least in relation to UA, you reject Einstein's Theory of General Relativity that claims mass/energy bends spacetime hence causing mass to appear to attract mass.

This looks like cherry-picking to me.