Yeah that and the absolutely incorrect assumptions about fuel/propellant efficency pretty much sums up the basic physics reasons why the engine can't do what Starship claims that it can.
I, Relativity Backpeddaling: Starship claims that reaction mass propulsion alone, not compensated for temporal or spacial relativity at all, can give you velocities (and inertias) above 1C, illustrated by the use of Newtonian reaction mass rocket equations. Being that Newton's equation is ultimatly wrong, albeit not by much at low speeds, the use of the equation for >0.10C rockets is fundimentally incorrect. Right math, wrong equation.
Then Starship turns to relativity, using time dialation to claim that his rocket can achieve effective speeds of >1C. Now I want to place special emphasis on the word effective here, because the ship never actually exceeds 1C. The ship never actually achieves inertias where V > 1C, which is forbidden by relativity, only that time slows down for the crew. This is what you calculated, I have not said anything about length contractions, which I am sure would support me anyway.
Oh, and using the relativistic mass increase of propellant as a means of extracting more energy from fission would never give you infinite energy needed to reach 1C because it is only an apparent increase in mass, and not a "real" one, the ship never actually gets any heavier it only takes more push to make it go. Even if it did, you'd have to be traveling at 1C to generate the infinite energy needed to reach or exceed 1C.
So... which is it? Newton's math showing superluminal inertia or Einstein's, which forbids superluminal inertia, time and space contractions "shortening" the trip but limiting your speed to <1C. There is some missing inertia between your Newtonian equation and your Relativity equations... an infinite amount actually... which is a gaping hole in Starships rockets' theory.
II, The efficency gap: Starship also doesn't seem to understand how fuel efficency works in reaction mass rockets; that the efficency of the rocket is controlled by how much energy you can derive for thrust from the mass of both the nuclear fuel and the propellant. Starship ignores the fact that the water or whatever propellant he is using does not produce energy of its own - unless you count "oxygen fission" which occurs by heating which is nonsense - so the average amount of useful energy produced per mass of nuclear fuel and propellant is very small.
If you could theoreticly build a nuclear engine where there was no propellant, and 100% of the energy released only went into pushing the fissioned atoms out the back, then you could reach ~1,000,000sec Isp... But not only does Starship weigh down his rocket with hundreds of tons of water, but the method he uses cannot transfer the energy that there is efficently. Solid core nuclear rockets like Starship's have been built before which operate at 3,000K (the maximum most solids tollerate) with the much better propellant Hydrogen and they only achieved Isp under 1,000sec and gas core rockets have been moddled running at 50,000K and have performance under 10,000sec... I find it very hard to reconcile the multiple order of magnetude discrepency with Starship's supposed mastery of the subject, given engines of similar mechanism have been built that have 1,000,000x lower efficency.
A real doctor of physics or math or whatnot who studied Einstein's works for years and has a deep understanding of thermodynamics of nuclear rockets would never make such terrible errors in the basic physics... It is not that you've done your math incorectly, the trouble is, you are using the wrong math to begin with.
And what is this ranting about proving negatives or proving this or proving that? What proof have you brought that shows that the whole of the physics community for the last half century is "all wrong" when they state that the 1C limit is fact? Why aren't particle accelerator experiments proof? The burden of proof is on yourself to show why they are wrong and you are right, not for them to show why you are wrong. I have not seen any proof from you that shows that the established law of relativistic mass (particle accelerator) and time dialation (atomic clocks) are incorrect in any way other than misconceptions quoted from crackpots and ranting about what Einstein didn't say.
Einstein is mostly correct about many things, but just as Newton was, he doesn't know everything. The 1C speed limit has been established by experiment time and time again for normal things and is an integral part of our physics which accuratly predicts real phenominons. And claiming that "no dector exsists" that can measure such high particle speeds doesn't make any sense to me since they operate if we can measure >0.99C speeds, why can't we measure >1.0C speeds?
Quantum Mechanics has advanced since Einstein's and Rutherfords' time, plus it has proven to be extraordinarily accurate, and when applied to the idealized atomic model it does accuratly describe the nature of the atom that accounts for your "constant motion" problem... but then you yourself have said you don't know anything about QM because you didn't bother to study it since it was "silly." I happen to know a bit, being I am a chemist and am concerned a little with the nature of the atom, and it has proven quite accurate in describing and confirming the basic tenants of the atomic model. No Strong Nuclear Force? No such thing as a nucleus? Oxygen fission? Nonsense. You have no proof at all about these far-out ideas other than quotes from fools and conspiracies.
So lets review shal we? You happen to hold multiple doctorates, the FBI/CIA/etc has been after you, you have atomic bomb parts in your back yard, you have worked for the USAF under some secret projects, you happen to know about a vast conspiracy to "steal The Bomb from Einstein" led by Fermi and censor all knowledge of nuclear power everywhere for a century, claim to be a professional physist but dismiss Quantum Mech as nonsense, you have "multiple atomic models" you invented, you don't seem to know anything about thermodynamics, you don't know what relativistic mass is, you have major mistakes with your understanding of rocket fuel energy density even though you've written a doctoral thesis about it...
...and you happen to know better about physics and relativity in general than essentially all the other members of the scientific community since "they were all taught wrong" or something. So, which is easier to believe? That you are not telling the truth and are wrong, or that you are right about all this stuff listed above? Thought so.