Hey, I said credentialed, not qualified. However, to that, I will leave those far more knowledgeable to do it, which they have. They will accomplish in minutes what would take me days.
@yuviarora ,
I know you don't respect the "math", but let me try to explain it. I will not try to justify the fudge factor of dark matter, as that is not possible, but that is just one item in a long long list.
Mathematical proofs are a lot like statistics.
If I say y = a + b, and I do an experiment, and y does equal A + B, that provides me a very narrow interpretation of the physical world and even then, a narrow confidence in its universal accuracy or applicability.
A statistical equivalent would be flipping a coin 10 times. I can have some confidence in what the statistics indicate, but not a lot.
Now what if I flip the coin a billion times, or better yet, what if I flipped 20 coins, 1 trillion times. Now I can be confident that the results is accurate with only the most minor minor chance it is not.
Mathematical proofs / models are like that. When I take say 10 equations, perhaps with 10 variables, and 10 constants, and I apply them to a new problem and come up with an answer, and then I do an experiment, and the experiment matches my mathematical model, then there is a very very high chance that the math IS an accurate representation of the physical reality. The reason is based in statistics. The odds that those equations, and those variables and those constants, randomly coming up with the exact answer is exceedingly low. The grey area, is "exact" and it will vary based on what you are modelling. And here is where the statistical strength improves. Often the answer is not 1 things, but a whole set of things, and the odds of all of those things happening and the models coming up with them, and the models doing it by accident become even more exceedingly rare.
This is why the electric model fails. It is incomplete, and only works in isolation. There are hand waving explanations for things that happened, but no unified model that takes into account everything that happens and all the outcomes, and all the phenomena observed.