It seems to me that when dealing with particle physics it is necessary to just start with relativistic methods and never do the approximations. Even at 5% of C the variation is more than 0.001 which loses a lot of precision in design. I am not really complaining, it is just a vehicle to show how simple it is implement complex math in python.

if__name__=="__main__":forxiinrange(0,99,5): x=xi/100.0 x2=x*x x3=(1/(math.sqrt(1-x2)))-1

0.05 0.00125234864352 0.1 0.00503781525921 0.15 0.0114434748483 0.2 0.0206207261597 .... 0.85 0.898315991505 0.9 1.29415733871 0.95 2.2025630761

Below follows on with using more elegant methods from numpy and list generation methods , which become ever more inscrutable but more elegant and concise.

if __name__ == "__main__": print 'Relativistic corrections.' for x in [k*k for k in numpy.arange(0.90,0.99,0.01)]: print math.sqrt(x), x,(1/(math.sqrt(1-x)))-1

0.9 0.81 1.29415733871 0.91 0.8281 1.41191535097 0.92 0.8464 1.5515518154 0.93 0.8649 1.72064780895 0.94 0.8836 1.9310519088 0.95 0.9025 2.2025630761 0.96 0.9216 2.57142857143 0.97 0.9409 3.11345034895 0.98 0.9604 4.0251890763

Personally, I don't feel that this way of expressing the relationships is all that obvious or useful in terms of what is taking place. It is a transform that depends on v_{rel}, but it affects many things. I will try to make a more generalized method of transforms that shows the relationships from a changing velocity framework or "accelerated frame of reference". I have stated before that a loose collection of particles that are logically assigned to a set due to their proximity and similar velocity is a thing that does not exist. It assigns "entity" to object sets and this is nonsensical.

I suppose I could just do this LINK to Wolfram (MeV) as mass.

ADDED: While analyzing this it becomes obvious that the way in which the calculations are made does not take into account the complete nature of the process and because it is only a small slice of the whole equation, it is less descriptive than it could be. By using simple anecdotal situations and not the complete framework it would seem that certain paradoxes may arise in the conclusions, that do not exist in the whole interpretation. This has long bothered me and now I may have a mathematical way to express that completeness that I see in the relationships. It makes it much more clear what is taking place in situations that would seem to resolve to paradox. I am still troubled by a 3-space universe where the Earth is at the center of the universe. It would seem that **if** telescopes are looking back to the big bang, then there would at least be some temporal or spatial variation to indicate the relative positions of the elements in three space. A 4-space interpretation would not absolutely ensure that effects in one direction would be observed in another, but that is one consequence. A model of 4-space and some scenarios placed upon it might clarify what one might expect to observe in such a situation. I am still looking for consistency in the patterns of mass, time, structure and radiation as well as total energy and momentum.

ADDED MORE: Clearly this is the wrong equation in the fact that it is incomplete. That seems to be the whole problem. It does work for the situations in which it is applied ( because it was devised from it! ) , however it is not a generalized solution. I can go through any data and find patterns and assign a mathematical formula to those relationships. Math is simply a formalized descriptive language which is assumed to have some absolute basis in fact. To some extent that is true. By reasoning from the small and absolute to the extreme with certainty at each step it can be accomplished and it does apply in *most* situations. E=IR can be determined experimentally and probably was initially and then backward devised as a special case of Maxwell's equations. So was gravity established, as an experimental relationship that was characterized in a formula.

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