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If you say the total charge must be conserved,
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I am not saying anything without knowing the facts, but I would like to help.
I am not the first in this thread to wonder what your direction is.
However you seem to have an oddly antagonistic attitude towards your physics classes.
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But I can't count the number of times I've noticed the contradictions in my physics class. Two charges, when touched, will have the same charge, so (q1+q2)/2. Except what if one of those starting charges was an odd multiple of the elementary charge, and the other even? I end up with two non-integer elementary charge multiples.
The relativity work I've done regards finding a number that expresses how much length contracts/time dilates at a given relative speed but, what if the length is 10 planck lengths? It shortens by a factor of some irrational number?
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If you are genuinely studying physics at a level to encounter relativity then this book may be of interest
On Space and Time edited by Majid - it explore exactly the granularity v continuity of space and time and contains essays from several famous physicists and mathematicians.
PS I still don't understand what you mean by (q
1 + q
2)/2 - nor does Google.
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