Dear Philip,
One again that time of year to bug you:) If you had seen my essay you can strike what I am about to say. Otherwise I am going to save you the trouble right here. based on the conversation you had with Dickau. I say
"The system can use both Real and Integer numbers, and in both systems you always get finite answer no matter how high your energy goes as when using Real mainly because the energy represented by line length summed up according to weights dictated by the interaction makes the short segments naturally lose their effect in long range interactions and the energies never blow up, even in short range.
As can be seen in the simulation of the electron mass (actually mp/me ratio) simulation the system is scale invariant, that is multiply the D0/D1 by any number the linearity makes the system scale invariant and you basically you get the same curves i.e. if you zoom in(or out) you get exactly the same curves. That is, when you are doing the electromagnetic interaction i.e. line crossing you always get the proton/electron ratio. because of the two special location which could be some phase change "
second
"Now suppose I ask you to tell me what will happen to some "object", but I don't tell you anything about it (how fundamental can you get) !! like what mass it has or what it will do if another thing is present. Ok, I'll give it a try. First I will say I will "invent a coordinate and since I don't know where it exists I will restrict it to be in some range and eventually make that range variable. This lonely thing would have a meaningless existence. i.e. it needs a partner. If we add another one next to it with similar setup and at some distance that can also be varied. Now, we can calculate all relative information just like our original idea in the essay.
Kaboom! both situations reached the same conclusion with generalization leading to all of physics ( at least the important) QM, QFT, Gravity like shown. In one instance we acted like GOD and decided to design a dynamic universe, in the other we are ignorant humans but figured out how things should work, and both match and are the FUNDAMENTAL building block. "
Thank you in all cases. and just in case
https://fqxi.org/community/forum/topic/3127
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