didn’t expect to see holofractal show up!
visualizing nature’s behavior is fun!
Thanks for the keyword; very interesting.
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After only a very brief look, the main distinction I would say is rooted in the debate about
mathematical realism. In a nutshell, is mathematics simply a human invention to describe nature? Is mathematics something we (humans) create as a model of the real world or is it something more fundamental? The counterargument is that the real world follows mathematics which leads to the term
mathematical realism.
In the present case, the interpretation of the reality of the
Poynting Vector as energy flux seems to lie squarely on the same question. Is it a real quantity or just a mathematical abstraction like imaginary numbers or potential energy that we don't see?
As per the holofractal theories, there are patterns in nature that are throughout. We can liken these to
a priori properties that CAN NOT be derived but always exist. The fundamental argument I put forth is that it is well accepted that mathematics is
a priori and so it is discovered NOT invented, and the physical laws of nature are as well
a priori no human-invented them. So are we to believe that there is no intersection between mathematics and the physical world? How can two
a priori property sets not be related? Well, they would have to be
independent but that is clearly not the case for independence means that we can not derive one from the other which is especially confounding except in the circular logic of
modal collapse. So when we "
work out the math", and we find some serendipitous relation between the math and the physical process it is because to a certain extent they are one and the same. Formally I would say that mathematics/logic is an inner model of the
a priori physical world.
The way that the Poynting math always points in the direction of energy flow, is the exact pattern in the propositional calculus for A<->B which is inseparable from and in fact defined by A->B and B-> A which is pure formal logic (propositional calculus) and the basis for the formal proof theory. This relation is called
material equivalence and at its core is the circular reference that establishes what we call
truth. For example in A<->B , this relation is true is A=B =True or A=B=False and is False in all other cases. If you have a longer chain of circular references A->B and B->C and .... etc Z->A the same is always true.
The physical interpretation then is that Truth implies Energy Flow independent of the direction of the E&M flows. I'm suggesting that it can't be any other way (due to the math/logic) and the Poynting vector is very real just as the E&M fields are.