Dear Lawrence,
You seem to see in my derivation of Planck's Formula Laplace transform. That may lead you to some deeper insights, but from my perspective I don't see the point. I just lose the physical meaning of that math.
All the results in my essay have a clear and simple physical meaning and are mathematically argued. What is the physical meaning of the Laplace transform you are arguing I inadvertently used in my derivation of Planck's formula? And does this also show what I am showing? Namely, that Planck's formula is a mathematical tautology that describes the interaction of measurement. This is why the experimental blackbody spectrum is indistinguishable from the one obtained from Planck's formula.
I do not argue with the mathematics used in physics. Rather, I argue with the physics in the mathematics used. What motivates me in this intellectual venture is my desire to understand physics physically. Modern Physics lacks physical meaning that makes sense. The 'man in the street' knows more about 'time travel', for example, than the theorist who with mathematical certainty asserts it.
We need 'physical realism'. I show in my essay this is possible. My derivation of Planck's Formula avoids energy quanta and discrete statistics. In this view, we gain a clearer understanding of what the Formula actually means.
Constantinos