Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.
Richard P. FeynmanThe shell game that we play ... is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate.
Richard P. FeynmanAny schemes - such as 'think of symmetry laws', or 'put the information in mathematical form', or 'guess equations'- are known to everybody now, and they are all tried all the time. When you are stuck, the answer cannot be one of these, because you will have tried these right away...The next scheme, the new discovery, is going to be made in a completely different way.
Richard P. Feynman