Max Planck's theory of 'Energetics'was on the right track - but it became complicated with things like Maxwellian waves, Transverse mass & Longitudinal waves, quantised energy and probabilistic wavefunctions etc as you point out).
Lacking a formally defined and visual model for their Mathematical solutions to the same,the situation then became even more confused as numerous answers [sqr Neg one, probabilities etc] became accepted scientific answers to quantum math.
Maxwell [had he lived ] would have been one of the first to point out that you must be able to build a physical model of any quantum system in order to justify the theory's accuracy and completeness.
I too agree with the comments concerning pi [C/D] vs Pi radians - it is a fine example in science of using 1 name for 2 distinct properties and as pointed out in Tetryonics we have been mistaking EQUILATERAL Pi radians for spherical Pi ratios in QM for over a century now.
This situation became very more complex in tetryonics where Pi [normally the property of a circle/sphere] becomes a property of Equilateral geometries. However in ET 1/2 pi really is 1/2 of the triangle and 2 ETs have internal angles adding up to 360 degrees so you win some - you lose some.
Fortunately TIME (having a spherical geometry) is usually measured by us as the time is takes light to travel 299,792,458 metres so it units are usually s. s^2 or c^2, c^4. [even though they are drawn as spheres.
I was tempted (early in my work) to use 'Tau' in lieu of Pi for my unified equation but dropped it as I thought it would create confusion in understanding my theory. [ie 4Pi & 36Pi quickly create the impression of geometry in most minds whereas 4T & 36T etc don't] and who am I to re-write mathematical descriptors - I am doing so much now correcting subtle but important misconceptions that arise from using Math without physical Models..
Sometimes you have to go with the accepted terms in order to have a new theory viewed seriously and to be understood by minds used to those particularly quirky
inconstancy...perhaps when the theory develops we can change these poor definitions .... after all seriously QUARKS, UP, DOWN, STRANGE, CHARMED, TOP, BOTTOM, GLUONS??
Perhaps when the theory grows in acceptance we can hold a international council to review some of the sillier names of fields & particles in Physics...I have gone far enough naming the tetrahedral quantum of Matter [the Tetryon]Attachment #1: 1_Figure_02.03__Tetryonics_and_Pi_radians_800x600.jpgAttachment #2: 1_Figure_01.03__Spatial_geometries_800x600.jpg