Cheshire Bifurcaton = 5 & 6 Dimensional Unification
The two discussions, Quantum Mechanics/ Photoelectric Effect/Particle Theory, and, the subject of relativity and field theory are generally considered antithetical/contrary-to each other...
The discontinuous fork in the formerly continuous road through theoretical physics.
In 1900, theoretical physics was near to recognizing, utilizing and pursuing continuous field theory to its fullest extents; when Max Planck's discovery of the 'constant h factor' emerged - a discontinuous, invariably uniform value (of 'photons') that the continuous field could be (and is in fact) reduced to (re: 'black body radiation').
This discovery deterred any further vigorous pursuit of the direction Maxwell was proceeding in, with his recently established continuous field theory.
Theoretical physics branched out, at Plank's introduced juncture of discontinuity; wherein and thenceforth (since 1900), theoretical physics in general was dichotomized, bifurcated.
Field Theory is about continuous waves.
Quantum Mechanics is about discontinuous ('wave mechanical'; so called) 'particles.'
The two subjects are considered mutually exclusive. Continuous Field Physics apparently contradicted by Discontinuous 'Particle' physics ('wave mechanics')...
Whereas, the apparently inherent contradiction is actually an illusion. Continuous Field theory begets Discontinuous Particles; there is no real 'contradiction': at the transition of the four dimensional mass, consisting of four ninety degree quadrants, producing 'quanta'.
Any more energy generated by that system, has no more room to occur inside that 360o 4-D mass/matter system, the 5th quadrant of ninety degrees - generated by and a result of the four dimensions constituting the material energy that generates it, moving at right angles out of 4-D matter, in a fifth 90o unit of electricity (the 5th dimension) 'quantum leaping' out of the four ninety degree quadrants of physical matter (sub atomic charges, i.e. 'particles').
Light and matter are both single entities, and the apparent duality arises in the limitations of our language. (Heisenberg)
(The record may be 'redundant' in the presentation of this issue, whereas, the repetitive descriptions wish to approach the unprecedented solution from several different perspectives. Thank you.)
This record describes the above explained ephemerality (the dynamics of Planck's 'constant "h" factor' known as the 'quantum leap'): as the 'translatory moment' - when the 5th 90o unit of electricity 'quantum leaps' out of the 4-D quadrant of 90o that generates furthermore, 90o of electricity, followed by 90o of magnetism; i.e. - the 5th and 6th dimensions of electricity and magnetism, respectively. Comprehensively and continuously emitted in discontinuous units, called 'quanta' and/or 'photons'; often referred to as 'photo-electric effect'. The 'translatory moment' is also when the apparently 'standing field' of actually expanding (ever acclerating) 4-D matter, projects the 5th and 6th dimensions of electromagnetism, abruptly accelerates beyond the accleration-rate of 4-D matter (an apparent 'standing field' <'obviously physical matter, corporeal reality at large, is not expanding'>, emitting the recognized electromagnetic field; in discrete - 90o units); 'quantum leaping' at light speed (relative to the apparently 'standing <'static'> field' from which it originates and by which it - electromagetism - is generated).
Illustration obtained from entering 'Geometry Junkyard' in Google.
(It also appears to be an expression of what is called the 'Golden Rectangle'...)
This shape, constructed by inscribing circular arcs in a spiral tiling of squares, resembles but is not quite the same as a logarithmic spiral. A similar spiral is used as the Sybase Inc. logo.
(Illustration of logarithmic spiral non-transferable at this location)
Above is a geometric expression of exponentially - extrapolating - spiral progression from a center source (in this case a rectangle rather than a circle). It is approximately the structure of a nautilus shell - pompilius nautilis linnae, as well as any number of sea shells, snails and an array of spiral shapes as they occur in Nature.
Referencing the above geometric expression; disregarding the rectangular center, there are four 90o quadrants exponentially progressing in clockwise motion, ending with the vertical straight line - where the evolution of the four segments preceding the vertical line fullfill a 360o whole.
360o divided by 90o equals four, followed by a 5th 90o 'pie chart' shape, extrapolated at right angles out of and far exceeding the - collective - area of the four 90o quadrants preceding it.
Repeat: note that the 5th 90o component occurs beyond 360o, and that, by way of extrapolation - exponential acceleration - the 5th component, although identical in 90o shape, very abruptly transforms to a size much larger than than all four combined 90o quadrants preceding it.
When the four 'sliced pie quarters' are gathered together in an equilateral circle , they complete a 360 degree whole. This represents a so called 'particle', more appropriately described as a 4 dimensional 'charge' of field energy.
The 5th section of 90o occurs outside of and at right angles to the described quadrant of four 90o segments. This record offers the (above diagrammatic) geometric expression - of an extrapolating spiral - as an example of 4-Dimensional acceleration of matter, generating a fifth 90o segment, representing the 5th dimension of electricity, contiguously extending - quantum leaping - at right angles out of the 360o, 4-Dimensional system from which it originates and by which it is generated; while the *6th 90o segment of 4-D charge-generated magnetism, exponentially extends at right angles out of the 5th.
(*Refer series of - immediate below - complementary illustrations, the first of which co-axially represents outwardly transient <5-D> electricity moving at right angles out of a central 4-D axis of apparently 'static', <corporeal> 'standing field' of material 'charge', aka, 'particle' <Note: a geometric 'point' occupies no space: whereas, the term 'Point charge' , refers to any 4-dimensional system of 'mass', i.e, sub-atomic 'particle' / 'charge'; that is, any electron, neutron or proton, individually or collectively constituting material reality; all of which Einstein established as four dimensional> Note <re: immediate below graphics>: a positive charge field moves outwardly; a negative charge field moves inwardly -alternative vector forces in nature:
...macrocosmically comparable to gravitationally impelling force and the repelling force of Lambda - the Cosmological Constant ).
Actually, the 5th dimension (5th ninety degree quadrant) doesn't ‘mysteriously’ leap out of 4-D matter at all, but rather is an inevitably extrapolated, continuous - inevitably accelerated - extension of it, appearing as a discontinuous unit - 'Planck's constant h', always having the same value, because it is always the 5th ninety degree unit extending out of the 4 physical dimensions that preceded and generated it.
The (5th) ninety degree units moving at right angles from the 4-D charges ('particles') are called photons, or 'quanta' and are the smallest fundamental, consistent unit of energy. They do not actually contradict continuous field theory, but rather, are generated by the 4-D space-time continuum of particular matter.
The 5th and 6th dimensions of electricity and magnetism respectively, are accelerating, just as the source from which they invariably originate (4-D matter), but the expansion of electricity and magnetism (electromagnetism) is exponentially extended from matter and therefore accelerating at a much faster - quantum leaping - rate...
Producing an illusion of 'contradiction' of continuous field theory, whereas the apparently 'discontinuous' particle is actually a 4-dimensionally and continuously expanding charge of electricity which generates 5 dimensional quadrants - photons - at right angles from it's (material, corporeal, concentric) 4-D 'boundaries'. Refer Fritjov Capra's Tao of Physics, which does not resolve the above but allows for *the illusion of apparent contradiction - which is actually mutually supportive - the central meaning of * 'Tao'.
Subsequent to this conceptual departure in what had formerly been the generally agreed conceptualization of continuous field physics, Eddington said:
"We'll call matter 'particles' on Mondays, we'll call it 'waves' on Tuesdays, and we'll call it 'waveicles' the rest of the week." - Paraphrased.
Eddington's Spartan sense of humor about the apparent dilemma directly implies that the alleged objective quandary is chimerical.
Continuous field physics does not contradict discontinuous particle physics, or conversely. They accompany one another; the latter being generated by the former. As gravity is both a push (at short distances) and a pull (at long distances - re: http://forums.delphiforums.com/EinsteinGroupie), so particles and fields are likewise non contradictory and supportively reciprocal. Covariantly existing together. The particles (5th ninety degree unit of four D matter) projected at right angles from and outside of the 4-D accelerating fields of expanding matter.
The question of why matter is expanding is so far undetermined by anyone, certainly including the minority of people who recognize the accelerating expansion (of physical - 'solid' - matter).
On the other hand we have the opportunity to understand that matter is definitely expanding, and that it - for whatever reason - generates electricity and magnetism, which move, respectively, at right angles out of matter. Electricity emitted perpendicular to 4-D matter, and magnetism moving at right angles to electricity (re: 'electromagnetism' - the 5th & 6th dimensions).