Substance, and accident, and their operations, All interfused together in such wise That what I speak of is one simple light. ~Dante 
Einstein, Helmholtz, Wigner, Sherrington, Mach, Schrodinger, Bohr, Tomonaga, Aharanov, Bohm  
Einstein Wigner Sherrington Schrödinger Bohr Tomonaga Aharonov Bohm Mach Cao Wittgenstein 
All the
fifty years of conscious brooding have brought me no closer to the
answer to the question: "What are light quanta?" Of course today every
rascal thinks he knows the answer, but he is deluding himself.
Einstein [If]
one entity
is influenced by another entity, in all known cases the latter one is
also influenced by the former. The most striking and originally the
least expected example for this is the influence of light on matter,
most obviously in the form of light pressure. That matter influences
light is an obvious fact — if it were not so, we could not see objects.
The influence of light on matter is, however, a more subtle effect and
is virtually unobservable under the conditions which surround us [...]
Since matter clearly influences the content of our consciousness, it is
natural to assume that the opposite influence also exists, thus
demanding the modification of the presently accepted laws of nature
which disregard this influence.
Wigner One
can only admire the colossal boldness
which led Weyl, onthe basis of a purelyformal correspondence, to his gaugegeometrical interpretation of electromagnetism. (London) When
a beam of light falls on the human eye, certain sensations are
produced, from which the possessor of that organ judges of the color
and luminance of the light. Now, though everyone experiences these
sensations and though they are the foundation of all the phenomena of
sight, yet, on account of their absolute simplicity, they are incapable
of analysis, and can never become in themselves objects of thought. If
we attempt to discover them, we must do so by artificial means and our
reasonings on them must be guided by some theory.
Maxwell It
turned out that,
once these foundations had been laid, symmetry could
be
of great help in elucidating the general character of the
spectra.
Weyl If
you ask a physicist what is his idea of yellow
light, he will tell you that it is transversal
electromagnetic waves of wavelength in the neighborhood of 590
millimicrons. If you ask him: But where does yellow
come in? he will say: In my picture not at all, but these kinds of
vibrations, when they hit the retina of a healthy eye, give the person
whose eye it is the sensation of yellow.
Schrödinger
We now proceed to the derivation of the laws of geometrical optics from the laws of wave optics. A rigorous and general derivation, however, requires a considerable amount of advanced mathematics so that we shall not go into details here. We shall be satisfied with observing the essential points by taking the simple example given above. The
problem is again that of the refraction
of monochromatic light
[...]
holds, as is apparent from the figure. In other words, the refractive index n is inversely proportional to the wavelength of the light wave in the respective media; i.e., n = k''/l The proportionality constant k'', however, may depend on the frequency or, in other words, on the color of the light. Tomonaga The science of colors becomes a speculation as truly mathematical as any other part of physics. ~Newton Hermann
Grassmann (along with William Rowan Hamilton) invented vector and
tensor algebra in 1844, but was unable to attract attention to the new
method.
He subsequently applied the methods of vector analysis to color in
order to calculate the outcomes of color mixtures.
In so doing, Grassmann proved that for every spectral color there
exists some other opponent color in the spectrum which when mixed with
the first color in the correct proportions will produce white light.
Boker
In the early 1990s, it was shown that the various superstring theories were related by dualities, which allow physicists to relate the description of an object in one superstring theory to the description of a different object in another superstring theory. These relationships imply that each of the superstring theories is a different aspect of a single underlying theory, proposed by Witten, and named "Mtheory". Mtheory
The Langlands
programme has, along these lines, something called the geometric
Langlands programme, which replaces the number fields by Riemann
surfaces. It is a very interesting theory which is much easier than the
number field case, but not trivial and still quite big. It is developed
by using the theory of vector bundles on Riemann surfaces. This theory
has been going on for quite a long time, has nice results and in it
there are geometrical analogues of the Langlands conjectures.
Atiyah

Eugene Wigner For
instance a star
which we perceive. The energy scheme deals with it, describes the
passing of radiation thence into the eye, the little light image of it
formed at the bottom of the eye, the ensuing photo chemical action in
the retina, the trains of action potentials traveling along the nerve
to the brain, the further electrical disturbance in the brain, the
action potentials streaming thence to the muscles of eyeballs and of
the pupil, the contraction of them sharpening the light image and
placing the best seeing part of the retina under it. The best 'seeing'?
That is where the energy scheme forsakes it. It tells us nothing of any
'seeing'. Everything but that.
Sherrington Erwin
("Mad Dog") Schrödinger
[It] was found possible to account for the atomic stability, as well as for the empirical laws governing the spectra of the elements, by assuming that any reaction of the atom resulting in a change of its energy involved a complete transition between two socalled stationary quantum states and that, in particular, the spectra were emitted by a steplike process in which each transition is accompanied by the emission of a monochromatic light quantum of an energy just equal to that of an Einstein photon. Bohr E = hv In the hands of
others, notably Issai Schur, Elie Cartan, and Hermann Weyl, the notion
of representation was extended to continuous groups, the most
important example being the group of rotations about a given point in
threedimensional space. This group has dimension three. For example,
if we are thinking of rotations of the earth about its center, we
have first to decide to what point we shall rotate the north pole. To
describe this point takes two coordinates. We have then to add a
third, because we are still free to rotate around the new pole through
an angle, whose size can be between 0^{◦} and 360^{◦}.
It is the representations of this group to which the oracular
pronouncement of Hermann Weyl about quantum numbers and group
representations applies.
The understanding of the fundamental role of this group and its representations in atomic spectroscopy and, ultimately, not only of representations of this group but also of many other groups as well in various domains of quantum physics led to a vigorous interest of the representation theory of finite and of continuous groups on the part of both physicists and mathematicians. The mathematical development remained for some time largely independent of the questions raised by spectroscopy and the later, more sophisticated theories of fundamental particles. There is not even, so far as I can see, a close relation between Weyl’s reflections on group theory and quantum mechanics and his fundamental contributions to the mathematics of group representations. Before describing how the concepts introduced by the physicists found their way back into mathematics, I recall briefly the issues that faced spectroscopists in the period after 1885, when the structure of the frequencies or wavelengths, thus the color in so far as the light is visible and not in the infrared or ultraviolet regime, of the light emitted by hydrogen atoms was examined by Balmer, and in the period after 1913, when N. Bohr introduced his first quantummechanical explanations. Langlands In classical mechanics, we recall that potentials cannot have such significance because the equation of motion involves only the field quantities themselves. For this reason, the potentials have been regarded as purely mathematical auxiliaries, while only the field quantities were thought to have a direct physical meaning. In quantum mechanics, the essential difference is that the equations of motion of a particle are replaced by the SchrÖdinger equation for a wave. This SchrÖdinger equation is obtained from a canonical formalism, which cannot be expressed in terms of the fields alone, but which also requires the potentials. Indeed, the potentials play a role, in SchrÖdinger equation, analogous to that of the index of refraction in optics. [...] The above discussion suggests that some further development of the theory is needed. Two possible directions are clear. First, we may try to formulate a nonlocal theory in which, for example, the electron could interact with a field that was some finite distance away. Then there would be no trouble in interpreting these results, but, as is well known, there are severe difficulties in the way of doing this. Secondly, we may retain the present theory and, instead, we may give a further new interpretation to the potentials. Aharanov, Bohm A
color is a physical object a soon as we consider its
dependence, for instance, upon its luminous source, upon temperatures, and so forth. ~Mach Is
there such a thing as a 'natural history of colors' and to what
extent is it analogous to a natural history of plants? Isn't the latter temporal, the former nontemporal? ~Wittgenstein
The principle
of duality in
projective geometry states that we can interchange point and line in a
theorem about figures lying in one plane and obtain a meaningful
statement. Moreover, the new or dual statement will itself be a theorem
— that is, it can be proven.
Kline
Surprisingly,
the Langlands dual group also appears in quantum physics in what looks
like an entirely different context; namely, the electromagnetic
duality. Looking at the Maxwell equations describing classical
electromagnetism, one quickly notices that they are invariant under the
exchange of the electric and magnetic fields. It is natural to ask
whether this duality exists at the quantum level.
Frenkel

quanta action color spectra EM photon E = hv optics refraction nonlocal 


