WHY QUANTUM? Here is why...
The photon no matter its frequency is an indivisible particle. This is a postulate of Quantum Mechanics, which if untrue, we must ask Why Quantum? In order to defend this postulate against logical and experimental assaults, and to prevent us asking the question, 'Why Quantum?', a number of mathematical escape routes have been invented.
Experiment already shows that light can be blocked or partially transmitted through a polarization filter. Transverse waves fit this bill easily as they can be partially transmitted through a polarization filter. Light as a particle however faces a dilemma because a single photon cannot be partially transmitted like a wave, since according to the quantum mechanical postulate a photon is not divisible. It either goes through a polarization filter as a whole or it does not.
To now fit the above experimental reality into the quantum particle jacket, rather than query the particle view further, it is decided to overcome the dilemma by using mathematics to reconcile the observed partial transmission through a polarization filter on the one hand, with the postulate of photon indivisibility on the other. When a polarization filter is suitably adjusted so that light is half transmitted, it is thus invented to interpret the scenario that half the time the photon passes as a whole through the filter and half the time it does not pass at all, rather than accepting that as a transverse wave, half the wave can pass through a 450 inclination. The overall mathematical objective is to achieve at any cost the experimentally observed reality that half transmission of incident light is physically possible by polarization. The cost is high. "Probability" is introduced as a price into physics because of this desire to make the particle picture fit the experimental reality that is observed and simply explained by the wave-picture.
Further, it is known that the polarization properties of the transmitted light in a wave picture is unaffected by the encounter with the filter. This agrees with experiment. However, there is another dilemma as this can not hold for the particle picture. Since a second trap (or filter) can be set to determine the light's properties, it is invented that in the particle picture, each transmitted photon can have its polarization state changed instantaneously to suit what the polarization filter or experiment predicts for the wave-picture, so both particle and wave results turn out the same.
In order that the photon can wear the garment of ability to be polarized which is logically worn by transverse waves, "Spin" is invented as a property for Quantum particles.
To next remove the logical need that a particle must at least be in some state at a given time in order to have classically resulted in some determined outcome that is observed, which logic may spell doom for the probability alibi used above to explain the overall observed outcome for polarized light, it is further decreed that it is impossible to know the initial state. Therefore, even though from an outcome, you can infer the initial state, to plug further loop holes in the particle picture plan to be foisted on physics, "Superposition" is invented, so that a particle cannot on its own even have a particular state, but possesses all the possible states at the same time so that probability can work.
Attempt to determine the falsity or truth of this alibi that the particle is in a superposition of states by measurement, always finds that the particle is not in such a state of superposition but rather can always be found in a particular state. Again to escape this dilemma, another alibi is invented. That the act of measurement is what makes the wave function to collapse (i.e. the act of measurement is what caused the previously co-existing different superposed states to collapse into that which is observed and measured).
There is no end. As more paradoxes and illogicalities are discovered, more alibi will be mathematically manufactured. Some enjoy this exercise. It is not a topic I like spending precious time on because the silliness of the whole endeavor is obvious to most except mathematicians. As Eckard would say Quantum nonsense!
Akinbo
*To distil some of what is written above I have had to browse through my copy of The Quantum World by J.C. Polkinghorne.