The question is thus: Why do you and I experience color the same way?
Having gained knowledge on how the human visual system works, as well as how the brain-eye system processes visual stimulation the answer follows from simply traversing the path of photons as they enter the eye. The journey proceeds as follows. The first stage involves photons of various energies released or reflected by the surrounding environment in the direction of the eye. Electromagnetic theory tells us that photon energy corresponds to photon wavelength in a definite way by way of the equation:
E = hv
where E is the energy , h is the Planck constant and v is not the Roman "vee" but rather the greek symbol "nu" and represents the frequency of the propagating photon. Since frequency is inversely related to wavelength , the equation could be written as:
where w is now the wavelength of the propagating photon. I won't get into the potentially sticky area of photons as propagating particles versus propagating waves, Physicists learned that in order for electromagnetic equations to provide consistent results both interpretations are required depending on what is happening at the interaction point. For our journey the interaction occurs at the back of the human retina, but before we get there, a bit about the wavelength and energy. It just so happens that photons with high frequency (therefore low wavelength) have higher energy than photons with low frequency or high wavelength. In my time studying quantum mechanics I've conceptualized this as a measure of the interaction probability for the propagating photon. High energy photons have high interaction probabilities while lower ones have lower interaction probabilities...unfortunately this fails to hold. The curious nature in which matter absorbs energy in quantized packets means that it is possible for high frequency photons to be completely ignored by certain materials if the quantum states required to stimulate those materials are not triggered. In particular, the mechanism of stimulation employed by eyes involves stimulation of photosensitive enzymes in the rod and cone sensors in the back of our retinas. The rods are sensitive to ANY photon energy while the cones have specific filter ranges of sensitivity. Like the aformentioned surfaces, the enzymes that form the sensitive material of these rods and codes reacts in specific ways. The rods are sensitive to a plethora of energies across the electromagnetic spectrum thus making them good gauges of intensity, where the cones have specific violet, red-blue and yellow-green sensitivity ranges. The perception of a rainbow of colors comes from our brains synthesis of the many signals coming from these tiny cones. These sensitivites are provided by enzymes that have specific molecular construction that is stimulated when photons of given energies or ranges impinge them. The molecules absorb part of the energy and emit additional photons that propagate down the optic nerve in a cascade of triggered stimulation and emmissions. Eventually these signals reach the brains visual system and are synethesized into the perceptions of color that we have.
The answer to the question of why we see the same is in fact hidden in the mechanism of transition. The cones consist of specific types, that will be stimulated only when photons having the required energy impacts them, the mechanism for this is explained by quantum jumps of photons from high to low orbital positions. These gap jumps are always the same because the unique molecules are constructed of the exact same elements. Thus a 445 nm photon hitting a cone sensitive to that wavelength of energy will always kick an electron to a different orbital and in so doing release a photon of a specific energy in return...thus continuing the cascade. The point is the underlying physics of the molecules is what normalizes the response to the original photons at the rod and cone sensitive surfaces. All photons that do not induce stimulation at a cone are filtered out of the response leaving only the pure responses to fixed energies. Since these responses are tied to the enzymes used to transmit the signal to the brain, and these enzymes are the same ones used in all human beings , the response at the brain processing region must be the same. However this is not sufficient to conclude that the "perception" of stimuli will be the same. Here is the consistency of neuronal cells comes into play, whatever neurotransmitters that are responsible for relaying the visual signals (now normalized) they cause the same effects at the neurons, so long as the quantities of neuronal stimulation are similar the perception will be the same. Note the key phrase "so long as", there are in fact examples of perception being different for different people. People with color blindness for example see a skewed pallette as a result of a different filtering of the stimuli at the rods and cones, similarly variations in the neurotransmitters between people can similarly lead to warped perceptions (as may be experienced by those under the effects of psychoactive drugs or other brain modifying agents) so the answer is not as cut and dried as it may seem to be from the outset. Perception does change when ever any stage of the stimulation, neurotransmission or neuronal processing is effected, otherwise the preeminence of the physics (the underlying photon stimulated emission cascades) leads to similar perceptions for all.