The inverted spectrum is the hypothetical concept of two people sharing their color vocabulary and discriminations, although the colors one sees—one's qualia—are systematically different from the colors the other person sees.
The concept dates back to John Locke. It invites us to imagine that we wake up one morning, and find that for some unknown reason all the colors in the world have been inverted, i.e. swapped to the hue on the opposite side of a color wheel, the complementary color. Furthermore, we discover that no physical changes have occurred in our brains or bodies that would explain this phenomenon. Supporters of the hypothesis of qualia as non-physical entities argue that, since we can imagine this happening without contradiction, it follows that we are imagining a change in a property that determines the way things look to us, but that has no physical basis. In more detail:
The argument thus states that if we find the inverted spectrum plausible, we must admit that qualia exist (and are non-physical). Some philosophers find it absurd that an "armchair argument" can prove something to exist, and the detailed argument does involve many assumptions about conceivability and possibility, which are open to criticism. Perhaps it is not possible for a given brain state to produce anything other than a given quale in our universe, and that is all that matters. The question, however, can arise how these critical philosophers, using the same armchair technique that they are criticizing, refute the robust argumentation of the Inverted spectrum experiment?
...there are more perceptually distinguishable shades between red and blue than there are between green and yellow, which would make red-green inversion behaviorally detectable. And there are yet further asymmetries. Dark yellow is brown (qualitatively different from yellow), whereas dark blue is blue[...] Similarly, desaturated bluish-red is pink (qualitatively different from saturated bluish-red), whereas desaturated greenish-yellow is similar to saturated greenish-yellow. Again, red is a "warm" color, whereas blue is "cool"—and perhaps this is not a matter of learned associations with temperature.
If the Hurvich–Jameson account of our color experiences is correct, then it is empirically impossible to change the profile of our subjective color responses to the world without changing in some way the response profile of our opponent cell activation vectors, as outlined, for example, in the preceding paragraph. From this reductive perspective, sundry qualia inversions are indeed possible, but not without the appropriate rewirings within the entirely physical H–J net that embodies and sustains all of our color experience. If we wish to resist this deliberately reductive account—as some will—then let us endeavor to find in it some real empirical failing. Imaginary failings simply don't matter.
In some cases, the inverted spectrum scenario is clearly possible. For example, if a world is simulated on a computer and we are looking at this world on a screen, perhaps through the eyes of one of the characters in the simulation, then clearly it is possible to invert the spectrum from our perspective. This is because some small changes to the code used for displaying the world would make it so that it would display in red what was displayed in green before, etc., without changing the underlying simulated physics. Though this would entail that code on a computer which represents a creature with sight is equivalent with a creature with sight. It is not clear whether we can conclude from such examples that an inverted spectrum is possible in ordinary life.
In his book I Am a Strange Loop, Douglas Hofstadter argues that the inverted spectrum argument entails a form of solipsism in which people can have no idea about what goes on in the minds of others—contrary to the central theme of his work. He presents several variants to demonstrate the absurdity of this idea: the "inverted political spectrum", in which one person's concept of liberty is identical to another's concept of imprisonment; an inverted "sonic spectrum" in which low musical notes sound like "high" ones and vice versa (which he says is impossible because low sounds can be felt physically as vibrations); and a version in which random, complex qualia such as riding a roller coaster or opening presents are reversed, so that everyone perceives the world in radically different, unknowable ways.