Colors and the Speed of Light: A Thought Experiment

Suppose that we are moving at the speed of red light through a vacuum. Suppose further that, directly in front of us, there is an object that is also red.

Let us first refresh ourselves on how color is actually perceived by the human eye. White light is comprised of equal parts of all the other colors (or types of light) in the visible spectrum, all which have different wavelengths, frequencies, and energy levels. When this light strikes an object, part of it is absorbed by the object, and part of it is reflected, deflected, and diffracted back in various ways. These lights are the ones that we interpret as colors. So, in terms of our red object, it is absorbing all the types of light that aren't red. The red light photon bounces off the object and into our eye, where it interacts with photopsins. The color that we thus see depends on the energy level of the photon that enters our pupil (in this case 1.77 eV, relating to red light), as this determines the strength of the electrical signal sent to the brain.

Now, since the color that we register is dependent on the energy of the photons that breach our eye, and since the energy level of light is calculated via multiplying Planck's constant by the frequency of the wave that accompanied those photons, the color that we detect is also ultimately related to the frequency of the light.

Since we are moving at the speed of red light, towards an object that is emitting red light, the frequency with which the red light waves coming from that object hit our eye should theoretically be doubled (assuming the object is aligned with our sight in a perfect 180 degree angle). Doubling frequency should then double the energy with which the photon interacts with our photopsins, doubling the strength of the electrical signal to the brain. Since double the energy of red light is 3.54 eV, what we actually see in front of us is not a red object, but a violet one (since 3.54 eV corresponds to violet light).

Some further interesting propositions can be gathered from all this. For example, if we were moving at the speed of red light and were instead approaching an object that was emitting infrared light (which we cannot see), it is possible that we would perceive that object as violet as well. On the other end of the spectrum, if we were still moving at the speed of red light and approaching say, a blue object, the object would now relatively be giving off ultraviolet light, which we also cannot see. Thus, the invisible becomes visible, and vice-versa.

All references to color energy were taken from Wikipedia.