I wasn't aware that the pigment in red cabbage works as a pH indicator, but I'm delighted to learn something new. One of my favorite web sites for answering these kinds of questions is this . In fact, the answer to your question is at .

Here's a summary:
Molecules that result in visible color are called pigments. They produce color because certain wavelengths of light energy are absorbed by electrons in the molecular bonds. All the wavelengths that are NOT absorbed are reflected back and result in color. (To produce reddish purple, a pigment would absorb orange, yellow, green and blue wavelengths.) Molecules that do not result in visible color simply do not absorb visible wavelengths of light.

Although all pigments produce color, there are many different kinds of pigments, depending on their molecular structure. The particular pigment that causes the red color in red cabbage is a type of pigment called anthocyanin, a flavenoid.

Many natural red pigments contain anthocyanin. Although many plant pigments do have metal atoms in their structure (e.g. chlorophyll-a), anthocyanins do not. The electrons forming the chemical bonds in the benzene ring structures are what absorb light energy. The pH of the pigment molecule's environment affects the strength of the chemical bonds in the benzene rings, which affects the vibration speed of the chemical bonds and in turn the wavelengths of light the electrons in those bonds absorb.