Can you define each of the 11 dimensions?

Answer 1

Dimensions can be defined mathematically without having a corresponding meaning in our observable four D universe. String/M theory has come up with higher dimensions in order to get results that correspond to observable quanta (like photons, muons, etc.) as they exist in four-D space-time. But the photons, muons, and such remain four-D quanta even though it took more dimensions to define them.

For example, we can define a 2-D square as a projection of a 3-D cube. So we use three dimensions to describe a two dimensional object. That's like casting a shadow of a box on a sheet. The box is 3-D, but the shadow is 2-D. In similar way, 10, 11, and even higher dimensions have been used to define things on our 4-D world. Why?

Because the math works and the solutions are often easier to find when working in higher dimensions. There is no indication that these higher dimensions were used because there were physical reasons to suspect the existence of higher dimensions.

Answer 2

Even those who know string theory inside out can't define any of the 11 dimensions other than as mathematical entities. Right now that's all they are.