The 4th derivative of a sine wave is itself. This, of course, not only is a fact, but can be used to define the sine wave. My question is, are there any theories relating the abundance of sine waves in QM to the fact that the largest dimensions of space-time are together 4 dimensional? For example, I have often heard string theory explained as vibrating branes. Vibration tends to imply sine wave, so does string theory explain the causes of this vibration in terms of a 4th derivative being equal to the undifferentiated function?