Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband? In DSP book by Proakis and as well as in this pdf, it is mentioned that practical causal digital filters cannot have an infinitely sharp transition from Pass-band to Stop-band. Why is it so? Can you please provide a detailed explanation (with proof)? 
Edit 1: In the book in was just mentioned that is a consequence of the Gibbs phenomenon, which results from the truncation of h(n) to achieve causality. I didn't understand how.
I don't have a concrete proof for this one. However, I can tell you this... 
Consider a perfect low pass filter. The time domain representation is a sinc. And for any system to have a sharp transition band, a base signal has to be multiplied with a rectangular waveform in the frequency domain. Which implies that, the time domain signal of the same has to be convoluted with a sinc in time domain. We know that sinc function is a non causal signal. 
Hence proved.