Yes. The author of "Information Theory, Inference and Learning Algorithms" had this to say about it:
http://www.amazon.com/review/R16RJ2PT63DZ3Q/ref=cm_cr_rev_de...
http://www.amazon.com/review/R16RJ2PT63DZ3Q/ref=cm_cr_rev_de...
It seems like PCA would already be a method that would only mean something if it was applied to comparable dimensions. What would transformed, dimensioned variables mean anyway? Chart A=mass - 3charge by B = mass + 2charge. What could a correlation mean.