Mutations do not have an ability to create new information.
What definition of information are you using here? Under any scientific definition I knoww of, mutations can increase the amount of information and change the information that is there. (If you are not sure, try looking up Shannon Entropy, bits or nats, and see if that is what you mean.)
That is scientifically proven.
No. It really isn't. This has been discussed over and over, and it is getting silly now.
Here is an example. Consider this length of DNA code (using Shannon's language, but other definitions produce similar results:
TAGCCTGCCTTA
How much info does it have? Each letter has four options, so two 'bits' of information (you have to ask two questions to get the answer: (1) is it either a G or C? No. (2) Is it an A? No. Then is is a T. More answers required, more information.)
12 letters, so 12 x 2 bits = 24 bits of information.
OK, lets have a point mutation. The code changes to TAGCCTG
ACTTA. How much info des this have? The same amount of information, 24 bits, but
different information.
So now we have a duplication mutation, leaving TAGCCTGACTTA
TAGCCTGACTTA. This has 25 bits of information (24 questions to determine the first 12 letters, then one more question to ask 'is it duplicated?')
Now another point mutation:TAGC
ATGACTTATAGCCTGACTTA. How much information? Rather more than 25, because the simple 'is it duplicated?' question won't completely specify the seqence. You'd probably have to go back to the '2 bits per letter' calculation, meaning 2 x 24 = 48 bits of information.
There you have it: a point mutation can change the information to produce different amino acids when translated, while transposition or duplication can dramatically increase the amount of information.
Mutations always, without exception, work on what already exists.
Yes, they must work on whatever genome there is there already, but they are not restricted to the pre-existing information. New information can be produced trivially.