If the EMH were true, price curves would always display maximum entropy, i.e. randomness, because there would be no spare redundant information that could be used to make predictions about the future. (This is based on Shannon's Communications Theory, but the maximal entropy bound applies to any system that mixes a predictable signal with random noise.)

It doesn't matter if you use an evolutionary explanation for price curves, as in AMH, or claim they're controlled by planetary alignments - because the prediction that price curves show maximum entropy is falsifiable regardless of possible causes.

And when it's tested, it is indeed falsified. See e.g.

http://www.turingfinance.com/hacking-the-random-walk-hypothe...

tl;dr There are standard tools for estimating entropy, and they all agree that markets aren't truly random. Therefore they can't be maximally efficient.

Quants make a living by mining the signal from the randomness. There's a lot of debate about the best way to do this, but there's no serious disagreement among quants that it's possible - and the people who make money by employing them tend to agree.