TITLE: Most 'obvious' open problems in complexity theory
QUESTION [14 upvotes]: What open problems in computational complexity theory have the most 'obvious' answers, regardless of whether that answer is true or false?  The problems I'm talking about certainly have more 'obvious' answers than P =?= NP.
I'll start this with
ZPP =?= EXPTIME

REPLY [2 votes]: A) Multiplication (of $n$--bit numbers) obviously takes longer than addition.
B) Sorting $n$ objects obviously takes longer than linear time.  (I suppose that this is obvious because it is true: there is a lower bound of $n \log n$ for comparison-based sorts.  However, radix sort of integers can be faster.  In fact, for any collection (of a particular type of object), there just might be a super clever way to sort it faster than $n \log n$....)