We present a fundamental theoretical obstacle that prevents quantum computers obeying 4 axioms from being more than a constant factor more powerful than classical ones. All presently known quantum error correction and quantum fault tolerant circuit ideas are defeated by this obstacle. The crucial question is whether "axiom #4" (concerning the nature of decoherence) is true in our universe. There are numerous previous decoherence models that both obey and disobey axiom 4. Previous arguments against quantum computers were of the form "although quantum computers may be valid theoretically, they seem extremely difficult to build in practice." In constrast, the present obstacle is theoretical, but may leave plenty of room for engineers to build quantum computers. That is because it merely shows there is some maximum number N_max of qubits in which one can hope to maintain coherence – but this upper bound might be enormous.Our argument also may be thought of as a partial explanation of why the macroscopic world appears classical. For that purpose, even a bound as weak as N_max<10³⁰ still seems interesting.[This resided on my web page since Mar.2003, and earlier versions of the manuscript were much older, e.g. I showed one to Peter W. Shor in the mid-1990s; now copying to VIXRA for archival purposes.]