[Edit: in the light of Nate Eldredge's answer below I rephrase the question]
P=NP is equivalent to the existence of a map of the following form:
Input: a polynomial-time non-deterministic Turing machine which accepts some language (call the language L) [Edit:wearenottoassumetheseNDTMscomewithanycertificateprovingtheyruninpolynomialtime--Ryanrequestedthisclarification,below]
Output: a polynomial-time deterministic Turing machine which accepts the language L
Is it known that if such a map exists then it cannot be computable?