In this paper we construct a theory of quantum mechanics based on Shannoninformation theory. We define a few principles regarding information-based frames of reference,including explicitly the concept of information covariance, and show how an ensemble of allpossible physical states can be setup on the basis of the accessible information in the localframe of reference. In the next step the Bayesian principle of maximum entropy is utilized inorder to constrain the dynamics. We then show, with the aid of Lisi’s universal action reservoirapproach, that the dynamics is equivalent to that of quantum mechanics. Thereby we showthat quantum mechanics emerges when classical physics is subject to incomplete information.We also show that the proposed theory is relational and that it in fact is a path integral versionof Rovelli’s relational quantum mechanics. Furthermore we give a discussion on the relationbetween the proposed theory and quantum mechanics, in particular the role of observation andcorrespondence to classical physics is addressed. In addition to this we derive a general formof entropy associated with the information covariance of the local reference frame. Finally wegive a discussion and some open problems.
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