Title: Quantum mechanics from an epistemic state space,
Abstract: We derive the Hilbert space formalism of quantum mechanics from epistemic
principles. A key assumption is that a physical theory that relies on entities
or distinctions that are unknowable in principle gives rise to wrong
predictions. An epistemic formalism is developed, where concepts like
individual and collective knowledge are used, and knowledge may be actual or
potential. The physical state $S$ corresponds to the collective potential
knowledge. The state $S$ is a subset of a state space $\mathcal{S}=\{Z\}$, such
that $S$ always contains several elements $Z$, which correspond to unattainable
states of complete potential knowledge of the world. The evolution of $S$
cannot be determined in terms of the individual evolution of the elements $Z$,
unlike the evolution of an ensemble in classical phase space. The evolution of
$S$ is described in terms of sequential time $n\in \mathbf{\mathbb{N}}$, which
is updated according to $n\rightarrow n+1$ each time potential knowledge
changes. In certain experimental contexts $C$, there is initial knowledge at
time $n$ that a given series of properties $P,P',\ldots$ will be observed
within a given time frame, meaning that a series of values $p,p',\ldots$ of
these properties will become known. At time $n$, it is just known that these
values belong to predefined, finite sets $\{p\},\{p'\},\ldots$. In such a
context $C$, it is possible to define a complex Hilbert space $\mathcal{H}_{C}$
on top of $\mathcal{S}$, in which the elements are contextual state vectors
$\bar{S}_{C}$. Born's rule to calculate the probabilities to find the values
$p,p',\ldots$ is derived as the only generally applicable such rule. Also, we
can associate a self-adjoint operator $\bar{P}$ with eigenvalues $\{p\}$ to
each property $P$ observed within $C$. These operators obey
$[\bar{P},\bar{P}']=0$ if and only if the precise values of $P$ and $P'$ are
simultaneoulsy knowable.