  We show that D=4 Minkowski space is an emergent concept related to a class of
operators in extended Hilbert space with no positive-definite scalar product.
We start with the idea of position-like and momentum-like operators (Plewa 2019
J. Phys. A: Math. Theor. 52 375401), introduced discussing a connection between
quantum entanglement and geometry predicted by ER=EPR conjecture. We examine
eigenequations of the simplest operators and identify D=4 Minkowski space as to
be spanned by normalized eigenvectors corresponding to the zero eigenvalue.
Both spacetime dimension and signature of the metric are fixed by the
regularization procedure. We generalize the result to the case of more general
operators, being analogues to quantum fields. We reproduce the Minkowski space
again, however, now in a holographic way, as being identified with the
conformal boundary of $AdS_5$. We observe an interesting analogy to string
theory and, in particular, to AdS/CFT correspondence.
