Impact of the Existence of One-Way Functionson the Conceptual Difficulties of Quantum Measurements
Abstract:One-way functions are functions that are easy to
compute but hard to invert. Their existence is an open conjecture; it
would imply the existence of intractable problems (i.e. NP-problems
which are not in the P complexity class).
If true, the existence of one-way functions would have an impact
on the theoretical framework of physics, in particularly, quantum
mechanics. Such aspect of one-way functions has never been shown
In the present work, we put forward the following.
We can calculate the microscopic state (say, the particle spin in the
z direction) of a macroscopic system (a measuring apparatus
registering the particle z-spin) by the system macroscopic state (the
apparatus output); let us call this association the function F. The
question is: can we compute the function F in the inverse direction?
In other words, can we compute the macroscopic state of the system
through its microscopic state (the preimage F -1)?
In the paper, we assume that the function F is a one-way function.
The assumption implies that at the macroscopic level the Schrödinger
equation becomes unfeasible to compute. This unfeasibility plays a
role of limit of the validity of the linear Schrödinger equation.
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