Physics and astronomy

Adjustment the orientation of remote devices

V. A. Zorich

Lomonosov Moscow State University

Abstract: It is well known that the Stern — Gerlach device orients the quantum particles of spin $1/2$ along the vertical axis arranging them into two beams of opposite polarizations.
We show how one can use this phenomenon to adjust the orientation of remote devices. We discuss only the mathematical concept without the technical aspects of the implementation that might be essential.
The main idea is as follows.
Use device $S$ to put the particle in state $+S$ (spin in the direction of the $z$ axis of device $S$) and send it to device $S'$.
The measurement of the received particle on device $S'$ can give either the $+S'$ state (spin in the direction of the $z'$ axis) or the $-S'$ state with probabilities $ p_{+} = \cos^2 {\frac{\alpha}{2}}$ and $p_{-} = \sin^2 {\frac{\alpha}{2}}$ respectively, where $\alpha$ is the angle between the $z$ and $z'$ axes of devices $S$ and $S'$ .
If we can use the $S$ device to put particles in the $+S$ state and in that state send them to the remote device $S'$ without interference, then, after performing a representative series of launches of such particles, according to the statistics of the states observed on device $S'$, one can calculate probabilities $p_{+}$ and $p_{-}$.
By either of values $p_{+}$ or $p_{-}$, (if they are calculated or measured reliably enough) one can find angle $\alpha = \alpha_z$ of the deviation of the $z'$ axis of device $S'$ from the $z$ axis of device $S$.

Keywords: quantum particle, spin, Stern — Gerlach device, orientation.

UDC: 517.5, 514.8, 53.06, 53.08
BBK: 22.161, 22.151, 22.311, 22.314

Received: 25.02.2019

DOI: 10.15688/mpcm.jvolsu.2019.2.6