Please show all steps and calculations. If you upload an image please make sure

Question

Please show all steps and calculations. If you upload an image please make sure it is clear and your writing is legible. Please write in print and not script or cursive.

Using a simple arrangement of Stern-Gerlach analyzers and detectors, and simple calculations and arguments, demonstrate:

a. The outcome of measuring the spin of a beam of particles in the x direction and z direction depends on the order in which you measure them.

b. You can know either the z component and x component of the spin of a beam with zero uncertainty (that is, complete certainty), but you cannot know both the spin z component and spin x component of a beam with complete certainty.

Explanation / Answer

A discrete-event simulation approach which provides a cause-and-effect description of many experiments with photons and neutrons exhibiting interference and entanglement is applied to a recent single-neutron experiment that tests (generalizations of) Heisenberg's uncertainty relation. The event-based simulation algorithm reproduces the results of the quantum theoretical description of the experiment but does not require the knowledge of the solution of a wave equation nor does it rely on concepts of quantum theory. In particular, the data satisfies uncertainty relations derived in the context of quantum theory.

1. Introduction

Quantum theory has proven extraordinary powerful for describing a vast number of laboratory experiments. The mathematical framework of quantum theory allows for a straightforward (at least in principle) calculation of numbers which can be compared with experimental data as long as these numbers refer to statistical averages of measured quantities, such as for example atomic spectra, the specific heat and magnetic susceptibility of solids. However, as soon as an experiment is able to record the individual clicks of a detector which contribute to the statistical average, a fundamental problem appears. Although quantum theory provides a recipe to compute the frequencies for observing events, it does not account for the observation of the individual events themselves [1

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