PHYS195 NotesChapter8

PHYS195 NotesChapter8 - Chapter 8 Quantum Measurement and...

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Chapter 8 Quantum Measurement and Bell’s Theorem The combination of the facts that there is a probability amplitude that superimposes states a from adding of all paths, a wavelike property, and the interactions being instantaneous and stochastic leads to what are often interpreted as paradoxes in the quantum behavior of things. These ideas are treated under the heading of measurement theory. Historically we could not do experiments on individual fundamental par- ticles and could only deal with ensemble systems and the language was developed in that context. We are now entering an era in which we can ma- nipulate individual fundamental systems. We are finding that all the rules that were developed in the ensemble language work for the fundamental systems. In the following we deal with light and photons as our fundamental enti- ties. This is a choice of convenience. Everything that I do here goes through for electrons. or any fundamental entity. The photon is a particularly simple system to deal with . 8.1 A Two Level System In order to understand the essence of quantum mechanics and the measure- ment process in particular, lets study the simplest system possible. We will work with a system that has only two states and thus can appear as only a superposition of these two possible states. The double slit is an example. The light had to come from either slit one or slit two. It turns out that light itself offers us an example of a two level system, 241
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242 CHAPTER 8. QUANTUM MEASUREMENT AND BELL’S THEOREM the two polarizations of light. In the classical wave picture of light, the light is oscillations in the value of the electric field, ~ E ( x, t ), and the magnetic field, ~ B ( x, t ). Maxwell’s equations determine that nature of the behavior of the electric and magnetic field. For light these equations require that the electric field be transverse to the direction of the motion of the light and that the magnetic field be perpendicular to both the electric field and the direction of propagation. Thus if we are given a direction for the light to travel, the electric field can only point in some direction in a plane, a two dimensional space. Figure 8.1: Electric Wave In one of our home experiments, we played with polarizers. These are sheets that absorb the light that has polarization transverse to a given direc- tion and allows light polarized in the given direction to pass. In other words, light traveling in given direction comes in two varieties, let’s say horizontal and vertical, which are at right angles with respect to each other. If we had measured carefully in our home experiment with polarizers,
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This note was uploaded on 01/20/2010 for the course PHYS 195 taught by Professor Anderson during the Spring '07 term at San Diego State.

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PHYS195 NotesChapter8 - Chapter 8 Quantum Measurement and...

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