Standard Quantum Mechanics, although successful in terms of calculating and predicting results, is inherently diffcult to understand and can suffer from misinterpretation. Entropic Dynamics is an epistemic approach to quantum mechanics based on logical inference. It incorporates the probabilities that naturally arise in situations in which there is missing information. It is the author's opinion that an advantage of this approach is that it provides a clearer mental image with which to picture quantum mechanics. This may provide an alternate means of presenting quantum mechanics to students. After a theory is presented to students, an instructor will then work through the paradigmatic examples that demonstrate the theory. In this thesis, we will be applying Entropic Dynamics to some of those paradigmatic examples. We begin by reviewing probability theory and Bayesian statistics as tools necessary for the development of Entropic Dynamics. We then review the topic of entropy, building from an early thermodynamic interpretation to the informational interpretation used here. The development of Entropic Dynamics involves describing a particle in terms of a probability density, and then following the time evolution of the probability density based on diffusion-like motion and the maximization of entropy. At this point, the review portion of the thesis is complete.
We then move on to applying Entropic Dynamics to several of the paradigmatic examples used to explain quantum mechanics. The rst of these is wave packet expansion. The second is interference, which is the basis behind many of the important phenomena in quantum mechanics. The third is the double slit experiment, which provides some interesting insight into the subject of interference. In particular, we look at the way in which minima can occur without a mechanism for destructive interference, since probabilities only add. The idea of probability flow is very apparent at this point in the discussion. The next example is that of the harmonic oscillator. This leads to an interesting insight concerning rotation and angular momentum as it corresponds to the flow of probability. The last example explored is that of entanglement. The discussion begins with a review of EPR, but then comes to the interesting conclusion that many of the problems inherent in the traditional approach to entanglement do not exist in Entropic Dynamics. The last topic covered in this thesis consists of some remarks concerning the state of education research as it pertains to quantum mechanics and the ways in which Entropic Dynamics might address them.
|Commitee:||Cafaro, Carlo, Knuth, Kevin, Lunin, Oleg, Robbins, Daniel|
|School:||State University of New York at Albany|
|School Location:||United States -- New York|
|Source:||DAI-B 79/09(E), Dissertation Abstracts International|
|Subjects:||Quantum physics, Physics, Theoretical physics|
|Keywords:||Interpretation, Maximum entropy, Probability, Quantum|
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