Sam Artigliere's Blog

I’ve begun work toward creating a page introducing Bohmian mechanics, a topic that plays a small but central role in my novel The Formula. I tried to come up with a way to make this introduction brief. However, after much deliberation, I feared that such brevity would make such a page like many popular science pieces-a string of generalizations and other unexplained statements that might pique a reader’s interest but leaves them with no real understanding of the topic. As stated in the introduction to this website, my goal is to move beyond such a popular understanding, but in a way that can be comprehended by an interested reader without extensive pre-existing knowledge of math and science. To do this, I believe that the details left out in popular science explanations must be filled in.

To gain such an understanding of Bohmian mechanics in particular, some background in (though not an exhaustive knowledge of) mathematics is needed. Accordingly, I’ve completed a page outlining the basics of Euclidean Geometry and have half completed a page on trigonometry. Next will be some information on calculus and differential equations. Finally, and most importantly, I’ll discuss linear algebra, a branch of math that is indispensable to comprehending quantum mechanics. For the time being, I’ll try to give just what I think is necessary to understand the subject at hand. At a later date, I’ll try to provide additional information that hopefully will create a more comprehensive presentation though, after starting work on this, I’ll probably have to do this by providing links to already established presentations 1) because I don’t think I can complete such an enormous task myself and 2) because comprehensive presentations are already available that are probably much better than I can ever produce.

After the math, I’ll need to provide an introduction to quantum mechanics. That introduction will need to proceed, at least, through a derivation of the Schrodinger equation since it is a modification of the Schrodinger equation that is central to Bohm’s theory. I’ll probably base my discussion on Quantum Mechanics: The Theoretical Minimum by renowned physicist, Leonard Susskind. It provides a detailed mathematical derivation of the Schrodinger equation but explains all the math in simple terms. (I strongly recommend The Theoretical Minimum series of books and free online lectures by Dr. Susskind for any interested amateur-like myself.) My ultimate goal with the page is to review Bohm’s original derivation of his so-called guiding equation, an equation that is the heart and soul of his theory.

Planning on what to include so as to streamline the text as much as possible has been a difficult task, one that has occupied most of the time elapsed since my last post. I’d like to say that I’ll have this article complete soon but, frankly, I’m not optimistic. We’ll see how it goes.