Category: Physics

Special Relativity and General Relatity Notes

It’s been a while since my last post. However, I’ve been working on new content during that time. Specifically, I published notes on special relativity – about a year ago, actually; hard to believe it’s been that long. And today, I published notes on general relativity. A few sections of the latter page are still under construction. I hope you find these pages useful.

The Formula – new addition, free

The Formula, 2nd edition, has now been published and is free from Sunday 5/17/2020 through Thursday 5/22/2020. Some of the math has been removed from the novel to improve the flow of the story. However, more detailed versions of chapters that have been shortened are available on this website as well as other supplementary material, for readers so inclined.

The Formula: Supplemental Material

On 9/12/2019, I made a post indicating my intention to publish articles on 4 topics – topics designed to provide explanatory material to supplement my novel, The Formula. These 4 topics were:

  1. RSA encryption
  2. Quantum encryption
  3. Bell’s Theorem
  4. Bohmian mechanics

My articles on these 4 topics have finally been published. Here are the links to those articles:

Some additional background material is also needed to understand the rather complicated subject of Bohmian mechanics. Here are links to those pages:

This project (at least for me) has been a massive undertaking. As noted in my last post, I’ve attempted to edit as best I could, but if any errors or inaccuracies have gotten by me, please let me know by clicking on the “Contact” link in the right upper corner of the page.

Bohmian Mechanics

My page on Bohmian mechanics has finally been published. Despite my initial (unrealistic) ambitions to the contrary, this could not have been made understandable without providing extensive background information. Accordingly, multiple additional articles have been published simultaneously. They include the following:

I attempted to edit this material as best I could but the project has been extensive. Therefore, it’s likely that some errors have slipped past me. If anyone finds any typos, inaccuracies or other problems, please let me know and I’ll attempt to address them.

I hope that you will find this material interesting and informative.

New Articles on Classical Physics

I have recently published three articles on non-Newtonian formulations of classical physics:

These articles provide important background information for a forthcoming article on Bohmian mechanics, an article that has been a long time in the making. Hopefully, it will be completed soon.

Bell’s Inequality 3

The series on Bell’s inequality is finally complete with the completion of Bell’s Inequality 3, a step-by-step explanation of Alain Aspect’s landmark paper “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities.” Physical Review Letters, vol. 49, no. 2, July 1982, pp. 91-94. A link to this third installment of the Bell’s inequality series is found below:

Bell’s Inequality 3

As stated in a previous post, the final series of the “next four topics” that relate to my novel The Formula will address Bohmian mechanics. And as suggested in that post, such an account of Bohmian mechanics will require a discussion of a fair amount of mathematics and basic quantum physics and will take some time. I hope to get started on this soon.

Bell’s Inequality 2

After over a month of writing, editing and re-editing, Bell’s Inequality 2 is finally ready to publish. I learned LaTex and put my equations directly into my page with a plugin call QuickLaTeX. It’s quite a tedious process, but as far as I can tell, it’s either that or create my pages as PDFs, as I did for Bell’s Inequality 1. Hopefully, I’ll get better at it as I go. I’ve investigated (and tried) a few other plugins but they haven’t worked very well. If anyone knows of an easier way, I would be eager to hear about them.

The article is a bit long, mainly because there are multiple explanations of subjects that are second nature to experts but probably confusing to the uninitiated. Frankly, I wish I would have had more such explanations when I was trying to learn about these topics. That’s why I included them. However, as I read them over, the explanations, themselves, are tedious. I would be interested in feedback about how I might deliver this content in a more efficient manner.

Bell’s Inequality 2 is about John Bell’s original paper, published in 1966, that provided a way to test whether quantum mechanics is a true description of reality or-as Einstein suggested-an incomplete theory; a theory that overlooks the fact that local hidden variables are actually at play to produce the results that quantum mechanic predicts. However, Bell’s paper raised theoretical questions but did not provide experimental evidence to answer them. The scientific world would have to wait a number of years for such answers. The paper that is usually cited as having provided a definitive answer to these questions is one by Alain Aspect in 1982. Aspect’s paper is the subject of the third installment in this series on Bell’s inequality, an article entitled Bell’s Inequality 3. I will begin work on it shortly, a project that will undoubtedly take some time. Meanwhile, a link to the second installment in this series can be accessed by clicking on the link below:

Bell’s Inequality 2

Bell’s Inequality 1

The next topic I’d like to discuss is Bell’s Inequality, a mathematical relationship that opened the door to validation of quantum mechanics. My goal is to do this in 3 installments. The first discussion on this subject can be found by clicking on the following link:

Bell’s Inequality 1

Next 4 topics

The next 4 topics that I would like to discuss on this blog expand upon subjects described in my novel, The Formula. They are:

  1. RSA encryption
  2. Quantum encryption
  3. Bell’s Theorem
  4. Bohmian mechanics

An explanation of RSA encryption is given in the long version of Chapter 62 from The Formula. It can be found elsewhere on this website. My page on RSA encryption will be, for the most part, the discussion in Chapter 62 (Long Version) presented in expository form. In keeping with my attempt on this site to avoid “black boxes,” I have included a detailed but slow and step-by-step derivation of the mathematical formulas used in RSA encryption. I’ve done this so the reader isn’t left scratching his or her head, wondering where those formulas came from. Because mathematical proofs have never been my forte, I’ve relied heavily on information gleaned from several on-line sources.

Likewise, my page on quantum encryption is largely an expository version of the treatment on this subject given in Chapter 79 (Long Version) from The Formula. This chapter can also be found on this website and can be reached by clicking here.

Because my treatments of RSA  and quantum encryption are essentially reformulations of the descriptions found in the above-mentioned chapters, it shouldn’t take too long to produce them. On the other hand, I plan to expand considerably on the discussion of Bell’s Theorem given in Chapter 79 (Long Version). Thus, I expect that my page on Bell’s Theorem will take a little longer to produce. Finally, the last page I wish to create that relates to The Formula has to do with Bohmian mechanics. Development of this page, quite frankly, will take some doing.

So RSA encryption should be coming up next. Slightly before or after my page on this subject is released, I anticipate posting news of a promotion involving The Formula: for 5 days, The Formula will be given away-free! On amazon.com.

So stay tuned.