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Category: Learning Quantum Mechanics

How can I teach myself quantum mechanics, step-by-step?

I have taught myself quantum physics but without the math. In other words, I can calculate only the tiniest bit of anything quantum mechanical, but I have some understanding of quantum physics concepts. I also have a conceptual understanding of some of the equations. However, I believe that if I continue my studies, I will be able to do quantum physics calculations. I have a college degree but no college math or physics. Actually I’ve never taken a physics course in school.

It’s taken me about 4 years, very part-time, to get through a basic understanding of classical physics, quantum physics, a review of high school math, and first year calculus. I have about average talent at math (though I really enjoy it), a below average talent at classical physics, and some talent at quantum physics.

What it takes is an intense interest in quantum physics, patience, perseverance, and, at least some of the time, enjoyment of the learning process. All the on-line resources I describe below are free. I bought books from Amazon.

Classical Physics First

To understand quantum mechanics, it’s necessary to first understand regular physics (classical physics). This is because much of classical physics applies to quantum physics. When it doesn’t apply, you’re supposed to be surprised. If you don’t know classical physics and aren’t surprised, you’re not going to get what’s so unique about quantum physics—you’re not going to get why physicists are puzzled and what puzzles that they’re trying to resolve.

I studied classical physics at PhysicsClassroom and Khan Academy. I started with kinematics and kept going until I felt that I had the basics. I also worked my way through a physics textbook, reading and doing the problems: Physics and Society by Art Hobson, published by Pearson, available on Amazon in softcover. This is an extremely brief review of classical physics and an introduction to relativity and quantum physics. A basic understanding of relativity is important to some aspects of quantum physics.

The on-line courses are free. These resources provide practice problems with answers so that you can check your work. No calculus needed.

Quantum Physics

I started my study of quantum physics with videos on Youtube. These are at all different levels. I only watched ones intended for laypeople. They have little or no math. I suggest starting with the series “Looking Glass Universe” and “Cracking the Nutshell.” Try to find the first videos on quantum mechanics in each series and go from there. I also watched a huge hodgepodge of other videos until I felt oriented.

I also read biographies of the early quantum physicists. These biographies included a little science—a good way to get your toes wet. The history of quantum physics very much helps in understanding the field. This is because you’ll run across many conflicting descriptions of quantum physics principles. They were either written by quantum physicists in different time periods or written by non-physicists who don’t know that the time period matters. This can be confusing unless you understand that views of quantum physics have changed over the years.

Then, I read books for laypeople on quantum physics. The best ones so far have been Quantum, a Guide for the Perplexed (Jim Al-Khalili) and Understanding Our Unseen Reality (Ruth E. Kastner). Both authors are working quantum physicists, but the books are written for non-physicists.

Math

Even if you want to learn quantum physics at only a conceptual level, like I have, it is desirable to have some understanding of calculus. It may not be essential, but it very much helps. For me, it gives me a general understanding of the quantum equations even though I couldn’t possibly solve them. (I plan to keep going with calculus and maybe one day I will be able to solve them.)

Each day, I study math for about half an hour and I study or write about quantum physics for about an hour.

I reviewed a lot of math on the Khan Academy website. I knew that I needed work on manipulating fractions, logs, and exponents. You will need these skills for calculus. You don’t need much geometry but you do need trigonometry and algebra. However, I started calculus without reviewing trig and algebra.

After reviewing fractions, logs, and exponents, I started the free on-line Ohio State first year calculus course (Calculus 1151). When I ran into difficulties because of insufficient algebra or trig, I went back to Khan Academy and also Paul’s On-Line Notes and Math Is Fun.

If I need more practice problems for calculus than the Ohio State website provides, I go to one of these other math websites that I’ve mentioned. I also google “problems and solutions” for whatever type of problem I’m looking for. There are lots of these on-line that instructors kindly supply.

Keys to Success

  1. As your question suggests, take things step-by-step. Study at least some classical physics before quantum physics. Study algebra and trig before undertaking calculus.
  2. In math, master each step before going on to the next. If you understand a subject, you should be able to do problems without errors. If you can’t do the problems or make a lot of “careless” errors, it means that you’ve not achieved mastery. I learned something—careless errors mean that you’re still struggling with the concepts. This is true for both physics problems and math problems.
  3. Look up words that you don’t understand. This may mean looking them up over and over. That’s what I’ve done. This is true for both regular English words and technical words. For technical words, find pictures and animations. Usually, Wikipedia is too technical, but it provides good pictures and animations. Pictures and animations are really important for understanding physics and, sometimes, math. Also, find pictures and animations by googling. Google your topic and then, click Images or Videos. Also, search on Youtube. I’m writing an encyclopedia of quantum physics for non-mathematicians on this website. It’s not yet complete, but you can find definitions of many classical and quantum physics terms there.
  4. If you find a good resource at your level, but you think that you could get more from it, do it over… and over. I’ve watched short videos 8 and 9 times. I’ve read most of my quantum physics books at least twice, one 7 times!
  5. If you find that what you’re studying is confusing or that you’re blanking out or getting less and less out of it, stop moving forward. Find where you were last doing very well. Find at the end of where you were last doing really well, what didn’t you fully get? Was it a word (regular English or technical)? Do you need to look at pictures or animations? Do you need to work problems? Fix the issue. And then, move forward again from that point. Or you may decide that this resource is just too challenging and find another that suits you better.
  6. This doesn’t mean that you must master each part of quantum physics before going on to the next. This is true for math, but not quantum physics. With math, unless you master each step, you’ll crash on the next one. But quantum physics is different. I cycle through videos/books on quantum physics, getting what I can from each and deciding upon completion if I want to re-do it immediately or move on to another and, possibly, come back later. My understanding of quantum physics has built up by reading different authors, watching different videos, and just getting the feel for what is going on.

Understanding quantum physics in a conceptual way doesn’t take great talent or college training—I’m the proof of that. It takes a lot of exposure to the concepts from many different viewpoints. And it takes patience, determination, and a willingness to tolerate counter-intuitive ideas.

For me, the notion that “no one understands quantum physics” isn’t true. Through all the exposure to various authors’ viewpoints and by trying to explain it all to my husband and also by writing my quantum physics encyclopedia, I’ve built up an ability to visualize what is going on. I’ve built up a feel for how it all works.

I find quantum physics an extremely rewarding field to understand. I want to know how this universe works. Quantum physics is one path in that quest. I feel that the more people understand quantum physics, the more able they are able to perceive the truth of what is really going on. I’m not going to explain that last statement. It may become clear when you study quantum physics.

I hope that what I have written will help you (and others) to decide if you want to study quantum physics. If you decide to undertake it, I truly wish you luck and good results. If you run into problems, you can always ask another question on Quora or search the many answers to Quora questions about quantum physics.

What are some good online resources that can help me understand physics better?

The Physics Classroom and Khan Academy both have excellent free on-line courses on physics, starting from the beginning. They’re step-by-step and give practice problems. On Khan Academy, if you sign in, it will keep track of your progress. It also gives “awards” like badges for good progress. Both websites are excellent. Khan Academy is a little more interactive. I have used both. To really gain understanding and certainty, I’ve done lessons on the same subject on both websites.

When I didn’t understand something in a particular lesson, I found videos on Youtube. I typed the subject into the Youtube search bar, for example, “inertia.” Then, I just started watching videos until I finally got it.

It’s important to understand all the jargon as it comes up. When terms came up I wasn’t sure of, like “mass,” I watched Youtube videos on the subject and/or googled the physics meaning. When googling, I often asked for images. Finding visuals really helps.

I’m writing definitions of physics terms in an on-line encyclopedia. It focuses on quantum physics, but many of the terms, like acceleration, are shared with classical physics. Classical physics is the first physics that you learn on websites like the PhysicsClassroom and KhanAcademy.org.

How do I get started in learning quantum mechanics?

Videos on the Youtube channel “Looking Glass Universe” provide the clearest intro to quantum mechanics that I’ve found. They don’t require math nor a prior knowledge of physics, and they take it slow. However, they really get you into the midst of quantum mechanics. It’s not a light once-over. Of course, start with #1 and take them in sequence. They’re each about 10 minutes and there are about 14 of them.

For more of a light once-over, documentaries hosted by Brian Greene on Youtube are excellent. He’s a quantum physicist and a noted science writer.

Good beginning book on quantum mechanics is Fields of Color by Rodney Brooks.

I’m assuming here that you already know the basics of Newtonian physics. If not, study these first. The Physics Classroom is an excellent free on-line course on Newtonian physics. It’s step-by-step and gives practice problems. Khan Academy also has excellent free lessons on Newtonian physics.

Whenever I didn’t understand something in a particular video or book on quantum mechanics, I found videos or on-line articles about that particular thing until I had more understanding of it.

I’m writing definitions of quantum physics jargon for people who are interested in quantum physics but don’t want to dive into the math of it. It’s the definitions and the illustrations and examples that I wish I had when I was first watching these videos and floundering around. I’m hoping that it will help others.

How can we tell when descriptions of quantum mechanics are woo-woo and not scientific?

[This article is under construction.]

Currently, there are over 20 theoretical interpretations of quantum physics. They mostly SOUND like woo. For example, the Many Worlds Interpretation proposes that innumerable universes are created by quantum events. The de Broglie-Bohmian Interpretation proposes that every event is connected with every other event in the universe, thus explaining the well-accepted phenomenon of quantum entanglement.

Serious physicists propose these kind of hypotheses and work on math regarding them. These are the easiest ones to describe—other interpretations are just as weird when you get down into the details. And I’m including the Copenhagen (orthodox) Interpretation as being weird because it proposes that quantum objects are not real and physical until they interact with another object. That’s a major reason that Einstein challenged it for decades, saying, “I like to think the moon is there even if I’m not looking at it.”

“Weird” here does not mean flaky, woo-woo, or wrong. It simply means unfamiliar to us who live in the world of chairs and tables and who don’t deal with electrons and photons on a daily basis.

It is easy to attack people who rely on quantum physics for some of their far-out philosophies. But when quantum physicists, themselves, propose Many Worlds or universal connectedness, one wonders who is calling the kettle black.

So, bottom line, I don’t think there is a way to distinguish between woo-woo and serious physics without a good background in quantum physics. Not yet. Quantum physics is currently an anarchy of interpretations, with each physicist supporting their own preferred view. This is not a good time to mock someone else’s interpretation or even a philosophy based on an interpretation that one isn’t familiar with.

Quantum physics is a mathematical theory that can be verified by experiment. Some might leap to the conclusion that someone talking about quantum physics is talking woo if he/she isn’t writing equations on the board. However, many popularizers of quantum physics spare their lay audiences the equations and are at the same time respected physicists. These include Brian Greene, James al Khalili, and Stephen Hawking.

While a lot of the math of quantum physics is understood by physicists and a lot of experiments have been done, there is a great deal more to know about both. This is an evolving science; more is being learned every day. In such a situation, it is premature to say that we understand what can be said legitimately about quantum physics and what is woo.

Theoretical quantum physicists do math and attempt to interpret the math and the experimental results so that they can envision new experiments. This has been the role of important physicists like Einstein and John Bell. Theoretical interpretations allow quantum physics to progress just as experiments do.

So, bottom line, I don’t think there is a way to distinguish between woo and serious physics without a heavy background in math and physics. Not yet. Quantum physics is currently an anarchy of interpretations, with each physicist either turning away from any interpretation at all or supporting their own preferred view. This is not a good time to make fun of someone else’s interpretation or of a philosophy based on an interpretation that one isn’t familiar with and, therefore, one supposes could not possibly have scientific support. It’s always good to keep in mind those who mocked and vilely threatened poor souls like Galileo who believed outlandish theories like the earth travels around the sun.

However, it’s an exciting time to try to understand as much as possible of the math, experimental results, and theoretical interpretations. With enough study, one can begin to draw one’s own conclusions about what is woo and what has theoretical, mathematical, and experimental support.

How can I learn Quantum Mechanics?

I will start by saying that I understand the math of Quantum Mechanics (QM) only in a highly conceptual way. Understanding the math to the point that one can calculate quantum mechanics problems, requires familiarity with matrix math and partial differential equations, and more. This requires several years of calculus.

However, I do have a basic conceptual understanding of QM. I understand its logic, which is my interest. If I were to be interested in using QM to work in electronics or as a physicist, I would need to take several years of calculus, classical physics, and QM. But that is not my interest.

I got interested in QM about 3 years ago. I’m interested in its implications for the nature of reality. But I didn’t have sufficient math nor classical physics to take a course in it. I had high school chemistry (no physics at all) and one semester of college calculus.

I started by reading biographies of quantum physicists, which usually contain some highly conceptual info about QM. I also watched beginner’s Youtube video lectures and animations. The best is a series called “Looking Glass Universe.” Even though I didn’t understand a lot of it, I would watch and re-watch, look up words, look for easier videos, anything needed to make progress.

Then, I studied four physics courses for non-scientists—meaning courses with very little math. These emphasized modern physics (QM and relativity). One was a textbook, Physics by Art Hobson, published by Pearson Custom Library, available on Amazon. The next two were audio books in The Great Courses series: Modern Physics and also Particle Physics for Non-Physicists. I listened to these while doing housework and cooking. They probably would each take a semester each if they were college courses. The fourth course was a DVD series by the Teaching Company: The Theory of Everything by Dr. Don Lincoln.

In between these courses, I read many books on QM for lay readers. The best of these were Quantum, A Guide for the Perplexed by Jim Al-Khalili and Understanding Our Unseen Reality by Ruth E. Kastner. They’re useful once you’ve read some biographies and looked at a lot of Youtube videos for beginners. I got something out of all the books that I read or listened to—the understanding slowly builds.   

I also reviewed all my earlier math with Khan Academy lessons—I had forgotten most of second year algebra, trig, and I had never learned matrix math. Then, I completed re-doing the first semester of calculus with an on-line free course that Ohio State University offers. Now, I’m into the second semester of calculus. I really enjoy math but have only average ability at it.

While I don’t attempt the math of QM, I find that having some understanding of calculus is quite helpful. I’ve pieced together a basic understanding of the Schrodinger’s Equation (a key QM equation), though I’m several years of calculus away from being able to calculate with it.

When I can’t understand something, I look up words on the Internet, watch videos about it on Youtube, and re-listen to audio books and re-listen and re-listen. I’ve listened to some of my audio book lectures maybe 15 times (I do a lot of housework and cooking!).

I think younger people make brain connections far faster than us oldsters (I’m 71). But I think that re-listening or re-reading, so long as one is looking up the words, is key. For me, the conceptual understanding comes slowly, and that is always what I’m going for.

I’m currently writing an encyclopedia of quantum physics for lay audiences (like myself) www.QuantumSkylight.com. That forces me to really understand—or I can’t write it. I’m learning more every day as I work on the encyclopedia.