New straighforward approach to teaching quantum mechanics

But despite the wild successes of QFT, when it comes to explaining things it is extremely hard to do without either using broken analogies or talking about Feynman diagrams, Lagrangians and Hamiltonians. To realistically depict what is going on you are replacing one branch of math with another more complex branch with the main advantage being that someone who has learned the math of classical mechanics can have a slightly stronger physical intuition.

The advantage of QIT is that because it is relatively simple already, a slightly simplified form is still easier to understand and more representative of the real thing than a highly simplified explanation of QFT. The other advantage of this is that the simplicity allows the raw structure to be exposed and tackled much more readily.

If I would bet I would say answers to questions like what is the wave function exactly , how does the macroscopic universe arise from the cloudy quantum picture, what is really going on in measurement etc will come from QIT. I get the impression that many physicist don't have much respect for foundations but these questions are still worth answering and would have a practical effect on our world right away.

QIT is young yet, there are advantages to being able to take multiple viewpoints of the same thing. The correct viewpoint can vastly simplify a problem. To quote Egan: " Everything becomes clearer, once you express it in the proper language."

Intuitive explanation: drift velocity is the overall streaming velocity of the moving electrons, fermi velocity is the velocity of a single electron. The reason these are different is that electrons move back and forth heavily, thus the fermi velocity is high. But under normal voltages, they move just slighly more in one direction than the other on average, which is the drift velocity. Of course this is highly simplified, and the real story is quantum mechanical.

Aaronson's explanation definitely is a step in the right direction. I still have a quibble however: he keeps mentioning "probability" as an analogy to amplitude. That confuses his explanation in my opinion. I'd rather have a straight explanation of QM math, then an explanation about its similarities with probability theory. And the mixed state paragraph seems to conflate subjective probability and actual distribution of amplitude. Ick.

Again, sincere thanks.

Including references to "God" in an attempted explanation of quantum mechanics is not "easily understandable". Moreover, it's rootedness in culture brings with it myriad histories that impact the way a reader understands what a writer intends. Explaining quantum mechanics by anthropomorphising a God-construct who "chose" to make something one way versus some other way is distracting to readers who do not inject God-construct into their own explanations specifically to avoid making understanding more difficult on the reader.

I can accept that this is a practice from the author's field and generation and still find it distracting and unhelpful without that equating to me being "that much biased." God does not elicit a mentally neutral concept that compresses "a pack of thoughts and emotions in just a few words" when discussing quantum mechanics. It would still be better for the author to not use "God", insofar as it eliminates mysterious language from his explanation, thus reducing the overhead of his reader needing to substitute a non-loaded term (especially when dealing with the sciences, where injecting the term "God" has a history rooted in Western culture of not being too helpful and enlightening).

I can accept it being a practice among the community. That, however, does not imply it is an easily understood, necessary, or sufficient shorthand.

And there's no reason the best way to create something has to be the way it was created the first time.

Definitely. However, it also happens to be the approach used since kindergarten up to high school, and in most universities. Whatever the field, as far as I know, students learn real science only when they start their PhD. Sometimes even later.

I would love to see a real science course, where students come up with theories and discard them, again and again, until they come up with something probably correct (or not). That would teach them to accept being wrong (I hope). Today, it's hard to do for anything but open questions, which tend to be pretty difficult.

So many great stories, and so much untapped storytelling potential... Wikipedia, History Channel, and random documentaries on Netflix aren't good enough!

Being equipped with some fundamentals first, makes exploring the history less confusing. I think Charles Petzold's book "Code", is a great example of blending historical narrative with core concepts - I highly recommend it.

When I was in grad school in math, I made the interesting discovery that if p and q are polynomials over a commutative ring, any polynomial that is symmetric in the roots of p and q is actually a polynomial in the original ring in the coefficients of p and q. (The construction works whether or not the ring can be embedded in a field where said roots actually exist.) Using this observation it is trivial, for instance, to write down in fully factored form a polynomial that has sqrt(2) + cube_root(3) as a root.

This construction was news to various mathematicians that I talked to, including a combinatorics prof who studied symmetric polynomials and a number theorist who worked on stuff related to the algebraic integers. Then finally I talked to a very old mathematician with an interest in history. He told me that I had rediscovered an old way to do things. At his encouragement I went to the library, and picked up an algebra book from the 1800s. My construction was taught, and there was a whole chapter full of problems where students were expected to use it to come up with polynomials with specific roots.

Furthermore as I looked into it both of the professors that I mentioned before worked in areas whose history dated back to the observation that I mentioned. It was used in the original proof that the algebraic integers form a ring, and that construction was the original reason that people were interested in symmetric polynomials.

For another demonstration of how little of their own history mathematicians know, ask anyone why the notation for the second derivative is d^2y/dx^2. Then ask them where the f' notation comes from. Then ask them what Cauchy was trying to do that lead to Cauchy sequences. Most will draw a blank on all three.

Don't read on until you're satisfied that you don't know the answers.

In the original infinitesmal notation, d was an operator. It could be defined by d(y) = y(x + dx) - y(x). And you'd calculate a slope as dy/dx (drop any infinitesmal bits). Well when you work out d(dy/dx)/dx it turns out that you get d(d(y))/(dx * dx) which is more compactly written d^2y/dx^2.

The f' notation was introduced by Lagrange in an attempt to get rid of infinitesmals by defining differentiation as a formal algebraic operation on polynomials and power series. This fell apart when Fourier demonstrated that apparently well-behaved power series could be used to construct pathological things like step functions.

Cauchy came up with Cauchy sequences while attempting to define infinitesmals rigorously. His approach fell apart on the seemingly trivial example of how you rigorously prove the chain rule when the derivative of the inner thing is 0. (He was trying to avoid 0/0, but in that special case you get 0/0 all over the place.)

Motivation is essential, but there are motivations other than the ones that historically lead to the creation of the field.

In number theory, one of my favorite examples, the motivations that lead people to be interested in it now come from modern cryptography, which flatly didn't exist when the field was founded but provides more interesting and relevant examples than the obsessions of century-old mathematicians.

Learn the history behind your subject, but separate it from the pedagogy. Otherwise you'll have a much harder time learning knowledge that you can actually apply.

I think you have an interesting idea of 'simple': A lot of software becomes orders of magnitude simpler to design and reason about once you have enough RAM to organize it in the obvious way.

For example, for many parsing tasks, a recursive-descent parser is the obvious way, but you can only design your software that way once you have a language that can directly express recursion and a computer that can grow a big enough call stack (on the stack or in the heap) to allow the parser to juggle nontrivial sentences. Otherwise, you're left the laborious, non-obvious, labor-intensive, but ultimately pointless task of turning your design into a program your tools can implement.

> So, it leaves me with an ability to be presented something new, or different and very quickly I can understand it.

Honestly, I think that says a lot more about your intelligence than your history. That's actually a pretty fair definition of intelligence, in fact.

How about this: Teaching networking now is teaching TCP/IP and everything that TCP/IP rests upon, such as Ethernet and Wi-Fi. Theory naturally flows from practice, and that is the practice.

The OSI Model? Gone. Out. Forget it. Nobody actually implements all seven layers; at most, we have four.

NCP? What? If you know what NCP stands for, congratulations, you know something entirely useless. "Jeopardy!" would love you.

So why teach the stuff we know is useless? It actively discourages students. It makes them think they're just wasting their time, primarily because they are.

The history of computer networking is a valid topic. It should be taught in its own course, it deserves its own course. It does not deserve to be shoved into a course on how networking actually works.

... which lead to the less-intuitive epsilon-delta proof framework replacing the much more intuitive infinitesimal framework calculus was originally founded on, until the 1960s when infinitesimals were reformulated as part of nonstandard analysis.

(Unless the controversy you're talking about is the utterly uninteresting one about Leibniz vs Newton.)

Another example where a historical development would lead students through a completely pointless diversion (epsilon-delta proofs) simply because Robinson was born in 1918 instead of 1618.