Re-writing Feynman’s Lectures?

I have a crazy new idea: a complete re-write of Feynman’s Lectures. It would be fun, wouldn’t it? I would follow the same structure—but start with Volume III, of course: the lectures on quantum mechanics. We could even re-use some language—although we’d need to be careful so as to keep Mr. Michael Gottlieb happy, of course. 🙂 What would you think of the following draft Preface, for example?

The special problem we try to get at with these lectures is to maintain the interest of the very enthusiastic and rather smart people trying to understand physics. They have heard a lot about how interesting and exciting physics is—the theory of relativity, quantum mechanics, and other modern ideas—and spend many years studying textbooks or following online courses. Many are discouraged because there are really very few grand, new, modern ideas presented to them. The problem is whether or not we can make a course which would save them by maintaining their enthusiasm.

The lectures here are not in any way meant to be a survey course, but are very serious. I thought it would best to re-write Feynman’s Lectures to make sure that most of the above-mentioned enthusiastic and smart people would be able to encompass (almost) everything that is in the lectures. 🙂

This is the link to Feynman’s original Preface, so you can see how my preface compares to his: same-same but very different, they’d say in Asia. 🙂

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Doesn’t that sound like a nice project? 🙂

Jean Louis Van Belle, 22 May 2020

Post scriptum: It looks like we made Mr. Gottlieb and/or MIT very unhappy already: the link above does not work for us anymore (see what we get below). That’s very good: it is always nice to start a new publishing project with a little controversy. 🙂 We will have to use the good old paper print edition. We recommend you buy one too, by the way. 🙂 I think they are just a bit over US$100 now. Well worth it!

To put the historical record straight, the reader should note we started this blog before Mr. Gottlieb brought Feynman’s Lectures online. We actually wonder why he would be bothered by us referring to it. That’s what classical textbooks are for, aren’t they? They create common references to agree or disagree with, and why put a book online if you apparently don’t want it to be read or discussed? Noise like this probably means I am doing something right here. 🙂

Gottlieb

Math, physics and reality

This blog has been nice. It doesn’t get an awful lot of traffic (about a thousand visitors a week) but, from time to time, I do get a response or a question that fires me up, if only because it tells me someone is actually reading what I write.

Looking at the site now, I feel like I need to reorganize it completely. It’s just chaos, right? But then that’s what gets me the positive feedback: my readers are in the same boat. We’re trying to make sense of what physicists tell us is reality. The interference model I presented in my previous post is really nice. It has all the ingredients of quantum mechanics, which I would group under two broad categories: uncertainty and duality. Both are related, obviously. I will not talk about the reality of the wavefunction here, because I am biased: I firmly believe the wavefunction represents something real. Why? Because Einstein’s E = m·c2 formula tells us so: energy is a two-dimensional oscillation of mass. Two-dimensional, because it’s got twice the energy of the classroom oscillator (think of a mass on a spring). More importantly, the real and imaginary dimension of the oscillation are both real: they’re perpendicular to the direction of motion of the wave-particle. Photon or electron. It doesn’t matter. Of course, we have all of the transformation formulas, but… Well… These are not real: they are only there to accommodate our perspective: the state of the observer.

The distinction between the group and phase velocity of a wave packet is probably the best example of the failure of ordinary words to describe reality: particles are not waves, and waves are not particles. They are both… Well… Both at the same time. To calculate the action along some path, we assume there is some path, and we assume there is some particle following some path. The path and the particle are just figments of our mind. Useful figments of the mind, but… Well… There is no such thing as an infinitesimally small particle, and the concept of some one-dimensional line in spacetime does not make sense either. Or… Well… They do. Because they help us to make sense of the world. Of what is, whatever it is. 🙂

The mainstream views on the physical significance of the wavefunction are probably best summed up in the Encyclopædia Britannica, which says the wavefunction has no physical significance. Let me quote the relevant extract here:

“The wave functionin quantum mechanics, is a variable quantity that mathematically describes the wave characteristics of a particle. The value of the wave function of a particle at a given point of space and time is related to the likelihood of the particle’s being there at the time. By analogy with waves such as those of sound, a wave function, designated by the Greek letter psi, Ψ, may be thought of as an expression for the amplitude of the particle wave (or de Broglie wave), although for such waves amplitude has no physical significance. The square of the wave function, Ψ2, however, does have physical significance: the probability of finding the particle described by a specific wave function Ψ at a given point and time is proportional to the value of Ψ2.”

Really? First, this is factually wrong: the probability is given by the square of the absolute value of the wave function. These are two very different things:

  1. The square of a complex number is just another complex number: (a + ib)2 = a+ (ib)+ 2iab = ai2b+ 2iab = a– b+ 2iab.
  2. In contrast, the square of the absolute value always gives us a real number, to which we assign the mentioned physical interpretation:|a + ib|2 = [√(a+ b2)]2 = a+ b2.

But it’s not only position: using the right operators, we can also get probabilities on momentum, energy and other physical variables. Hence, the wavefunction is so much more than what the Encyclopædia Britannica suggests.

More fundamentally, what is written there is philosophically inconsistent. Squaring something – the number itself or its norm – is a mathematical operation. How can a mathematical operation suddenly yield something that has physical significance, if none of the elements it operates on, has any. One cannot just go from the mathematical to the physical space. The mathematical space describes the physical space. Always. In physics, at least. 🙂

So… Well… There is too much nonsense around. Disgusting. And the Encyclopædia Britannica should not just present the mainstream view. The truth is: the jury is still out, and there are many guys like me. We think the majority view is plain wrong. In this case, at least. 🙂