The experimental verification of the existence of the Higgs particle in CERN’s LHC accelerator three years ago (July 2012), and the award of the Nobel prize to the scientists who had predicted its existence (including Peter Higgs and François Englert), led me to buy Roger Penrose’s Road to Reality, A Complete Guide to the Laws of the Universe. So I started to try to read and understand it, and I also started writing this blog to externalize my frustration as I tried to cope with the difficulties involved. But now this site is getting quite a few hits and, hence, I’ll just continue it and see where it goes.
I consider myself to be of average intelligence only. However, I also consider myself to be a ‘citizen of this world’ and, hence, I think this is something we all should understand somehow. I don’t shy away from the math, however. So this is not a Guide to the Universe for Dummies. However, I hope it may help to guide some Not-So-Dummies. 🙂
Oh… And as for Penrose’s book, I put it aside and start reading Feynman’s Lectures instead, which is why I’ve got two site addresses for this blog: Reading Penrose and Reading Feynman. I have to admit it’s basically about reading Feynman nowadays. Maybe I’ll start reading Penrose again in some distant future. But probably not: I feel he writes more about math than about physics, and I am more interested in the latter.
3 March 2016
I started this blog almost two and a half years ago. I am not where I had hoped to be. Not yet. But I do feel like I have a good grasp of quantum electrodynamics now. It feels good—like climbing Mont Blanc. 🙂 There is a lot more to learn before I’ll really get what Higg’s particle is all about. But—Hey! Feynman once wrote the following: “I think I can safely say that nobody understands quantum mechanics.” Well… I am not sure I fully understand it either—but I proved that the underlying math is structurally the same as that used in classical electrodynamical theory. So… Well… Perhaps we don’t ‘understand’ classical electrodynamics either.
19 March 2016
You probably heard about the discovery of gravitational waves by Caltech’s LIGO Lab. This makes our picture of the Universe pretty complete. As far as I am concerned, it confirms the wavefunction is, effectively, a propagation mechanism that is common to all forces. The fundamental question remains: what is the wavefunction? What are those real and imaginary parts of that ubiquitous complex-valued wavefunction?
I think I have an answer to that question now: the wavefunction does not only describe some oscillation in spacetime; it actually is an oscillation of spacetime.
Maxwell, after jotting down his equations for the electromagnetic wavefunction, wrote the following back in 1862: “The velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”
We now know there is no medium – no aether – but we still haven’t answered the most fundamental question: what is it that is oscillating? We haven’t gone beyond the abstract math. I dare to say now that it must be spacetime itself. In order to prove this, I’ll have to study Einstein’s general theory of relativity.
The idea is the following here: we like to think of the wavefunction as the dependent variable: both its real as well as its imaginary part are a function of x and t, indeed. But what if we’d think of x and t as dependent variables? In that case, the real and imaginary part of the wavefunction would be the independent variables. It’s just a matter of perspective, isn’t it? I mean… We can sort of mirror our function: we switch its domain for its range, and its range for its domain, as shown below.
It makes a lot of sense to me. Think of it: space and time appear as separate dimensions to us, but they’re intimately connected through c, ħ and the other fundamental physical constants. Likewise, the real and imaginary part of the wavefunction appear as separate dimensions too, but they’re also intimately connected through π and Euler’s number, i.e. through mathematical constants. That cannot be a coincidence: the math and the physics of what we’re looking at somehow reflect each other through the wavefunction, just like the domain and range of a function reflect each other through the function itself. So physics and math must meet in some kind of union—at least in our mind, as Penrose put it.
So, yes, I feel it’s quite natural to look at the wavefunction not only as an oscillation in spacetime, but also as an oscillation of spacetime. But so that’s beyond the undergraduate stuff I’ve been studying so far. In short, I need to move on now! 🙂
PS: Feynman’s developed his series of famous Lectures at Caltech. For some reason I don’t quite understand, it gives me immense satisfaction that the LIGO Lab is a Caltech initiative… Or… Well… I should add that Caltech arch-rival (MIT) is also involved. While it’s one of these things the scientific community had to find, I am so happy they did! 🙂 We live in exciting times!
6 June 2016
About three weeks ago, I brought my most substantial posts together in one document: it’s the Deep Blue page of this site. For those who’d like to read it in an e-book format, I also published it on Amazon/Kindle, and I also published an abbreviated and more philosophical version of it on a separate site. It is best to read it online – because the e-book does not have the animations.
This crowns many years of self-study, and many nights of short and bad sleep – as I was mulling over yet another paradox haunting me in my dreams. It’s been an extraordinary climb but, frankly, the view from the top is magnificent.
The offer is there: anyone who is willing to go through it and offer constructive and/or substantial comments will be included in the book’s acknowledgements section when I go for a second edition (which it needs, I think). First person to be acknowledged here is my wife though, Maria Elena Barron, as she has given me the spacetime 🙂 and, more importantly, the freedom to take this bull by its horns. 🙂
While this site is getting a few thousand visitors every month, the book may or may not sell well, but then that was – and has never been – the purpose of this exercise. The only purpose was to find those words – those words that the Buddhist psychoanalyst, Robert Langan, refers to:
“We are in the words, and at the same time, apart from them. The words spin out, spin us out, over a void. There, somewhere between us, some words form some answer for some time, allowing us to live more fully in the forgetting face of nonexistence, in the dissolving away of each other.” (Robert Langan, in Jeremy Safran (2003), Psychoanalysis and Buddhism: an Unfolding Dialogue)
As all of physics is expressed in the language of math, I should substitute the “words” in that quote for “the math”: it’s the math that spins me out now, not the words—over some void. And the math forms some answer, for some time at least. 🙂 I also do think it allows me to live more fully – in the face of existence, or nonexistence. I am not sure which, but then existence and nonexistence are just dual mathematical spaces, so they must describe the same reality. 🙂
27 July 2016
My last post discusses Feynman’s last Lecture of the 150-odd lectures in the whole series. I am done with Feynman now. It was an exciting adventure. I realize I should re-structure my site, and add new chapters to my book. In fact, I set up a separate site to do just that: organize my thoughts and bring it all together in a more coherent structure. I just don’t know if I’ll have much time to work on it in the coming months. Probably not. 😦 But then perhaps you should feel encourages to continue the work. 🙂 🙂
Have fun and be good! 🙂