A few weeks ago, looking to make some inroads into the shelves of unread books around our house, I picked up Faster than the Speed of Light by João Magueijo. Published around 2003, this is a non-fiction, popular science account of a family of theories called VSL. These are theoretical models in which the speed of light is allowed to vary, particularly in the early universe, and for reasons that help resolve some of the nagging puzzles in canonical Big Bang cosmology, such as the "horizon" and "flatness" problems. I remembered the splash of publicity around the book at the time it came amount, perhaps helped by the fact that the book's author, one of the co-discoverers of VSL, was unafraid of badmouthing the scientific establishment, from university administrators to the academic traditions of peer review. The book is appropriately grouchy and full of grievances and name-calling, unusually so for a publication by a (then young) scientist still fully embedded in the field.
But once he gets beyond the score-settling, it's actually a pretty lucid and well-organised introduction to VSL. First of all we have to be walked through a couple of areas, though. There's a good, entry-level discussion of Special Relativity (SR) done with thought experiments involving fields of cows, for the most part, and then a quick grounding in standard Big Bang cosmology as it now stands - or did in 2003, taking in inflation and its various spin-off theories, before going on to show how VSL might make some of the outstanding problems evaporate. To be clear, this isn't about FTL in the science fictional sense, so the title is largely misleading; it's about epochs in the universe when the speed of light might have been much, much higher than it is now, allowing widely separated regions to be in causal contact in ways that can't be reconciled with the good old slow speed of light as we now measure it. But nothing ever moves faster than light at any given epoch. The exception to this is discussed only briefly, in the context of cosmic strings, where it's said that the speed of light might get faster the closer you get to one of these strings, allowing the possibility of very rapid travel without (to a high approximation) any time dilation. Obviously, I'd have liked more on this.
Not being any kind of insider in either theoretical physics or cosmology, I wasn't in a position to judge how well VSL has endured in the intervening seventeen years, but it does at least come up in the context of paper abstracts, so I presume there is still some mileage in the idea. However, it fairly obviously hasn't become the dominant theory either.
One thing Faster than the Speed of Light barely contains is any mathematics. There's an old sentiment, probably apocryphal, that every equation put into a popular science book halves the audience. But while I could take or leave VSL itself, the recapitulation of SR did make me want to re-engage my brain cells with a more mathematically grounded treatment, the sort of thing I had to understand at undergraduate level.
I then turned to a book I'd picked up relatively recently, which was volume three in the "Theoretical Minimum" series by Leonard Susskind and co-authors. Volume 3 covers SR and classical field mechanics. Susskind is a lecturer in physics, but also one of the architects of string theory. His recent popular status, though, draws on a series of courses he ran for educated non-physicists, including a fair bit of mathematics, and which led to Youtube videos and then this series of books.The treatment of SR is exactly what I wanted, in that it's careful and lucid, starting at absolute first principles, and then walking you through the arguments step by step, until you get to the juicy bits like time dilation, length contraction and such head-scratchers as the barn-pole paradox. What I really liked about the approach of Susskind and his collaborator, in this case Art Friedman, is that they didn't start from the usual thought experiments that one tends to encounter in entry-level derivations of SR. These often involve such things as pulses of light being bounced between mirrors on railway cars - all perfectly good but I appreciated a somewhat different angle of attack this time, even if it arrived at the same place. Ultimately, following Susskind and Friedman's discussion, one arrives at a derivation of E=mc^2, and it's hugely satisfying to reach this minor summit in modern physics, and feel that one vaguely followed all the steps on the way.
Once I started pushing into the second part of the book, dealing in field mechanics, I felt myself to be on much less solid ground. This is no fault of the authors. But SR was something I studied at undergraduate level, retained an enthusiasm for, and have revisited from time to time since. Even though it was good to be reacquainted with the derivations, it was more a case of re-training old mental muscles than having to develop a completely new set. Once the book began to steer into the foundations of field theory, involving Lagrangians and Hamiltonians, I knew I had to do some backtracking. To be fair, the authors are clear on this: at various points in the book, it advises refreshing concepts from the first volume before proceeding. I had indeed perused the first volume - but some while ago, and evidently not deeply enough.
Volume one was initially published as just "The Theoretical Minimum: What You Need to Start Doing Physics", by Susskind and George Hrabovsky, but it's since been retitled as Classical Mechanics: The Theoretical Minimum. Mine was the earlier edition, but as far as I'm aware the contents are unchanged. Suitably chastened by my bruising encounter with the concepts needed for the second half of Volume three, I'm now reworking my way through the first book. It begins with stuff that will be familiar to anyone who's studied physics or mathematics at (the very least) undergraduate level, and probably high-school/sixth form as well, such as coordinate spaces, vectors, vector algebra, differential and integral calculus, partial derivatives, and so on. None of this was etched firmly in my brain to the point where I'd have been confident to wade in without a textbook, but it was all stuff I'd known once, even if very little of it was applicable to the sort of work I actually did as a jobbing scientist. However, it was good to be reacquainted.
Now I am forging into the parts which gave me trouble in Vol 3 - Lagrangians, Hamiltonians, Euler-Lagrange equations and so on - and I must confess that I don't honestly remember whether I was taught any of this material at degree level. I suppose I must have been, but after thirty two years it's hard to be sure. Our standard year-one mechanics textbook was Kleppner and Kolenkow, which is still in print, and which I considered one of the few academic books worth hanging onto in later life. But a quick glance at the index reveals nothing on Lagranges, Hessian matrixes etc. So perhaps this will all be new, and exciting. Who knows.
I've said nothing about the second volume in the Susskind series, by the way, because I don't yet own it. The second book covers Quantum Mechanics. However, having reaffirmed my enthusiasm for the first and second titles, I've now tracked down a matching hardcover of the second, and which is on its way to me.
Speaking of textbooks, and keeping them or throwing them away - how's that for a segue - Deep Six Textbook is the first track on the first album by Let's Eat Grandma, an avant pop/synth pop/sludge pop (take your pick) group originating in Norwich and which consists of two schoolfriends, Rosa Walton and Jenny Hollingworth. They were fifteen when they recorded the first album, I Gemini, and followed it up in 2018 with I'm All Ears, by which time they were long past it at nineteen. I bought the first album a couple of years ago, and liked it very much, recognising an abundance of weird ideas and off-the-wall originality. The second album, I'm sorry to say, didn't quite grab me the way I'd hoped it would. On first listen, it sounded like a maturation of the approaches on the first record, without quite going anywhere surprising. I played it once or twice, then let it gather dust. How wrong I was, though. When I actually did what I should have done, and gave the album the time and attention it deserved, it left me floored. Insidious, is how I'd describe it: one of those recordings that doesn't give up its treasures too readily, but gradually sinks hooks into your subconscious, until you begin to doubt that any other music will ever sound interesting again. Let's Eat Grandma really are remarkable, and without burdening Walton and Hollingworth with impossible expectations, I can't wait to hear where they go next.
A couple of years ago, I took a stab at rederiving all of special relativity using rapidity instead of velocity. This is simply a variable substitution, where beta = v/c = tanh(r) where r is rapidity. It's easy to show that gamma = cosh(r). Later on momentum is mc sinh(r) and energy is mc² cosh(r).ReplyDelete
When you set up integrals to figure out things like how much Earth time passes when a rocket accelerates for one year of ship time, the integrals are all pretty easy. (I think this whole idea of rapidity originated with someone who discovered himself doing the same hyperbolic substitution over and over again.)
The crowing glory of using rapidity is when you compute the relativistic rocket equation and get a clean, simple answer instead of the god-awful thing that Robert Forward came up with in his paper "A Transparent Derivation of the Relativistic Rocket Equation."
The downside is that you have to get comfortable with hyperbolic trig functions. But that turns out to be very little effort, and the reward of getting clean expressions for so many things in relativity is well worth it in my opinion.
Thanks, Greg. I says much for my ignorance that I wasn't aware of the notion of rapidity as a concept in physics.ReplyDelete
It does feel awesome diving deep into sciences like that. You have prior knowledge thought, albeit rusted down by the erosion of time. I've never dabbled in quantum physics or anything of the sort, not even during my education. Now I'm discovering this boundless realm of curiosity therein and I have to say I'm absolutely loving it.ReplyDelete
On some primal level, dealing with such exotic matters gives an extra sense of purpose to one's life - learning. I find it very liberating from the prison of the everyday reality. Currently I'm exploring the concepts of quantum entanglement, superposition, retrocausality, and all things black holes. I really want to use those as foundation for writing something interesting in the future when I finally get down to putting all my ideas into a sci-fi novel.
Let's Eat Grandma sound very fresh and peculiar. I like it. There's an Australian band I found a few years ago called Lime Cordiale whose music I absolutely fell in love with. Check them out. I think you'll enjoy them as well. Just filter to their most popular songs on YouTube.
It’s been a while since I’ve listened to Let’s Eat Grandma. Thanks for the reminder! I enjoyed their second record when it came out, but I didn’t revisit it after an initial few listens. Coming back to it now, I think I’m enjoying it even more than I did the first time around. I love the zany, occasionally gothic production and the bombastic vocal performances and songwriting.ReplyDelete
Someone in your Facebook fan group posted a link to an interview you gave for the Middletown public library’s science fiction book club. I thought it was a fun read, and I was flabbergasted that you regularly manage to put down two to three thousand words a day. I understand that you’re a professional, but none of the novelists I’ve heard speak about these things are ever that productive. In my scattered and largely pathetic attempts at writing fiction, I’ve rarely managed to come up with more than five hundred words in a day that are worth keeping when I review them the next morning.
I’m also intrigued by your reference to War & Glass. With a name like that, I’m holding out hope that it’ll be your Russian epic à la War & Peace or Life & Fate.