History of Science
drorzel | December 16, 2011To end this week, we wrap up electricity and magnetism with the fourth and final of Maxwell's equations. this one includes Maxwell's own personal contribution to these:
This is sort of the mirror image of Faraday's Law from yesterday, with the curl of the magnetic field on the left, and stuff related to a change in the electric field on the right. There are two terms instead of just one on the right, though, because when you're dealing with electric fields, you can get a change in the field in two ways: by changing the field directly, or by moving charged particles around.
The first term…
drorzel | December 15, 2011Moving along through our countdown to Newton's birthday, we have an equation that combines two other titans of British science:
This is the third of Maxwell's equations (named after the great Scottish physicist James Clerk Maxwell), but it originates with Michael Faraday, one of the greatest experimentalists of the day. Faraday was a fascinating guy, who came from humble origins-- he was an apprentice bookbinder who managed to get a job as Humphrey Davey's assistant-- to become hugely influential in both chemistry and physics. He also played an important role in science communication and…
drorzel | December 13, 2011As the advent calendar moves into the E&M portion of the season, there are a number of possible ways to approach this. I could go with fairly specific formulae for various aspects, but that would take a while and might close out some other areas of physics. In the end, all of classical E&M comes down to four equations, known as Maxwell's equations (though other people came up with most of them), so we'll do it that way, starting with this one:
This is the first of Maxwell's equations, written in differential form, and this relates the electric field E to the density of charge in…
drorzel | December 12, 2011We kicked off our countdown to Newton's birthday with his equations of motion, so it seems fitting to close out the section on classical mechanics with another of Newton's equations, this time the Law of Universal Gravitation:
Like all the other equations to this point, I'm cribbing this from the formula sheet for my just-completed intro mechanics class, which means it's in the notation used by Matter and Interactions. This is sub-optimal in some ways-- I prefer to have subscripts on the r to remind you which way it points, but I don't care enough to re-do the equation.
So, this is the…
drorzel | December 8, 2011One of the things that is sometimes very frustrating (to me, at least) about popular physics books is that they rush very quickly through the physics that we already know, in order to spend time talking about wildly speculative ideas. This not only gives some of these books a very short shelf life, as their wilder speculations get ruled out, but it does a dis-service to science. Because as cool as some of the things that might be true are, the stuff that we already know is pretty awesome in its own right, and even more amazing for being true.
Happily, Frank Close's new book, The Infinity…
drorzel | December 6, 2011It's hard to go more than a couple of days without seeing another "imminent death of publishing" article somewhere, predicting the ultimate triumph of ebooks, There's one category of books that I expect to remain safe for the foreseeable future, though, namely books that are specifically constructed to be aesthetically pleasing. In other words, coffee-table books.
Clifford Pickover's new Physics Book is one of these. It's a very attractive and well-made book, pairing some 250 full-page images representing milestones in physics, paired with one-page descriptions of the underlying scientific…
drorzel | December 6, 2011For the sixth day of our advent countdown to Newton's birthday, we have the first equation that really departs from the usual notation. I've gotten to kind of like the way the Matter and Interactions curriculum handles this, though, so we'll use their notation:
This is what Chabay and Sherwood refer to as the Energy Principle, which is one of the three central principles of mechanics. The term on the left, ΔE represents the change in the total energy of a system, while the two terms on the right represent the work done on that system by its surroundings, and any heat energy flow into or out…
drorzel | December 5, 2011Moving along in our countdown to Newton's birthday, we start to deal with equations that Sir Isaac never would've seen, because they deal with more abstract quantities than he worked with. The first and in some ways most important of these is energy:
This is the full and correct expression for the energy of a particle with mass m moving at speed v. The notion of energy traces back to Newton's contemporary and rival Gottfried Wilhelm Leibniz, but this particular equation involves the same square-root factor as Saturday's definition of momentum. That tells you for sure that this particular…
drorzel | December 4, 2011Continuing our countdown to Newton's birthday, let's acknowledge the contributions of one of his contemporaries and rivals with today's equation:
This is, of course, Hooke's Law for a spring, which he famously published in 1660:
ceiiinosssttuv
Clears everything right up, doesn't it? OK, maybe not. This one's not only in Latin, it's a cryptogram, unscrambling to "ut tensio sic vis," which translates roughly to "as the extension, so the force," giving the correct proportionality between the force exerted by a spring or other elastic material and the amount that material has been stretched.…
drorzel | December 3, 2011We kicked off the countdown to Newton's birthday with his second law of motion, which is almost but not quite everything you need to understand and predict the motion of objects. The missing piece is today's equation:
This is the full and correct definition of momentum, good for any speed all the way up to the speed of light. Newton's second law tells us how the momentum changes in response to a force, but in order to use that to predict the future, you need to know what momentum is, and that's where this equation comes in.
(Wouldn't it make more sense to do this first, and the second law…
drorzel | December 2, 2011We kicked off our countdown to Newton's birthday with his second law of motion, so the obvious next step is to go to his third law of motion:
This one was also originally in Latin, because that's how Ike liked to roll:
Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.
In English, this comes out as:
Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
That first…
drorzel | December 1, 2011It's that time of year again, when we count down the days to Isaac Newton's birthday (according to the Julian calendar, anyway), and how better to mark this than with mathematics? Thus, I'll post an equation a day until either Christmas Eve or I run out of ideas, and talk about what it means and why it's important for physics.
Since this is, after all, a celebration of Sir Isaac, let's kick things off with arguably his most famous equation:
OK, it might not look familiar in this form, but this is, in fact, the full and correct statement of Newton's Second Law (written in modern notation),…
drorzel | September 23, 2011The final sentence of the neutrino paper that everybody is buzzing about:
We deliberately do not attempt any theoretical or phenomenological interpretation of
the results.
From a somewhat older work in physics:
Rationem vero harum gravitatis proprietatum ex phænomenis nondum potui deducere, et hypotheses non fingo. Quicquid enim ex phænomenis non deducitur, hypothesis vocanda est; et hypotheses seu metaphysicae, seu physicae, seu qualitatum occultarum, seu mechanicae, in philosophia experimentali locum non habent. In hac philosophia Propositiones deducuntur ex phaenomenis, et redduntur…
drorzel | June 1, 2011One of the interesting things about reading David Kaiser's How the Hippies Saved Physics was that it paints a very different picture of physics in the mid-1970's than what you usually see. Kaiser describes it as a very dark time for young physicists, career-wise. He doesn't go all that deeply into the facts and figures in the book, but there's plenty of quantitative evidence for this. The claim of the book is that this created a situation in which many younger physicists were pushed to the margins, and thus began to work on marginal topics like quantum foundations, which thus began be be…
drorzel | May 31, 2011I heard David Kaiser talk about the history of quantum foundations work back in 2008 at the Perimeter Institute, and while I didn't agree with everything he said, I found it fascinating. So when I heard that he had a book coming out about this stuff, How the Hippies Saved Physics, I jumped at the chance to get a review copy.
This is, in essence, a book-length argument that I owe Frijtof "Tao of Physics" Capra, Gary "Dancing Wu Li Masters" Zukav, and even J*ck S*rf*tt* a beer.
The book expands on things that Kaiser said in that PI talk (which was really good-- you could do worse than to spend…
drorzel | May 18, 2011Today's lecture topic was position-space and momentum-space representations of state vectors in quantum mechanics, which once again brought up one of the eternal questions in physics:
Why do we use the symbol p to represent momentum?
I did Google this, but none of the answers looked all that authoritative. And, anyway, I'm sure that the readers of this blog can come up with fanciful speculations that would be far more interesting than the real answer. So, have at it.
(I'm too overextended and exhausted to post anything more substantive right now; maybe later this afternoon.)
drorzel | May 10, 2011When I was looking over the Great Discoveries series titles for writing yesterday's Quantum Man review, I was struck again by how the Rutherford biography by Richard Reeves is an oddity. Not only is Rutherford a relatively happy fellow-- the book is really lacking in the salacious gossip that is usually a staple of biography, probably because Rutherford was happily married for umpteen years-- but he's an experimentalist, and you don't see that many high-profile biographies of experimental physicists.
When you run down the list of famous and relatively modern scientists who have books written…
drorzel | May 9, 2011While I've got a few more review copies backlogged around here, the next book review post is one that I actually paid for myself, Lawrence Krauss's Quantum Man: Richard Feynman's Life in Science, part of Norton's Great Discoveries series of scientific biographies. I'm a fan of the series-- past entries reviewed here include Richard Reeves's biography of Rutherford, Rebecca Goldstein's biography of Goedel, and David Foster Wallace on Cantor's work on infinity (which is less of a biography than the others). I'm not a huge reader of biographies, but I've liked all the books from this series that…
drorzel | May 5, 2011NASA held a big press conference yesterday to announce that the Gravity Probe B experiment had confirmed a prediction of General Relativity that spacetime near Earth should be "twisted" by the Earth's rotation. A lot of the coverage has focused on the troubled history of the mission (as did the press conference, apparently), but scientifically it's very impressive.
The shift measured is very, very small-- 0.04 arcseconds over the course of a year, or 0.000011 degrees-- but agrees nicely with the predictions of relativity. I'm not sure whether to try to work this into the book-in-progress as I…
drorzel | May 2, 2011Last summer, there was a fair bit of hype about a paper from Mark Raizen's group at Texas which was mostly reported with an "Einstein proven wrong" slant, probably due to this press release. While it is technically true that they measured something Einstein said would be impossible to measure, that framing is a little unfair to Einstein. It does draw media attention, though...
The experiment in question involves Brownian motion, and since I had to read up on that anyway for something else, I thought I might as well look up this paper, and write it up for the blog.
OK, so what did they do that…