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This link recently saved by orzelc on July 08, 2011
By the 1860s, the classical theory of electricity and magnetism was on a very solid theoretical footing. Maxwell's equations describing the interplay of charges and currents with electric and magnetic fields were on paper by 1862, and with some changes in notation they're the exact same today. Relativity wouldn't be invented for another half-century or so, and that makes it all the more remarkable that Maxwell's equations don't actually need to be modified at all to work in a relativistic framework. Lorentz covariance is built right in, though it's a bit hidden.
But Maxwell and Faraday and Ampere and the rest didn't know that. There were some tantalizing hints though, and in fact it was the exploration of classical electrodynamics that led Einstein to the theory of special relativity. It's entertaining to take a look at some of those hints, which are lurking right there in second-semester intro physics.
This link recently saved by orzelc on June 12, 2011
"Here is a picture of (I think) Maru the cat playing in a bag. He loves bags.
Here is the same picture of Maru, at half the size:
Now imagine that Maru is a physicist and the pictures are not pictures but instead windows into the universe he occupies, separate from ours with (possibly) its own unique set of physical laws. The only difference between the two universes is that one has the lengths of everything reduced by a factor of 2.
Can the parallel versions of Maru tell which universe they're in - the smaller or the larger? "
This link recently saved by orzelc on December 05, 2010
"Isaac Newton, when he wasn't revolutionizing mathematics and almost single-handedly inventing physics as a systematic discipline, wrote some really ridiculous stuff. Alchemy, occult esoterica, you name it. In his defense, it was the 1600s. He didn't have a whole lot of prior scientific understanding to help him sort the wheat from the chaff.
Until he reached the age at which the position is traditionally handed to a successor, Stephen Hawking occupied Isaac Newton's chair at Cambridge University. I don't know what his excuse is."
This link recently saved by orzelc on November 14, 2010
"Once lasers were invented however, high intensities became available. One of the more important discoveries was second harmonic generation, which happens when light of frequency f is sent into a medium with nonlinear properties and light of frequency 2f is generated. Most green laser pointers work this way, frequency-doubling infrared light of 1064 nm wavelength into visible green light of 532 nm wavelength.
This second harmonic generation was first reported in Phys. Rev. Lett. 7, 118-119 (1961) by researchers at the University of Michigan with pulsed ruby laser light of around 3 kilowatts instantaneous power focused into a very tiny area. The paper they published is now unfortunately not just a famous paper in laser physics but a famous publishing screw-up in laser physics:"
This link recently saved by orzelc on November 08, 2010
"[T]he idea of function as a machine is such a powerful and intuitive one that it tends to be used pretty universally until you have a good reason to abandon it. Non-mathematicians rarely encounter such reasons, even in the more mathematically demanding disciplines like physics, computer science, and engineering. In fact, most of the time we tend to double down and promiscuously apply the "function as machine" picture to operators. If a function is a machine that turns numbers into other numbers, and operator is a machine that turns functions into other functions. One such operator is called the Laplace transform, after the french mathematician Pierre-Simon Laplace. But I think we'll stick to calling these posts Sunday Functions, even if we take the occasional look at operators."
This link recently saved by orzelc on October 20, 2010
"You're taking your morning shower and a thought occurs to you. "In classical electrodynamics, an accelerating charge radiates. In general relativity, acceleration is equivalent to a gravitational field. Therefore a stationary charge should radiate simply by virtue of being in a gravitational field. What's up with that?"
You wonder about what the radiated power would be for a given gravitational field. You figure maybe you could use the Larmor formula with the Stefan-Boltzmann law to estimate the equivalent thermal radiation but you don't remember either one of those equations exactly and you're pretty sure you'd have to finagle some spatial factors anyway (the Stefan-Boltzmann law has a factor of surface area).
One alternative is to try to construct a quantum field theory in curved spacetime, but this is ludicrously tough even if you're not in the shower without pen and paper. But we might be able to just juggle some constants around and get an estimate."
This link recently saved by orzelc on October 18, 2010
This link recently saved by orzelc on June 09, 2010
"Let's say you want to prove that all the dominoes are going to fall. One way to do this would be to prove that the fall of one causes the fall of the next, and that the first domino falls. Those two statements combined prove that all the dominoes will fall.
Mathematical induction works much the same way."
This link recently saved by orzelc on June 02, 2010
"Occasionally you'll hear some intrepid thinker propose to use this as a source of power. If the particle always has that minimum energy, why can't we bleed off energy from the particle as nature constantly replenishes it to keep it at the zero-point value? Unfortunately it doesn't work. As weird as quantum mechanics is, it still doesn't give us away around thermodynamics."
This link recently saved by orzelc on May 24, 2010