mspringer | November 19, 2009Ok, see counselor Troi firing her phaser?
You see this kind of thing all the time on film in scifi. Whether it's Star Trek, Star Wars, or pretty much anything else, energy beams fired from future weapons are visible. Usually someone will point out that in fact laser beams are not visible in this manner. To see light, it has to reach your eyes. This is clearly not possible when all the light is actually traveling down the beam path. You can see this in action with laser pointers - only the spot where the light hits and diffusely reflects is visible. The path is not.
Writers of TV shows…
mspringer | November 18, 2009There's a little bit of buzz burbling around over Al Gore's scientific goof during a Conan O'Brien interview. Discussing geothermal energy, he said the following:
It definitely is, and it's a relatively new one. People think about geothermal energy -- when they think about it at all -- in terms of the hot water bubbling up in some places, but two kilometers or so down in most places there are these incredibly hot rocks, 'cause the interior of the earth is extremely hot, several million degrees, and the crust of the earth is hot ...
Of course the interior of the earth is extremely hot, but…
mspringer | November 15, 2009We're doing two functions today. If I'm not mistaken we've done each of them separately, but there's a famous and interesting relationship between the two that's always interesting to look at. Like very many interesting mathematical facts, it has to do with the prime numbers.
As such the first function is the log integral Li(x), usually defined in the following way:
We'll plot it in a minute, but if you're interested in a rough idea of it's behavior it so happens that Li(x) ~ ln(x)/x. That is, those two functions have a smaller and smaller percentage difference as x becomes larger.
Now…
mspringer | November 13, 2009Whew! Interesting day around here yesterday, no? There's more controversial topics out there: abortion, health care, gay marriage, Iraq, and a few others. But not many. It's good for sparking discussion, but I also know that some large (probably majority!) fraction of you would prefer to hear about physics. Which is good because generally I prefer writing physics, and I know that I can get irritated when my otherwise favorite nonpolitical blogs go off on political crusades for causes I dislike. So as always I'll try to continue to keep the partisan politics to relatively rare and easily…
mspringer | November 11, 2009God help me, I resisted mightily. If my fellow SB friend Greg wants to spin the Ft. Hoot shooting as a cause for gun control then frankly there's pretty much nothing further to say. You'd think a @#$% major in the @#$% army on a @#$% army base just might not have been terribly inconvenienced in procuring weaponry even if every civilian gun in the hemisphere vanished in a puff of sunshine and wishful thinking. But I was going to leave it alone, assuming that that particular point makes itself. To each his own.
But he wrote a follow-up post asserting a few points of fact, pretty much all of…
mspringer | November 11, 2009On Veterans Day we commemorate the living veterans of the American armed forces. On Memorial day we commemorate those who lost their lives. We should also spend a moment to remember those who helped make sure more soldiers fit into the first category. Though I've made the point before on this blog, I'd like to commemorate two men in particular who between them likely saved the lives of tens or hundreds of thousands of Allied soldiers during the Second World War, simply by doing brilliant science. Their names are Alan Turing and Robert Watson-Watt.
Turing was a mathematician and computer…
mspringer | November 9, 2009Again I have to apologize for the sparseness of posting lately, but I've got two research projects going full blast and time has not been something I have a lot of. I'll still be writing at least a few times a week, and you can't beat the price. ;) In any case once things cool down just a little I should be back to a more regular schedule.
Today's function isn't interesting because of the function itself, the interest comes from what we'll do with it. Let's say we have a function like this:
If we want to see where the function is equal to zero, it's clear that 0 = x^2 - 2 is solved by x…
mspringer | November 7, 2009Of late president Obama has taken a little bit of heat for his frequent (and mostly male) golf outings. Before him, president Bush took the same sort of heat for his golf and vacations. If you were willing to dig a bit through the news archives, I'd bet you could find similar tut-tutting about previous presidents taking time off. It's a common theme for criticism of just about any important federal officeholder - it's no coincidence that so many congressional "fact-finding" missions are to tropical paradises or European vacation spots. In that case it's a criticism I vigorously share, as…
mspringer | November 6, 2009Here's a question which pretty much everyone gets wrong. But the readers of this blog aren't just a random sample, so I bet most of you will get it right:
Two identical vehicles A and B, both traveling at speed V directly toward the other vehicle, collide exactly head-on. At another test track, car C collides with an indestructible concrete barrier at speed V'. All other things being equal, the crash-test dummy occupants of vehicles A, B, and C will experience the same forces (and therefore injuries) if...
1. V' = V/2
2. V' = V
3. V' = 2V
4. Something else (explain)
How might the answer…
mspringer | November 4, 2009For most of human history, our ability to perceive and understand very fast optical events has been limited by the temporal resolution of the human eye. Things that happened too fast were a blur, and all we had to go on was guesswork. Take, for instance, this 1821 painting of a horse race:
If it looks a little bizarre, it's because it guesses wrong on the character of one of those very short events - in this case, the position of a horse's feet during a gallop. Not until the invention of high-speed photography later on in the 19th century could the gallop be better resolved and understood…
mspringer | November 2, 2009These days pretty much everyone knows that mass and energy are two sides of the same coin, as discovered by Einstein. In fact this is so well known that the average man on the street - knowing nothing at all of physics - would still recognize the expression even if he didn't know what it meant or how to use it:
E is energy, m is mass, c is the speed of light. As with all such formulas, you need to have properly matching units. You can't just use mass in pounds, e in British thermal units, and speed in furlongs per fortnight. But any properly consistent set of units will work; for…
mspringer | October 30, 2009There's an interesting article in New Scientist that purports to describe "seven questions that keep physicists up at night". The list is very heavy on the "deep questions" that tend to percolate around the more esoteric quarters of the high-energy physics world, and not so much on the vast bulk of physicists who (ad Chad and I like to harp on) do physics that's much more directly connected to the real (i.e., observable) world. For instance, it's the question of high-temperature superconductivity probably dominates the dreams of lots of solid state physicists, but it's not on the list. So…
mspringer | October 28, 2009Grab a book, or an empty DVD case, or anything else that's a uniform rectangular solid. If it's a book, you might want to secure the book closed with tape or a very lightweight clip, because we'll be throwing it in the air. We want to test a theory.
In classical mechanics we know that each solid object has three special rotational axes, called "principal axes". Intuitively, imagine the object is shaped from styrofoam. The principal axes are the axes along which you can spear the object with a wooden dowel, and the object doesn't try to "wobble" when you rotate the dowel. Aligning a car…
mspringer | October 26, 2009There's a stereotype that it's declasse for us intellectual aesthetes to enjoy football, but I don't care. I enjoy it anyway. Whether you spent any time this weekend watching football or not, I'd like to pose a quick and (maybe!) easy vaguely football-related problem to exercise your brain to make up for all the boob tube time:
You're standing on the goal line of a standard football field and walk the 100 yards to the opposite goal line at a uniform speed of 2 miles per hour. Upon reaching the other side, you immediately turn around and jog back. How fast do you have to jog so that your…
mspringer | October 23, 2009The deserts of New Mexico can get blazingly hot and bone-chillingly cold, extremes of temperature familiar to the outdoorsman in that kind of terrain. A few hundred feet below the ground in Carlsbad Caverns, the temperature is essentially stable in the mid-50s no matter how scorching or frigid the air a few feet above happens to be.
Fig 1: Experimental physicists also tend to live in caves.
You can think of the earth's surface in New Mexico as subject to two superimposed sinusoidal periodic heat pulses. One has a period of 24 hours and corresponds to the heat rising and falling over the…
mspringer | October 19, 2009There's a question that gets posed toward the beginning of intro physics classes to gauge the students' understanding of acceleration. If you fire a bullet horizontally while at the same instant dropping a bullet from the same height, which hits the ground first?
The point is to think clearly about the equation describing accelerated motion. The equation is this:
The bold letters represent vectors. Lower case r is position, a is acceleration, v is velocity. The vectors with 0 subscripted represent the starting values, so v0 is the initial velocity and r0 is the initial position.
But the…
mspringer | October 18, 2009Edit: The previous version of this post required some fixing, as I boneheadedly mixed up the O and Ω notations. The rest of it should still be good.
When you invest in stocks, bonds, mutual funds, or just about any other major investment vehicle, you'll hear a standard but important disclaimer. "Past performance is not a reliable indicator of future returns." And it's wholly true. The hottest mutual fund of the last five years will very frequently revert to the mean over the next five. Or, start a Harley Davidson and an F-22 on the same runway and for the first few seconds the motorcycle…
mspringer | October 16, 2009Today Texas A&M was a bit of a madhouse. Huge crowds, hundreds of police, unseasonably-suited and grim-faced men with mirrored sunglasses, unmarked helicopters circling overhead, TV cameras circling below, and completely borked traffic.
Why? Not just one but two Presidents of the United States are making speeches this afternoon. Obviously most of the fuss is about President Obama, but George H.W. Bush is there as well since he's the one putting on this particular shindig. It's is a non-partisan service-oriented civic pride sort of thing. I'd like to see them it but it's an invitation-…
mspringer | October 15, 2009I propose a Fermi Problem.
Over the lifetime of an average light bulb, what is the total mass of all the electrons that have flowed through?
Work on that if you have an idea how to proceed, or just take your best plausible guess. Remember it's a Fermi problem, so we're looking for estimates rather than detailed calculations. My suggested solution method under the link.
Ok, here's my rough shot. Each electron will transfer energy to the bulb roughly equal to the energy associated with the potential of the electric field produced by the voltage at the plug. For wall current, that's about…
mspringer | October 14, 2009Supposedly there's no such thing as bad publicity, and indeed just about every large organization from business to charity spends tremendous amount of time and money trying to get noticed by the public. You'd think therefore that it would be a good thing that particle physics gets the press it does. You'd think, but then you see news stories like this, from which we can get the gist by quoting the second paragraph:
...Then it will be time to test one of the most bizarre and revolutionary theories in science. I'm not talking about extra dimensions of space-time, dark matter or even black…