mspringer | June 17, 2010As you might expect for a guy who does experimental optical physics, I get to spend a tremendous amount of time in labs with some fairly snazzy lasers. Most of them are fairly specialized pieces of equipment that aren't really designed simply to dump huge amounts of power in industrial applications. As far as danger goes, they're not going to come to life and murder you in your sleep. But still, we have open beamlines of infrared lasers with average powers on the order of 1-4 watts. Unfocused they usually won't do much to exposed skin other than make you uncomfortable (for instance, like a…
mspringer | June 13, 2010A while back I mentioned the St. Petersburg paradox. It's a hypothetical gambling scenario where you win money based on the outcome of a coin toss. If you get your first tails on the first throw, you get $1. If you get one head before your first tails, you get $2 dollars. If you get two heads before tails, you get $4. If three heads before tails, you get $8, and so on doubling each time.
How much should you be willing to pay to play this game? If you work out the mathematical expected value of the game, it turns out to be infinite. Play this game enough times and it doesn't matter how much it…
mspringer | June 9, 2010This is a poster in a hallway here in the Texas A&M physics building:
Sort of an odd question, but an interesting one. Sound waves carry energy, and if that energy we being absorbed by your coffee because you were yelling at it, how long would you have to do so before it was piping hot?
But let's put that question aside for a minute and talk about sound levels. Most of the time you'll hear sound intensity quoted in decibels. Decibels confuse a lot of people because it's a logarithmic scale rather than a linear one. Logarithmic scales are useful for measuring quantities that can span a…
mspringer | June 6, 2010Back in 2003, I was a college freshman sitting in my first college math class - Honors Calculus I. On what was probably the second or third day of class, the professor gave us a surprise quiz. It was something like: "Give the formal statement of the principle of induction". It was my first graded assignment of my college career, and like most of the class I got a 0 on it.
Which was the professor's point - he had gone over it in great detail previously and was baptizing us by fire into the world of mathematical rigor. We didn't yet understand that mathematics both requires great attention to…
mspringer | June 1, 2010Grab a particle and put it in a box.
According to elementary quantum mechanics, that particle isn't described by the classical model in which it can have any value of energy as it bounces around. Instead, the possible energy levels of that particle are described by a discrete set. When you measure the energy of that particle in the box, it will always have one of those specific energy levels and nothing else. Exactly which level it will occupy depends on the details of how you put it into the box, but whatever you do you're constrained to having the particle in those levels or at least a…
mspringer | May 27, 2010Before we get to the heart of yesterday's quiz, let me briefly define solid angle for those who may not be familiar with it. Regular angles are measured in degrees or radians, and solid angles are to angles as square meters are to meters. Solid angle is more or less angular area, and is measured in steradians (or sometimes square degrees). Here's one steradian, from Wikipedia. There are 4π steradians in a sphere:
Now let's take a look at the sun. Make yourself a square frame made with 1-meter sides. Fly down and stand on the surface of the sun (this is a thought experiment, after all), and…
mspringer | May 26, 2010Pop quiz! The picture below is a solar power facility wherein light from the sun is collected by mirrors and focused onto the top of a collecting tower. Fluid within the tower is heated by this light and the hot fluid is used to generate power. We won't care about that in this quiz though; we're just assuming that all the energy goes into heating the tower until its own radiant heat output is equal to that coming in from the mirrors.
Here's the quiz setup. There's nothing stopping you from adding as many mirrors as you want to this installation - for the purposes of this question you can put…
mspringer | May 23, 2010You're a member of the French Resistance in the height of WWII. You're part of a network of resistance members who have to work with other resistance members they've never met before. For instance, an agent from Paris might have to meet up with an agent in Normandy to work together on sabotage before the invasion. But resistance is not something the Nazis take lightly, and they've deployed double agents who attempt to infiltrate the resistance. The agent in Normandy needs some way to verify that this person from Paris is in fact a resistance member rather than an enemy double agent.
One…
mspringer | May 22, 2010I can't let this week go by without mentioning that it is - officially - the 50th birthday of the invention of the laser.
Officially, anyway. On the 16th of May 1960, Theodore H. Maiman produced the first working optical laser. There was actually recently a huge slap-fight in the letters to the editor of Physics Today over the priority of his work compared to the work of some guys at Bell Labs. Still, it seems like Maiman was the first to actually have a working optical laser in his lab.
I say optical because at microwave wavelengths the maser had been previously invented in the mid-50s by…
mspringer | May 19, 2010Space Shuttle mission STS-132 is currently orbiting over our heads. It's scheduled to land a week from now. After that, there's two more launches and that will be that for the program. At that point the US will officially be out of the business of launching people into orbit, and there's not a lot of prospect of getting back into that business in the near future. I don't really regret the end of the shuttle program as such - it was never a really good human spaceflight strategy - but it's a real shame we have nothing to replace it.
Oh well. To commemorate STS-132, how about a quick physics…
mspringer | May 16, 2010Consider this not-so-difficult sum:
It consists of just a string of fractions up to whichever N you happen to choose. Add them up, and you certainly and unambiguously have a number. If you chose to stop at N = 10, you'd find that f(10) = 1627/2520, which is about 0.645635. If you chose to stop at N = 100, you'd find f(100) = 0.692647. If you've taken calculus in college, you can show without too much trouble that as you make N larger and larger, f(N) will close in on the value 0.6931471806..., which happens to be the natural logarithm of the number 2. As such you could say the sum of…
mspringer | May 13, 2010CNN has a headline up: Fate or Fluke: Air crash sole survivors. ON the homepage itself the banner reads "Fate or Physics?"
(CNN) -- Some will see it as divine intervention, others a simple quirk of fate, fortune or physics, but one boy's cheating of death in an air crash in Libya this week adds another name to a small roll call of aviation disaster sole survivors.
The boy, identified as Ruben van Assouw, suffered multiple fractures in his lower limbs when the Afriqiyah Airways Airbus A330-200 crashed Tuesday at Tripoli International Airport killing 92 passengers and a crew of 11.
...…
mspringer | May 7, 2010I recently learned about a great blog by S.C. Kavassalis of the University of Toronto called The Language of Bad Physics. She discusses, among other things, the way language is used in physics. She's got an interesting piece on the use of the word "theory". This is always a hot area of discussion, but in physics it has particular resonance because so many non-physicists like to come up with their own "theories" about how nature might work.
I put "theory" in scare quotes not because amateurs can't make contributions to physics - they can and do - but because there's a heck of a lot of cranks…
mspringer | May 4, 2010This semester I took a course on quantum optics. I'm an AMO guy and quantum optics is one of our department's particular strengths, so it was both a very useful class and a pleasure to take. One of the graded requirements of the class is to write a paper from a list of quantum optics with the stipulation that it couldn't be from our own research. Essentially the paper is supposed to be sort of a review article / tutorial on that topic for our own edification, graded for clarity and grasp of the topic. I wrote on which-way detectors and quantum erasers. It's a bizarre and fascinating topic…
mspringer | May 2, 2010It's been a while since we've done a Sunday Function, so let's get back into the swing of things with a weird one. This is Thomae's function, and using Wikipedia's conveniently typeset definition:
If you're new to the concept of rational and irrational numbers, it's pretty simple. A number is rational if it can be written as a fraction p/q. Otherwise it's irrational. Numbers like pi or the square root of two fit this description. For this function we assume that the fraction p/q is reduced as far as possible, so if x = 1/3 we have p = 1 and q = 3. This is opposed to something like p =…
mspringer | April 29, 2010I'm not quite convinced Iron Man is entirely realistic.
"Proposterous!", you say, "Hollywood makes its superhero films to near-documentary accuracy!" No, hear me out. Iron Man can fly, using rockets in his hands and feet. We know from the commercials that the suit can in fact fit in a briefcase and be carried around by hand, so as an estimate let's say the Iron Man suit + Tony Stark weighs 200 pounds even. In more proper physics-style units, that's 889.6 newtons. Just to hover, let alone fly into the air at high speed, his rockets are required to generate at minimum 889.6 newtons of…
mspringer | April 23, 2010Back in the 1600s science was much less specialized. You didn't really have biology, chemistry, physics, and even mathematics for that matter as fully separate disciplines. If you did science, you were a "natural philosopher" and that was that. Now even physics by itself could be argued to be about a half-dozen separate disciplines whose overlap is not always so large.
Astronomy is often considered to be a sub-discipline of physics depending on the context, and in fact many universities have a "Department of Physics and Astronomy". My undergrad university does, my current university was…
mspringer | April 21, 2010There's a really snazzy physics blog run out of Cornell called The Virtuosi. Sort of like this blog, they're big fans of looking at interesting scenarios through the equations of physics. Not long ago, they had an interesting post looking at whether or not laser guns would have recoil.
I'm not going to duplicate the steps of the problem here, as you should go read it on their excellent site. I'll just state the conclusions: if the laser pulse has energy roughly comparable to a bullet, the momentum imparted to the gun will be tiny - on the order of 10^6 times smaller than that even of the…
mspringer | April 14, 2010Here's an experiment to try. It's a thought experiment - it would be almost impossible to carry out in reality, though more delicate experiments roughly along these lines have been done.
You're in one of the space shuttles, or the Discovery One, or your favorite fictional but realistic spacecraft. It has a hallway extending the length of the spacecraft from bow to stern. You stand at one end of the hallway with a laser pointer, and shine a brief pulse of light down the other end. Make that a very brief pulse. You want the physical length of the pulse as it flies down the hall to be short…
mspringer | April 9, 2010In every cop drama there's a scene where a suspect is being questioned in an interrogation room. The room contains a large mirror, and behind that mirror the detectives and district attorneys are observing and arguing about the progress of the case. The mirror is a two-way mirror.
These kinds of mirrors aren't complicated. Light shines on them, and some fraction is reflected back while some fraction passes through. The suspect in the brightly lit room can't see the dark room beyond the mirror because the bright room light washes out the much smaller amount coming from the adjacent dark…