If you were to put a lens, with a focal length 1/4 of the distance between the prisms, right in between the prisms, you’d definitely bring the light back to nearly a point at the first surface of the second prism. However, the angles of each color will not be what they need to be so that they’ll all come out parallel to each other out the second face.
How do I know this? Because I know what it takes to get all the colors to come out parallel (though not on top of each other).
Monthly Archives: October 2011
Drs. Larry, Moe and Curly, I Presume?
Experimentalists Aren’t Idiots: The Neutrino Saga Continues*
Linking not just because Chad links to my post from yesterday but because he goes into more depth than the blurb I whipped up just before going to bed.
But since we’re on the topic, in case anyone is tempted to do yet another “I know the fundamental error you made” article: GPS clocks have their frequency adjusted to compensate for relativity — the clocks in space do keep nominal earth time already. On the ground, they would run slow by about 38 microseconds per day. In space, the gravitational shift is about 45 microseconds faster, opposed somewhat by the kinematic dilation of 7 microseconds. It’s not clear from my very quick scan if the authors of that paper had taken that into account or were trying to argue for some other effect.
Also, people do time transfer (i.e. synchronization) with GPS all the time. It’s called Common View GPS Time Transfer (though you can do it with any satellite that broadcasts). One might have gotten the impression that the neutrino experiment tried something novel to synch up their clocks.
*I am an experimentalist, and I am occasionally an idiot. Nobody is immune, really. But I have excellent colleagues who act as idiocy filters so at work, at least, any work that gets out to the public has been screened.
Cautionary Tale From Neutrinoland
There’s one main reason I don’t care how many non-experts rail against topics like we see with global warming or evolution. It’s because they are NOT EXPERTS. When you get into the details, science is subtle and tricky, and even though you might understand the big chunks, there comes a point where the non-expert — even a very intelligent one — will be out of his or her depth.
I offer up an example from the brouhaha of the month, the neutrino experiment. (I trust I don’t have to say no, not that one, the other one.) Followup: FTL neutrinos explained? Not so fast, folks.
There are two issues here. One is the paper itself on which Phil is commenting; the author seems to assume that the GPS satellite use for synchronization is always traveling in the same direction as it passes over the experiment, which I don’t think is the case. But I’m not a GPS expert. The second is that if this purported timing offset weren’t already accounted for in GPS receivers, it would show up as a positioning error. 1 nanosecond is 1 foot, roughly. (3 ns is a meter). So from just this one source we’re talking 10 – 11 meters of error. GPS does better than that. It’s kind of silly to assume that this wouldn’t be accounted for in setting up the system. So my initial reaction is that it’s bunk.
The second part is what Phil posts
I had thought of something like this as well. CERN and OPERA are at different latitudes, and since the Earth rotates, they are moving around the Earth’s axis at different speeds. Could that be it? I did the math, and the answer is no. Too bad; it would’ve been fun to be the person to have figured this out!
As I’ve mentioned at least once before, the rotation of the earth has no effect on clocks. The rotation causes deformation of the earth (we are oblate spheroid, mighty mighty oblate spheroid) and it turns out that the slowing from the kinematic time dilation is offset by a speedup cause by being slightly higher in the gravity well. So on the geoid, clocks all run at the same rate, and you only have to account for elevation changes.
It’s not surprising that an astronomer wouldn’t know that. Hell, I didn’t know that for the first few years I worked with clocks, and when I asked the question, the people I talked to weren’t sure why latitude corrections weren’t necessary. I went and found the answer in Neil Ashby’s “Relativity in the Global Positioning System”
Considering clocks at two different latitudes, the one further north will be closer to the earth’s center because of the flattening – it will therefore be more redshifted. However, it is also closer to the axis of rotation, and going more slowly, so it suffers less second-order Doppler shift. The earth’s oblateness gives rise to an important quadrupole correction. This combination of effects cancels exactly on the reference surface.
What does all this mean? Smart people outside of their field will not be familiar with subtle but very important effects. They may, as happened here, raise what seem to be legitimate objections that are well-know to people who actually work in the field.
No, Don't Tell Me. I'm Keen to Guess
Monty Python was less help than I had hoped.
Though it’s now obvious you could re-do the sketch as The Font Shop.
Well let’s keep it simple, how about Helvetica?
Well, I’m afraid we don’t get much call for it around these parts.
Not much call? It’s the single most popular font in the world!
Not ’round these parts, sir.
That's Some Catch, That Catch-22
‘Catch-22’: A Paradox Turns 50 And Still Rings True
There was only one catch and that was Catch-22, which specified that a concern for one’s safety in the face of dangers that were real and immediate was the process of a rational mind. [Bomber pilot] Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. … Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.
One of my favorites, even if I didn’t “get” some of it the first time I read it back when I was a teenager.
Soon to be a Major Motion Picture
By golly, I wish I’d had this book as an undergrad.
As it was, I had to wait until this past January, at the ScienceOnline 2011 conference. These annual meetings in Durham, North Carolina feature scientists, journalists, teachers and students, all blurring the lines between one specialization and another, trying to figure out how the Internet can help us do and talk science. Lots of the attendees had books recently published or soon forthcoming, and the organizers arranged a drawing. We could each pick a book from the table, with all the books anonymized in brown paper wrapping. Greg “Dr. Skyskull” Gbur had brought fresh review copies of his textbook. Talking it over, we realized that if somebody who wasn’t a physics person got a mathematical methods textbook, they’d probably be sad. So, we went to the table and hefted the offerings until we found one which weighed enough to be full of equations, and everyone walked away happy.
The “we” includes me, because I scored a copy as well, and was in on the activity of sizing and weighing the anonymized books. There were probably more of these books than physicists (perhaps we can do better this year), though, so I imagine some species of biologist and/or journalist (statistically speaking) was disappointed.
I Do Not Think it Means What You Think it Means
We are stuck on the idea that 300,000 kilometres a second is a speed limit, because we intuitively believe that time runs at a constant universal rate. However, we have proven in many different experimental tests that time clearly does not run at a constant rate between different frames of reference. So with the right technology, you can sit in your star-drive spacecraft and make a quick cup of tea while eons pass by outside. It’s not about speed, it’s about reducing your personal travel time between two distant points. And that has a natural limit – of zero.
A decent little tutorial. One approach that can also be used is to note that the invariant speed, given by the velocity four-vector, has a constant length of c. The three spatial components are the velocity and the time component is \(gamma\)ct. If you are stationary, as we all are in our own rest frame, time ticks normally. But when one is moving — the spatial velocity vector is nonzero — the time component of the vector shortens compensates.
Update: Chad points out some sloppiness on my part. The vector is given by \({v_x}^2+{v_y}^2+{v_z}^2-gamma c^2\) so the components get bigger while the resultant stays constant.
That Which Will Occupy Your Time
Kern Like Everyone is Watching
Your mission is simple: achieve pleasant and readable text by distributing the space between letters. Typographers call this activity kerning. Your solution will be compared to typographer’s solution, and you will be given a score depending on how close you nailed it. Good luck!
Going On and On and On About Archaeology
Tiny drone helps reveal ancient royal burial sites
The machine tested in a remote area in Russia called Tuekta was a four-propeller “quadrocopter”: the battery-powered Microdrone md4-200. The fact it is small — the axis of its rotors is about 27 inches (70 cm) — and weighs about 35 ounces (1,000 grams) made it easy to transport, and researchers said it was very easy to fly, stabilizing itself constantly and keeping at a given height and position unless ordered to do otherwise. The engine also generated almost no vibrations, they added, so that photographs taken from the camera mounted under it were relatively sharp. Depending on the wind, temperature and its payload, the drone’s maximum flight time is about 20 minutes.