Category Archives: Physics

Then You Are Set With a Capital 'J'

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When you’re a Jet,
You … stay … a … Jet!

Why Dropping a Stone Makes a Jet

The splash of a solid object into water–be it a coin or an Olympic high diver–is capped off by a thin jet of fluid shooting straight up from the surface. The detailed explanation of this seemingly simple event has proved elusive. Now researchers publishing in the 23 January Physical Review Letters think they have a more complete explanation than their predecessors. Using a combination of theory, simulation, and experiment, they studied the collapse of the air cavity trailing the submerged object, concluding that it ejects water like toothpaste squeezed rapidly from its tube.

Phys. Rev. Lett. 102, 034502
(issue of 23 January 2009)

How Atomic Clocks Don't Work

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I was listening to a podcast recently that delved into timekeeping and atomic clocks, and was surprised that they got a couple of details wrong. I haven’t done a post explaining how atomic clocks work, because that’s something easily found on the intertubes, and so I’m not particularly motivated to recreate Wikipedia or HowStuffWorks.

But someone was wrong on the internet, and the basis of that “wrongness” has some physics behind it. The claim was made in explaining clocks that when electrons absorb energy they jump up a level, and then radiate it when they jump back down. And while that’s true, it’s not the basis for a Cesium or Rubidium clock. The thing is that you don’t want the atom to radiate on its own if you are going to make a clock out of it. Transitions between atomic states are not infinitely narrow, i.e. there is an uncertainty in the energy of the emitted photon. This is known as the linewidth of the transition, and for a good clock you want a really narrow transition so that you know what the frequency is. While there are several factors that can increase that linewidth, the fundamental width is due to the Heisenberg Uncertainty relation between energy (or frequency) and time.

The uncertainty of the frequency and the lifetime of the transition are inversely related, and \(Delta omega Delta t = 1 \) (that should be greater than or equals, but latex is choking on that for some reason)

In order to get a narrow transition, you want a long-lived state. So you don’t want something that radiates readily on its own, and atomic clocks don’t. Cesium and Rubidium devices are passive: you shine radiation on them, and then read out whether or not your radiation was on resonance by looking at which state the atoms are in. Active masers do radiate, but as the acronym tells us, the radiation is stimulated, rather than being spontaneous. (Left on its own, the lifetime of the Hydrogen atom state is about 10 million years) The search for long-lived states becomes even more important for optical clocks, since the larger energy differences tend to lead to shorter lifetimes. What is generally done is to search for so-called forbidden transitions, in which the strong coupling of electric dipole transitions aren’t present, and you are left with other types of transitions or ones that must couple through other states and end up taking much longer.

I Get No Kick from Champagne

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So tell me why should it be true?
That I get a kick out of you

gg writes up the recent paper on the Abraham-Minkowski controversy

Measuring the ‘kick’ of a photon leaving a fiber!

The difficulty lies in the fact that any discussion of the momentum of light in a medium must properly account for the total momentum of the system, which includes the momentum of the medium itself. When traveling into a medium of refractive index much greater than unity, the light is strongly interacting with the material and it becomes almost arbitrary to distinguish between the momentum of the photon and that of the matter: the two are completely intertwined. With this perspective, one would say that the designation of ‘light momentum’ and ‘medium momentum’ are completely arbitrary, merely different ways to slice ‘total momentum pie’. Differences in experimental results can be explained away as a failure to completely account for the interaction between the light and the medium.

Are You the Keymaster?

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Gatekeeping at Faraday’s Cage

[I]t bothered her that in the sciences and engineering there are often classes used as “weeders”, the principal being that the “unfit” are not able to survive the rigors of the fundamentals classes and will drop out before too much time and money has been invested by either party.

The teacher called this “gatekeeping”. It’s a concept with which I am familiar because, unfortunately, I’ve been on both ends of it. I also have a lot of mixed feelings on the topic, and it helped me to hear that this philosophy bothers other people.

And I Say, It's Alright

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Here comes the sun, or at least its shadow, at Dot Physics: When is the Sun directly overhead?

There’s a nice little video that accompanies the post which also demonstrates some of the foibles of doing experiments

What I want to do is change the question a little bit. Rhett points out that one of the common answers is “Everyday at noon,” which can never be correct if you are outside of the tropics. But let’s change this to “When is the sun on the N-S line that goes directly overhead?” The answer still isn’t “everyday at noon.”

Why? Because the earth’s orbit isn’t a circle, and we orbit the sun fastest when we are near perihelion (in January) and slowest near aphelion (in July), with the difference being about a kilometer per second. If we define our time in terms of the sun being on that overhead line — i.e. we use a sundial — then the length of the day will vary, and this is why we generally don’t use solar time (when we’re using solar time) without modifying it. What we do is apply the equation of time, which gives rise to the figure-eight-ish analemma (found on globes as well as sundials). This takes into account both the inclination of the sun and the eccentricity, to give a correction to solar time and correct the reading. While this makes our day 24 hours again, it also means that the sun will be on that overhead line as much as 15 minutes or so before or after actual noon, as kept by our clocks.

New Quantum Teleportation Result

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Via both Physics and Physicists and Uncertain Principles, I see that there is a new result in quantum teleportation between ions that were about a meter apart. Both posts have short summaries (along with Chad considering doing a more thorough write-up) and other links.

I think the Science Daily or Eureka Alert (which I think are identical) are the better ones, since they actually explain how the entanglement occurs:

You excite the two ions so they well drop back down into one of two complementary states, and in doing so they release photons that would be different in energy if they represent the two different transitions.

Before reaching the beamsplitter, each photon is in a superposition of states. After encountering the beamsplitter, four color combinations are possible: blue-blue, red-red, blue-red and red-blue. In nearly all of those variations, the photons cancel each other out on one side and both end up in the same detector on the other side. But there is one – and only one – combination in which both detectors will record a photon at exactly the same time.

In that case, however, it is physically impossible to tell which ion produced which photon because it cannot be known whether the photon arriving at a detector passed through the beamsplitter or was reflected by it.

Thanks to the peculiar laws of quantum mechanics, that inherent uncertainty projects the ions into an entangled state. That is, each ion is in a correlated superposition of the two possible qubit states

Moving in Stereo

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Life’s the same, except for my shoes

Stereograms! Make Your Own 3D Camera for $15 or Less

If you happen to have two digital cameras, you can skip some of the steps, like getting the film developed and scanning the pictures. I was able to get my hands on a second camera; I found that butt-end joining got the lenses close together. I also tried side-by-side, using some optics posts and attaching to the camera tripod mounts. Unfortunately I did not have a third camera, so I can’t show the full rig.

Here is a laser table stereogram. I tested this on a few people, and not all could get it to work. But I can, and that’s good enough, for I am the benchmark for many things.

Tips for 3-D “cross-viewing”

Also, you can see that the two pictures appear to diverge from each other, an example of the leaning tower illusion