Visualizing the geometric phase of light!

Another post inspired by my book on Falling Felines and Fundamental Physics! I talk about geometric phases in the book in the context of falling cats, but here I focus on the polarization of light.

I regularly argue that most physics isn’t as scary and complicated as most people think. Once you get past the mathematics, which is analogous to a foreign language for the non-fluent, many of the concepts and ideas are intuitive, and even logical. This is, in fact, the motivation behind all the physics posts on this blog!

But some concepts are resistant to easy explanation, and can be quite difficult to understand, even when you are familiar with all the math involved!  One topic that has vexed me, from an intuitive perspective, for a number of years is the concept of geometric phase.  Broadly recognized as a general phenomenon in physics due to the groundbreaking work of Michael Berry in the 1980s, the basic idea is as follows. Some physical systems can be brought from an initial condition, or “state,” changed through a variety of intermediate states and back into its original condition, yet nevertheless have something different about it.

The easiest example of this to visualize is Foucault’s pendulum, a free-hanging pendulum on the Earth, which I have discussed in detail before. Because the pendulum is oscillating on the Earth, and the Earth is effectively turning underneath it, the pendulum changes the direction of its swing during the day.

For a pendulum at the North Pole, the Earth spins 360º underneath it during a day, making the pendulum appear to change direction by 360º. A pendulum at the equator doesn’t change direction at all over the course of a day. But this means that a pendulum at some intermediate latitude, such as Paris, changes direction by less than 360º during the course of the day. Although the Earth has rotated back to its starting position, the pendulum has not ended up swinging in the same direction — that discrepancy is what we call the geometric phase.  It is “geometric” because its unusual behavior is related to the spherical geometry of the Earth.

So this case is somewhat easy to understand, but there is also a geometric phase associated with the behavior of light!  This phase, called the Pancharatnam phase for reasons which we explain below, is a bit trickier to explain. Recently, however, I found a very nice way to visualize this change, and how it connects to “geometry.” This is what I will (hopefully) show in this post!

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Old School Dungeons & Dragons: Part 12

Time again for another compilation of old School Dungeons & Dragons posts from twitter! I am still not tired of exploring the history and mechanics of classic RPGs and the adventures written for them.

Bughunters (1993), by Lester Smith. We begin with a look at a non-D&D roleplaying game produced by TSR in the early 90s, whose core conceit is pretty much given away in the title!

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Posted in Entertainment, Fantasy fiction | 7 Comments

Fake Book Titles Extravaganza #3!

Time for another round of Fake Book Titles that I’ve done, compiled from twitter!  You can see compilation 1 and compilation 2 at the links. These have proven to be a welcome distraction in stressful times. And, wow, I’ve done a lot since part 2!

As always with these, content warning for language, innuendo, and politics!

Original title: The Caves of Mars.

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Posted in ... the Hell?, Silliness | 4 Comments

About a cat flip video!

Okay, even though my book is now out in the world and I spent years working on it, I still manage to come across new things that surprise me about the problem of the falling cat!  A good example of this came across my twitter feed the other day: a video of a cat doing some pretty incredible acrobatics.  I include a gif of the relevant action, which includes a slower-motion version of the flip, below.

Gif of a cat flipping while walking, ending up facing the opposite direction.

The cat, and the people, are startled by the sound of a passing car. The cat almost instantly does a complicated maneuver that results in it turning to cat the possible threat.

What surprised me about this: assuming that this video has not been altered, and I have no reason to think that it has, we have a cat that is using the cat-righting reflex to do something quite distinct from making sure it lands on its feet! In particular, it is using the “cat flip” to change its horizontal orientation, rather than its vertical orientation.

Being that I am now evidently the world cat flip expert by default, I thought I would take a closer look at this video to see if I can analyze the motion being done.

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Posted in Animals, Physics | 3 Comments

A few more Falling Felines bits of news!

If you’re still not tired of Falling Felines and Fundamental Physics news, yesterday was a good day for new posts, which I thought I’d compile here, along with some earlier stuff I forgot to share!

The Curiosity Daily Podcast interviewed me late last year, and that interview went up yesterday! You can listen to the podcast here.

I wrote a blog post for BBC Science Focus giving an introduction to the science and history of falling felines, a bit of a “Cliff Notes” for the book, and it also appeared yesterday. You can read it here!

I somehow neglected to share this cool interview that my friend Jennifer Ouellette did with me about the book that appeared on Christmas Day, which you can read here!

It’s a small thing, but my longtime friend and colleague Scott Carney, when he announced the end of my term as an editor for the Journal of the Optical Society of America A, gave my book a shoutout!

I also did an early morning interview on Sirius XM’s Doctor Radio show about the book, but I don’t know if it is saved online — will investigate further…

Finally, I should mention that I will be doing my first “official” book event on Thursday, January 16th, at Park Road Books in Charlotte! I’m planning to read a bit from the book, sign copies, and try and demonstrate cat-turning techniques using an ice-skating spinner, so it should be an entertaining time if you’re in Charlotte or Charlotte-adjacent!  The event starts at 7:00 pm.

I had to take a screencap for myself!

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Falling Felines at BBC Science Focus!

In case you’re not tired yet of hearing about my book on Falling Felines and Fundamental Physics, I wrote a post for BBC Science Focus Magazine about the falling cat phenomenon, which you can read here.  A sample of the article:

With the recognition of conservation of energy, physicists soon decided that a cat simply cannot flip over on its own in freefall once it begins falling. The consensus view was that a cat, at the moment it begins to fall, must push off of its perch to give itself some initial rotation that leads to it ending on its feet. The cat generates its angular momentum by imparting the opposite angular momentum to its perch and, consequently, the Earth itself.

But this explanation was demolished in a fateful meeting of the French Academy of Sciences on October 22, 1894, by the physiologist Etienne-Jules Marey. Marey presented a sequence of high-speed photographs taken of a falling cat, the first of their kind, showing clearly that the cat begins falling upside-down without any rotation but nevertheless manages to turn over to land on its feet.

The revelations of the photographs threw the meeting into disarray. One member of the Academy declared that Marey “had presented them with a scientific paradox in direct contradiction with the most elementary mechanical principles.”

I’ll be back with more posts soon!

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A decade of history of science!

I’ve picked up a significant number of new followers on the blog lately, and this combined with the wrap-up of the decade seems like a good time to share some of my favorite history of science posts of the past ten years, for those who might have missed them. I can’t say that I’ve written at a particularly fast pace, but I do manage to find some of the strangest, most obscure, and most interesting tales about science and how it has been done! What follows is a list of posts, by year, and a short description of what makes them special to me.

Here’s hoping for another ten years of fascinating science and science history!

April 28, 2010: Mythbustin’: 1808 edition (the incombustible man). Science has a long history of debunking supposed supernatural powers, and a great and relatively little-known example of this was early efforts to explain how some performers seemed to be immune to heat and fire! A fun post that delves into both science and theatrics.

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