Archive for the 'Physics' category

Rolling out the (optical) carpet: the Talbot effect

Mar 04 2010 Published by under Optics, Physics

ResearchBlogging.orgOne of the wonderful things about having a career in science is that a deeper understanding of the science leads to a greater appreciation of its beauty.  In physics, this usually requires a nontrivial amount of mathematics, but there are some phenomena that are self-evidently beautiful; unfortunately, many of these are also not very well known!

In working on my textbook on optics, I delved rather deeply into one of these phenomena, known as the optical Talbot effect.  First observed in 1836 by Henry Fox Talbot, the effect went unnoticed for nearly fifty years before being rediscovered by the great Lord Rayleigh in 1881. The true subtlety of the phenomenon was still not understood, however, for another hundred years!

In short, the Talbot effect can be described as the self-imaging of a diffraction grating: at regular distances from the grating, the light diffracted through it forms a nearly perfect image of the grating itself. This simple statement does not do justice to the Talbot effect, however, which results in stunning images such as:

This is an example of what is known as a Talbot carpet,  presumably because it is reminiscent of an ornate Persian rug:

(Why isn't it called a "Talbot rug"?  That I can't answer.)

There's a lot to explain in order to understand the significance of the Talbot carpet, starting with an explanation of what exactly a diffraction grating is!

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A WTF scientific paper from Edinburgh, 1884

Feb 24 2010 Published by under ... the Hell?, History of science, Physics

I'm still quite busy finishing off my book, and a grant proposal in the meantime, but I thought I'd share a very odd paper from the Proceedings of the Royal Society of Edinburgh 13 (1884), 23-24, entitled, "Extraordinary occurrence at House No. 7 York Place".

One of the fun things about old journals are the miscellaneous "reports" sent in about unusual phenomena seen in the field, often by non-scientists.  Perhaps my favorite example of this comes from the very first volume of the Philosophical Transactions of the Royal Society in 1665, "An account of a very odd monstrous calf," by Robert Boyle.  This was the fifth paper ever published in a scientific journal, a fact that I find very amusing for some reason.

The paper I want to describe carries the sub-heading, "(The following notice was sent to the General Secretary, from the Office of Messrs Hunter, Blair and Cowan, W.S.)".  I can't really do it justice without quoting it in its entirety:

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Announcing: Mathematical Methods for Optical Physics and Engineering!

Feb 10 2010 Published by under Optics, Personal, Physics

I've mumbled various random things in the past about my upcoming textbook project; this week, I finally got approval from the publisher to start hyping it on the blog.  (Actually, they never prohibited it, but I just got around to asking them last week if it was okay.)

Announcing:  Mathematical Methods for Optical Physics and Engineering, by Greg Gbur, to be published by Cambridge University Press!  The raw image that I have submitted to be turned into beautiful cover art is shown below:

(I'll leave it for the readers to guess what the image represents; feel free to speculate in the comments.)

There are plenty of "mathematical methods for physics" books out there -- why did I feel the need to write another one?  Well, I've been teaching a graduate course on mathematical methods in my department for five years -- and actually taught one while still a grad student, too.  My department focuses on optical science and engineering, so most of the students I get are (a) interested specifically in optics, and (b) often coming from an engineering background with much less abstract mathematics.

Most mathematical methods for physics books are geared towards a general student of physics.  This was a bit irksome for both me and the students while I taught the class, because optics requires a slightly different set of mathematical tools, in particular more emphasis on signal processing, integral transforms, and Green's functions.

Furthermore, math methods books typically draw from a wide variety of physical topics for exercises and examples.  This is, in my opinion, sometimes futile -- for most students, examples drawn from general relativity (or even statistical mechanics) are no better than abstract mathematical ones.

Optics has become a significant field of science in its own right, with dedicated schools in Arizona, Rochester, Orlando, and Charlotte (my home base).  Plenty of other departments of physics and engineering have a strong focus on optical science.  I decided to take a stab at revising the curriculum for those optics-centric programs, and introduce my own mathematical methods book that would complement an optics undergraduate or graduate education.

One of the biggest problems in teaching mathematics is making the connection between the math itself and the application of said math.  To try and address this, (almost) every chapter begins with an introductory application for the technique to be studied, and ends with a more detailed study of how the math is used in solving an optical problem.  I've tried to pick optical problems that don't typically appear in other optics textbooks, for instance: the Talbot effect, Zernike polynomials and aberrations, optical vortices, X-ray crystallography, computed tomography, and even optical cloaking!  I've also taken the unusual step of including essay questions in the exercises: read a given scientific paper and answer questions about its relation to the given mathematical topic.

Though academic optics programs are becoming more common, I'm hoping the book will catch the attention of instructors teaching general math methods for physics courses.  I've tried really hard to approach many of the traditional topics from a slightly different angle.  I'm endeavoring to pass through a very narrow opening between "qualitative understanding" and "mathematical rigor" -- I only include the rigor when it genuinely helps in applying the given methods.

I've also tried to make this book a little more portable!  Most math methods books are well over 1000 pages, but mine is targeted at 850.

Obviously, this book won't be for everybody, and probably won't appeal to many of the readers of my blog, for instance those interested in non-technical explanations of optical phenomena!  (This project was conceived long before I started a blog; my next writing project will be a more popular science/history book.)  Hopefully everyone will benefit from my efforts, however -- over the next few months, I'll write non-technical descriptions of many of the optics examples that I've used in the book.  I'll also give more descriptions of the book and the process of finishing the book at time progresses.

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To describe, or not to describe...

Jan 29 2010 Published by under Physics

In a recent post, Chad at Uncertain Principles addresses an interesting criticism of one of his posts.  In short, he attempted to summarize the essential features of quantum mechanics that set it apart from other, classical theories of physics.  As Chad notes,

So, what's the issue? The strongest single objection probably comes from Peter Morgan, who didn't like my element 2):

2) Quantum states are discrete. The "quantum" in quantum physics refers to the fact that everything in quantum physics comes in discrete amounts. A beam of light can only contain integer numbers of photons-- 1, 2, 3, 137, but never 1.5 or 22.7. An electron in an atom can only have certain discrete energy values-- -13.6 electron volts, or -3.4 electron volts in hydrogen, but never -7.5 electron volts. No matter what you do, you will only ever detect a quantum system in one of these special allowed states.

He commented:

NOOOO!!!!! You need to talk about measurement operators, not about states, if you want to say "discrete".

Perhaps: Measurement operators that have discrete spectra are used to represent measurement apparatus/procedures that produce discrete measurement results. Measurement operators that have continuous spectra are idealizations that do not correspond to real experimental data that is written in lab books or in computer memory.

The state space is usually taken to be vectors in a Hilbert space over the complex field, or density operators (arguably always one of these, by quantum physicists?), which are pretty much continuous linear spaces.

Leaving aside the technical details, the real issue between poster and commenter is one that's often on my mind: how much description is necessary to properly explain a physical phenomenon?  This is relevant not just to authors of blog posts, but also to educators in general.  Science is complicated, and we want to simplify it as much as possible for our students/readers.  There is clearly some point, however, at which the simplifying just becomes misleading.  The question, then, is: how does one draw the line?

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Mythbusters were scooped -- by 130 years! (Finger in the barrel)

Jan 10 2010 Published by under Entertainment, History of science, Physics

During my first evening in San Antonio, I sequestered myself in my hotel room to polish up my presentation.  Fortunately, there was a Mythbusters marathon on the Discovery Channel at that time, so I was able to keep myself marginally sane by watching the 'Busters abuse places, things, and themselves for the cause of science.

One of the episodes that played during the marathon contained the "finger in the barrel" myth -- the idea that a person can stick a finger in the barrel of a rifle or shotgun as it fires, causing the barrel to split like a banana peel without harm to the finger!  The initial investigation of the 'busters clearly demonstrated that a finger would certainly be lost in the attempt, and that a barrel would not split in the manner suggested.  An updated investigation two years later, however, demonstrated that a rifle barrel could be split if sufficiently weakened by use.

In a remarkable case of serendipity, the next evening I was browsing the Proceedings of the Royal Society of Edinburgh and came across an article with the title, "On the bursting of firearms when the muzzle is closed by snow, earth, grease, &c."!  The article, by Professor George Forbes, is a theoretical explanation of the bursting of firearms and was published in the 1878-1879 session of the Royal Society, meaning that Forbes' investigation was some 130 years before the Mythbusters!  The calculation and explanation are short and entertaining, and I thought it would be fun to take a look at them.

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Lord Kelvin vs. the Aether! (1901)

Dec 29 2009 Published by under History of science, Physics

The more I study the history of aether physics, the more I feel that modern physicists underappreciate both the huge influence the theory had on the development of physics and how it indirectly spurred many positive scientific discoveries, even though it is an incorrect theory. The "aether", for those not familiar with it, was a hypothetical substance theorized in the early 1800s to be the medium in which light waves propagate, just as water waves travel through water and sound waves travel through air.  Many papers were written speculating on the nature of the aether before Einstein's special theory of relativity (1905) argued convincingly that the aether was unnecessary.

Nevertheless, these speculations resulted in a number of interesting results.  For instance, we have noted previously that Earnshaw's theorem (1839), an important result in electromagnetic theory, arose from an attempt to determine the forces that hold the aether together.  In 1902, Lord Rayleigh attempted to detect the aether-induced "length contraction" by measuring the birefringence of moving objects, an ingenious attempt that gave a negative result.

In the broadest sense, a "good" theory is one which raises interesting questions that may inevitably be tested by experiment.  Even if it proves to be fundamentally incorrect in the end, it has spurred numerous theoretical and experimental results.  This can be contrasted with sham "theories" such as intelligent design (the "theory" that living creatures are too complex to have developed without the aid of a creator), which has resulted in no testable predictions and exists only as a way to push religion into the classroom.

By 1900, the aether remained a vexing mystery, and perhaps the foremost scientific problem, for the physicists of the era.  It is not surprising that many famous scientists expended considerable energy to try and elucidate its properties.  In 1901, a paper appeared in the Philosophical Magazine (Ser. 6, vol. 2, 161-177) by the famous (even infamous) Lord Kelvin, entitled, "On Ether and Gravitational Matter through Infinite Space."  It is not, in fact, an original publication; as Kelvin puts it,

This is an amplification of Lecture XVI, Baltimore, Oct. 15, 1884, now being prepared for print in a volume on Molecular Dynamics and the Wave Theory of Light, which I hope may be published within a year from the present time.

In fact, the article begins with a reprinting of material from 1854, nearly fifty years old!  This is, if nothing else, a measure of how baffling the aether was to physicists of the time -- material fifty years old was still, in some sense, "state of the art".

The 1901 paper, as a whole, summarizes Kelvin's theoretical musings on the nature of the aether, and highlights how perplexing the topic remained before Einstein's wonderful theory came along and shattered the aether hypothesis once and for all.

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Lord Rayleigh's comments on invisibility (1884)

Oct 07 2009 Published by under History of science, Invisibility

Found it! I pointed out in my previous invisibility post that R.W. Wood attributes an early discussion of invisibility to Lord Rayleigh in his Encyclopædia Britannica article on optics; however, I couldn't find the quote after browsing Rayleigh's articles and wondered if Wood had miscited Rayleigh's work.

A bit of closer inspection, however, shows that I overlooked Rayleigh's comment, which was buried in a footnote in his article on geometrical optics (Encyclopædia Britannica, vol. 17 (1884, 9th ed.), 798-807), in what I would have considered an unlikely place, namely his discussion of achromatic object-glasses (p. 805).  The footnote is as follows:

Even when the optical differences are not small it is well to remember that transparent bodies are only visible in virtue of a variable illumination.   If the light falls equally in all directions, as it might approximately do for an observer on a high monument during a thick fog, the edge of (for example) a perfectly transparent prism would be absolutely invisible.  If a spherical cloud, composed of absolutely transparent material, surround symmetrically a source of light, the illumination at a distance would not be diminished by its presence.

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The first paper on invisibility? (1902)

Oct 02 2009 Published by under Invisibility, Optics

When discussing the history of invisibility physics, I typically cite Ehrenfest's 1910 paper on radiationless motions as the first publication dedicated to the subject.  Ehrenfest's paper, which attempts to explain how electrons could oscillate in a classical atom without radiating, is a direct precursor to the long history of nonradiating sources and nonscattering scatterers that I've been chronicling on this blog.

However, it turns out that Ehrenfest was not the first author to discuss some form of invisibility!  I recently stumbled across an article in an early issue of the Physical Review: "The invisibility of transparent objects," by R.W. Wood, 1902.  It is not an earth-shattering paper, but it presents some intriguing ideas and suggests that visions of invisibility may go even further back in the sciences... Continue Reading »

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Quasicrystals... now all natural!

Sep 09 2009 Published by under Physics

This result came out a few months ago, and I've been looking for the time to write about it ever since: in a paper published in the June 5 issue of Science, scientists reported the discovery of the first natural quasicrystal!

Of course, in order to get excited about this result, one needs to know what a quasicrystal is!  In this post, we'll take a look at what we mean by the terms 'crystal' and 'quasicrystal', and then explain why the discovery of a natural quasicrystal is significant.

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Computed tomography as art

Sep 03 2009 Published by under Physics

A friend (h/t David) sent this to me a bit over a week ago, and now that I'm less distracted by work, I thought I'd pass it along!  On August 23rd, The Daily Mail reported on a new science-based art form: making art out of images generated via computed tomography!

Hong Kong radiologist Kai-hung Fung takes the data generated during a CT scan and colors them using a 'rainbow technique' of his own design.  The images which result are quite striking, such as this image of the back of the nose:

I've always been intrigued by the intersection of art with science; with today's software, it is possible and even useful to present scientific data with an eye towards beauty as well as clarity.  Add to that amazing imaging technology like CT scans (which I discuss in this old post), and one can make jaw-dropping art.

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