Teaching physics ? A view from Mr.Zz

Teaching Physics To Kids (And Dogs)

For the longest time, I resisted myself from making any comments on this. I respect other physicists who spend time and effort trying to educate the public on various aspects of physics. It isn't easy, not just because of the nature of the subject, but because we have to be very careful on what we say and how we say certain things. This is because we can mean one thing when we say it, but the public may understand things in a very different way because of the different "vocabulary" that we some time use. So trying to explain something, or writing a book, on physics is an endeavor that requires a lot of self-exploration and self-evaluation.

I've read a bit of Chad Orzel's book "How to Teach Physics to Your Dog", and I've read many reviews about it. It's a fun book, and I highly recommend it. However, I am a bit uncomfortable with the title of the book, and I will try to explain it here. I only hope the reasons don't become confusing and I end up sounding as if I'm criticizing the book, which is far from my intention.

What do we mean when we try to teach someone something? If I tell you that Newton's 2nd Law says "F=ma", have I taught you anything? If tell you that the largest planet in the solar system is Jupiter, have I taught you anything? To me, teaching means the imparting of knowledge, not simply the imparting of information. There's a difference there. Information can be a series of disconnected, disjointed items, whereas a knowledge is not just information, but how these items connect to each other. In other words, you know not only that "F=ma", but you know what it means, and how to use it. This isn't automatic. Many people know F=ma. In fact, we write it early in our class in intro physics. Yet, give these students a simply projectile problem to do right after you introduce that equation and see how many can use it to solve such a problem. This clearly shows that just because you have that information, it doesn't mean that you have the knowledge of what it is.

So that brings us back to whether you can teach your dog, or your kids, physics. At some level, you can. You can certainly show simple concepts until the kids see a pattern, and they now understand how something behaves. They might even be able to replicate such a thing with other examples. So yes, that would be teaching. But how do you teach kids (and dogs) quantum mechanics, for example? All the pop-science books meant for the public have done it simply by telling the readers the "weird" properties of QM, how a quantum system behaves, and what possible implication it could mean. But these are nothing more than telling someone a series of information. In fact, when done this way, these series of information, more often than not, appear disjointed and disconnected. People learn about the Schrodinger cat, for example, but do not realize that the same principle (superposition) is what makes quantum entanglement so weird. Without that principle, quantum entanglement is no more strange than the classical case of a simple conservation of (angular) momentum. Or would people realize that the Heisenberg Uncertainty Principle isn't really a "principle", or that it is not separate from the wavefunction itself and how we define what we call "observables"? The HUP is almost always automatically there when we deal with the Schrodinger equation wavefunction.

To me, this is not teaching physics. It is teaching ABOUT physics. There's a difference. There is value in teaching about physics, and many pop-science books do a tremendous service to the field by introducing people to it. But it should not be confused with teaching physics. The latter involves imparting knowledge in such a way that the recipient obtains the ability and skill to use and apply the information. I consider being able to use F=ma and solve kinematical problems as a sign that someone has a knowledge of F=ma. In Mary Boas's "Mathematical Methods in the Physical Science", she stated:

To use mathematics effectively in applications, you need not just knowledge, but skill. Skill can be obtained only through practice. You can obtain a certain superficial knowledge of mathematics by listening to lectures, but you cannot obtain skill this way.

And I would apply that to the difference between information and knowledge, physics and about physics, as used in this context. One needs to clearly differentiate the superficial understanding of something versus learning something. This should be done both by the instructor (or author) and the student (or the reader).

There's plenty of worthiness in a book that teaches physics, and a book that teaches ABOUT physics. One can only hope that a reader does not confuse the two.

Zz.

Lecture series on physics by Leonard Susskind:

http://www.youtube.com/results?search_query=leonard+susskind+lectures&search_type=&aq=0

And more things can be found here:

http://www.openculture.com/2008/07/susskindlecture.html

Why is it dark at night ?

If I'm asked, what might contain the key to a theory of everything, my reply would be that, let us collect more information about the cosmos. There are indeed quite a few interesting long-standing puzzles regarding how our universe is. One of such puzzles is, 'why is it dark at night ?' . Here is an Wiki page discussing this.

Engineering a quiet road

In HK, the roadside noises are really annoying. Buses are very loud. This is of course not unique with HK. It is also ture in many other countries. Although physicists have accquired a good understanding about the noise resources--the pavement and tires, a quiet road is still not a reality.

Neutrino helps shielding seismic waves

This experiment is said to be a significant step toward a better understanding of the chemical makeup inside the earth. Glad to know that, knowledge of neutrino can be useful even in predicting seismic events, which recently happened frequently.

phonon laser ?

After decades of lasers, recently people came up with phonon laser setups. The underlying physics is essentially this: phonons, as photons, are bosons. Bosons tend to amplify themselves. In this work [1,2] the authors observed amplification but not lasing so far. So, real phonon laser has to be seen afar.

[1] Phonon Laser Action in a Tunable Two-Level System

Ivan S. Grudinin, Hansuek Lee, O. Painter, and Kerry J. Vahala

Phys. Rev. Lett. 104, 083901 (2010) – Published February 22, 2010

[2] Coherent Terahertz Sound Amplification and Spectral Line Narrowing in a Stark Ladder Superlattice

R. P. Beardsley, A. V. Akimov, M. Henini, and A. J. Kent

Phys. Rev. Lett. 104, 085501 (2010) – Published February 22, 2010

Experimentally measuring transmission matrix of light

These authors now opened a new road to manipulating light and utilizing it. They came up with a way to measure the so-called transmission matrix, which is supposed to contain essential information of the media through which a light propagates. They demonstrated how such matrix can be used to focus light and to spot an object before the media. In a word, it is quite interesting and practical. However, I need more time to get a full understanding of their method.

PRL 104, 100601 (2010)

An introduction is enclosed below:

Optical elements such as lenses and polarizers are used to modify the propagation of light. The transformations of the optical wave front that these elements perform are described by simple and straightforward transmission matrices (Fig. 1). The formalism of transmission matrices is also used to microscopically describe the transmission through more complex optical systems, including opaque materials such as a layer of paint in which light is strongly scattered. A microscopic description of this scattering process requires a transmission matrix with an enormous number of elements. Sébastien Popoff, Geoffroy Lerosey, Rémi Carminati, Mathias Fink, Claude Boccara, and Sylvain Gigan of the Institut Langevin in Paris now report in Physical Review Letters an experimental approach to microscopically measure the transmission matrix for light [1]. Knowledge of the transmission matrix promises a deeper understanding of the transport properties and enables precise control over light propagation through complex photonic systems.

At first sight, opaque disordered materials such as paper, paint, and biological tissue are completely different from lenses and other clear optical elements. In disordered materials all information in the wave front seems to be lost due to multiple scattering. The propagation of light in such materials is described very successfully by a diffusion approach in which one discards phase information and considers only the intensity. An important clue that phase information is very relevant in disordered systems was given by the observation of weak photon localization in diffusive samples [2, 3]. Even extremely long light paths interfere constructively in the exact backscattering direction, an interference effect that can be observed in almost all multiple scattering systems. Interference in combination with very strong scattering will even bring diffusion to a halt when conditions are right for Anderson localization [4]. Since light waves do not lose their coherence properties even after thousands of scattering events, the transport of light through a disordered material is not dissipative at all, but coherent, with a high information capacity [5].

A propagating monochromatic light wave is characterized by the shape of its wave front. By choosing a suitable basis, the wave front incident on a sample can be decomposed into orthogonal modes. Typical choices for this basis of modes are the orthogonal modes of a waveguide or a basis of plane waves in free space. As only propagating waves need to be considered, the number of modes is finite and they form the basis in which the transmission matrix is written. The transmission matrix of the sample specifies the transmitted field amplitude for each combination of incident and transmitted modes. From a theoretical viewpoint, transmission matrices are useful tools to understand correlations in transport of light and other waves. Much insight into the properties of the transmission matrix has been gained in the framework of mesoscopic transport theory [6]. The transmission matrix has played a less important role in experiments due to its enormously high dimensionality: it is an N×N matrix of complex numbers, where N represents the number of modes of the incident (and transmitted) light field coupled to the sample. Each incident mode corresponds to a discrete incident angle, and the number of resolvable discrete angles is N=2πA/λ² [7], with A the illuminated surface area, λ the wavelength, and where the factor 2 accounts for two orthogonal polarizations. Hence, a 1-mm² sample has about a million transversal optical modes. Until recently, measuring a matrix with the corresponding large number of elements was beyond technological capabilities. Progress in digital imaging technology has now enabled measuring and handling such large amounts of data. In particular, spatial light modulators—computer-controlled elements that control the phase in each pixel of a two-dimensional wave front—are now creating a digital revolution in optics and are at the heart of the experiment by Popoff and colleagues.

In their experiment they used a spatial light modulator to precisely control the wave front of a monochromatic laser beam, which permitted them to address different incident modes of a strongly disordered sample. By cleverly using part of the transmitted light as a phase reference, they were able to capture amplitude and phase information on a two-dimensional CCD array of 16×16 pixels. Thanks to this parallel detection, they measured 16⁴ elements of the transmission matrix in only 16² steps. Their method enables a deep characterization of light transport through turbid media, which enables them to control light propagation, as they demonstrated by transforming their sample into a focusing and detection element. To focus light they used the information in the transmission matrix to construct wave fronts that formed a tight focus after being scattered by the sample. Their approach is more flexible than first-generation “opaque lens” experiments [8] since the data to produce a focus at any desired position is already in the transmission matrix. To detect objects placed in front of the scattering sample they compared the transmitted field with the information stored in the transmission matrix.

Direct access to the individual elements of the matrix makes it possible to perform statistical analysis on them. The statistical properties of the transmission matrix are described using random matrix theory, an analytic approach that focuses on symmetries and conservation laws rather than detailed interactions (for an introduction see Ref. [9] and references therein). For example, the transmission matrix elements are correlated due to the fact that none of the matrix elements or singular values can ever be larger than unity, since in that case more than 100% of the incident power would be transmitted [10]. However, this correlation is subtle and can only be observed if the complete transmission matrix is measured.

In the current experiments the number of measured matrix elements is impressive (65536), yet the transmission matrix of the full area of the sample is even larger. Nevertheless, the matrix measured by Popoff et al. was sufficiently large to test an important baseline prediction of random matrix theory: The histogram of its singular values should have a peculiar quarter-circle shape [11, 12]. The fact that the data follows this quarter-circle law means that the matrix elements are not significantly correlated, which is a good indication that the experimental procedure does not introduce spurious correlations. By measuring considerably larger matrices, intrinsic correlations can be brought to light. In a large enough matrix, the singular value distribution will deviate from the quarter-circle law and converge to a bimodal distribution consisting primarily of completely transmitting (open) and completely reflecting (closed) channels (for reviews, see Refs. [13, 14, 15]). Using the information in such a matrix it will be possible to create a perfect wave front that couples only to the open channels and is transmitted through an opaque medium for a full 100%.

Another interesting experiment will be to measure the transmission matrix of samples with extreme disorder. As three-dimensional samples approach the Anderson localization threshold, the transmission matrices will give direct insight in the localized regime, where the modes of the transmitted light should have intriguing properties [13, 16, 17, 18, 19] . Similarly, it would be extremely interesting to study the transmission matrix of a so-called Lévy glass [20], in which light propagates according to a strongly modified diffusion law, or of photonic crystals, which have inevitable disorder [21] in addition to intricate band structure.

In relatively transparent materials, the transmission matrix can be used to obtain a tomographic reconstruction of the sample [22], which can be used to track processes inside living cells. It is not yet clear whether this approach can be generalized to stronger scattering materials, but it is hoped that information can be obtained from inside nontransparent biological tissue [23, 24]. Algorithms to gain information on hidden targets from ultrasound measurements (see, e.g., Ref. [25]) could be ported to optics.

The approach of Popoff and colleagues marks the beginning of a highly exciting road towards a deeper understanding of light transport. Technological progress will enable the measurement of larger and larger matrices that contain all available information about the samples. Ongoing developments in random matrix analysis (see, e.g., Ref. [26]) will allow one to make sense of these enormous quantities of information. When the information in the transmission matrix is fully known, any disordered system becomes a high-quality optical element (Fig. 1). From a technological point of view this has great promise: quite possibly disordered scattering materials will soon become the nano-optical elements of choice.

Universality of beings

Yesterday in a talk with Kevin, I came to a question, which I think may be interesting to wiserU minds. So I'll post it here, in the hope of sparkling discussions. I'm nearly ignorant of biology and pls take tolerance.

The question emerges this way. In January this year, I attended a speech on langevity presented by Francois. From it I learned that, there is a great univerality existing among various speacies, covering bacteria and humans. What appears remarkable to me is that, despite their apparent differences in life forms, the mortality rates of a variety of organisms plotted against ages follow essentially the same trend, very high at infancy, declining all the way as it grows till its adolescence, then increasing without return throughout the rest of its life. I got stuck to this similarity, because this is something in sharp contrast with what might be conceived based on naive reasoning. Think about this: a bacteria has only one cell but a human has billions of cells, and it is natural to think that, aging process for a human involves inter-cell communications while for a bacteria no such communications are possible, and therefore, one naively expects their mortality curves should differ distinctly. This is the argument I held when I talked with Kevin. But Kevin told me that, a bacteria can interact with another bacteria. Aha, a good fact ! Perhaps it is just these interactions that are playing the same role as inter-cell communations for many-cell individuals. Then I asked, what would happen to a single isolated bacteria ? Does aging process essentially reflect the way cells interact ?

I feel that, the universality is perhaps deeply connected to the interactions between cells. Otherwise, it would be hard to understand such universality. Another implication is that, all cells may take similar mechanisms in contacting one another.