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Chap 7 (vision) archived stories

Sunday, February 01, 2009

Chapter 7 (vision). Here are the updates and new stories, including many video links and journal citations. Many more links and citations for this chapter are available at

http://www.flyingcircusofphysics.com/pdf/Chapter7_Ref_Com.pdf

Reference style and difficulty dots
Dots · through · · · indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

7.3 Decapitation with the blind spot
Jearl Walker www.flyingcircusofphysics.com
April 2007   Even if you have full sight, you are blind in a small region of your retina where the optic nerve is connected to the light detectors along the retina. To find this blind spot, fix your gaze on a distant object while you bring a small object across your field of view. Moving a small eraser at arm’s length will do but don’t follow the eraser with your eye; keep your gaze fixed on the distant object. If you bring the eraser to a point about 15º to the temple side of the gaze, the eraser might disappear because its image then falls on the blind spot.
   You do not normally notice the blind spot because the visual system fills it in, almost as if it does not want you to worry about the lack of image there. By filling in, I mean the visual system completes the scene. For example, if you are looking at a wall, you automatically perceive the wall in the blind spot. Recently, Lothar Spillmann, Tobias Otte, Kai Hamburger (of the University Hospital, Freiburg, Germany), and Sevin Magnussen (of the University of Oslo) found that the filling in of both texture and color depends on the visual scene immediately next to the blind spot (as close as 0.05º from the edge of the blind spot). The visual system apparently samples that adjacent texture and color and then blends it across the blind spot.
    However, this blending in does not always work, especially if you know enough to “look” for the blind spot. In The Flying Circus of Physics book I describe how one physiological psychologist amused himself by closing one eye and then positioning the blind spot of his open eye on the head of an irritating dinner guest to visually behead the guest. If you are ever bored to tears in a lecture (golly, surely it could not a physics class and surely it could not be my physics class!), you might try positioning the blind spot of one eye on the head of the lecturer.

· Spillmann, L., T. Otte, K. Hamburger, and S. Magnussen, “Perceptional filling-in from the edge of the blind spot,” Vision Research, 46, 4252-4257 (2006)

Want more references? Use the link at the top of this page.

7.8 Eye oscillations, pretzels, and monitor screens
Jearl Walker www.flyingcircusofphysics.com
April 2007     In The Flying Circus of Physics book, I describe how you can hum in order to “strobe” a television screen. The television image is created line by line and each image line lingers for a short time after it is created. If you hum at the right frequency (and can hold the frequency), the vertical oscillations of the retina allow you to see one or more horizontal black lines on the screen. A black line occurs when an image line has faded and has not yet been replenished by the next cycle of line production. When I wrote about this effect in Scientific American, I quickly realized that I could not hold the frequency of my humming steady enough to see the black lines. So I pressed a controllable oscillator onto my face and then slowly changed the frequency until the black lines appeared. (Ok, I fully understand just how weird this sounds, and you are right---it really was weird and not something I would do in public.)
    Professor Matt Anderson of San Diego State University recently described a more tasty method. Crunch down on a large hard pretzel while watching a television screen from a distance. As you crush the pretzel in your mouth, your skull vibrates, briefly oscillating your eyes. If you stand about 20 meters from the tube-type of television or computer monitor, with the screen fully lit up with an image rather than just being blank, you can see brief distortions and black lines across the screen. I cannot see this effect on flat screens but I am not yet convinced that I tried enough pretzels. Let me know what you see if you try this.

· Williams, P. C., and T. P. Williams, “Effect of humming on watching television,” Nature, 239, 407 (13 October 1972)
· “Humming up an odd vizhual effect,” New Scientist, 63, 230 (1 August 1974) (vizhual is correct spelling)
· Werner, M. S., “Synchronous stabilization of visual perception by voice vibration,” Journal of the Optical Society of America, 64, 890 (June 1974)
· · · Mastebroek, H. A. K., and J. B. Van Der Kooi, “The effect of humming on vision,” Physics Education, 14, 253-254 (1979)
· Walker, J., “How to stop a spinning object by humming and perceive curious blue arcs around a light” in “The Amateur Scientist,” Scientific American, 250, No. 2, 136-145 (February 1984)

Want more references? Use the link at the top of this page.

7.9 Catching arrows
Jearl Walker www.flyingcircusofphysics.com
Dec 2008 Most of the action we see in a modern martial art movie is faked or computer-generated, making the movie little more than an animation film. However, some of the stunts can really be performed by skilled fighters. For example, a person really can catch an arrow in flight, as seen in this video:

http://www.youtube.com/watch?v=uLj8eK814o0

You might think that to catch an arrow means that you must follow it with your eyes, from the bow to when it is alongside you in flight. However, the eyes cannot follow such motion, as shown in studies with baseball players. When he stands at the plate with a fastball coming toward him, a major league baseball player can see the ball until it is about 5.5 feet away from the plate, but thereafter the motion is a blur. The problem is that the eyes cannot rotate fast enough for the vision to be fixed on the ball. However, some ball players can track the ball during the first part of its flight and then, anticipating where the ball will cross home plate, jump the vision to that point, in order to see the ball as it is hit with the bat.

An arrow-catcher might do the same vision jump in order to catch the arrow as it passes him. But the arrow-catcher in the video does not use the sight of the arrow at all. Instead, he depends on the sound emitted as the bow as it launches the arrow to trigger his grab into the air. If he moves quickly, the time he takes to clinch his hand matches the time the arrow takes to reach him. As you see in the video, the strategy does not always work. Not only can the timing be off, but the arrow may not be exactly the right place to be grabbed. Of course, this demonstration is highly dangerous for the obvious reason --- the arrow-catcher might end up catching the arrow with his body or head instead of his hand.

References
Dots · through · · · indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Hubbard, A. W., and C. N. Seng, “Visual movements of batters,” Research Quarterly, 25, 42-57 (1954)
· Johansson, G., “Visual motion perception,” Scientific American, 232, No. 6, 76-88 + 128 (June 1975)
· Regan, D., K. Beverley and M. Cynader, “The visual perception of motion in depth,” Scientific American, 241, No. 1, 136-151 + 162 (July 1979)
· Bahill, A. T., and T. LaRitz, “Why can't batters keep their eyes on the ball?” American Scientist, 72, 249-253 (May-June 1984); see also letters on page 433
· Allman, W. F., “The swing's the thing,” Science 85, 86-87 (April 1985)
· McLeod, P., “Visual reaction time and high-speed ball games,” Perception, 16, 49-59 (1987)
· Watts, R. G., and A. T. Bahill, Keep Your eye on the Ball, W. H. Freeman and Company, 1990, Chapters 7 and 8, ISBN 0-7167-2104-X
· Masood, E., “Howzat! Why the best players don’t always watch the ball,” New Scientist, 168, 22 (25 November 2000)
· · Land, M. F., and P. McLeod, “From eye movements to actions: how batsmen hit the ball,” Nature Neuroscience, 3, No. 12, 1340-1345 (December 2000)
· Bahill, A. T., D. G. Baldwin, and J. Venkateswaran, “Predicting a baseball’s path,” American Scientist, 93, No. 3, 218-225 (May-June 2005)

Related references
· Voisin, A., D. B. Elliott, and D. Regan, “Babe Ruth: with vision like that, how could he hit the ball?” Optometry and Vision Science, 74, No. 3, 144-146 (1997)
· Loomis, J. M., “Looking down is looking up,” Nature, 414, No. 6860, 155-156 (8 November 2001)

7.13 The “rotating snakes” illusion of motion
Jearl Walker www.flyingcircusofphysics.com
July 2008 Skilled artists can paint images that range from realistic to impressionistic but the images are always static, even if they suggest motion. At best they are snapshots and not movies. However, there is a certain type of art, dubbed op art for “optical art,” in which most people perceive motion. When I look at certain examples of op art, I sense motion in my peripheral view (off the direct line of sight), as if sections of the art are sneaking around like mice on a kitchen floor. When I turn my gaze toward the moving regions, the motion there stops, as if the mice freeze in place.

The most startling example of op art I have seen is “rotating snakes,” which was created by Professor Akiyoshi Kitaoka of Ritsumeikan University in Japan. It consists of circular arrangements of colored tiles. When I look casually at the art, the circular arrangements in my peripheral view undergo noticeable rotation but when I look directly at any one of those arrangements, the motion immediately disappears, as if the tiles don’t want to be seen while they move. Here’s the link to “rotating snakes,” but let me first warn you that if you are adversely affected by shimmering lights, you probably should not use the link:

http://www.ritsumei.ac.jp/~akitaoka/index-e.html

Illusions of motion in a static picture fascinate many types of researchers because they provide tantalizing clues as to how not only vision works (which we only poorly understand) but also how the brain works (which we understand even less). The colors of the “rotating snakes” illusion are actually irrelevant. Instead, the important features lie in the contrast in the luminance (loosely said to be the brightness) of adjacent tiles in each circle of tiles. Along each circle the tiles have this repeated arrangement:

black, dark gray, white, light gray, black

The perceived motion is rightward through this arrangement.

No one can explain the illusion in detail but here are some of the main points:

1. When I look at an edge that divides regions with different luminance, the speed of the visual processing needed to bring the image to consciousness depends on both the luminance and the contrast between the two regions. Larger luminance and larger contrast results in faster processing. For the arrangement of tiles, we have

black, dark gray, white, light gray, black

↑ ↑ ↑ ↑

contrast: small large small large

So, the processing of the different tiles occurs at different rates:

black, dark gray, white, light gray, black

↑ ↑ ↑ ↑

contrast: small large small large

↑ ↑

processing: quick delayed

2. When I perceive one edge and then, shortly later, an adjacent edge, the motion sensors in my brain can signal that something moved from the first edge to the second edge. This seems to be the source of the motion illusion.

black, dark gray, white, light gray, black

↑ ↑ ↑ ↑

contrast: small large small large

↑ ↑

processing: quick delayed

perceived motion →

3. If I could stare at the pattern without moving my eyes, not only would I not perceive motion but the pattern itself would probably fade out. The brain quickly ignores constant (unchanging) signals. So, if the pattern remains fixed on my retina, it would soon be ignored.

However, even if I try to fixate my view of the pattern, my eyes still undergo slight motions, drifts and jumps. Part of the normal visual processing is to allow for that motion and bring a steady view up to consciousness. In the “rotating snakes” illusion, the natural drifting of the eyes seems to act as a “screen refresher” because it moves the pattern over the retina, disallowing the brain to fade it out. Because the pattern is continuously being refreshed on the retina, I can then perceive the illusion of motion due to the processing speed of different edges that separate regions with different luminance.

Professor Kitaoka has a wealth of other optical illusions on his web site. After you explore them, you might like to try your hand at creating new designs of op art. There is a lot left in visual science to be explored.

· · Oster, G., “Optical art,” Applied Optics, 4, No. 11, 1359-1369 (November 1965)
· Zanker, J. M., M. Doyle, and R. Walker, “Gaze stability of observers watching Op Art pictures,” Perception, 32, No. 9, 1037-1049 (2003)
· Zanker, J. M., and R. Walker, “A new look at op art: towards a simple explanation of illusory motion,” Naturwissenschaften, 91, 149-156 (2004)
· Zanker, J. M., “Looking at Op Art from a computational viewpoint,” Spatial Vision, 17, No. 1-2, 75-94 (2004)
· Leviant, I., “Does ‘brain-power’ make Enigma spin?” Proceedings of the Royal Society of London B, 263, 997-1001 (1996)
· · Murakami, I., A. Kitaoka, and H. Ashida, “A positive correlation between fixation instability and the strength of illusory motion in a static display,” Vision Research, 46, 2421-2431 (2006)
· Gori, S., K. Hamburger, and L. Spillmann, “Reversal of apparent rotation in the Enigma-figure with and without motion adaptation and the effect of T-junctions,” Vision Research, 46, 3267-3273 (2006)
· Kumar, T., and D. A. Glaser, “Illusory motion in Enigma: A psychophysical investigation,” Proceedings of the National Academy of Sciences of the USA (PNAS), 103, No. 6, 1947-1952 (7 February 2006)
· Hamburger, K., “Apparent rotation and jazzing in Leviant’s Enigma illusion,” Perception, 36, No. 6, 797-807 (2007)

Want more references? Use the link at the top of this page.

x
7.15 Reading in the dark – a weird illusion
Jearl Walker www.flyingcircusofphysics.com
Sep 2009 Here is another of my examples of “physics for the first date,” and it is also one of the weirdest illusions I have ever experienced. First you and your date need to dark adapt your eyes by waiting in darkness for about 10 to 15 minutes. Place an open magazine in front of you at about normal viewing distance. Of course, in the dark, you cannot see it.

After your eyes have adapted to the dark, illuminate the magazine with a flash of light, such as with a camera or a cell phone with a built-in camera. During the flash, the magazine is too brightly illuminated for your dark-adapted eyes to see any details of it. But hold your gaze steady (don’t move your eyes around). As the glare of the flash fades, a detailed image of the magazine begins to appear. It is said to be a positive afterimage because the white regions on the page appear as white regions in the afterimage and the dark regions (such as words or photographs) appear as dark regions. Moving your eyes will immediately erase the afterimage, but if you hold your gaze steady, you can move your attention over the afterimage to read words and pick out details in any photographs or drawings. This image lasts for about 15 seconds and then is replaced by a negative afterimage, with black and white reversed.

Reading in the dark may be curious but here is the weird part. Trigger the flash twice as, say, a coin falls and then again hold your gaze steady. You will see two afterimages of the coin during the fall, as if they were shot in a stroboscopic photograph. Next, place your hand in front of you, trigger the flash, and then grab the back of your neck with the hand. As the afterimage appears, you clearly see the hand in front you while you clearly feel it on the back of your neck. The sensation is most strange.

Even stranger is this: Look down at the floor, trigger the flash to illuminate the floor, and then (without changing your gaze), squat. When the afterimage appears, you see the floor at its normal distance from your eyes, but from a lifetime of experience you know that from the squatting position it must be much closer. If you flash when squatting and then stand for the afterimage, the floor appears to be cutting through you at about chest level. I sure that you and your date can think of other experiments.

The positive afterimage is the more striking of the two afterimages you see in these demonstrations. Unfortunately there is little known about positive afterimages and no commonly accepted explanation.

The negative afterimage is better understood and is usually attributed to the saturation (bleaching) of the photoreceptors on the retina, especially the cone cells, by bright light or prolonged exposure to light. When light reaches the retina, certain chemical reactions occur which then trigger nerve signals to be sent to visual cortex of the brain. However, over stimulation of the photoreceptors temporarily depletes the chemicals, and those regions of the retina then appear to be darker than the surrounding, undepleted regions, giving the bright-dark reversal that characterizes a negative afterimage. This much is the common explanation of the effect, but experimental evidence indicates that negative afterimages are also due to changes in the processing of the nerve signals in the visual cortex following a bright or prolonged exposure.

References
Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Brindley, G. S., “The discrimination of afterimages,” Journal of Physiology, 147, No. 1, 194-203 (1959)
· Gregory, R. L., J. Wallace and F. W. Campbell, “Changes in the size and shape of visual after-images observed in complete darkness during changes of position in space,” Quarterly Journal of Experimental Psychology, 11, No. 1, 54-55 (1959)
· Brindley, G. S., “Afterimages,” Scientific American, 209, No. 4, 84-91 (October 1963)
· Miller, N. D., “Positive afterimage following brief high-intensity flashes,” Journal of the Optical Society of America, 56, No. 6, 802-806 (June 1966)
· Robinson, J. O., The Psychology of Visual Illusion, Hutchinson, 1972, pages 243-245
· Gregory, R. L., Concepts and Mechanisms of Perception, Charles Scribner's Sons, 1974, Chapter 22
· MacLeod, D. I. A., and M. M. Hayhoe, “Rod origin of prolonged afterimages,” Science, 185, No. 4157, 1171-1172 (1974)
· Hayhoe, M. M., D. I. A. MacLeod and T. A. Bruch, “Rod-cone independence in dark adaptation,” Vision Research, 16, No. 6, 591-600 (1976)
· Gosline, C. J., D. I. A. MacLeod and W. A. H. Rushton, “The dark adaptation curve of rods measured by their afterimage,” Journal of Physiology, 259, No. 2, 491-499 (1976)
· Sakitt, B., “Psychophysical correlates of photoreceptor activity,” Vision Research, 16, No. 2, 129-140 (1976)
· Friedman, H., and A. L. Marchese, “Positive after-image, PAI: early erasure by saccadic eye movement or Jendrassik manoeuvre,” Experientia, 34, 71-73 (1978)
· Adelson, E. H., “Visual persistence without the rods,” Perception & Psychophysics, 26, No. 3, 245-246 (1979)
· Kriegman, D. H., and I. Biederman, “How many letters in Bidwell's ghost? An investigation of the upper limits of full report from a brief visual stimulus,” Perception & Psychophysics, 28, No. 1, 82-84 (1980)
··· Geisler, W. S., “Increment threshold and detection latency in the rod and cone systems,” Vision Research, 20, No. 11, 981-994 (1980)
· Power, R. P., S. Hausfeld, and A. Gorta, Workshops in Perception, Routledge & Kegan Paul, 1981, Chapter 21
·· Adelson, E. H., “The delayed rod afterimage,” Vision Research, 22, 1313-1328 (1982)
· Power, R. P., “Apparent movement induced by afterimages,” Perception, 12, 463-467 (1983)
· Walker, J., “Bidwell's ghost and other phenomena associated with the positive afterimage” in “The Amateur Scientist,” Scientific American, 252, No. 2, 122-128 (February 1985)
· Walker, J., “The Amateur Scientist,” Scientific American, 252, 122 (March 1985); see page 126
· Bross, M., “Emmert’s law in the dark: active and passive proprioceptive effects on positive visual afterimages,” Perception, 29, No. 11, 1385-1391 (2000)
· Suzuki, S., and M. Grabowecky, “Attention during adaptation weakens negative afterimages,” Experimental Psychology, 29, No. 4, 793-807 (2003)

7.28 Ornamental ball visual effect
Jearl Walker www.flyingcircusofphysics.com
December 2007 Around Christmas time some years ago, Michael Berry, who is famous for a variety of physics insights, including the Berry phase in quantum physics, made a remarkably simple observation about the reflection by a convex curved surface, such as in this photo by Iaanba. You can easily repeat that observation. If you examine the image of a small lamp in the side of a shiny ball, such as commonly used to decorate a Christmas tree, the shape of the image depends on the room illumination. When the illumination is normal, the reflection forms a small image that you can clearly identify as that of the lamp. However, if the room lights are dimmed, the image gradually elongates and the final distorted image may not be recognizable.

The distortion involves the way light reflects from the convex surface and how the pupil of your eye changes in response to the general illumination. Light rays from the lamp are reflected in a wide range of directions by the curved surface. When your eye intercepts some of those rays, the only ones that reach the retina and result in a visual sensation are the ones that pass through the pupil, the optical opening to the eye. When the general illumination is relatively bright, the diameter of the pupil is relatively small and so the rays that enter the eye must have about the same angle in their reflection from the ball. The angular spread of those rays is small enough that your visual system can make sense of the rays by mentally extending them back into the ball. What is brought up to consciousness is the image of a small source of light seemingly located behind the surface, much like an image of you is seemingly located behind your bathroom mirror when you look into the mirror.

When you dim the room illumination, your pupil gradually expands to allow in more light, so that you become “dark adapted.” (I usually allow about 10 or 15 minutes for such adaptation.) The now larger pupil allows a larger angular spread of the rays reflected from the curved surface, and the rays can no longer be mentally extended backward to a single point. Instead, they seem to extend back to a line that lies in the plane formed by your eye, the lamp, and the point on the ball closest to your eye. The effect works better if the lamp is tiny, such as a common Christmas tree light or a pinhole pierced into a sheet of aluminum foil that is mounted over the front end of a desk lamp.

If you switch on the room illumination after the line forms, the pupil diameter quickly decreases and the line quickly collapses to a point.

· · · Berry, M. V., “Reflections on a Christmas-tree bauble,” Physics Education, 7, 1-5 (1972) 1972. Available at

http://www.iop.org/EJ/article/0031-9120/7/1/301/pev7i1p1.pdf?request-id=MO4iqgKd3BGJYvcY3Ai7Kg

· · · van Beveren, E., F. Kleefeld, and G. Rupp, “Images in Christmas baubles,” European Journal of Physics, 27, 337-346 (2006)

7.46 Cosmic rays and airplane flights
Jearl Walker www.flyingcircusofphysics.com
July 2010 Earth is continuously bombarded by cosmic rays, which are particles that originate either in our Milky Way galaxy or from other galaxies. Most of the particles are protons that are generated by well understood processes, but the generation of the very energetic protons is currently not understood.

As the particles penetrate the higher reaches of the atmosphere, their collisions with air molecules produce secondary particles, including electrons, positrons, and pions. The protons and electrons lose their energy as they continue downward through the atmosphere, and each positron soon combines with an electron along the way --- the pair annihilate each other, producing two gamma rays. The pions quickly decay to produce muons. Muons then decay by transforming into neutrinos and either electrons or positrons. Again, the electrons and positrons quickly lose their energy or undergo annihilation.

Most of the particles reaching sea level are muons. At first glance, they should not be able to travel all the way down to sea level because their average life time is only 2.2 microseconds, as measured when they are stationary. With such a short lifetime, they should decay well before reaching sea level. However, the muons are moving so fast that the relativistic effect known as time dilation applies, and their lifetime as measured in the frame of the ground is much longer than 2.2 microseconds. That longer lifetime allows many of them to reach sea level before they decay.

If you move to greater altitudes by, say, climbing a mountain, the rate of particles reaching you increases. Not only do you intercept more of the muons, but you begin to intercept some of the other particles in the secondary particle shower.

With careful measurements, including proper statistical analysis, you might be able to measure the increase in the particle rate by carrying a Geiger counter along with you as you climb a mountain. In such a device, the passage of a particle (such as a muon), x ray, or gamma ray through the interior causes a cascade of charged particles, which produces a pulse of current in the meter. Collectively, these particles and rays are called ionizing radiation because they can remove electrons from atoms, thus ionizing the atoms. Each pulse generates a signal with an audible click (as you might have heard in movies involving radiation dangers, atomic war, giant insect creatures, and so on). Each pulse also produces a flash of light in a bulb. Thus, the rate of particles passing through the device is indicated by the rate of clicks and flashes.

Mountain climbing with a Geiger counter is actually a difficult way to show that the rate of particles increases with altitude because the rock itself produces ionizing particles and rays due to its radioactive content. Thus, the rate of clicks and flashes does not measure only the particles resulting from cosmic rays.

Recently Francesco Blanco, Paola La Rocca, and Francesco Riggi of the University of Catania and the INFN (both in Catania, Italy) described experiments in which Geiger counters were carried by students on commercial air flights. The count rate was measured as a function of time during the flight, rather than as a function of altitude, because the altitude could not be measured. However, the normal cruising altitude of the flights was known to be between 9 and 10 kilometers. On average, the measured rate at the cruising altitude was about 8 times that at sea level.

The authors point out two complications in interpreting the result in terms of the muon rate. (1) The Geiger counters were somewhat shielded by the airplane body. (2) Although the rate of protons and electrons at sea level was close to zero, their rate at the cruising altitude was about half that of the muons. Still, the experiments admirably demonstrate the increase in muon rate with altitude.

Down below here are links to videos made by other people who happened to carry Geiger counters on airplane trips. Let me explain the units of microsieverts per hour that you see in some of the videos.

The radiation dose (the energy) that, say, you absorb when exposed to radiation is measured in grays (Gy), where 1 gray is the absorption of 1 joule per kilogram in your body. (An older unit of absorbed is the rad, where 1 rad = 0.01 gray.)

However, different types of radiation cause different amounts of damage to your body. So normally we multiply the dose in grays by a number known as the RBE factor, to account for the severity of damage. For example, electrons and muons have an RBE of 1.0, whereas protons have an RBE of 5 to 10 (the value is debated in the research literature). The result of the multiplication is the dose equivalent, measured in units of sieverts (Sv). (An older unit is the rem, where 1 rem = 0.01 sievert.)

What you see in the videos is useful only in a relative sense --- you can see that the count rate at the cruising altitude is significantly higher than that at sea level. However, to interpret the readings in terms of sieverts would require better information about the type of radiation setting off the Geiger counter.

Radiation exposure is of no concern to occasional passengers but not to flight crews who are routinely at high altitudes. If you would like to read my earlier story about the flight-crew concern, click on this next link to the archives and scroll down to item “7.46 Cosmic rays and airplane flights.”

http://www.flyingcircusofphysics.com/News/NewsDetail.aspx?NewsID=43

If you want to watch a video that I produced about time dilation for the web material associated with my textbook, go to the Facebook site for The Flying Circus of Physics at

http://www.facebook.com/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?v=app_23798139265&ref=ts#!/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?v=wall&ref=ts

and click on “The Relativity of Time.” Using only algebra and Einstein’s own simple explanation, I derive the time dilation equation. You might also watch “The Relativity of Length,” which uses only algebra and the time dilation equation to derive the length contraction equation.

Reference
Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
·· Blanco, F., P. La Rocca, and F. Riggi, “Cosmic rays with portable Geiger counters: from sea level to airplane cruise altitudes,” European Journal of Physics, 30, 685-695 (2009)