Bubbles

I had the distinct pleasure of benefiting from the resources of two of New York City's elite high schools.  I attended Brooklyn Technical High School in the late 1950s, and then, after an already long career teaching English in other schools, had a twelve-year stint at Stuyvesant High School from 1992 until 2003, when I retired.   Although my formal education had been in the humanities, I have had a life-long interest in science, particularly in astronomy and physics, and, so, I came to enjoy the opportunity to have informal conversations with my students about some of the issues about which I had questions.  I can recall one such conversation in which I shared with a group of students my dismay and annoyance at the way science text books represent reality.  Based on these conversations, I got the impression that in the forty years (1959 to 1999) that had passed since I was a student that while science had changed a great deal, pedagogy had not kept pace.

      What exactly is a wave?  Throughout all of our schooling we are taught about waves--sound waves, light waves, radio waves, ripples in ponds and waves in the ocean.  The stylized radio antenna depicted above has been reproduced in countless texts.  What this iconic image purports to show is an antenna emitting radio waves.  What we actually see is a series of broken concentric circles with their source at the tip of the antenna.  I could never understand how those broken circles even came close to actually depicting waves.  If anything, I suspected, a more accurate depiction would be a series of concentric spheres, in effect, bubbles within bubbles emanating from the antenna.  Similarly, the often offered alternate image of ripples made by a rock thrown into a still body of water, a pond, seemed to have a similar drawback.   While it is true that, in this case, we seem to have advanced to both concentric circles and the standard image of a wave, if we take the added step of visualizing the ripples in cross section, our cross-section seems restricted to the surface of the water.  That is, the trough of the ripple/wave still does not depict what may be going on beneath the surface.  Even the oscilloscope, another standard device that is understood to depict waves electronically, seems merely to be a line of light having a certain amplitude and frequency (height or intensity and time period between pulses).
     Thus all three of the most common depictions of waves, namely fret lines, ripples, or squiggly lines of light on an oscilloscope's screen, seem merely to be shorthand methods of showing us what a wave is.  I struggled to find some way to better understand and visualize what was actually taking place.  I imagined a light going on in a room or a hand clapping.  In both cases, whether I was considering light or sound, it was obvious to me that there was no linear wave emission from either source.  Whether at the speed of light or the speed of sound, whatever was being created at the source reached everyone in the room regardless of where they were. Some way of illustrating something akin to an expanding sphere of some force or energy seemed to be called for.

When I found the image on the left, of a guide in a children's museum blowing bubbles within bubbles, what was going on seemed closer to what my instincts told me actually emanated from a point at which light or sound (and thus anything said to take the form of waves) might be depicted.  At this point, however, I had the sinking feeling that a knowledge of calculus might be a good thing to have.  I knew enough about the construct underlying calculus to know that it dealt with objects in motion.  Had I arrived at one of those junctures where only mathematics could express what was going on, and that what I wanted to see simply illustrated no more surrendered itself to pictorial explanation than all those rubber sheets and curving graph lines through black space could succeed in depicting Einstein's theory of General Relativity?
     I searched for one more common device that might help--a cheap fiber optic lamp.  (I have even bought one online so I can stare at it and await enlightenment.)  This last seems closest to what I envision happening when any object emits or even reflects light.  But where is the wave?
    I applied myself to the problem.  It now seemed to me that a combination of the bubbles within bubbles and the fiber optic lamp might offer a solution.   But there are problems.  If you turn on the lamp, you instantly see the points of light emerging from the end of each plastic fiber.  Given the speed of light, one would not expect to see the photons gradually traveling from their source to the end of each individual fiber.  It would be ideal, I thought, if one could make two important modifications to my table-top toy: first, slow down the speed of light to a degree that one could see the light travel from its center to the end of the fibers, and, second, so increase the number of fibers so that, rather than seeing pinpoints of light, the lamp would ultimately produce something closer to a perfect sphere of light.  If the light were traveling slowly enough what one would see is a gradual transformation--from a small sphere at the moment one turned on the lamp, to a larger sphere whose radius would be determined by the length of the fibers.
     You have probably guessed that my "solution" raised more questions than it answered.  When, in my conversations with students, I shared some of these speculations and offered that, ultimately, if we could actually see all of the waves in the room we were in, radio waves, television waves, X-Rays, ultra-violet rays,etc., coming into the room, bouncing off one another, reflecting one another, we would find that we were in a dense "soup" of bubbles and intersecting bubbles, (are those the strings of string theory?), a cosmic foam of bubbles, several of them told me that, "Hey, there are some scientists we have heard about who also believe in bubbles.  You're not alone."

...to be continued.