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(E21)   Waves in Space     

    (This section is optional: consider reading it for general outlook, without concern for every detail.)

Light

    Allegedly it was Galileo who one night tried to measure the velocity of light, using two hooded lanterns and a helper. The helper with one lantern was posted at a far-away spot and was instructed to uncover his lantern the moment he saw light from Galileo's. When Galieo uncovered his lamp, the returning flash came almost instantaneously. He then told his helper to repeat the experiment at a much greater distance. The delay was just as short as before and Galileo concluded that is was mostly due to the reaction time of the helper, and that light spread very rapidly, maybe instantaneously.

    The first actual estimate of the velocity of light in empty space was made in 1676 by Ole Roemer, a young Danish astronomer at the observatory of Paris, as a by-product of a method to determine longitude in mapping the Earth. It was a clever feat of deduction, but has already been described elsewhere in this collection, so the reader is encouraged to look up there

    By the 1800s, a lot had been learned about light. Eyeglasses, telescopes and microscopes were in use--all based on the property that light slowed down in transparent materials. It was known to spread as a wave, propagating in empty space at about 300,000 km per second--a velocity nowadays denoted by the letter c--and slightly more slowly in air. A wave is a spreading disturbance associated with an oscillating phenomenon (mathematics has a more precise definition), giving it a wavelength λ (lambda, Greek lower case L), and a frequency ν = c / λ, the number of up/down oscillations per second when the wave passes any point in space (ν is nu, the Greek lower case N).

    Sound is such a wave, an oscillation which can spread through air, water, walls and solids. Its wavelength can be inferred from the size of the instrument producing it, e.g. a plucked string--and the bigger the source, the longer the wavelength (centimeters to many meters) and deeper the sound (Big dog: woof, woof! Little dog: yip, yip!). Its velocity in air, demonstrated by the time lag between lightning and thunder, is about 330 meters per second.

    Light also has its wavelength, but it is very small, as indicated by the sharpness of visible images. Only with very small objects, of size comparable to a wavelength, is the image fuzzed out. With half-closed eyes, in bright light, we see "floaters" in our eyeballs, specks of dust or short threads in the eyeball fluid, and these indeed are "fuzzed out" by wave effects, to tiny bright circles inside dark circles, or bright threads between dark parallel borders. The particles are actually too small for details to show up, all we see is the pattern of light waves they produce.

    Microscopes and telescopes similarly have limited powers of magnification depending on wavelength, beyond which one only gets magnified blurs. Patterns of light that has passed a thin slit, the colors of patches of kerosene floating on water (whose thickness is comparable to the wavelength λ, dependent on color) or (these days) the colors reflected by the narrow grooves of a computer's compact memory disk--all these are related to the wave nature of light.

    But what sort of wave? Sound does not spread in vacuum, but light does. Scientists in the 1800s therefore speculated that all space was filled with a "lumineferous (light carrying) aether" (will come back to that). A great achievement of 19th century was to show that light was linked to electricity--that it was an electromagnetic wave, part of a large family of such waves which grew with new discoveries to include infra red, ultra-violet, radio, microwaves, X-rays, gamma-rays and more.

Units of Electricity

    The study of electricity in the 1800s uncovered an interesting relationship. The electrostatic law found by Coulomb, giving the force between electric charges q1 and q2 a distance r apart, was

F  = k1 q1q2/ r2

    The choice of the constant k1 allows one to define a "natural" unit of electricity, linked to fundamental measurables like (meter, kilogram, second). By choosing k1=1, for instance, a unit of electric charge is defined as the amount attracting or repelling an equal charge at a distance of 1 meter with a force of one Newton (about the weight of 100 gram or 3.5 ounces)--defined from the fundamentals by Newton's laws of motion.

    Magnetic forces, on the other hand, allow one to define a unit of electric current i, by the force formula

F  = k2 i1i2 [ s1s2/ r2 ]
giving the force between parallel wire elements of length s1 and s2 separated by a distance r. Ignore now the ratio in the square brackets--whatever units length is measured in, it remains the same (e.g. convert from inches to centimeters--any distance is multiplied by a factor 2.54, which then cancels out). If here F is again in Newtons and we choose k2=1, this defines a natural unit of electric current i.

    However, electric current and electric charge are related! A unit of electrical current should also correspond to a unit of electric charge moving at some velocity! Hidden somewhere in this haystack of units is a velocity which is a natural constant of nature.

    It turns out to be the velocity of light c--possibly with factors like the ratio of the circumference of a circle to the diameter (π=3.141526...) which would actually be part of the formula. This may carry two kinds of message:

    (1) Electricity, magnetism and light are somehow related.
    (2) The velocity c is some how "built into" the structure of
                nature, just as the number π is built into mathematics.

It turns out both hold true. Light is indeed an electromagnetic phenomenon, while c appears unexpectedly in formulas like Einstein's E = mc2


    Note: At one time physicists actually used different "electrostatic" and "electromagnetic" systems of lectrical units, defined by one or the other equations given above. Engineers meanwhile stuck to amperes and volts, which had practical orders of magnitude. Today's system is the MKS (meter-kilogram-second) system which includes somewhat arbitrary values of k1 and k2, bringing into the equations of electricity arbitrary "constants" ε0 and μ0 (epsilon-zero and mu-zero) but retain the ampere and the volt. The coulomb and farad turn out to be inconveniently large, but that's how it is.

"Ray Vibrations"

    Sound in air is a pressure wave, advancing in the same direction as the force it produces. Light is altogether different, a "transverse wave" with effects in the directions perpendicular to its advancing front--like a sideways jiggling of a bowl of jelly pudding, or certain types of earthquake waves. Ordinary light vibrates in all directions, but certain crystals (known to Faraday) can separate vibrations into components polarized in two directions, perpendicular to the advance of light and to each other. The human eye can barely detect any difference, but Polaroid eyeglasses with crystals embedded in mutually perpendicular directions can separate two differently polarized images, and thus give us 3-D film images. Faraday also knew that light reflection from transparent surfaces (but not from ordinary mirrors with thin metal coating!) depended on the polarization of its components (in reference to the direction of the source), and that the blue color of the sky, from scattered sunlight, also had a preferred polarization, depending on the location of the Sun.

    Polarized waves are somewhat like waves propagating on a long rope when one end is vigorously shaken. Shake the end up and down, and the waves are all in a vertical plane. Shake it sideways, and the waves are horizontal. And when the shaking is in random directions, so are the waves, though a vertical slit (like a polarizing crystal) will only allow vertical waves to pass, and a horizontal slit, only horizontal ones.

Faraday lecture

    Faraday wondered if magnetic field lines filling space could oscillate like such ropes, and whether light, with its polarizations, consists of such oscillations. In April 1846 he gave an impromptu lecture Thoughts on Ray Vibrations on his speculations. In his report on the lecture, he wrote:

        The view which I am so bold to put forth considers, therefore, radiation as a kind of species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavors to dismiss the aether, but not the vibration. The kind of vibration which, I believe, can alone account for the wonderful, varied, and beautiful phaenomena of polarization, is not the same as that which occurs on the surface of disturbed water, or the waves of sound in gases or liquids, for the vibrations in these cases are direct, or to and from the centre of action, whereas the former are lateral. It seems to me, that the resultant of two or more lines of force is in an apt condition for that action which may be considered as equivalent to a lateral vibration; whereas a uniform medium, like the aether, does not appear apt, or more apt than air or water.

    This beginning of the electromagnetic theory of light occurred in somewhat unusual circumstances. Faraday was schedule dto introduce a Friday lecture at the Royal Institution by Charles Wheatstone, remembered nowadays for his "Wheatstone bridge" for measuring electrical resistance (his talk however was on a timing device). Wheatstone came to the lecture hall, but developed an anxiety and left again before the talk began (allegedly, since the it has been customary at the Royal Institution to lock speakers in a room half an hour before the presentation).

    With and audience but no speaker, Faraday gave the talk (he knew the subject), but with a lot of free time left at the end, added a talk about his own ideas. A hesitant speculation, not a polished talk, but that is what brand-new scientific ideas often look like. Once you know the answer, it may look deceptively simple and obvious; Faraday recaptures the uncertain mix of guess and hypothesis which precedes knowledge. He himself ended his report with these words:

        I think it likely that I have made many mistakes in the preceeding pages, for even to myself, my ideas on this point appear only as the shadow of a speculation, or as one of those impressions on the mind which are allowable for a time as guides to thought and research. He who labours in experimental inquiries knows how numerous these are, and how often their apparent fitness and beauty vanish before the progress and development of real natural truth.

Today one might argue that Faraday was on the right path, but only at its beginning. It is true that oscillating magnetic field lines in a vacuum are just a mathematical abstraction. But the notion that they represent a possibility of magnetic force turned out to be the seed of the idea of fields in space.

    But a key ingredient was still missing: because of magnetic induction, (discussed in what follows) there also existed an oscillating electric field--a possibility of sensing an electric force in the region where the wave is spreading.

    The complete idea of an "electromagnetic wave" propagating in what is otherwise empty space was later correctly worked out by James Clerk Maxwell, and it fit all known properties of light; the velocity of propagation was a natural consequence of the two basic laws, cited above. And we no longer claim that the waves propagate in some "aether" filling space, because that would be a most unusual substance, one whose motion was unobservable. We just call the environment of propagation "space"--sometimes "space-time", or simply "the vacuum."



 

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Last updated: 24 July 2010


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