History of Science -- Part Six: Electromagnetic Force

Michael Faraday

A piece of silk rubbed on glass is attracted to the glass but repelled by another piece of silk also rubbed on glass. Walk across a rug dragging your feet and, when you touch a door knob, you’ll get a nice blue spark as electricity jumps to the door knob. Such “electric charge,” seen when different materials are rubbed together, was known in ancient times. The crucial step in understanding it was the bright idea of Benjamin Franklin. He noticed that when any two electrically charged attracting bodies came into contact, the attraction lessened. He realized that attracting charged bodies canceled each other’s charge.

Cancelation is a property of positive and negative numbers. Franklin therefore assigned algebraic signs, positive (+) and negative (-), to charged objects. Bodies with charges of opposite sign attract each other. Bodies with charges of the same sign repel each other.

Unfortunately, what Franklin didn’t realize was that the carrier of the charge was the electron. It flowed onto the objects that he called “negative” leaving a shortage of negative charge on the object providing the electrons making it “positive.” Later, when scientists figured out just what was “flowing,” it was the “negative electricity.” That makes some of the equations of electricity and especially circuit theory use negatives. It isn’t a big deal, but a lot of modern electronics engineering imagines a positive current flow in the opposite direction to the electron flow. This is called “conventional flow” and is positive. It just makes the mathematics a tiny bit easier.

We all wish Franklin had chosen the opposite bodies to be positive and negative, and then we wouldn’t need this fiction of “conventional current” to make the math a little bit easier. But, you can’t go back and change history. We’re just lucky that Franklin didn’t kill himself flying kites in thunderstorms.

Franklin’s work on electricity is in good part responsible for the existence of the United States. As ambassador to France, it was not just Franklin’s wit, charm, and political acumen, but his stature as a scientist that allowed him to recruit the French aid that was so crucial to the success of the American Revolution.

We now know that atoms have a positively charged nucleus made up of positively charged protons and uncharged neutrons. Electrons, each with a negative charge equal in magnitude to that of a proton, surround the nucleus. The number of electrons in an atom is equal to the number of protons, so the atom as a whole is uncharged. When two bodies are rubbed together, it is the electrons that move from one to the other.

A glass rod that is rubbed with a silk cloth, for example, becomes positively charged because electrons in the glass are less tightly bound than those in the silk. Therefore, some electrons move from the glass to the silk. The silk, now having more electrons than protons, is negatively charged and is attracted to the positively charged glass. Two negatively charged pieces of silk would repel each other.

An early scientific device for exploring these charge is called an electroscope. One such device, the gold foil electroscope, is made up of two thin leaves of gold suspended in a glass jar. The gold-leaf electroscope was developed in 1787 by British clergyman and physicist Abraham Bennet. It was a very sensitive device to detect charge. It consists of a vertical metal rod, usually brass, from the end of which hang two parallel strips of thin flexible gold leaf. A disk or ball terminal is attached to the top of the rod, where the charge to be tested is applied. To protect the gold leaves from drafts of air they are enclosed in a glass bottle, usually open at the bottom and mounted over a conductive base. When a charge is applied to the metal ball, it flows down to the gold leaves, causing them to spread apart. If the charge is negative, then the excess electrons on the two leaves repel since they are like charges. Same with a positive charge which is a shortage of electrons.

Coulomb's law describes the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb, and was essential to the development of the theory of electromagnetism. Like gravity, this force is an inverse square law. That is, the intensity of the attraction or repulsion is proportional to the inverse square of the distance between the two objects. Double the distance and you get one over two squared or one-fourth the attractive force. With this law you can calculate the forces in any arrangement of charges. That seemed to be the whole story of electric force — there was nothing more to say, or so thought most physicists in the early nineteenth century.

But Michael Faraday found the electric force puzzling. Let’s back up a bit. At the age of fourteen, Michael Faraday, the son of a blacksmith, was apprenticed to a bookbinder. Faraday, a curious fellow, was fascinated by some popular science lectures by Sir Humphrey Davy. He took careful notes, bound them into a book, presented them to Sir Humphrey, and asked for a job in his laboratory. (There is a lesson there for any young person wishing to break into a new field of endeavor.) Though hired as a menial assistant, Faraday was soon allowed to try some experiments of his own.

How, Faraday wondered, could one body cause a force on another through empty space? That the mathematics of Coulomb’s law correctly predicted what you would observe did not satisfy him. He therefore postulated that a charge creates an electric “field” in the space around itself, and it is this physical field that exerts forces on other charges. Faraday represented his field by lines emanation from a positive charge and going to a negative charge. Where the lines were most dense, the force of the field exerted would be greatest.

Most scientists, claiming that Coulomb’s law said it all, considered Faraday’s field concept to be superfluous. Faraday’s ignorance of mathematics, they noted, required him to think in pictures; abstract thinking was no doubt difficult for this young man from the “lower classes.” The field concept was ridiculed as “Faraday’s mental crutch.”

Actually, Faraday went further and assumed that the field due to a charge takes time to propagate. If, for example, a positive and a nearby negative charge of equal magnitude were brought together to cancel each other out, the filed would disappear in their immediate neighborhood. But it seemed unlikely to Faraday that the field would disappear everywhere immediately. (He as so, so right about that!)

The remote field would, he thought, exist for a while even when the charges that created it canceled each other and no longer existed. If true, the field would be a physically real thing in its own right, and not just a crutch.

Moreover, Faraday reasoned, if two equal and opposite charges were repeatedly brought together and separated, an alternating electric field would propagate from this oscillating pair. Even if they stopped oscillating and just canceled each other, the oscillating field would continue to propagate outward.

Faraday’s intuition was sound. A few years later James Clerk Maxwell, picking up Faraday’s field idea, devised a set of equations that encompassed all electric and magnetic phenomena. He combined Faraday’s law of moving charges with Ampère’s law that relates the magnetic field around a closed loop to the electric current passing through the loop and Gauss’s law which is the magnetic analog of Ampère’s. Finally, he added a term to Ampère’s law. Ampère’s law with Maxwell’s correction states that magnetic fields can be generated in two ways: by electrical current (this was the original "Ampère's law") and by changing electric fields (this was "Maxwell's correction"). Maxwell's correction to Ampère's law is particularly important: it shows that not only does a changing magnetic field induce an electric field, but also a changing electric field induces a magnetic field. I consider these four equations the pinnacle of Classical Physics. Like much of Classical Physics, they are just approximations and require some correction both to fit the requirements of Relativity and also Quantum Theory. In fact, in many ways, this set of equations open the door to these twin discoveries of the twentieth century that relegate all that came before as “Classical Physics” and just an approximation of Nature’s true methods.

James Clerk Maxwell was a Scottish physicist and mathematician and he published his results between 1861 and 62. His striking prediction was the existence of waves of electric field propagating along with waves of magnetic field — “electromagnetic waves.” Maxwell noticed that the speed of these waves was exactly what had been measured for light. He therefore proposed that light was an electromagnetic wave.

The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of Michael Faraday's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch who had measured the speed of light. But it wasn't until 1884 that Oliver Heaviside, concurrently with similar work by Willard Gibbs and Heinrich Hertz, grouped the four together into a distinct set. This group of four equations was known variously as the Hertz–Heaviside equations and the Maxwell–Hertz equations, and are sometimes still known as the Maxwell–Heaviside equations. But, in most modern texts, all credit for the equations is given to Maxwell.

Maxwell's contribution to science in producing these equations lies in the correction he made to Ampère's circuital law in his 1861 paper On Physical Lines of Force. He added the displacement current term to Ampère's law and this enabled him to derive the electromagnetic wave equation in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrate the fact that light is an electromagnetic wave. This fact was then later confirmed experimentally by Heinrich Hertz in 1887. The physicist Richard Feynman predicted that, "The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."

The concept of fields was introduced by, among others, Faraday. Maxwell then combined all these ideas into this keystone of electro-magnetics. Albert Einstein wrote:

The precise formulation of the time-space laws was the work of Maxwell. Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarised waves, and at the speed of light! To few men in the world has such an experience been vouchsafed … it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow workers —(Science, May 24, 1940)

As Faraday had predicted, the jiggling of charges produces electromagnetic radiation. The frequency of the jiggling is the frequency of the wave produced. These are the waves we associate with radio and television broadcasts and, at higher frequencies, they are light. Infrared and red are lower frequency and violet and ultraviolet are higher. Even higher frequencies are X-Rays and Cosmic Rays.

Today the most fundamental theories in physics are formulated in terms of fields — Faraday’s “mental crutch” is a pillar upon which all of physics now rests.

The electromagnetic force in very important in many branches of science from electronics to chemistry. Along with gravity, it is the only force we normally experience.

When we touch someone, the pressure of our touch is an electric force. The electrons in the atoms of our hand repel the electrons in the atoms of the other person. Reach out and touch someone by telephone, and it is the electric force that carries the message over the wires and through space. The atoms making up solid matter are held together with electric forces. Electric forces are responsible for all of chemistry and therefore underlie all biology. We see, hear, smell, taste, and touch with electric forces. The processes in our brains are electrochemical, therefore ultimately electrical.

Is our thinking, our consciousness, ultimately to be explained wholly in terms of the electrochemistry taking place in our brains? Some believe so.

There are forces in nature besides gravity and the electromagnetic force. But, we only know of two others: the so-called “strong nuclear force” which binds the protons in the nucleus of an atom together and overcomes the repulsion of like charges, and the “weak force” which is involved in radioactive decay. Current theories combine the weak force and the electromagnetic force. Science is still looking for a combination of all four forces and it is possible there are additional forces we have not yet discovered. Since the strong and weak forces only operate over the very short distances found in the nucleus of atoms, gravity and electric force are what we encounter in our day-to-day lives.

The method used by Faraday is something that interests me personally. I know scientist that work entirely in the abstract realm of mathematics and don’t really worry much what it “looks like.” On the other hand, some of the greatest scientists of all time, including Einstein and Richard Feynman, seemed to use intuitive vision as much as mathematics to understand the physical world. I’m trying to decide which group I belong to. Sadly, in my day, there was a greater emphasis on geometry and especially solid geometry that ties together this visualization and mathematics. These topics are not as common in modern schools with the emphasis shifting to the pure math and away from vision. With computers taking over much of the calculation, I think the time is right to focus more on visualization and ask more "why" questions. That is one of many reasons I’ve added “Art” and “Design” to my “STEM” focus.

I’m as interested in the "why" and "how" as I am of the "what" and "where" and "when." Perhaps that is the source of my great interest in the history of ideas and science. Hopefully you share this interest with me and have found these discussions to your liking. There are other powerful ideas that have led to many scientific breakthroughs. One of those universal ideas is “conservation,” which turns out to be a function of “symmetry.” That is what I’ll explore next as I continue with the History of Science and look at “energy.”

The History of Science -- Part Seven

History of Science -- Part Five: Light

Newton discovered many physical properties of light. Newton bought his first prism in an attempt to disprove French Philosopher Rene Descartes’ wave theory of light. He argued that the geometric nature of the laws of reflection and refraction could only be explained if light was made of particles, which he referred to as corpuscles, as waves do not tend to travel in straight lines. After joining the Royal Society of London in 1672, Newton stated that the 44th trial in a series of experiments he had conducted earlier that year had proven that light is made of particles and not waves.

Advocates of the wave theory had previously stated that light waves are made of white light and that the spectrum that can be seen through a prism is formed because of corruption within the glass. This means that the more glass the light travels through, the more corrupt it will become.

In order to prove that this was false, Newton passed a beam of white light through two prisms which were held at such an angle that it split into a spectrum when passing through the first prism and was recomposed, back into white light, by the second. This showed that the spectrum was not caused by glass corrupting the light. Newton claimed that this was a “crucial experiment.”

A crucial experiment is any experiment devised to decide between two contradictory theories, whereby the failure of one determines the certainty of the other. Since almost everyone agreed that light must either be composed of particles or waves, Newton used the failure of the wave theory to prove that light is made of particles. (Ironically, this experiment did not prove a thing. In fact, if we consider the colors of light to be different frequencies of waves, then the spectrum is a better demonstration of a wave property of light.)

Newton concluded that light is composed of colored particles, which combine to appear white. He introduced the term “color spectrum” and, although the spectrum appears continuous, with no distinct boundaries between the colors, he chose to divide it into seven: red, orange, yellow, green, blue, indigo, and violet.

Newton chose the number seven as this reflected the Ancient Greek belief that it is a mystical number because there are seven “wandering stars” (the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn) and seven days in a week. Recall he was a bit of a mystic. A little bit of science, a little bit of magic, a little lucky guessing, that has been the path science has followed even up to the present day.

Newton showed that every color has a unique angle of refraction that can be calculated using a suitable prism. He saw that all objects appear to be the same color as the beam of colored light that illuminates them and that a beam of colored light will stay the same color no matter how many times it is reflected or refracted. This led him to conclude that color is a property of the light that reflects from objects, not a property of objects themselves. On this he was most correct.

Despite Newton's confidence that his theory had been proven, it still faced several problems and was not accepted right away. Within a year of his announcement fellow Royal Society member Robert Hooke argued that diffraction is not a new type of refraction as Newton had claimed and that it could only be explained by assuming that light is a wave.

Many other members joined Hooke in criticizing Newton's particle theory. Some denied that the Newton's color spectrum existed at all and others denied that his 44th trial really proved that light is not composed of waves. Those that tried to replicate Newton's experiment often failed. Prisms were not commonly accepted as scientific instruments at that time. They were sold as simple forms of entertainment and there was little technical work on their design or improvement. Venetian glass was regarded as the standard against which other glasses were compared, but even this was full of air bubbles and flaws.

Newton did not help matters by concealing the details of his trials. He did not explain how to produce a spectrum from the first prism or specify the size or geometry of the second. Further, he used glass made in London that was superior to the Italian glass prisms. However, with his usual disdain for conflict, he bowed out of the discussion.

Newton had good arguments for his conclusion that light was as stream of tiny particles. Objects obeying his universal equations of motion, light travels in straight lines unless it encounters something that might exert a force on it. His particles of light scatter widely when they hit something irregular, but bounce off a mirror at the same angle that they hit, as would a tennis ball. Newton even ascribes color to the sizes of these bodies.

Actually, Newton was conflicted. He investigated a property of light we now call “interference,” a phenomenon uniquely characteristic of waves. Nevertheless, he came down strongly in favor of particles. Waves seemed to require a medium in which to propagate, and this medium would impede the motion of the planets that his universal equation of motion seemed to deny. This problem of “just what is waving” if light is a wave is a fundamental issue that we will hear of again.

Other scientists proposed wave theories of light that also matched Newton’s experiments of reflection and refraction, but the overwhelming authority of Newton meant that his “corpuscular theory,” that light is a hail of little bodes, dominated for more than 100 years. Ironically, the “Newtonians” were more certain of Newton’s corpuscle than was Newton — until about 1800.

Thomas Young was a precocious child who, reportedly, read fluently at the age of two. He was educated in medicine, earned his living as a physician, and was an outstanding translator of hieroglyphics. But his main interest was physics. At the beginning of the nineteenth century, Young provided the convincing demonstration that light was a wave.

On glass coated with soot, Young scribed two closely spaced parallel lines. Light shining through these two slits onto a wall or reflecting screen produced a pattern of bright and dark bands we call an “interference pattern.” Interference is the conclusive demonstration of wave behavior. Not only does this experiment demonstrate the wave property of light, but it will be integral in our story later as scientists explore the properties of waves and matter. This is an important result, so lets spend some time exploring it.

You can picture a “wave” as a moving series of peaks and valleys, or crests and troughs … like an ocean wave. Such crests and troughs can, for example, be seen through the flat side of an aquarium as ripples on the water surface. Another way to depict waves is a bird’s eye view where you can draw lines to indicate the crests. Waves on the ocean seen from an airplane look like this. I’ll draw some diagrams using that method to demonstrate the principles of wave propagation and interference patterns.

Waves from a small source such as a pebble dropped into water spread out in all directions. Similarly, light from a tiny glowing object spreads in all directions. Light from a large or a distant source will appear more as a row of parallel lines. However, when waves like that encounter a small slit, it will spread out from the slit like from a point source.

Light coming through two closely spaced slits might be expected to illuminate the screen twice as brightly as the light from a single slit. That is the behavior we would expect if light were a series of tiny particles like Newton supposed. But what Young saw when he shined a light through his experimental slits was bands of bright and dark on the screen — a stream of particles could not account for this.

The explanation of the interference pattern is that light from each slit travels a different distance to the areas across the screen. At some points the crests from the light through one slit combine with the crests from the light passing through the other slit. That creates an area of brightness. However, on other parts of the screen, the crest of one wave combines with the trough of the other wave and the light “cancels out” just like adding +5 and -5. This cancelation produces the dark bands. This is the unique wave behavior of light combining and canceling out.

Since one wave is the same as the next, this effect is repeated across the screen of adding and canceling producing bands of bright and dark. “Interference” is actually a misnomer. Waves from the two slits are not interfering with each other, they just add and subtract, like deposits and withdrawals from a bank account.

If you think about the geometry a bit, you can see that the greater the spacing between the slits, the smaller the spacing between the bright bands of the interference pattern. To be truly noticeable, this effect is best produced by two slits very close together. That is what was missing in earlier experiments of this type.

But the essential point to remember is that the interference pattern shows that the light waves reaching each point on the screen must come from both slits. Were light a stream of particles, there would be no interference pattern. Little bullets, each coming through one slit or the other, could not cancel each other out to produce the pattern depending on the slit separation.

Is Young’s argument airtight? Probably not. When Young presented it, it was hotly disputed. Young’s English colleagues were strong in the Newtonian particle school of thought. Plus, wave ideas were favored by the French, and that alone was a good enough reason for a loyal Britain to reject the theory. You see, science is not immune to the prejudices that infect the human race. However, before long, further experiments overwhelmed the objections to wave theory and it was adopted as the true explanation of the form of light.

This isn’t the end of the story. This double slit experiment and its results will appear again as we explore the path of modern science. But, for now, we will follow the trail of electromagnetic force, which is a wave theory. We also need to address the progress science made in studying “heat” and “energy,” a study that had very practical applications in the age of steam engines.

The History of Science -- Part Six

History of Science -- Part Four: Isaac Newton

Isaac Newton was born in 1642, the year that Galileo died. With the wide acceptance of the experimental method, there was a sense of scientific progress, though Aristotle’s erroneous physics was still being taught. The Royal Society of London, a major scientific organization, was founded in 1660. Its motto, Nullis in verba, translates loosely as, “Take nobody’s word for it.” It would have delighted Galileo.

Newton, a handy fellow, was supposed to take over the family farm. But more interested in books than plows, he managed to go to Cambridge University by working at menial tasks to help pay his way. He did not shine as a student, but science fascinated him. In those days it was called “natural philosophy.” When the Great Plague forced the university to close, Newton returned to the farm for a year and one-half. And what a time it was, for Newton and the rest of the world.

Young Newton understood Galileo’s teaching that on a perfectly smooth horizontal surface a block, once moving, would slide forever. A force is needed only to overcome friction. With a greater force, the block would speed up, it would “accelerate.” Galileo, however, accepted the Aristotelian concept that falling was “natural” and needed no force. He also had planets moving “naturally” in circles without force. Galileo just ignored the ellipses discovered by his contemporary, Kepler. To conceive his universal laws of motion and gravity, Newton had to move beyond Galileo’s acceptance of Aristotelian “naturalness.”

Newton tells that his inspiration came as he watched an apple fall. He likely asked himself: Since a force was needed for horizontal acceleration, why not a force for vertical acceleration? And if there’s a downward force on an apple, why not on the moon? If so, why doesn’t the moon fall to Earth like the apple?

His solution was very simple. Here’s a picture. Assume you have a cannon on a mountain. If you drop a cannon ball, it will fall straight down. If you shoot it out horizontally, it will travel a great distance, but still fall to the ground. In fact, it will hit the ground at the same time as the dropped ball if you are shooting it short distances and assume the Earth is flat. But what if you shoot it for a longer distance? Newton knew, as we do, that the Earth isn’t flat. So if you shoot the cannon ball far enough, it will actually fall a ways around the round Earth. If fact, if you shoot the ball fast enough, it will actually miss the Earth, falling around it the whole time. It will move horizontally around the Earth, continuing to fall, and actually be in orbit. In fact, it will come all the way back around and hit the cannonier in the back of the head.

Of course, on the surface of the Earth, air resistance would rob the cannon ball of velocity and it would eventually fall to Earth. But on a planet without air, like the moon, this would actually work. Here on Earth we just shoot our satellites up above the atmosphere with enough velocity that they fall around the Earth in a stable orbit.

The moon doesn’t crash to Earth only because it, like that fast cannon ball, has a velocity perpendicular to Earth’s radius. Newton realized what no one had before: The moon is falling.

Galileo thought that uniform motion without force applied only to motion that was parallel to the surface of the Earth, in a circle about the Earth’s center. Newton corrected this to say that a force is needed to make a body deviate from a constant speed in a straight line.

This is Newton’s first law of motion, often called “Inertia”: A body at rest will remain at rest unless acted upon by an outside force, and a body in motion will remain in motion (in a straight line) unless acted upon by an outside force. So the moon would keep going in a straight line if it were not for the force drawing it to the Earth: gravity.

Further, Newton figured out just how much force is needed. The more massive the body, the more force required to accelerate it. Newton speculated that the force needed was just the mass of the body times the acceleration produced or F = ma. That is Newton’s second law. Force equals mass times acceleration.

If you measure the mass in kilograms and the acceleration in meters per second per second (I’ll explain later), then the force is one Newton in honor of Sir Isaac. This is Newton’s universal law of motion. Note the first law is really a statement of the second law when F = 0.

Let’s explore a little mathematics and define some terms that may not be clear. Let’s start with “velocity,” or as it is commonly known “speed.” Velocity is the rate of change of location or distance. On your car speedometer you read “miles per hour.” At 60 mph you are traveling 60 miles in an hour.

Here is a precise way to calculate that. You might be on a highway with mile markers and you have a watch with a second hand. So you note the starting mile post and the time. Call the milepost x₀ and the time t₀. The zero is the start time and start distance. Drive for some time and then note the new milepost (x₁) and time (t₁). You can now calculate the average speed or velocity by calculating the distance traveled and the time it took. The total distance is the final milepost minus the initial milepost and the time is calculated the same way. You then divide the distance by the total time. If the distance is in miles and the time is in hours, you will get “miles per hour.”

Where
v = velocity
x = distance
t = time

So velocity (or speed) is the rate of change of distance. The calculation shown here is the average velocity over a period of time. Newton explored the instantaneous velocity. If you travel at a constant speed, the average and instantaneous is the same value. But what if speed is increasing, like a drag racer that starts from standing still and accelerates over the quarter mile? Newton had to invent a new kind of mathematics to perform these instantaneous calculations. We now call that new math “The Calculus.” In Calculus, the rate of change is called the “derivative.” Newton would show the derivative with respect to time by putting a dot over the variable letter.

In Calculus “speak” we say that velocity is the first derivative of distance or location. Acceleration is the rate of change of velocity, so acceleration, then, is the second derivative of distance.

If you are measuring velocity in feet per second, then acceleration would be “feet per second per second” or "per second squared."

Newton put two dots for this second derivative.

So it was a busy year and one-half for Newton as he worked out the universal laws of motion, gravity, lunar orbits, and created the mathematics that would allow him to calculate all these values.

When the plague subsided, Newton returned to Cambridge. Isaac Barrow, then the Lucasian Professor of Mathematics, was soon so impressed with his one-time student that he resigned to allow Newton to take the Lucasian chair. The quiet boy became a reclusive bachelor. Newton was reserved and moody and was often angered by well-intended criticism. You’d rather spend an evening with Galileo.

Newton’s ideas needed testing. However, his force of gravity between objects that he could move about on the Earth was far too small for him to measure. So he looked to the heavens. Using his equation of motion and his law of gravity, he derived a simple formula. A chill, no doubt, ran down his spine when he saw that his formula was precisely the unexplained rule Kepler had noted decades earlier of the time it took each planet to orbit the sun.

Newton could also calculate that the orbital period of the moon was consistent with a falling object gaining a speed of ten meters per second each second — something experimentally shown by Galileo. His equations of motion and gravity governed apples as well as the moon — on Earth as it is in Heaven. Newton’s equations were universal.

Newton realized the significance of his discoveries, but controversy over the first paper he ever wrote had seriously upset him. The idea of publishing now terrified him.

Some twenty years after his insights on the farm, Newton was visited by the young astronomer Edmund Halley (of the famous comet). Knowing others were speculating on a law of gravity that would yield Kepler’s elliptical orbits for the planets, Halley asked Newton what orbits his law of gravity would predict. Newton immediately answered, “ellipses.” Impressed by the quick response, Halley asked to see the calculations. Newton could not find his notes. “While others were still seeking a law of gravity, Newton had already lost it.”

After Halley warned him that others might scoop him, Newton spent a furious eighteen months producing Philophiae Naturalis Principia Mathematica. What is now just referred to as Principia was published in 1687 with Halley footing the bill. Newton’s fears of criticism were realized; some even claimed he stole their work.

Though Principia was widely recognized as the profound revelation of Nature’s laws, being mathematically rigorous and in Latin, it was little read. But popularized versions soon appeared. Newtonianism for Ladies was a best seller. Voltaire, aided by his more scientifically talented companion, Madame du Chatelet, in his Elements of Newton claimed to “reduce this giant to the measure of the nincompoops who are my colleagues.”

The revealed rationality of Nature was revolutionary. It seemed to imply, in principle at least, that the world should be understandable as the mechanism of clocks. This was later dramatically demonstrated by Halley’s accurate predictions of the return of a comet. Until then, comets were commonly thought to foretell the death of kings.

Principia ignited the intellectual movement known as the Enlightenment. Society would no longer look to the Golden Age of Greece for wisdom. Alexander Pope captured the mood when he wrote, “Nature and Nature’s laws lay hid in night. / God said, Let Newton be! And all was light.”

When he needed better mathematics, Newton invented Calculus. His studies of light transformed the field of optics. He held a chair in Parliament then returned to Cambridge. He became Director of the Mint and took the position seriously. In his later years, Sir Isaac — the first scientist ever knighted — was perhaps the most respected person in the Western world. Paradoxically, Newton was also a mystic, immersing himself in supernatural alchemy and interpretations of Biblical prophecies.

Although there were some scary moments when mathematicians realized some subtleties in The Calculus such as “continuity requirements for Integration,” but all worked out in the end as an army of somewhat lesser minds filled in the missing spaces in Newton’s mathematical creation.

Newton did have a rival in the invention of Calculus. Recall that Newton didn’t publish his work for twenty years, and, during that time, a European named Gottfied Leibniz independently invented The Calculus. Unfortunately, that ultimately led to a feud between the two men and separated the scientific communities of England and the Continent for many years as each championed their “home boy.”

Sadly, Leibniz had created a better notation for Calculus that was more flexible and easier to use than the dot notation Newton favored. Since the English scientists adopted the “dot” in defense of Newton, it set English science back for nearly one hunderd years and advancements in Calculus exploded on the Continent.

The advance of science is not only dependent on brilliant ideas, but how well those ideas can be taught and spread to the public, and good notation always helps.

A similar occurrence will be discussed later when I describe the beginnings of Quantum Mechanics and how the original work in an awkward and little known mathematical method called “Matrices” was overshadowed by later work that used a simpler formulation and math. Science and the advance of science is often tied to its acceptance and understanding by scientists and the general public alike. Calling the Higg’s Boson “The God Particle” is part of the modern hype that I hope to reduce. But we’ve got to climb a few more foothills before we get to the top of that mountain.

My next chapter will expand on Newton’s legacy and the beginning of what is now called “Classical Physics” in deference to “Relativistic” and “Quantum Physics,” the twentieth century inventions. But first we need to cover the preceding three centuries as Kepler's, Galileo's, and Newton’s Genesis is brought to fruition.

The History of Science -- Part Five

History of Science -- Part Three: Galileo Galilei

In 1591, at only twenty-seven years of age, Galileo Galilei became a professor at the University in Padua, but he soon left for a post at Florence. Today’s university faculty would understand why: He was offered more time for research and less teaching. (Not me, I prefer teaching!) His talent included music and art as well as science. Brilliant, witty, and charming, Galileo could also be arrogant, brash, and petty. We could envy his skill with words. He liked women, and they liked him. He was, what we call now, a renaissance man.

Galileo was a convinced Copernican. That is, he was certain the Earth revolved around the Sun and not vice-versa. The simpler system made sense to him. But unlike Copernicus, Galileo did not merely claim a new technique for calculation; he argued for a new worldview. A humble approach was not his style.

The Church had to stop Galileo’s call for independent thought — the business of the Church was saving souls, not scientific validity. Found guilty by the Holy Inquisition and given a tour of the torture chambers, Galileo recanted his heresy of a sun-orbiting Earth. For his last years, Galileo lived under house arrest — a lesser penalty than that of Copernican Giordano Bruno, who was burned at the stake.

Recantation not withstanding, Galileo knew that the Earth moved and that Aristotle’s explanation of motion could not survive on a moving Earth. Friction, not desire for rest in the cosmic center, caused a sliding block to stop, and air resistance, not less desire, caused a feather to fall more slowly than a stone.

Contradicting Aristotle’s claims, Galileo asserted, “In the absence of friction or other impressed force, an object will continue to move horizontally at a constant rate.” And, “In the absence of air resistance, heavy objects and light objects will fall at the same rate.”

Galileo’s ideas were obvious — to him. How could he convince others? Rejecting Aristotle’s teaching for the motion of matter was not a minor issue. Aristotle’s philosophy was an all-encompassing worldview. Reject a part, and you appear to reject it all.

To compel agreement with his ideas, Galileo needed examples that conflicted with Aristotle’s mechanics — but that conformed to his own ideas. But looking around, he could see few examples, so he decided to create them!

Galileo would contrive special situations: “experiments.” An experiment tests a theoretical prediction. This may seem an obvious approach to us here in the twenty-first century, but in that day it was an original and profound idea.

In his most famous experiment, Galileo supposedly dropped a ball of lead and a ball of wood from the leaning Tower of Pisa. The simultaneous click of the wood and the thud of the lead proved the light wood fell as fast as the heavy lead. Such demonstrations gave reason enough, Galileo argued, to abandon Aristotle’s theory and to accept his own.

Galileo used inclined planes to “reduce” the acceleration of gravity, and measured the acceleration of objects rolling down the planes measuring time with his own pulse. He also developed early telescopes and made many discoveries including the phases of Venus (further proof of an heliocentric solar system) and discovered the moons of Jupiter as well as sunspots. Through experiments and observations, Galileo was rapidly filling in new science and discarding incorrect theories.

Some faulted Galileo’s experimental method. Though the displayed facts could not be denied, Galileo’s demonstrations were contrived situations, therefore insignificant because they conflicted with matter’s intuitively obvious nature. Moreover, Galileo’s ideas had to be wrong because they conflicted with Aristotelian philosophy. Galileo had a far-reaching answer. Science should deal only with those matters that can be demonstrated. Intuition and authority have no standing in science. The only criterion for judgment in science is experimental demonstration.

Within a few decades, Galileo’s approach was accepted with a vengeance. Science progressed with vigor never seen before. The experimental method had been discovered. The scientific age had dawned.

Now we’re really getting to the “crux of the biscuit.” I know most of my friends are not scientists and mathematicians. That’s OK. I’m writing this series specifically for those people. You may not be a scientist or a technologist, but I’m certain you are aware that we now live in a highly scientific and technological world. It can be very confusing and difficult to understand. I hope this will help you understand.

Science is not politics, it is not philosophy, and it is not religion. Nor is it opposed to any of those concepts. This idea of experimental confirmation is how you “do science.” Let me explain.

Let’s agree on some rules of evidence for accepting a theory as reliable science. They will stand us in good stead when we consider quantum theory and will serve as a test for any ideas that theory might inspire.

But first, a remark on the word “theory.” We speak of quantum theory but Newton’s laws. Why? “Theory” is the modern word. I can’t think of a single twentieth- or twenty-first-century “law” in physics. Plus, Newton’s “laws” have been proven incorrect, replaced — or more specifically, “corrected” by Einstein’s theories and the experiments that demonstrate Einstein’s superiority in cases of high velocity or high gravity. Although “theory” is, at times, used in science for a speculative idea, it does not necessarily imply uncertainty. Einstein's relativity theory is, as far as is known, completely correct. Newton’s laws are an approximation.

For a theory to compel consensus, it must, first of all, make predictions that are testable with results that can be displayed objectively. It must stand with a chip on its shoulder challenging would-be refuters.

“If you truly believe, then you will go to heaven.” That prediction may well be correct, but it is not objectively testable. Religions, political stances, or philosophies in general are not scientific theories. Aristotle’s testable theory of falling — that a two-pound stone will fall twice as fast as a one-pound stone — is a scientific theory, albeit an incorrect one.

A theory making testable predictions is a candidate for being reliable science. Its predictions must be tested by experiments that challenge the theory by attempting to refute it. And the experiments must be convincing, even to skeptics. For example, theories suggesting the existence of extra-sensory perception (ESP) makes predictions, but, so far, tests have not been convincing to skeptics.

To qualify as reliable science, a theory must have many of its predictions confirmed without a single disconfirmation. A single incorrect prediction forces a theory’s modification or abandonment. This scientific method is hard on theories — one strike and you’re out. Actually, no scientific theory is ever totally reliable — it is always possible that it will fail some future test. A scientific theory is, at best, tentatively reliable.

The scientific method, setting high standards for experimental verification, is hard on theories. But it can also be hard on us. If a theory meets these high standards, we are obligated to accept it as reliable science — no matter how violently it conflicts with our intuitions. And that is the rub where quantum mechanics is involved. QM definitely violates our intuitions. Yet the experimental evidence is solid. And that is how we do science.

But, before we can get to these modern theories of how tiny particles that make up atoms and the like work, we need to introduce the giant of Classical Physics, the science that came before Quantum Physics and Relativity.

The History of Science -- Part Four

History of Science -- Part Two: Medieval and Renaissance Astronomy

From ancient times, the position of the stars in the sky foretold the change of the seasons. What, then, was the significance of the five bright objects that wandered through the starry background of the fixed stars? An obvious conclusion was that the motion of these planets (“planet” means “wanderer") foretold erratic human affairs and warranted serious attention. Astronomy’s roots are in astrology.

In the second century A.D., Ptolemy of Alexandria described the heavenly motions so well that calendars and navigation based on his model worked beautifully. The astrologer’s predictions — at least regarding the positions of the planets — were likewise accurate.

Although the stars moved in a steady progression across the sky on a yearly cycle, the planets not only moved differently (from the stars and even from each other). What was most odd is that some planets would actually change the direction of their motion against the fixed stars and go backward for a short time before reversing again. This was called “retrograde” motion.

Ptolemy’s explanation was based on a stationary Earth as the cosmic center, requiring planets to move on “epicycles,” complicated loopy curves made up of circles rolling on circles within yet further circles. Thus was preserved Aristotle’s “perfect circles” in the perfect heavens.

King Alfonso X of Castile, having the Ptolemaic system explained to him, supposedly remarked “If the Lord God Almighty had consulted me before embarking on Creation, I would have recommended something simpler.” Nevertheless, the combination of Aristotle’s physics and cosmology with Ptolemy’s astronomy was accepted as both practical truth and religious doctrine, and enforced by the Holy Inquisition.

In the sixteenth century, an insight upsetting the whole apple cart appeared within the Church itself. The Polish cleric and astronomer Nicolas Copernicus felt Nature had to be simpler than Ptolemy’s cosmology. He suggested that the Earth and five known planets orbited a central, stationary sun. The retrograde motion of planets such as Mars against the starry background was the result of observing the orbit from the third planet from the Sun, also in motion. The outer planets would seem to move backward when the Earth was overtaking them in its own orbit. (Inner orbits move faster than outer orbits. That is to come too.) The Earth was just the third planet from the Sun. It was a simpler picture.

However, simplicity was hardly a compelling argument. The Earth obviously stood still. One felt no motion. A dropped stone would be left behind on a moving Earth! If the Earth moved, since air occupied all space, a great wind would blow!! Moreover, a moving Earth conflicted with the wisdom of the Golden Age and the authority of Aristotle. Such arguments were hard to refute. And, most disturbingly, the Copernican system was seen to contradict the Bible, and doubting the Bible threatened salvation.

Copernicus’ work, published shortly after his death, included a foreword, probably added by a colleague, announcing his description as a mathematical convenience only — it did not describe actual motions. Any contradiction of the Church’s teachings was disavowed.

Enter Tycho Brahe … the man with a metal nose. (Don’t ask.) He was a Danish nobleman who refuted the Aristotelian belief in an unchanging celestial realm. His reputation started when he discovered a new star in the sky, a nova in the constellation Cassiopeia. Prior to his time, comets were considered atmospheric phenomenon. After all, the heavenly realm was perfect and unchanging. Through Brahe’s careful observations and calculations, he proved that comets existed beyond the orbit of the moon … amongst the celestial spheres. So much for the unchanging heavens.

Tycho Brahe was granted an estate on the island of Hven and the funding to build an early research institute by the King of Denmark. He built large astronomical instruments and took many careful measurements. On the island he founded small factories such as paper-making to provide material for printing his results. After disagreements with the new Danish king Christian IV in 1597, he was invited to Prague, where he became the official imperial astronomer. He built the new observatory at Benátky nad Jizerous. Here, from 1600 until his death in 1601, he was assisted by Johannes Kepler.

Brahe died under unusual circumstances in 1601. Not suspicious, just unusual. He suddenly contracted a bladder or kidney ailment after attending a banquet in Prague, and died eleven days later. According to Kepler's first hand account, Brahe had refused to leave the banquet to relieve himself because it would have been a breach of etiquette since the royalty in attendance had not left the party. After he had returned home he was no longer able to urinate, except eventually in very small quantities and with excruciating pain.

Upon his death, Kepler “inherited” the results of over twenty years of precise planetary measurements. With that windfall of data, Kepler began working on a system of planetary movements and orbits.

Although he believed in the Copernican system with the Sun at the center of the solar system, he adopted many of Aristotle’s views. He tried to fit the measurements and data to circular orbits and attempted to model the space between the orbits using the five Platonic Solids (for example, tetrahedron, cube, octahedron, etc.). He even invented new planets to try to get the scheme to work.

For many years he struggled trying to find a model that matched the data. Sadly, the solution actually was a common shape, one of the conical sections. Although the orbits were nearly circular, they were actually an oblong shape called an ellipse or elliptical.

Kepler eventually developed his first two laws: (1) The obit of every planet is an ellipse with the Sun at one of the two foci; and (2) A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

These laws stated that, not only weren’t the orbits perfect circles, but the planets actually sped up when approaching closer to the sun and slowed down on the distant part of their orbit.

Several years later he added his third law: (3)The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. These models not only worked for the known planets, but, years later, when additional planets were discovered, they also followed these laws.

Kepler's laws were not immediately accepted. Several major figures such as Galileo and René Descartes completely ignored Kepler's results. Many astronomers, including Kepler's teacher, Michael Maestlin, objected to Kepler's introduction of physics into his astronomy. Some adopted compromise positions. Ismael Boulliau accepted elliptical orbits but replaced Kepler's area law with uniform motion in respect to the empty focus of the ellipse while Seth Ward, English Astronomer and Mathematician, used an elliptical orbit with motions defined by an “equant,” an element of Ptolemy’s theory.

Kepler did great astronomy and was an excellent mathematician, but science didn’t guide his worldview. Initially, he considered the planets to be pushed along their orbits by angels, and as a sideline he drew horoscopes, in which he likely believed. He also had to take time from his astronomy to defend his mother from accusations of witchcraft.

However, his three laws were good scientific progress based on careful observation and cunning calculations and insight. However, Kepler did not explain any reason for why these relatively simple relationships existed. But they did provide a much simpler and very precise method to analyze planetary motions. An explanation for why Nature worked this way would have to wait for eight decades and Sir Isaac Newton to provide, but Kepler did live to see discoveries using the new instrument of the telescope and the discovery of moons on several of these planets and observation of the phases of Venus, definitely proving the solar-centric theory.

The History of Science -- Part Three

History of Science -- Part One: Greek Science

We owe the philosophies of ancient Greece credit for setting the scene for science by seeing Nature as explainable. Prior to that, explanations of the natural world were all wrapped in gods and magic. When Aristotle’s writings were rediscovered, they were seen as the wisdom of a “Golden Age.” From the ancient Greek, via Arabic, and translated into Latin in the Middle Ages, beginning in the 12^th and 13^th centuries.

Aristotle noted that everything that happens, even the sprouting of acorns into oak trees, for example, is essentially the motion of matter. He therefore started by treating the motion of simple objects using a few fundamental principles. This is the way we do physics today, even though Aristotle got several ideas that were wrong. But Aristotle’s method of deriving fundamental principles was the correct method. Unfortunately, the Greeks did not favor experiment, and they assumed these fundamental physical properties could be intuitively perceived as self-evident truths.

Here are a couple of his errors. A material object sought rest with respect to the cosmic center, which “clearly” was Earth. An object fell because of its desire for the cosmic center. A heavy object, with its greater desire, would therefore, without doubt, fall faster than a light object. In the perfect heavens, on the other hand, heavenly objects moved in that most perfect of figures, the circle. These circles were on the “heavenly spheres” centered on the cosmic center, Earth.

Greek science had a fatal flaw. It had no mechanism to compel consensus. The Greeks saw tests of scientific conclusions no more necessary than were tests of politics or aesthetics. Conflicting views could be argued indefinitely.

Just through pure thought and philosophy, however, on occasion the Greeks came up with good science. The theory of atoms, and the name “atom” originated from a Greek Philosopher named Democritus who lived around 400 BC. He proposed that all life and matter is made up of tiny particles which he called atoms. The word “atom” comes from the Greek word “atomos” meaning indivisible.

Further, the pure thought and rules of logic did lead to the development of mathematics. But what separates mathematics from all the other sciences is experiment. The basis of modern science is on the results of experiments. Experiments that demonstrate the validity of theories and experiments suggested by theories and used to “prove” the theories correct.

To quote the Nobel Prize winning physicist, Richard Feynman, “It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” All science from physics to chemistry to biology is based on experimentation. Mathematics is unique in that regard because it is entirely based on axiomatic reasoning and proofs.

We do owe the Greek thinkers a great deal of gratitude for putting mathematics on an axiomatic basis. On occasion, their guesses and philosophies about physical science were correct or at least close. But they could be way off and mislead the advancement of science for hundreds of years of appeal to authority.

In general, the Greeks not only didn’t use experiments, they considered them below their station in life. Experiments were a form of manual labor and that was reserved for the common workman, while the scientists of the Greek age simply argued for the truth. There were some exceptions.

A very notable exception is Eratosthenes, a Greek who lived around 200 years before Christ. He was the first person to use the word "geography" in Greek and he invented the discipline of geography as we understand it. He invented a system of latitude and longitude and was the first person to calculate the circumference of the earth by using a measuring system using “stades,” or the length of stadiums during that time period with remarkable accuracy.

He was the first to calculate the tilt of the Earth’s axis (also with remarkable accuracy). He may also have accurately calculated the distance from the Earth to the Sun and invented the leap day. He also created the first map of the world incorporating parallels and meridians within his cartographic depictions based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology. He endeavored to fix the dates of the chief literary and political events from the conquest of Troy. He also proposed an algorithm for determining prime numbers that is still used today in computer programs that determine if a given number is prime.

His accomplishments and use of experiments, data, and mathematics would yield a Nobel Prize in today’s modern scientific culture and I’m always surprised how unknown he is compared with the other great Greek thinkers.

The thinkers of the Golden Age launched the scientific endeavor, but, without a method to establish agreement, progress was impossible. Though Aristotle established no consensus in his own day, in the late Middle Ages his views became the official dogma of the Church, mostly through the efforts of Thomas Aquinas.

Aquinas fitted Aristotle’s cosmology and physics together with the Church’s moral and spiritual doctrine to create a compelling synthesis. Earth, where things fell, was also the realm of morally “fallen” man. The heavens, where things moved in perfect circles, were the realm of God and His angles. At the lowest point in the universe, the center of the Earth, was Hell. When, at the beginning of the Renaissance, Dante used this cosmological scheme in his Divine Comedy, it became a view that profoundly influenced Western thought.

Yet the Greeks founded modern mathematics, discovered both magnetism and electricity, and set the world to ponder on the source and motive power of the celestial orbs.

Aristotle attributed the first of what could be called a scientific discussion on magnetism to Thales of Miletus. The term “magnet” comes from the name “Magnesia-on-the-Maeander,” an ancient Greek city where mysterious stones were found. They could attract or repel each other. We now know this mineral as Magnetite (Fe₃O₄).

And the term “Electricity” comes from the Latin word “electrum” and from the Greek “elektron.” Both words for the mineral "amber." If you rub amber with a wooly cloth, it will then attract small bits of paper with what is sometimes called “static electricity.”

So the ancient Greeks were right at the heart of the mysteries of physics, if not arriving at the correct solution. They studied gravity, magnetism, electric force, and the heavenly orb, as well as putting mathematics on a strong foundation and making advances in many other areas of science from medicine to botany and zoology. In fact, that search for the correct solution, the explanation of all in the physical realm, continues to this day and new discoveries are as fresh as today’s newspaper.

The History of Science -- Part Two

It's Just a Joke

Here’s a little story I heard a while ago. There was this married guy that didn’t get along well with his wife and wanted to get rid of her. He couldn’t divorce her because it was a community property state and he didn’t want to give her anything.

He didn’t know what to do, but one day he was explaining his problem to a guy he knew at the gym who was in the Mafia. The Mafia guy asked if he had thought about murdering his wife. The guy explains he wouldn’t have the guts to do that. So the Mafia guy says to just hire a killer. The married guy says he wouldn’t know how to do that, and the Mafia guy says he’ll send around his personal hit man and do it as a favor.

So, pretty soon the married guy meets up with the Mafia hit man named Arthur, but he prefers just “Artie.” He says he would be glad to rub out the guy’s wife and would do if for free as a favor. The married guy says that wouldn’t be fair because Artie is a professional and he should be paid for his work. So the hit man says, “If that’s so important to you, then just pay me a dollar.”

So the hit is arranged. Artie explains that he will follow the wife until she’s at the grocery store. He says that is the perfect place because he can find a deserted aisle and there will be no witnesses. He explained that he just strangles the victim because then there is no noise or blood or any murder weapon to tie him to the crime. With no witnesses, it is a perfect crime.

So the hit man follows the wife to the grocery store and waits until she is in a deserted aisle and grabs her and strangles her. Just as he’s finishing, a clerk comes out of the back room and sees him. Since he can’t have any witnesses, he strangles the clerk too. But, by then, a shopper comes into the aisle with her cart. So, the hit man has no choice but to strangle her too. But, by then, he’s spent too much time in the store and the cops arrive and he’s arrested.

The next day the newspaper headline reads, “Artie chokes three for a dollar at Safeway.”