What's Classical Physics All About?

By Donald E. Simanek

Around 1900, give or take a decade, surprising new experimental evidence, primarily about atoms and molecules, showed us that these small-scale phenomena behave in ways not anticipated by classical theory. This ushered in a new era called "modern" physics. New laws and methodology were developed to deal with the rapidly expanding experimental evidence. Relativity and quantum mechanics added new tools to the study of nature. These did not make classical physics "wrong", for the old laws were working just as they always had, within their limited scope—which was the study of large objects (not atomic scale ones) moving relatively slowly (not near the speed of light).

So classical physics is still the starting point for learning about physics, and constitutes the bulk of the material in most introductory textbooks. It is the theory underlying the natural processes we observe everyday. It is the key to understanding the motion of pulleys, machines, projectiles and planets. It helps us understand geology, chemistry, astronomy, weather, tides and other natural phenomena.

Let's look at the key ideas of classical physics as they developed historically.

• Motion. The ancient greek philosophers thought a lot about motion. What makes things move? Why doesn't a thrown projectile move forever? What causes it to stop? Why does a stone fall when we drop it? The theories they invented to account for these things are now forgotten except to historians of science. But they were asking the right questions.

• The Heavens. All early civilizations paid attention to the motion of stars, sun, moon and planets in the sky. The regularity and predictability of these motions was recognized very early. Most thought these motions were special, having causes quite distinct from the causes of earthly motions of projectiles. Aristotle accepted this difference as a fundamental principle.

• The Physics of Aristotle. Aristotle's physics (a synthesis of ideas from many Greek philosophers) accepted the fixity (immobility) of the Earth. The Earth was assumed to be the center of the universe. The Greek theory of matter postulated that everything on Earth was made up of just four elements: earth, water, air and fire, and these had settled from an initial chaotic condition to a relativly stable situation with earth being at the lowest level (being heaviest), water above the earth, air above that, and finally there was a shell of invisible fire above everything. This hierarchy represented the four elements in their "natural place". The evidence for fire being above everything was the fact that fire leapt upward, and like all the elements, was seeking its "natural place" in the scheme of things. So unsupported things made of earthen materials fell down toward the earth. Water flowed down mountain streams to the oceans, and hot air balloons moved upward into the air.

  Motion of things toward their natural place was called "natural" motion. Any motions that displaced things from their natural place was called "violent" motion. Natural motion happened for no other reason than the body's "desire" to get to its natural place. Violent motions were caused by forces. Natural and violent motions were mutually exclusive and could not occcur simultaneously. When a projectile was thrown (by action of a force) it moved in a straight line for a while (violent motion), until it used up the motion it had been given. Then it immediately moved in a straight line downward (natural motion), toward Earth. All motions on Earth were made up of a succession of straight line motions.

• The Ptolemaic Universe. Claudius Ptolemy (about 85 - about 165 CE), astronomer, synthesized earlier ideas about planetary motion into a geocentric (Earth-centered) model in which the sun and all the planets moved in circles around the Earth. Why circles? Because the Pythagorean numerology had declared circles the most perfect geometric figure, and Aristotelian physics declared everything outside of the earh to be in some sense "perfect". So all celestial motions were considered to be circles, or a superposition of circles. But naked-eye astronomers had accumulated rather good data on planetary positions over time, so Ptolemy's system had to be a complicated combination of circles (cycles and epicycles) to account for the data well. It did work, but it did only one job, predicting planet's positions in the sky, and it had some problems dealing with Mercury and Venus.

• Scholasticism. The Catholic Church dominated education in Europe. It tried to unite science and religion into a unified system of thought. St. Thomas Aquinus was one of the most visible in this effort, and the result was a system consisting of Aristotelian physics and Christian theology, called "Scholasticism." It accepted the Greek four element theory, the immobility of the Earth, Aristotle's physics and the Ptolemaic system. All of this was considered church dogma, to be accepted without question. This was the "science" taught in the schools when Galileo was at the University.

• The Copernican Revolution. Nicolas Copernicus (or Koppernigk; Polish: Kopernik) (1473 – 1543) is credited with the demise of the Ptolemaic planetary system. Copernicus' heliocentric (Sun-centered) model assumed that the Sun (not the Earth) was the center of the solar system, with all the planets moving in circles about the Sun, and Earth's moon moving in a circle around Earth. This model kept the idea of epicycles (it had to to account for observations), but fewer of them. Exactly six fewer—those planetary epicycles that had identical periods of 365+ days. (That's a clue to what's going on.) The Catholic Church denounced the idea, and banned Copernicus' book de Revolutionibus (1543), but Copernicus had died before the controversy erupted. Martin Luther also denounced the idea. Galileo publicly championed Copernicus' heliocentric model, so he took heat for it.

• The Experimental Revolution. Though the ideas of the Greeks, as expressed by Aristotle (384 BCE–322 BCE), persisted until the time of Galileo, there were many who seriously questioned much of it, and even did experiments to show that Aristotle was wrong. John Philoponus (490–570) (John the Grammarian) experimentally disproved Aristotle's assertion that heavy bodies fall faster than lighter ones. This experiment (dropping heavy and light balls from a height) was repeated by others, including Simon Stevin (1548/49–1620). Their work constituted a gradual revolution in how physics was done, one that showed the importance of deliberate experiments designed to study natural processes. Previous physics had mostly relied on passive observation of phenomena. One exception was the work of the Greek mechanicians, such as Archimedes, Ctestibius and Hero(n).

• Galileo Galilei (1564–1642) challenged Aristotelian physics with vigor, and suffered the consequences of arguing against the Catholic Church's Aristotelian teachings about physics. He showed that freely falling bodies accelerate (increase their speed). He made use of his "principle of superposition" to analyze motion of projectiles. He also effectively used this method of argument to explain why objects of different mass fall in the same way. His telescopic discoveries in astronomy are well known: four moons of Jupiter, sunspots, craters of the moon, and much more. Galileo is sometimes called the "father of experimental physics", but as we noted above, the experimental spirit arose earlier. Still, Galileo deserves credit for his total commitment to the experimental methods that paved the way for others.

• Johannes Kepler (1571–1630) spent many years trying to understand the reasons for the motions of planets, especially the orbit of Mars. Along the way he tried, and abandoned many hypotheses (proposed models) of the planetary system. His early guesses were in the "magical" or "mystical" tradition of astrology and numerology, but he was objective enough to realize that those approaches were not useful. His final, correct, solution was purely mathematical, his three laws of planetary motion. One major value of this model is that it introduced elliptical orbits for planets, doing away with all of the epicyles and other gimmicks of Ptolemy's and Copernicus' models.

• The Newtonian Revolution. Isaac Newton (1643 [1642 O.S.]–1727) knew the work of these pioneers of experimental science, and he sought to develop a larger and more comprehensive synthesis of their work, one that would unify the motions of things near Earth (falling bodies, projectiles) with the motions of planets in the heavens. He achieved this only after he invented mathematical tools to deal with the problem, tools that we now know as calculus. Gottfried Wilhelm von Leibniz (1646–1716) invented another form of calculus at about the same time, one that was later found to be mathematically equivalent to Newton's version. Today calculus notation combines contributions of both men. Newton's solution to the problem of motion was his three laws of motion, combined with his universal gravitation theory. These introduced a refined definition of force, giving precise meaning to force and relating it, through his famous equation F = ma, to mass and acceleration. Newton's synthesis of these ideas is considered the first important theory in physics, and Newton may be justifiably called the first theoretical physicist. However you charactize his work, it set the standard and goal for physics to this day.

• Newton's style. Newton's theory changed the way scientists thought of nature. It introduced a view of force that many found hard to swallow. The idea that the force due to gravity could act between material bodies even at a distance, without them touching each other and without anything between them—well, that seemed an "occult" idea to some. Newton was pressured to explain "why" gravity worked that way. Newton declined to do that saying "I make no hypotheses." He was using the word hypothesis to mean "conjecture" or "explanation". He was content to simply describe how his theory worked, not why. Even though he was a deeply religious man, and even did alchemy and numerology, he wisely never mentions (nor uses) religious, magical or mystical ideas in his writings about physics. This is a style most scientists still follow in their work.

• The Mechanical Universe. Newton's mechanics presented a view of nature that was dominated by objects moving under the influence of forces. This view was soon applied to all sorts of phenomena, from the collision of billiard balls to the motions of mechanical parts in machines. It viewed everything as having underlying mechanical interactions. Once you knew the positions of bodies and the forces acting on them you could (using mathematics) predict what they would do as time goes on. Newton's mechanics pictured the universe as a huge clockwork, all of its component parts obeying Newton's laws. Those of religious inclination supposed that this meant that God devised those laws, created matter and then let the laws take over. The clockwork of the universe could then run forever without further attention, strictly following Newton's laws. What room did this leave for miracles? What use was prayer? In this universe, do we really have free will? It was a deterministic view of the universe. Those philosophical questions are still debated today, but physics goes on without troubling itself about philosophical questions, which are considered outside of its domain.

• Conservation Laws. In this short space I can't do justice to the "discovery" of the conservation laws of energy, momentum and angular momentum. These arose from the question of how best to characterize motion of a body. Should it be a quantity dependent on velocity (mv, called momentum) or should it be dependent on the square of the velocity (mv², called "vis viva")? It turned out that both were necessary for a complete description of motion, and the vis viva morphed into kinetic energy, mv²/2. Finally we learned that in closed systems, total energy within the system remains constant (is conserved). Earlier we had learned that in such systems momentum is conserved, and so is angular momentum. In fact Kepler's third law anticipated the conservation of momentum, and one of Galileo's laws of motion anaticipated the conservation of energy. Nowadays we know that all conservation laws arise from the geometry of the universe, from symmetries of a physical system's geometric properties under certain kinds of transformation, translation in space, time, or rotation. It now appears that the conservation laws are the most fundamental and powerful laws of the universe, from which many other major laws may be derived. They have withstood all of the advances and revolutions of physics described below.

• Successes of Newton's Mechanics. One thing we expect of a good theory is that it suggests directions for further investigation, and that it is applicable to new information that comes along. One major success of Newton's mechanics was the kinetic theory of gases. By modeling gases as very tiny, perfectly elastic particles zipping around at high speeds, and colliding with the walls of their container, the empirical gas laws were found to be derivable from Newton's laws. For example, from Newton's laws you can derive the famous "ideal-gas law" PV = nRT, relating pressure, volume, amount of gas, the gas constant and gas temperature. By relaxing the "idealized" conditions to allow larger particles, and occasional collision of particles with each other one could even do better at modeling real gases and deriving their laws, in agreement with experiment.

• New Insights Another thing we expect of a good theory is that it clarify other things that were previously puzzling. For example, what are the fundamental mechanisms of heat and temperature? Kinetic theory showed us that temperature is the average kinetic energy of the particles in a gas, and internal thermal energy in a gas is just the total energy of its particles.

• James Clerk Maxwell (1831–1879) is responsible for the second highly successful theory in physics: his four laws of electrodynamics. These built upon the experimental work of such pioneers as Michael Faraday (1791–1867) and William Thomson, (1st Baron Kelvin) (1824–1907). Maxwell's four laws unified and correctly described the diverse (and sometimes puzzling) results obtained by experimenters who studied electric circuits, magnets, motors, generators and a whole host of electromechanical phenomena. But even more remarkable, a little mathematical work with these equations allows one to derive unanticipated predictions. (This does require calculus.) For example with a few steps of math one can show that electromagnetic waves can occur, and they propagate with the speed of light. Hertz and others demonstrated this in the laboratory, producing what were called "radio" waves, and others soon used these waves to send information over great distances. The vacuum speed of light that appears in the equations was no accident, for light itself was found to be an electromagnetic wave, obeying Maxwell's equations.

• The Atomic Revolution. Experimental physicists, around the period 1890 to 1910 were making many astounding discoveries. X-rays were discovered. Michelson measured the speed of light and to everyone's surprise, it was found to be constant and did not seem to depend on the motion of the light source or the observer. The charge and mass of the electron were measured. And Ernest Rutherford (1st Baron Rutherford of Nelson) (1871–1937) was bouncing protons from atoms in order to find out what was going on inside atoms. Previous physics was found not to be helpful in understanding some of these things. New hypotheses were proposed, and a new theory of atoms was devloped.

• The Bohr Theory of the Atom. Some thought that atoms were like a "pudding" of small charges in a larger mass of the opposite charge: the "plum pudding" model. Rutherford's scattering experiments showed that that was not so. The positive charge in an atom was confined to a very tiny volume at the center of a much larger cloud of negative charge. Bohr proposed that the atom might be a "miniature solar system", with the electrons orbiting a positive nucleus like planets orbit around the sun.

• Successes of the Bohr Theory. This Bohr model could be analyzed with Newtonian mechanics, combined with what we knew about the forces of attraction of charges. Experimentalists had already shown that atoms could absorb and emit very particular frequencies of light, the frequencies being unique to the particular kind of atom. These frequencies constituted the "spectrum" of light from atoms, and spectroscopy (thanks to physicists' understanding of classical optics) could measure frequencies precisely to 10 decimal places. Any model of the atom must account for these very precise results, so it was a challenging problem.

• Problems with the Bohr Theory. One problem of the Bohr theory was obvious to all. The electrons orbiting the nucleus were in constant acceleration, and Maxewll's theory clearly said that whenever a charge acclerates it must emit some of its energy as an electromagnetic wave. Therefore the electron would be constantly losing kinetic energy, and would spiral into the nucleus and crash into it. But experiment showed that the electrons don't do that. They radiate only when they change orbital radius, and while in a circular orbit they don't radiate at all. Yet if this inconvenient fact was ignored, the Bohr model was very successful in predicting atomic spectral frequencies with accuracies up to 10 decimal places. So Bohr added an "ad hoc" postulate declaring that the electron in a circular orbit does not radiate, and the question of why that is so could be swept under the rug until later.

• More Success With the Bohr Theory, and More Problems. Initially the Bohr model had circular orbits. But as experimentalists accumulated more data it was found necessary to allow elliptical orbits, but only with specific eccentricities. This helped a lot, and was "successful". But one of the orbits, the one for zero angular momentum states, was a very narrow ellipse that actually would extend to the very center of the atom, within the nucleus, passing throuugh the nucleus like a ghost through a brick wall. How could that be?

• The Quantum Revolution. On other fronts, new theoretical physics was being developed, resulting in what we now call quantum mechanics. This gave a completely new model of small scale phenomena, one that included the Heisenberg uncertainty principle [Werner Heisenberg (1901–1976)]. That principle told us that certain pairs of measurable quantites, such as position and momentum, and energy and time, called "conjugate" quantities, could not be simultaneously measured with perfect precision. For example, if you know a particle's position very precisely, the simultaneous measurement of momentum would be very poor. But if you measured the momentum of a particle precisely, you'd have only a vague measure of its position. You wouldn't know where it was when the measurement was made. This was not merely a problem of experimental method or inadequate measuring instruments. It was a fact of nature about which we could do nothing to improve.

• The Demise of the Bohr Atom Once quantum mechanics was shown by experiment to be correct and useful, physicists realized that to think of electrons as moving in orbits within an atom was impossible to experimentally verify. We knew the momentum of the electrons in each "orbit" very well, so we had no idea of the position (or path) of the electrons. Our "picture" of the atom was now a small positive nucleus surrounded by a "cloud" of negative charges, and while the charges could have definite energy and momentum states, that's about all we could know about them.

• The Ether Problem. Newton had said that time and space were absolute, a framework underlying all of physics, unchanging and unchanageable by anything we do in carrying out experiments. This idea seemed reasonable, and went unchallenged until the early 20th century. In the late 19th century physicists thought that all of space was filled with a tenuous substance called the "luminiferous ether". Many attempts were made to measure the motion and properties of the ether. All were failures. Albert Abraham Michelson's (1852–1931) measurements of the speed of light were really attempts to see the effects of motion of the ether, or our motion relative to the ether. He was disappointed because all his very careful experiments showed no evidence of the ether. Oliver Joseph Lodge (1851–1940) did some experiments with the same purpose, and sadly concluded that his experiments were not good enough, saying "The experiments may have to be explained away."

• The Relativity Revolution. A number of physicists were troubled by the fact that Maxwell's laws and Newton's laws treated relative motion differently. Albert Einstein (1879–1955) tried to reconcile these two great theoretical pillars of physics, and he succeeded with his special theory of relativity, and later a more general theory of relativity. These new theories concluded that there is an upper limit to velocities in the universe and that limit is the speed of light. It also showed that measurements of time and space are not absolute, but depend upon observer's motion relative to each other—on the relative velocity of their frames of reference. There is no absolute frame of reference. But, most importantly, this whole theory of relativity had no mention of the luminiferous ether! Relativity theory was found to work remarkably well when put to experimental tests. Gradually the luminiferous ether was forgotten, and it was admitted that there never had been any conclusive evidence for it.

History is seldom neatly linear. Running parallel to the timeline sketched above were other "traditions" of thought about the nature of the universe. There were mystical, magical and religious traditions in early history of science, up to about the time of Newton. Several of Kepler's early ideas about the planetary system were in these traditions. One question he wanted to answer was "What keeps the planets in motion around the sun?" Remember, gravity hadn't been invented then. One of his first ideas was in the religious tradition: the popular notion that each planet had a dedicated angel to continulally push it around and around. He also tried Pythagorean mysticism, assuming that the solar system had an invisible framework of spheres nested within the five Pythagorean regular polyhedra, and the planets moved around those spheres. But he realized that the numbers didn't match those from experiment, and abandoned the idea. Then, from reading Gilbert's 1600 book de Magnete he assumed that the sun was a great magnet, and so were the planets, and the "magnetic influence" of the sun kept the planets moving. Clearly he hadn't understood Gilbert's book. It was only when Kepler abandoned such notions that he found a purely mathematical solution to the problem, unencumbered with mystical, magical or religious ideas.

There were also many interesting byways and dead ends in the history of science. We mentioned only one—the luminiferous ether. We could have mentioned numerology, astrology, alchemy, homeopathy, mesmerism, the search for perpetual motion and many other examples of scientific mistakes. Some historical ieas, such as the geocentric models of the solar system, are not clear-cut mistakes, for they were of some limited use, but were replaced by better models as the old models became cumbersome in accounting for new evidence. They are all instructive, and some can be found discussed elsewhere on my web pages. It has been said that the essence of science is defined by its mistakes, and how well scientists learn from them. The procedures we call "scientific method" are no more than the strategies we have devised to help us avoid jumping to wrong conclusions about nature.

[More to come, someday, maybe.]