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My position is that Newtonian mechanics is the glue that holds the universe together and is in large part responsible for the theory of relativity.  The other argument is that quantum mechanics is going to replace Newtonian mechanics.  I believe this to be totally false.  So I set out to conduct a little research.

What follows is mostly direct quoted material with references, of that research.

Search Results for: Newton’s laws Results 1-25  of 222 

Newton, Sir Isaac

Born: 1643  Died: 1727
Occupation: physicist, astronomer, mathematician

Natural laws allow for the prediction of the effects of forces such as gravity and processes such as motion. While humans have been able to predict such consequences and even use natural laws to their advantage for thousands of years, Sir Isaac Newton was the first to formulate such laws precisely and use mathematics to prove them rigorously. Scientists and engineers, as well as athletes and artists, still use principles that he delineated in his two major works, Principia and Opticks. Newton also invented the branch of mathematics called calculus and made significant contributions to many other areas of mathematics. In addition, he designed the first reflecting telescope, which has allowed the human race to explore farther into space than ever before.

He concluded that each individual color was a component part of white light—white light was due to the presence of all the colors. What was happening was that the individual colors were refracted, or bent, by the prism to different degrees; the red was bent the least, and the blue light was bent the most. Thus a circle of white light entered the prism and exited as an elongated spectrum of the individual colors.

The German astronomer Johannes Kepler had proposed that planets orbited elliptically around the Sun, that their speed changed along their orbits, and that the length of time it took to complete one orbit was related to the distance the planet was located from the Sun. Newton was learned in Kepler’s laws concerning planetary motion, but he wondered what kept the planets and the Moon in their orbits. He spent a lot of time pondering this question, and legend has it that one day as he sat under an apple tree, with his mind primed to discover the law of universal gravitation, an apple fell to the ground. (Another version of legend has the apple falling on Newton’s head.) Newton contemplated why the apple fell downward. Was Earth pulling the apple toward itself?

Years later, in 1684, while Newton remained hidden away in his lab, three other members of the Royal Society, Hooke, Christopher Wren, and Edmond Halley, were discussing the problem of elliptical orbits while drinking coffee together. They had figured out that the force needed to move planets in a circle around the Sun obeyed the inverse square law. This meant that a planet twice as far from the Sun would only require one-fourth the force exerted by the Sun to keep it in orbit. But these three extremely intelligent men could not figure out why they traveled in elliptical orbits. After months without success, Halley set out to visit Newton. He was shocked when he presented the problem to Newton only to hear Newton remark that he had solved that problem 15 years ago. This was an amazing accomplishment, and Halley could hardly believe Newton had kept it to himself. Newton could not locate the calculations immediately, however, and he promised to redo them. Several months later, Newton mailed his proof to Halley. By 1686, Newton had fleshed out the nine-page proof into his most famous work, which described the workings of the universe using mathematics.

Principia

The full title of this work is The Mathematical Principles of Natural Philosophy, though it is most often referred to by the abbreviation of its Latin name, Principia. Because of shortness of funds, the Royal Society almost did not publish it. Halley himself arranged the financial support for the publication of this work. In addition, Hooke again was angered, claiming that Newton stole his ideas. Newton balked, but Halley smoothed matters over, and the world is forever in his debt.

The first volume of Principia described what are known today as the three laws of motion. The first law summarizes inertia, the tendency originally articulated by the Italian astronomer and mathematician Galileo Galilei—unless acted upon by an outside force, an object in motion remains in motion at a constant speed in a straight line and an object at rest remains at rest. Because air resistance and friction act upon most earthly motions, Newton’s first law is not apparent. If you kick a ball, it will not roll forever at constant speed: it will eventually stop. However, in space, where there is no air and no friction, the first law is manifest. The second law of motion states that force is equal to the product of mass and acceleration. This law explains why it is harder to throw a bowling ball than a tennis ball. The third law maintains that when one object exerts a force on another object, the second object exerts an equal but opposite force on the first. (This is often expressed imprecisely in the form: For every action there is an equal and opposite reaction.) For example, when someone pushes off the ground to jump vertically, the force her feet exert on the ground is equal in magnitude to the force that the ground simultaneously exerts back on her feet.

Using these laws, Newton calculated the gravitational force between Earth and the Moon, proving that it followed the inverse square law: the force was directly proportional to the product of the two masses (the mass of Earth times the mass of the Moon) and inversely proportional to the square of the distance between the centers of Earth and the Moon. Previously, it had been assumed that the universe and Earth followed different sets of natural laws. Amazingly, Newton went on to prove that his predictions concerning gravitational forces could be applied throughout the universe. Thus, Newton was able to explain mathematically Kepler’s laws of planetary motion and demonstrate why the planets orbited the Sun in elliptical orbits (rather than in circles, as had earlier been assumed).

The third volume applied Newton’s new theories to the Moon, planets, and comets. It contained predictions using the laws of motion and gravity, which he formulated. One prediction he made was that gravity should cause Earth to be a perfect sphere, but the rotation of Earth about its axis should cause a bulge at the equator. Newton predicted the size of this bulge; it has since been proven correct to within 1 percent accuracy. He also predicted that many comets would follow elliptical paths just as planets do, but that they would have more elongated paths. Halley was quite excited by the realization that the motion of comets could be predicted using Newton’s laws. Credited for discovering the comet named for him, he was able to use Newton’s laws and methods to predict the return of this comet every 76 years. The comet has indeed reappeared every 76 years since.

Rosen, J. & Gothard, L. Q. Newton, Sir Isaac. In Science online. Retrieved from http://www.fofweb.com/activelink2.asp?ItemID=WE40&SID=5&iPin=EPS0143&SingleRecord=True

general relativity

Albert Einstein’s general theory of relativity, known in short as “general relativity,” is the theory of gravitation that Einstein proposed in 1915. A generalization of the special theory of relativity (“special relativity”), this theory, too, is formulated in terms of four-dimensional space-time. In contrast to the way it is in the special theory, space-time is not flat in the general theory: rather, it curves as an effect of and in the vicinity of masses and energies. According to the theory, gravitation is not a force, like, say, the magnetic force, but rather is an effect of the curved geometry of space-time. That comes about in this way. In the theory, force-free bodies obey a generalization of Newton’s first law of motion. Their free motion, or inertial motion, however, is not in a straight line, but follows a path that is the closest to a straight line in curved space-time, called a geodesic. This is referred to as geodesic motion, motion that is the analog in curved space-time of straight-line motion at constant speed in ordinary space. The result is motion that appears in ordinary space as neither in a straight line nor at constant speed, in general, and manifests the effect of gravitation on the bodies.

As an example, consider the motion of Earth around the Sun. Viewed nonrelativistically, in the hypothetical absence of the gravitational force of the Sun (and ignoring all other solar-system objects), Earth would move inertially (i.e., in accordance with Newton’s first law) in a straight line at constant speed. The gravitational force of the Sun on Earth makes the situation dynamic, however, and Newton’s second law applies. The resulting dynamic motion turns out to be motion in an elliptical orbit around the Sun. The general theory of relativity describes conditions differently. According to the general relativistic view, the Sun causes a deformation of space-time. No forces act on Earth, which therefore moves inertially. Inertial motion is geodesic motion in space-time, as described earlier. When Earth moves inertially (freely) along a geodesic in space-time, it appears to be moving dynamically (under the effect of a force) along an ellipse in ordinary space.

Here is a description of an often-presented model, to give some idea of what is going on. Set up a horizontal stretched sheet of rubber to represent flat space-time. Place a heavy marble on the sheet. The marble represents a massive body. Because of the marble’s weight, the rubber sheet is stretched downward at the location of the marble and assumes a somewhat conical shape with the marble at the apex. This shape represents curved space-time in the presence of and in the vicinity of mass. Now, toss light marbles or ball bearings onto the rubber sheet so they roll at various speeds and in various directions. Some might orbit the heavy marble. Low-speed ones will spiral into the marble. High-speed ones will escape capture but still have their trajectory affected. This behavior represents the effect of space-time curvature on bodies as an explanation of gravitation.

The General Theory

One of the basic postulates of the general theory, which is a straightforward generalization of a basic postulate of the special theory, is that the laws of physics are the same in all reference frames, no matter what their relative motion. (In the special theory, the reference frames are restricted to relative motion at constant velocity, i.e., at constant speed in a straight line.) Einstein designed the general theory to produce Newton’s law of gravitation, under appropriate conditions.

The general theory of relativity has passed all the tests it has been given. It explains the deviation of the orbit of the planet Mercury from the prediction of Newtonian mechanics, and it correctly gives the amount of deflection from a straight-line trajectory of starlight as it passes near the Sun. Its prediction of the gravitational redshift—the change in frequency of light or of any electromagnetic wave as it passes through the gravitational field—has been confirmed. The theory also predicts the existence of gravitational waves.

As for practical applications, the theory is routinely invoked in connection with the navigation of spacecraft and in the design and operation of the Global Positioning System (GPS).

Arthur Eddington an English astronomer and physicist participated in organizing and leading expeditions to those islands. The weather cooperated during the eclipse, although just barely for the Principe group under Eddington, and both groups photographed the star field near the Sun. Upon return to England, Eddington compared the stars’ apparent positions during the eclipse with their usual positions. The result confirmed the prediction of the general theory of relativity. Since then, additional such observations have strengthened confirmation of the theory.

Rosen, J. & Gothard, L. Q. General relativity. In Science online. Retrieved from http://www.fofweb.com/activelink2.asp?ItemID=WE40&SID=5&iPin=EPS0092&SingleRecord=True

Among physicists, however, classical physics stands in contrast only to quantum physics, while relativistic effects are included in it. Quantum physics is characterized by the Planck constant, h = 6.62606876 × 10–34 joule·second (J·s), which is nature’s elementary unit of a quantity called action. While nature is fundamentally quantum in character and quantum physics seems to give an excellent understanding of it, classical physics can be valid to high accuracy for situations involving actions that are large compared to h, what is referred to as the classical domain. This includes everyday phenomena, of course, and furthermore ranges over lengths, durations, and masses that are not too small, that are in general larger, say, than the atomic and molecular scales.

Characteristics of Classical Physics

Some of the characteristics of classical physics, which, to a good approximation, reflect properties of nature in the classical domain, are definiteness, determinism, continuity, locality, wave-particle distinction, and particle distinguishability.

Definiteness. Every physical quantity that is relevant to a physical system possesses a definite value at every time. Even if we do not know the value of such a quantity, it nevertheless has a definite value. For instance, speed is a physical quantity that is relevant to every body. So at any instant every body possesses a certain value for its speed. And that is true whether one has measured and knows its speed’s value or not.

Determinism. The state of a physical system at any instant uniquely determines its state at any time in the future and, accordingly, is uniquely determined by its state at any time in the past. It follows that a full understanding of the working of nature and a complete knowledge of a system’s state at any time allow, in principle, prediction of the system’s state at any time in the future and retrodiction of its state at any time in the past. Limitations on such predictability and retrodictability, even when the laws of nature are known, are the result of incomplete knowledge of the system’s state. In practice, such incompleteness is unavoidable, since all measurements possess only finite precision. (And even if infinite precision were hypothetically possible, inherent quantum uncertainties exist in the values of physical variables.) For example, determinism allows astronomers, using their present-day data on the positions and velocities of the heavenly bodies, to tell us what the sky will look like at any time in the future and how it appeared at any time in the past.

Continuity. Processes occur in a continuous manner, so that physical quantities that vary in time do so continuously—no sudden jumps. Also, the ranges of allowed values of physical quantities are continuous: a physical quantity can possess a certain value, then it can also take values as close to that value as one might like. For instance, if a system can possess 3.14159 joules (J) of energy, then in general the same system is also capable of possessing 3.14158 J of energy.

Locality. What happens at any location is independent of what happens at any other location, unless some influence propagates from one location to the other, and the propagation of influences occurs only in a local manner. What this means is that influences do not instantaneously span finite distances. (Such a hypothetical effect is known as action at a distance.) Rather, the situation at any location directly affects only the situations at immediately adjacent locations, which in turn directly affect the situations at their immediately adjacent locations, and so on. In this way an influence propagates at finite speed from its cause to its effect. For example, if one wiggles an electric charge in Washington, D.C., that action will in principle affect all electric charges everywhere in the universe. However, the effect is not instantaneous: rather, it propagates at the speed of light in vacuum, which is approximately 3.00 × 108 meters per second (m/s).

Wave-particle distinction. A wave is a propagating disturbance, possibly characterized, for instance, by frequency and wavelength. It possesses spatial extent, so is not a localized entity. A particle, on the other hand, is localized. It is characterized by mass, velocity, position, energy, and so forth. Waves and particles are distinct from each other and bear no relation to each other.

Particle distinguishability. All particles are distinguishable from each other, at least in principle. For example, this hydrogen atom and that one can always be distinguished one from the other.

In fact, though, nature does not possess any of these characteristics. Quantum theory recognizes that and takes into account nature’s uncertainty, indeterminism, discontinuity and discreteness, nonlocality, wave-particle duality, and particle indistinguishability. For example, physical quantities in general possess intrinsic uncertainty in their value over and beyond any uncertainty in knowledge of the value due to inherently imprecise measurement. And as another example, there is no property of a hydrogen atom by means of which two hydrogen atoms in the same state can be distinguished. Nevertheless, classical physics can and does deal with nature to a high degree of accuracy, as long as it is not pushed beyond nature’s classical domain.

History of Classical Physics

The approach to the comprehension of nature that led to science as we know it today originated in ancient Greece. One name that stands out is that of Aristotle, who lived in the 300s BCE. He observed nature and developed ways of thinking logically about it.

Some of the events and people in the development of classical physics are these:

  • The Italian physicist and astronomer Galileo Galilei, commonly referred to as Galileo, whose life straddled      the 16th and 17th centuries, investigated motion and demonstrated the      validity of the heliocentric model of the solar system. He is attributed      with dropping objects from the Leaning Tower of Pisa in order to study      free fall.
  • The German astronomer and mathematician Johannes Kepler, a contemporary of Galileo’s, found the three laws of      planetary motion named for him.
  • Isaac Newton, the English physicist and mathematician who lived in      the 17th and 18th centuries, discovered the three laws of motion and law      of gravitation named for him, among his other accomplishments, which      included inventing calculus.
  • The English chemist and physicist Michael Faraday, most of whose life was in the 19th century, made      important discoveries in electromagnetism.
  • James Clerk Maxwell, the 19th-century Scottish physicist, formulated the      laws of classical electromagnetism.

Rosen, J. & Gothard, L. Q. Classical physics. In Science online. Retrieved from http://www.fofweb.com/activelink2.asp?ItemID=WE40&SID=5&iPin=EPS0038&SingleRecord=True

laws and physics

Scientists discover laws by searching for and finding patterns in experimental and observational data. Laws are based on a finite amount of data. The amount might be very large, but it is always limited. The mathematical relation that expresses a law forms a summary of the relevant data, but it offers more than that—it allows the prediction of the results of new experiments or observations. Thus the law can be tested and confirmed, or tested and contradicted.

When a law has been confirmed by overwhelming evidence for its validity, that is, by many successful results of predictions, it becomes accepted as correct and can serve as a useful, predictive tool.

Every law possesses a limited known range of validity. What this means is that every law is known to be correct only for certain ranges of values of the physical quantities that enter into it.

Sir Isaac Newton’s law of gravitation fails for strong gravitational fields and for high speeds. Albert Einstein’s general theory of relativity fixes that but is expected to fail at very small distances, since it is incompatible with quantum physics.

Consider another example of the discovery of a law. Galileo Galilei performed many experiments on the behavior of uniform spheres rolling down straight, inclined tracks. He released spheres from rest and measured the distances d they roll from rest position during various elapsed times t. In this way, Galileo collected a lot of experimental data in the form of d-t pairs. He studied the numbers, performed calculations on them, and perhaps plotted them in various ways, all in search of pattern and order. What he found was, for a fixed angle of incline, the distance a rolling sphere covers from rest position is proportional to the square of the elapsed time from its release, d = bt2 .This mathematical relation summarizes Galileo’s experimental results and forms a law. Although it is based on only a finite number of d-t pairs, the relation is able to predict the distance covered for any elapsed time, whether Galileo actually had that d-t pair among his data or not. Thus, it predicts the results of new experiments. The predictive power of the law allows it to be tested, and it has been tested and confirmed sufficiently to be considered correct. The law is valid as long as the mass of the rolling sphere is not too small nor its speed too high (i.e., as long as the force of gravity acting on the sphere is sufficiently greater than the retarding force on it due to the viscosity of air).

Rosen, J. Laws and physics. In Science online. Retrieved from http://www.fofweb.com/activelink2.asp?ItemID=WE40&SID=5&iPin=EPS0218&SingleRecord=True

mathematics and the laws of thermodynamics

Thermodynamics is that branch of science that deals with the relationships that exist between heat and work. It touches on important questions about why physical systems evolve in some ways but not others. It is one of the conceptually richest areas of classical physics.

The history of thermodynamics traces its roots to experiments performed by the Italian physicist and mathematician Galileo Galilei. Galileo is often given credit for being the first to devise a thermometer. Galileo’s invention was an important innovation because two objects at the same temperature often feel as if they are at different temperatures. For example, if we touch a slab of wood and a slab of iron, both of which are at room temperature, the iron feels cooler. Thermometers provide an objective way of comparing temperatures, but they do not offer much insight into what temperature is.

…a little-known repairman named James Watt (1736–1819). While repairing the Newcomen engine, Watt saw a way that the efficiency of the engine could be substantially improved. In 1769 James Watt applied for his first steam engine patent. It was the first of many patents that Watt received for improving the steam engine. By the time he had finished his work on the steam engine, Watt’s engines were installed in mines and factories throughout Britain, and Watt had become a wealthy and celebrated man. The British Industrial Revolution was now in full swing, and it was powered by the Watt steam engine. The race to understand the relationship between heat and work had begun.

Joseph Black (1728–99) In physics Black undertook one of the first serious studies of the nature of heat. His experiments with heat and his theory of heat are his most important contributions to the history of the science of thermodynamics.

The change of any substance from vapor to liquid, or liquid to vapor, or the change of any substance from liquid to solid, or solid to liquid, is a phase change. (Matter generally exists in one of three phases: vapor, liquid, or solid.) Black’s experiments showed that when a material undergoes a phase change, the temperature remains constant until the phase change is complete. Black responded to these observations by defining heat in terms of what it does rather than what it is. He called heat that causes a change in temperature sensible heat. He called heat that causes a change of phase latent heat.

After he had developed a significant body of experimental results, Black created what he called the caloric theory to explain what he had observed. Caloric, he hypothesized, is a fluid that can flow from one body to another. When a warm body is placed in contact with a cool body, caloric flows out of the warm body into the cool one. The temperature of the warm body diminishes as the temperature of the cool body increases. Furthermore as caloric flows from one body to the other, the volume of the warm body diminishes and the volume of the cool body increases. Having hypothesized the existence of caloric, he was able to deduce various properties that it must have in order to make his theory consistent. The most important of these properties was that caloric is conserved; that is, Black’s idea was that caloric, as well as momentum and mass, cannot be created or destroyed. Black had proposed a new conservation law.

Sadi Carnot

Carnot is remembered for a single slim book that he published, Reflexions sur la puissance motrice du feu (Reflections on the motive power of fire), Unequal heating of the atmosphere causes the winds. The source of rain and snow is water that is evaporated off the surface of the oceans. The water vapor then condenses and falls to the surface as precipitation. Heat is what causes the evaporation. Without heat there can be no weather. He also recognized that eruptions of volcanoes are, in the end, thermal (heat-driven) processes. Without heat life would be impossible. Carnot begins his book with a list of phenomena that are heat-driven. He demonstrates that the study of heat is a field unto itself.

Carnot accepted Black’s ideas about caloric, a sort of heating fluid that always flows from warmer regions to cooler ones. To understand how Carnot incorporated these ideas into his own theory of heat engines, it is helpful to think about water turbines: Water always flows from higher elevations to lower ones. Engineers build dams to raise the water level on the upstream side of the dam. They then use pipes to direct the flowing water past turbines. The flowing water causes the turbines to spin, and the spinning motion of the turbines is then harnessed to do work. As the moving water pushes against the turbine, the water slows, but it does not stop. It flows past the turbine, down a pipe, and back into the river. No less water exits the pipe that directs it away from the turbine than enters the pipe that directs it toward the turbine. The water does its work, but the mass of the water is conserved.

Carnot imagines the caloric flowing from the hotter thermal reservoir to the cooler thermal reservoir. (The expression thermal reservoir, or simply reservoir, has since become part of the standard vocabulary in the science of thermodynamics.) As the heat flows from the hot reservoir to the cold reservoir, the steam engine enables the user to convert some of the energy of the flowing caloric into useful work, but just as the water turbine does not convert all of the water’s energy of motion into work, the steam engine does not convert all of the moving caloric into work. Some of the caloric flows right past the steam engine into the cooler reservoir. The question then is, How much work can be extracted from the caloric as it flows from the high temperature reservoir to the low?

To appreciate the usefulness of a Carnot engine, some knowledge of its theoretical properties is helpful. A Carnot engine operates between a high-temperature reservoir and a low-temperature reservoir. It is generally described as a single cylinder that is closed off by a piston. Enclosed within the cylinder is a gas, the working fluid. Heat is transferred to and from the gas in the cylinder via a sequence of carefully controlled steps. At each step the piston is either raised or lowered. At the completion of the cycle the Carnot engine has produced some work—how much work depends on the temperature difference between the two reservoirs and the size of the engine—and the temperature and volume of the working fluid inside the cylinder have been precisely restored to what they had been before the cycle began. This restoration is an important characteristic of the engine: The Carnot engine is a cyclic engine. It repeats the same procedure with the same results over and over again.

Soon after completing his masterpiece, Carnot made a disconcerting discovery: The caloric theory is wrong. Carnot had based his book on the caloric theory and later concluded that the caloric theory of heat was flawed. Instead Carnot began to perceive heat as “motive power”; that is, heat (caloric) can be converted to motive power and motive power converted to heat. The exchange is exact: The amount of heat lost equals the amount of motive power gained, and vice versa. This is a deep insight into nature, and Carnot took this to be an axiom, a law of nature. With these insights Carnot had essentially discovered what would later be known as the first law of thermodynamics, one of the most important of all natural laws.

James Prescott Joule

He studied electricity, heat, and the relationship between heat and work. One of his first discoveries was that a current flowing in a wire produces heat. The main problem with which Joule was concerned was the identification of the “mechanical equivalent of heat.” Essentially he wanted to know how much heat has to be expended to produce one unit of work, and vice versa.

What Joule discovered was that as the paddle spun in the water, the temperature of the water increased slightly. Joule was essentially creating “caloric” by stirring water. The heat was the result of friction between the paddle and the water, between the water and the walls of the container, and inside the water itself as one region of water flowed past another. The resulting friction raised the temperature of the entire system. Joule had created heat, and he had done so in a way that enabled him to state how much work had been performed in the creation of the heat. Joule’s experiments disproved the caloric theory.

The First Law of Thermodynamics

The work of Joule and Carnot was the foundation on which the science of thermodynamics was built. The first person to recognize how Joule’s and Carnot’s ideas about work and heat could be incorporated into a coherent theory was the German physicist and mathematician Rudolf Clausius (1822–88). Clausius was the first to state what is now known as the first law of thermodynamics.

Clausius asserted that the change in energy of a system can be completely accounted for by the sum of the heat flow into or out of the system and the work performed. This result, called the first law of thermodynamics, is often stated like this:

(Change in energy of a system) = − (work done by the system) + (heat flow across the boundary)

Here is how Clausius expressed the first law: The energy of the universe is constant.

The discovery of energy and its relationship to heat and work is one of the great milestones in the history of science. It is a cornerstone of modern scientific thought. No one, for example, has ever seen energy consumed or created. Of course only a few hundred years ago many scientists spent their working life studying physics without ever observing the consumption or the creation of heat (caloric), whereas today these kinds of observations pose no problem at all to the curious high school student. Will we one day be able to point to exceptions to the first law of thermodynamics? The best that can be said about the validity of the first law is that since it was first formulated by Clausius, no scientist has ever erred in assuming its validity.

The Second Law of Thermodynamics

Of course, no one has ever seen this occur, but there is nothing in the first law to rule it out, either. In the case of the heat engine’s running on “backward”-flowing heat, the first law is satisfied provided that the decrease in energy of the lower-temperature reservoir equals the sum of the work performed by the engine plus the amount of heat rejected to the higher-temperature reservoir. The theory of heat is still incomplete.

The second law is fundamentally different from previous natural laws. It is negative. It states the impossibility of certain processes. By contrast the conservation laws are all positive. They state that some property is conserved. The mathematical form of the second law is also different from the form of all previous laws of nature. Unlike conservation laws, which are written as equalities, the mathematical statement of the second law of thermodynamics is an inequality. The scientific, mathematical, and philosophical implications of the second law continue to draw the attention of thoughtful people to this day.

Negative statements cannot be proved experimentally: There is no experiment that can rule out the existence of another experiment that does not conform to the second law. Nevertheless, no experiment that violates the second law has ever been devised. There is nothing else in science to compare with the second law of thermodynamics.

Here is one version of what is usually called Clausius’s statement of the second law of thermodynamics:

It is impossible to construct a cyclic engine whose only effect is the transfer of heat from a body at a lower temperature to one at a higher temperature.

In his book Carnot emphasized the motive power of heat. Heat drives all the processes on which life depends, but heat flows only when there are temperature differences.

It is impossible to construct a cyclic machine whose only effect is to perform work using heat extracted from a single reservoir that is the same temperature throughout.

Like Clausius’s version of the second law, Kelvin’s version is a negative statement. It, too, states a basic law of nature in terms of the impossibility of constructing a certain type of machine. Kelvin used a heat engine in his formulation; Clausius used a refrigerator.

Notice that if Kelvin’s formulation of the second law were false, then we could attach a cyclic heat engine to a single thermal reservoir—the surface of the Earth, for example—and run it as long as we wanted. The engine would have no other effect than that of cooling Earth’s surface as it converted heat into work. Given the amount of thermal energy in the Earth, this would be, for all practical purposes, a perpetual motion machine. This kind of machine has never been constructed. The failure to build this type of device is one of the principal arguments supporting the truth of the second law of thermodynamics.

Energy is one of the most important concepts in science, and its importance has only increased in the years since Clausius published his discoveries. It is now a fundamental concept in understanding the inner workings of galaxies and the inner workings of atoms. It is as important in the philosophy of science as it is in the design of refrigerators. It is, perhaps, the only physical principle to find such wide applicability. The discoveries of Clausius and Kelvin are among the most important in the history of science.

Tabak, J. Mathematics and the laws of thermodynamics. In Science online. Retrieved from http://www.fofweb.com/activelink2.asp?ItemID=WE40&SID=5&iPin=HMMLN0008&SingleRecord=True

Newton’s laws of motion

Three laws of mechanics formulated by Sir Isaac Newton in 1687. They can be stated as:

(1) An object continues in a state of rest or constant velocity unless acted on by an external force.

(2) The resultant force acting on an object is proportional to the rate of change of momentum of the object, the change of momentum being in the same direction as the force.

(3) If one object exerts a force on another then there is a simultaneous equal and opposite force on the first object exerted by the second. The first law was discovered by Galileo, and is both a description of inertia and a definition of zero force. The second law provides a definition of force based on the inertial property of mass. The second and third laws combined give the law of conservation of momentum.

Daintith, J. & Rennie, R. Newton’s laws of motion. In Science online. Retrieved from http://www.fofweb.com/activelink2.asp?ItemID=WE40&SID=5&iPin=FDPF1297&SingleRecord=True

 

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