the advent of the quantum theory and relativity in the early years of the 20th century, Newtonian physics was replaced by modern physics which basically states that Newtonian principles need to be revised when we consider very small objects such as atoms and very fast moving objects such as light. Modern physics does not posit a deterministic universe. It is intrinsically impossible to make an exact measurement of all the quantities such as position, velocity, etc. of even a single atom, leave alone billions of atoms. Not only is precise measurement impossible, but prediction is also ruled out by the laws of quantum mechanics. Thus determinism has collapsed. One can no longer use Newtonian physics to argue against the possibility of free will. The philosophical debates regarding free will became far more sophisticated as a result of quantum theory.
2.8Summary
The heavenly bodies appear to be moving in a circular motion round the earth. But the cumulative results of painstaking observations made by astronomers through the centuries enabled Copernicus to conclude that the sun and not the earth is the center of the solar system. But if the earth also moved in a circular orbit, then one could no longer accept the ancient belief that circular motion was a special property of the heavenly bodies.
The Copernican worldview required a scientific explanation for this perpetual motion of the planets round the sun. Newton was the first scientist to explain the kinematics of both celestial and terrestrial objects. He provided a simple mathematical system that explained all sorts of motion. The force of gravity attracts all objects to each other. The force between two objects is proportional to the product of the masses and inversely proportional to the square of the distance between them.
In addition to the law of gravity Newton also enunciated the three laws of motion. All objects have this property called inertia, whereby they tend to remain at rest or move in a straight line with constant speed. In order to change this state, an external force has to be applied. This force is numerically equal to the product of the mass of the object and its acceleration under this force. Moreover, when one object applies a force on another, the second object simultaneously applies an equal and opposite force on the first.
Newton’s laws of motion and gravity form the basis of all classical mechanics, the branch of physics dealing with motion and forces. These laws successfully explained the motion of the planets as well as all motion on earth. They seemed to be absolutely infallible rules followed by all matter in the universe. This led many people to believe that the universe is deterministic. Everything happens the way it does because it cannot happen any other way. All things have been predetermined by the laws of motion.
1I use the word Planet with a capital P to denote the term as it was used in antiquity — meaning the five visible planets plus the sun and the moon.
2The day/night difference and the seasonal variations would be greater in regions further removed from the equator than Egypt.
3The United States continues to use the outdated British FPS system. This is an example of systemic inertia.
The ratio sin θ is defined as shown.
4Consider a triangle with one right angle = 900. The side opposite to this right angle is called the hypotenuse. If θ is one of the other two angles, then the side between the 900 angle and the angle θ is called the adjacent side of the angle θ and the third side is called the opposite side. We define cos θ as the number obtained by dividing the length of the adjacent side by the length of the hypotenuse.
Chapter 3
Statistical Mechanics
3.1Atoms
The Greek philosopher Democritus (460–370 BCE) proposed that material objects cannot be divided into smaller and smaller pieces ad infinitum, but that a stage would be reached when it would be impossible to divide matter any further. Thus all matter was made of very tiny grains which were so small that they could not be seen. Democritus claimed that these tiny grains could not be divided any further, and so he called such a grain an atom, which in Greek means “indivisible”.
What evidence is there for the existence of atoms?
Democritus argued that odors and aromas are caused by atoms breaking off from the material and flying through the air and eventually entering our nostrils. This explanation is valid even today, though we would use the word “molecule” rather than atom to describe the smallest particles of the substance that we are smelling.
The first visible proof of Democritus’ hypothesis of these atoms was the observation of the random erratic motion of pollen grains and saw dust grains suspended in water when seen through a powerful microscope. This motion is called Brownian motion, after the botanist R. Brown who reported his observation in 1827.1 The pollen grains were seen dancing about in a zigzag haphazard manner. The explanation is that the tiny invisible particles of water were hitting the pollen grains from different directions at different speeds, and the pollen grains were reacting to these collisions by moving in random directions. Today we know that the smallest particles of water are not really atoms, but molecules. Brownian motion provided the first visible proof that matter is made of small indivisible particles.
The atomic theory of matter is able to explain the observations of chemistry. Chemistry investigates reactions whereby elements combine with other elements to form compounds, and compounds react with other elements or compounds to produce other substances, both elements and compounds. Around 1880 the chemist John Dalton found that when elements combine to form compounds they do so in fixed proportions by weight. As an example, 1 gram of hydrogen combines with 8 grams of oxygen to form 9 grams of water, and 2 grams of hydrogen combine with 16 grams of oxygen to form 18 grams of water. This seems to suggest that substances are made of atoms which have fixed masses, because this observation would make sense if each substance was made of small microscopic particles all having the same mass and that the masses of these fundamental particles varied from one substance to another. So Dalton’s observation offered a good indirect proof for the existence of atoms.
Another major victory scored by the atomic theory is that it has been able to explain our most basic experiences of heat and cold. Temperature is something everybody experiences. The application of heat to effect useful changes — particularly for cooking food — had been recognized since the discovery of fire. The industrial revolution took off when heat was recognized as a form of energy that could be harnessed to do useful work such as in the steam engine and the automobile engine. The study of the relationship between heat and mechanical energy is called thermodynamics. Physicists made considerable progress in discovering important laws of thermodynamics before they understood the nature of heat. The atomic theory finally explained that heat is nothing but the sum total of the energies of the individual atoms or molecules of a material object — solid, liquid or gas. Temperature is simply a measure of the average kinetic energy of the microscopic atoms or molecules of an object.
We shall do a quick review of the laws of thermodynamics and show how these laws make sense in the light of the atomic theory of matter.
3.2The laws of thermodynamics
The word “thermodynamics” is a combination of “thermo” meaning heat and “dynamics” meaning the effects of forces.
So in the study of thermodynamics we are interested in the interplay between heat and work. Let us recall that we learned earlier (Ch. 2) that work is done when a force causes a body to undergo a displacement.
When a dynamo is made to rotate swiftly, it produces electricity. One way of causing a dynamo to rotate is to attach paddles to it and place it under a waterfall. The falling water has mechanical energy due