History of Classical Mechanics - Modern Age

Modern Age

It wasn't until Galileo Galilei's development of the telescope and his observations that it became clear that the heavens were not made from a perfect, unchanging substance. Adopting Copernicus's heliocentric hypothesis, Galileo believed the Earth was the same as other planets. Galileo may have performed the famous experiment of dropping two cannon balls from the tower of Pisa. (The theory and the practice showed that they both hit the ground at the same time.) Though the reality of this experiment is disputed, he did carry out quantitative experiments by rolling balls on an inclined plane; his correct theory of accelerated motion was apparently derived from the results of the experiments. Galileo also found that a body dropped vertically hits the ground at the same time as a body projected horizontally, so an Earth rotating uniformly will still have objects falling to the ground under gravity. More significantly, it asserted that uniform motion is indistinguishable from rest, and so forms the basics of the theory of relativity.

Sir Isaac Newton was the first to unify the three laws of motion (the law of inertia, his second law mentioned above, and the law of action and reaction), and to prove that these laws govern both earthly and celestial objects. Newton and most of his contemporaries, with the notable exception of Christiaan Huygens, hoped that classical mechanics would be able to explain all entities, including (in the form of geometric optics) light. Newton's own explanation of Newton's rings avoided wave principles and supposed that the light particles were altered or excited by the glass and resonated.

Newton also developed the calculus which is necessary to perform the mathematical calculations involved in classical mechanics. However it was Gottfried Leibniz who, independently of Newton, developed a calculus with the notation of the derivative and integral which are used to this day. Classical mechanics retains Newton's dot notation for time derivatives.

Leonard Euler extended Newton's laws of motion from particles to rigid bodies with two additional laws.

After Newton, re-formulations progressively allowed solutions to a far greater number of problems. The first was in 1788 by Joseph Louis Lagrange, an Italian-French mathematician. In Lagrangian mechanics the solution uses the path of least action and follows the calculus of variations. William Rowan Hamilton re-formulated Lagrangian mechanics in 1833. The advantage of Hamiltonian mechanics was that its framework allowed a more in–depth look at the underlying principles. Most of the framework of Hamiltonian mechanics can be seen in quantum mechanics however the exact meanings of the terms differ due to quantum effects.

Although classical mechanics is largely compatible with other "classical physics" theories such as classical electrodynamics and thermodynamics, some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. When combined with classical thermodynamics, classical mechanics leads to the Gibbs paradox in which entropy is not a well-defined quantity. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the energy levels and sizes of atoms. The effort at resolving these problems led to the development of quantum mechanics. Similarly, the different behaviour of classical electromagnetism and classical mechanics under velocity transformations led to the theory of relativity.