The World Of Physics

4. Classical physics

Physics that does not make use of quantum mechanics or the theory of relativity. Newtonian mechanics, thermodynamics, and Maxwell's theory of electromagnetism are all examples of classical physics. Many theories in classical physics break down when applied to extremely small objects such as atoms or to objects moving near the speed of light. Classical mechanics refers to the classical physics of bodies and forces, especially Newton's laws of motion and the principles of mechanics based on them. Compare quantum mechanics.

Classical physics is widely assumed to provide a friendly environment for determinism. In fact, determinism must overcome a number of obstacles in order to achieve success in this setting. First, classical spacetime structure may not be sufficiently rich to support Laplacian determinism for particle motions. Second, even if the spacetime structure is rich, uniqueness can fail in the initial value problem for Newtonian equations of motion if the force function does not satisfy suitable continuity conditions. Third, the equations of motion that typically arise for classical particles plus classical fields, or for classical fields alone, do not admit an initial value formulation unless supplementary conditions are imposed. Fourth, even in cases where local (in time) uniqueness holds for the initial value problem, solutions can break down after a finite time.

The following subsection takes up the first of these topics — the connection between determinism and the structure and ontology of classical spacetimes. The others are taken up in due course.

By the late nineteenth century the laws of physics were based on Mechanics and the law of Gravitation from Newton, Maxwell's equations describing Electricity and Magnetism, and on Statistical Mechanics describing the state of large collection of matter. These laws of physics described nature very well under most conditions, however, some measurements of the late 19th and early 20th century could not be understood. The problems with classical physics led to the development of Quantum Mechanics and Special Relativity.

Some of the problems leading to the development of Quantum Mechanics are listed here.

Black body radiation : Classical physics predicted that hot objects would instantly radiate away all their heat into electromagnetic waves. The calculation, which was based on Maxwell's equations and Statistical Mechanics, showed that the radiation rate went to infinity as the EM wavelength went to zero, ''The Ultraviolet Catastrophe''. Plank solved the problem by postulating that EM energy was emitted in quanta with.

The photo effect : When light was used to knock electrons out of solids, the results were completely different than expected from Maxwell's equations. The measurements were easy to explain (for Einstein) if light is made up of particles with the energies Plank postulated.

Atoms: After Rutherford found that the positive charge in atoms was concentrated in a very tiny nucleus, classical physics predicted that the atomic electrons orbiting the nucleus would radiate their energy away and spiral into the nucleus. This clearly did not happen. The energy radiated by atoms also came out in quantized amounts in contradiction to the predictions of classical physics. The Bhor atomic postulated an angular momentum quantization rule,  for , that gave the right result for hydrogen, but turned out to be wrong since the ground state of hydrogen has zero angular momentum. It took a full understanding of Quantum Mechanics to explain the atomic energy spectra.

Compton scattering : When light was scattered off electrons, it behaved just like a particle but changes wave length in the scattering; more evidence for the particle nature of light and Plank's postulate.

Waves and Particles: In diffraction experiments,light was shown to behave like a wave while in experiments like the Photoelectric effect, light behaved like a particle. More difficult diffraction experiments showed that electrons (as well as the other particles) also behaved like a wave, yet we can only detect an integer number of electrons (or photons).

Quantum Mechanics incorporates a wave-particle duality and explains all of the above phenomena. In doing so, Quantum Mechanics changes our understanding of nature in fundamental ways. While the classical laws of physics are deterministic, QM is probabilistic. We can only predict the probability that a particle will be found in some region of space.

Electromagnetic waves like light are made up of particles we call photons. Einstein, based on Plank's formula, hypothesized that the particles of light had energy proportional to their frequency.

The new idea of Quantum Mechanics is that every particle's probability (as a function of position and time) is equal to the square of a probability amplitude function and that these probability amplitudes obey a wave equation. This is much like the case in electromagnetism where the energy density goes like the square of the field and hence the photon probability density goes like the square of the field, yet the field is made up of waves. So probability amplitudes are like the fields we know from electromagnetism in many ways.

DeBroglie assumed for photons and other particles and used Lorentz invariance (from special relativity) to derive the wavelength for particle like electrons.

The rest of wave mechanics was built around these ideas, giving a complete picture that could explain the above measurements and could be tested to very high accuracy, particularly in the hydrogen atom. We will spend several chapters exploring these ideas.