Historical Background

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1.1 Historical Background

1.1.1 Success of Classical Physics

Physics started from the ancient Greeks (around 300 BC) evolved through different stages of development by contributions from several scientists of different countries. Motivated by the curiosity about natural processes, initially their study was mainly about the mass, motion, forces etc. The landmark developments in this pursuit may be mentioned as follows: the heliocentric (Sun-centered) model of our solar system by Copernicus (1543), three laws of planetary motion by Johannes Kepler (1571–1630), classic method of experimentation by Galileo Galilei (1564–1642), comprehensive theoretical synthesis into the laws of motion and the theory of universal Gravitation by Isaac Newton’s (1643–1727) etc. The discovery of the conservation laws of energy, momentum and angular momentum which have been the most basic and comprehensive was significant since they have stood the test of time. Newtonian Mechanics was deterministic and worked in the reference frame of absolute space and time. Given the information about the position and velocity/ momentum of a particle at any time, it was possible in principle, to predict these quantities for moving bodies in the universe at any other time. Invention of mathematical tools like Calculus by Newton and Leibniz was useful for the development of other branches in addition to mechanics e.g. for modeling gases, deriving gas laws, development of kinetic theory of gases, understanding the basic mechanisms of heat and temperature, to develop the laws of thermodynamics etc. Maxwell-Boltzman Equipartition theorem was useful to describe systems with a large number of degrees of freedom which formed a separate branch called as Statistical Mechanics. Wave nature of light was well established. Following the discoveries by scientists like Gauss, Ampere, Michael Faraday (1791–1867) etc. James Clerk Maxwell (1831–1879) had presented the synthesis of electrodynamics in his celebrated equations and the separate branches of Electricity, Magnetism and Light were united into one discipline. Mathematical work of Maxwell’s equations enabled to make unexpected predictions like the existence of electromagnetic waves and their propagation with the speed of light. The assumptions and results of these theories were found to be consistent in the physics of the macroworld. Separate branches like Mechanics (including Gravitation), Waves, Light, Heat and Thermodynamics, Sound, Electricity, Magnetism were united in the system called Classical Physics.

These developments enabled to fabricate machines based on heat and electric power leading to industrial revolution. The theoretical background was mathematically consistent and was proved repeatedly in experiments. It seemed as if the main theories and important discoveries in physics were made and only a few minor details remained. Classical physics at the end of 19 th century, was found to be quite satisfactory to understand the order underlying the working of objects of the every day universe which belonged to the classical domain i.e. the objects of the macroworld which can be studied with unaided human senses and moving with velocities far less than the velocity of light.

At the beginning of twentieth century some experimental observations were found to be unexplainable using the theory of classical physics. It was only because they were outside the classical domain. Still the above mentioned achievements of Classical Physics cannot be underestimated. Professor S\,. Pollock has rightly remarked that “Classical Physics is the giant on whose shoulder we stand today, as we move into new realms of study, into modern physics, or contemporary biology, or any of a number of modern disciplines."

1.1.2 Inadequacy of Classical Physics

In spite of the great success of classical physics, in the beginning of the 20th century, there were some areas in which discrepancies between the classical model / theory and experiments were observed. The prominent among them were Blackbody Radiation, the Photoelectric effect, Basic Atomic Theory, Compton Scattering etc. as follows

Blackbody Radiation

A lot of experimental data showed that a heated solid object (called as Blackbody) emits radiation which consists of continuous energy distribution having frequency range from ultraviolet to infrared. This data related to the phenomenon of exchange of energy between radiation and matter could not be explained properly by the theories of Classical physics (Maxwell's equations in Electrodynamics and Boltzman’s Equipartition Theorem in Statistical Mechanics). According to the classical theory, the radiant energy density approaches infinity as the frequency of light is increased in the ultraviolet (UV)\, region. This problem was known as the "UV\, catastrophe". However, this trend was not observed in the experiments. On the contrary, the radiant energy density was found to decrease with the increasing frequency in the UV\, spectrum. Also there was not a single formula which could model the experimental observations throughout the entire radiation spectrum.

The Photoelectric effect

When light falls on certain metals, electrons are knocked out of solids. This phenomenon known as the photoelectric effect was found to be difficult to explain on basis of electromagnetic theory and Maxwell's equations due to the experimental observations as follows

\ast There was no emission of electrons for frequencies of the incident radiation below a particular frequency (called as the threshold frequency, v_{th}\,), characteristic of the material.

\ast The number of ejected electrons increases for increase in intensity above v_{th}\,

\ast The kinetic energy of the ejected electrons does not depend on the intensity of radiation

\ast There is no time lag between the emission of electrons and irradiation for frequency > v_{th}\,

Basic Atomic Theory:

Fig. Consequences of the Rutherford’s Atomic Model

According to the Rutherford’s planetary model of the atom, electrons revolve around the nucleus in circular orbits. But according to classical electromagnetic theory, accelerated charged bodies (orbiting electrons in the atom) would emit energy as electromagnetic radiation of continuously increasing frequency and produce a continuous spectrum. Due to this emission, electrons should lose energy and spiral into the nucleus i.e. electron orbits would be unstable. However it was observed that atoms were stable.

From numerous experiments, large data was available that showed that emission and absorption of light from luminous gases did not comprise of a continuous range of wavelengths, but it consisted of discrete lines having a regular series of different frequencies (colors) which were characteristic /unique for different gases (unique radiation fingerprint). An empirical formula for the frequencies of spectral lines was fitted by Balmer (1885) as follows

v = C\ast\left(\frac{1}{2^2}-\frac{1}{n^2}\right) where n = 3,\,4,\,5,\,6

ν = Frequency of radiation, n= no. of the orbit, C = Balmer’s Constant

However, the physical basis of above formula could not be explained by classical theory. Thus the two facts the existence of a stable atom and the discrete spectral lines due to radiating gas atoms were contradictory to each other. It had remained an unsolved puzzle.

Compton Scattering:

In the experiments on the interaction of X-rays with matter, it was seen that when a beam of X-rays is targeted at an atom, an electron is ejected and is scattered through an angle \theta\,. According to Classical electromagnetism theory, the wavelength of scattered rays should be equal to the initial wavelength. However, the wavelength of the scattered X-rays was found to be greater than the initial wavelength in different experiments. This observation could not be explained on the basis of wave phenomena of light.

Summary

Classical Physics accurately described most systems of the macro-world that can be easily observed with naked eyes. Objects that were of a "normal" size (larger than a molecule), at a "normal" temperature (of the order of room temperature), moving at a normal speed (values significantly less than the speed of light) behaved consistent with the models developed in classical physics. However, when the system under observation was found to go beyond these limits (i.e. belonged to the micro-world as in the above cases), then the laws of Classical Physics were seen to be violated.

References:

\ast http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=1295#wrapper Steven Pollock, “Great Ideas of Classical Physics”

\asthttp://www.lhup.edu/~dsimanek/ideas/allabout.htm Donald E. Simanek, “What's Classical Physics All About?”

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