Lecture III : Jan 30, 2017

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1 Lecture III : Jan 30, 2017 Prequantum Era Particles & Waves Reading Assignment: Chapter 2 and 3 from Quantum Physics for Poets. Summarize your thoughts with some questions/comments. ( One page writeup Due Next Monday, Feb 6, 2017 ) Classical or prequantum era rests on two pillars: Galilean/Newtonian mechanics ( 17 century ) Laws of Electricity, Magnetism and Light ( Maxwell s Equations ) Nature is complex. However, mathematics provides a universal language that reveals secrets of nature, showing its simplicity, universality and common sense symmetries. Physics has a history of synthesizing many phenomena into a few theories. We believe that there is one theory ( or perhaps just one equation ) that can explain everything... THEORY OF EVERYTHING... Laws of Physics The language of mathematics reveals itself unreasonably effective in natural sciences...a wonderful gift which we neither understand nor deserve..... Eugene Wigner, 1960 How do we find the laws.. Guess... To check the laws, scientists try to test them in real world, in their laboratories.. After many testing, the guess gets accepted and becomes a Law. Some people continue to doubt the law ( even though the majority accepts it ) and this sets the stage for next revolution... For example, almost all physicists who developed QM did not believe in the validity of their own work... Like Planck, Einstein, Schrödinger,... 1

2 We start with what is known as the Newtonian Period or Newtonian Science ( ). Sir Isaac Newton explained how particles move... Laws of Motion. PARTICLES: The Classical or Newtonian physics, is solely based on one single mathematical equation that describes the motion of the particle. This equation, known as Newton s equation says that Force acting on a particle is equal to its mass m times acceleration. F = ma (1) The beauty of this equation is, it applies to all particles, no matter whether it is on the earth, or in space or on Mars. It applies to all kinds of forces, such as gravitational force or electric or magnetic force. In those days, Sir Isaac Newton s theory could explain motion, sound, heat etc... For example, phenomena of sound can be understood as motion of atoms in the air... Heat is also related to random motion of particles... So it is all Newton s theory..., heat, sound and motion of planets or anything else.. WAVES In classical physics, particle and waves are two different things... When we think of waves, we think about waterways, sound waves and also light waves.. After the synthesis of the phenomena of motion, sound and heat, there was discovery of a number of other phenomena that we call electrical and magnetic. In 1873 these phenomena were synthesized with the phenomena of light, and in fact all other radiations like X-rays, ultraviolet, radio waves... There is a single theory that describes all these, theory by James Clerk Maxwell. Maxwell combined theory of electricity, magnetism and light in four equations, known as Maxwell s equations. You might wonder what light has to do with electric and magnetic phenomena. It turns out 2

3 light or X-rays are waves that travel in vacuum ( unlike sound waves that require medium like air ) and these waves are made up of oscillating electric and magnetic fields... ( will talk more about it later...) Can you think of some phenomena that you believe fall outside these theories.. ( except beauty, love.. sorry, happiness..) A. Characterization of Waves Figures 1 and 2 illustrate how to characterize waves. Note the following: Humans can hear sound waves with frequencies between about 20 Hz and 20 khz. Sound above 20 khz is ultrasound and below 20 Hz is infrasound. In air at standard temperature and pressure, the corresponding wavelengths of sound waves range from 17 m to 17 mm. Other animals have different hearing ranges. Loudness ( energy) is associated with the amplitude of the wave and pitch is associated with the frequency. Compare this with light: for light waves, intensity is determined by amplitudes and color is determined by frequency. Visible light is usually defined as having wavelengths in the range of nanometres (nm),, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). This wavelength means a frequency range of roughly terahertz (THz) T Hz = Speed of sound is approximately 300 = m/sec. Compare this with the speed of light which is m/sec. There are two main types of waves (1) Mechanical waves propagate through a medium. Examples are sound waves and water waves. Sound waves propagate via air molecules colliding with their neighbors. When air molecules collide, they also bounce away from each other. This keeps the molecules from continuing to travel in the direction of the wave. Wave equation in this case can be obtained 3

frequency = 1/period velocity=frequency * wavelength FIG.

(2) Electromagnetic Waves: The second main type of wave, electromagnetic waves, do not require a medium.

particles, and can therefore travel through a vacuum.

4 frequency = 1/period velocity=frequency * wavelength FIG. 1: Schematic diagram characterizing waves from Newton s equation. (2) Electromagnetic Waves: The second main type of wave, electromagnetic waves, do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles, and can therefore travel through a vacuum. These waves include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. These waves are described by equations called Maxwell s equations which cannot be obtained from Newton s law. 4

5 FIG. 2: Colors of the waves from the sun Spectrum of radiations from H-atom. Note the unit nm means nano meters, that is 10 9 m. 5

Lecture I REVOLUTION that began in To check the laws, scientists try to test them in real world, in their laboratories..

Revolutions are celebrated when they are no longer dangerous...... Pierre Boulez, on!3 Jan, 1989 on bicentennial celebration of the French Revolution 1 Lecture I REVOLUTION that began in 1900... Quantum