Lecture IV : Feb 1, 2017

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1 Lecture IV : Feb 1, 2017 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 ) Can you think of some phenomena that you believe fall outside Newton and Maxwell s theory.. ( except beauty, love.. sorry, happiness..) Einstein s Theory of Relativity I. THEORY OF RELATIVITY Newton s equation fail when particles travel at speed of light c = 10 8 m/sec. Proposed in 1905 ( called special theory of relativity ) and General theory of Relativity (1916) were not revolutionary theories.. There were considered extension of Newton s theory to particles moving close to speed of light It can be viewed as a kind of mini-revolution, as speed of light emerged as the largest speed possible in Newtonian world, in some sense linking particles and light. Brief Introduction of Einstein s theory The key point was the idea of space-time, space and time are correlated and mathematically treated on equal footing. Also, E = mc 2. (1) The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source. That means, two individuals, traveling on two trains moving in same direction will not feel that they are not moving... (2) Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion. 1

2 (3) Time dilation: Moving clocks are measured to tick more slowly than an observer s stationary clock. (4) Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer. Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable. Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum. General Theory of Relativity General relativity is a theory of gravitation developed by Einstein in the years Einstein first proposed that space-time is curved. equations which relate the curvature of space-time with matter and energy. In 1915, he devised the Einstein field General relativity generalizes special relativity and Newton s law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or space-time. In particular, the curvature of space-time is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations. R ab 1 2 Rg ab = 8πGT ab (1) The above equation means that space-time curvature = energy density. R and g describe the structure of space-time and T matter or energy that determines this structure. NOTE: YOU DO NOT NEED TO UNDERSTAND THIS EQUATION. However, you may find it fascinating that these few weird symbols encode all the complexity of the theory and that is what physicist call Mathematical Beauty. Some of the consequences of general relativity are 2

3 (1) Orbits precess in a way unexpected in Newton s theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars). (2) Rays of light bend in the presence of a gravitational field. General theory of Relativity is the key to GPS... something Einstein did not envision when he discovered his theory.. Distinguishing Particles and Waves in an Experiment Double Slit experiment distinguishes particles and waves: Particles: N 12 = N 1 + N 2 Waves: N 12 N 1 + N 2 Here N 1 represents particles, or intensities of waves ( or probability ) when slit 1 is open & Here N 2 represents particles, or intensities of waves ( or probability ) when slit 2 is open Here N 12 represents particles, or intensities of waves ( or probability ) when both slits 1 and 2 are open. Is electron a particle or a wave.. We do not know we cannot see it. We hoped that double-slit experiment can tell us... However, it cannot!!! Wave particle duality is at the heart of quantum physics... a revolution... II. SOME SCALES AND NUMBERS IN NATURE Size of an atom m = Angstrom.. Size of the Nucleus m = Fermi Smallest length scale Planck length m...the Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, 3

4 and the gravitational constant. The Planck length l p is defined as, G l P = m c 3 Note G, the gravitational constant and c the speed of light are constants from classical physics and is the constant from quantum physics. The Avogadro constant (named after the scientist Amedeo Avogadro) is the number of atoms, that are contained in the amount of substance given by one mole. That is one gram of H has atoms and so is the 238 grams of Uranium. NEXT REVOLUTION... Present Theory is inadequate... as there is no quantum theory of gravity.there will be a next revolution.. When.. We do not know... Newtonian physics survived for 200 years... How long Quantum Physics will survive, It has survived little more than 100 years... By that we mean there has been NO experiment that has violated the theory Although there has been no violation of the theory, it cannot explain gravity?? III. ALL FUNDAMENTAL FORCES AND ALL ELEMENTARY PARTICLES In this complex world, there are only four fundamental forces. All other forces can be expressed in terms of these four. Also, all particles of nature are build out of few particles shown in the table below. Note that There are two types of particles: Fermions and Bosons... Protons and neutrons are not elementary particles. They are made up of Quarks. Mass of the particles of expressed in the unit of energy divided by speed of light square ( E = mc 2 : m = E/c 2 ). To understand this, note that the mass of the electrons is about 0.5 and that of proton is about 1000 in this unit. 4

5 FIG. 1: Fundamental forces 5

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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