A GRAND TOUR OF PHYSICS MATHEMATICS) · The Elegant Universe: Superstrings, Hidden Dimensions, and...
Transcript of A GRAND TOUR OF PHYSICS MATHEMATICS) · The Elegant Universe: Superstrings, Hidden Dimensions, and...
QUANTUM MECHANICS
GENERAL RELATIVITY
A GRAND TOUR OF PHYSICS
DR. GEORGE DERISE PROFESSOR EMERITUS, MATHEMATICS THOMAS NELSON COMMUNITY COLLEGE SPRING 2019
(WITH A BIT OF MATHEMATICS)
MAR 22-APR 26, 2019 1:30 – 3:30 TNCC ROOM 328.
A GRAND TOUR OF PHYSICS
DR. GEORGE DERISE PROFESSOR EMERITUS, MATHEMATICS THOMAS NELSON COMMUNITY COLLEGE SPRING 2019
MAR. 22, 2019 1:30 – 3:30 TNCC ROOM 328.
CLASSICAL MECHANICS
LECTURE 1
A GRAND TOUR OF PHYSICS-DR. GEORGE DERISE PROFESSOR EMERITUS, MATHEMATICS THOMAS NELSON COMMUNITY COLLEGE (HISTORIC TRIANGLE) FRIDAYS; MARCH 22 – APRIL 26, 2019: 1:30 – 3:30; ROOM 328.
GOOD WEBSITES: Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/ Khan Academy: https://www.khanacademy.org/ Wikipedia: first paragraphs or introduction usually accessible. YOUTUBE LECTURES: Just search appropriate topic "… youtube"
BOOKS: The Fabric of the Cosmos: Space, Time, and the Texture of Reality: Brian Greene The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory: Brian Greene Fearful Symmetry: A. Zee Particle Physics in the Cosmos (Readings from Scientific American Magazine)
TOPICS: 1. CLASSICAL MECHANICS 2. ELECTRICITY AND MAGNETISM SPECIAL RELATIVITY 3. QUANTUM MECHANICS 4. PARTICLE PHYSICS 5. GENERAL RELATIVITY 6. ADVANCED THEORIES- SUPERSYMMETRY QUANTUM GRAVITY- STRING THEORY CONSTRUCTING THE UNIVERSE ?
CONCEPTS: SYMMETRY BEAUTY IN PHYSICS - IN MATH? SIMPLICITY; ONE ‘THEORY OF EVERYTHING’? GENERALIZATION A BIT OF MATH??
Symmetry is a type of invariance: the property that something does not change under a set of transformations.
“ I am quite convinced; and, believe me, if I were again beginning my studies, I should follow the advice of Plato and start with mathematics, a science which proceeds very cautiously and admits nothing as established until it has been rigidly demonstrated. ”
GALILEO GALILEI LINCEO DIALOGUE ON THE TWO CHIEF WORLD SYSTEMS 1632
If you wish is to become really a man of science, and not merely a petty experimentalist, I should advise you to apply to every branch of natural philosophy, Including mathematics.
If an integer n is greater than 2, then the equation has no solutions in non-zero integers a, b, and c.
FERMAT’S LAST THEOREM (NUMBER THEORY)
𝑎3 + 𝑏3 = 𝑐3
𝑎4 + 𝑏4 = 𝑐4
𝑎5 + 𝑏5 = 𝑐5
. . .𝑎𝑛 + 𝑏𝑛 = 𝑐𝑛
Any relevance to physics at all?
AXIOMATIC METHOD (example: EUCLIDEAN GEOMETRY)
1. Undefined terms ( point, line; plane; between) 2. Axioms ( given two distinct points, there exists one
and only one line connecting them.) 3. Definitions (angle, triangle, polygon) 4. Theorems (the sum of the angles of any triangle is
exactly 180 degrees… the Pythagorean Theorem... …There exists exactly Five Platonic Solids)
The primary criterion for an axiomatic system is...
consistency
the order of magnitude of the earth-sun distance is 1011 m.
speed of light, c = 3 x 108 m/s; the order of magnitude of c is 108 m/s.
the size of the Milky Way Galaxy is 10 orders of magnitude greater than
the earth-sun distance.
KEPLER’S MYSTERIUM COSMOGRAPHICUM (1596) “Geometry is one and eternal shining in the mind of God”. (letter to Galileo, 1610 )
WILLIAM THOMSON - LORD KELVIN
THE THEORY OF VORTEX ATOMS (1867)
Stability of atoms accounted for by the stability of knots.
Large number of knot types can accommodate all the different elements.
Vibrational oscillations of knots could be the mechanism for atomic spectral lines.
“Geometry, which before the origin of things was coeternal with the divine mind and is God himself.” HARMONICES MUNDI 1619
KEPLER: THREE LAWS OF PLANETARY MOTION (1609-1619)
1. The orbit of every planet is an ellipse
with the Sun at one of the two foci. (1609) 2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. (1609) 3. The square of the orbital period of a planet is directly proportional to the cube of the semi major axis of its orbit. (1619)
CURRENT VALUES: Orbital Period 29.5 years Semi-Major Axis 9.58 AU D= 890.56 million miles
886.65 million miles
s = 16 t 2
400 = 16 t 2
25 = t 2
5 = t
How long would it take to die when leaping off a 40 story building?
SIR ISAAC NEWTON (1642-1726)
THREE LAWS OF MOTION, LAW OF GRAVITATION, INVENTED CALCULUS PHILOSOPHIAE NATURALIS PRINCIPIA MATHEMATICA
John Couch Adams Urbain Le Verrier
MATHEMATICAL DISCOVERY OF NEPTUNE 1846
LAPLACE'S DEMON the first published articulation of causal or scientific determinism, Pierre-Simon Marquis de Laplace (1814). If the Demon knows the precise location and momentum of every atom in the universe, their past and future values for any given time known by him, the future and the past can be known precisely from the laws of classical mechanics.
Pierre-Simon Laplace, "A Philosophical Essay on Probabilities” 1814
BASIC ASSUMPTIONS OF CLASSICAL MECHANICS
Classical dynamical variables, e.g. position, x momentum, mv kinetic energy, 1/2mv2 take on continuous values.
These dynamical variables satisfy a law (usually a differential equation) GLOBAL initial conditions and / or boundary conditions LOCAL
CLASSICAL MECHANICS: DETERMINISTIC
A state of a system is represented by giving the positions and velocities
of all the particles at a given time t.
This is equivalent to require the uniqueness of the solution of the
Newton's equations once initial conditions are specified.
LAW OF CONSERVATION OF ENERGY In a closed system the total amount of energy is conserved i.e. does not change. Energy may change from one form to another, but the total amount of energy in the closed system remains constant.
2015-04-22 at 2230 GMT,
left to right:
Europa, Io, Ganymede, Callisto. https://astronomy.stackexchange.com
Newtonian Mechanics A.P. French. 1971. p289
FOR ONE PARTICLE TRAVELING IN 3 SPACE WE NEED SIX COORDINATES; THREE TO SPECIFY POSITION THREE TO SPECIFY MOMENTUM, THUS WE HAVE A 6 DIMENSIONAL SPACE.
whatever shape a bubble has initially, it will try to become a sphere.
sphere - the shape that minimizes the surface area the shape that requires the least energy
“ACTION PRINCIPLE” IN PHYSICS
“Les loix du movement…” 1746
“I…have discovered a universal principle on which all
laws are based… This is
the principle of least action
(a physical quantity called ACTION
tends to be minimized)
a principle so subtle as to be worthy of a supreme
being.”
Pierre-Louis Moreau de Maupertuis
WHY DOES THE BALL FOLLOW A PARABOLIC TRAJECTORY?
THERE IS A MATHEMATICAL EXPRESSION CALLED THE ACTION MINIMIZE THE ACTION: THAT WILL GIVE YOU THE EXACT PARABOLIC TRAJECTORY!
RICHARD FEYNMAN: it [the particle] smells all the paths in the neighborhood and chooses the one that has the least action by a method analogous to the one by which light chose the shortest time.
NOETHER’S THEOREM: CONSERVATION LAWS FOLLOW FROM THE SYMMETRY PROPERTIES OF NATURE.
If a system has a continuous symmetry, then there are corresponding quantities whose values are conserved in time.
SPACETIME SYMMETRIES
INDEPENDENCE OF TIME → ENERGY CONSERVATION.
INDEPENDENCE OF POSITION → MOMENTUM CONSERVATION.
INDEPENDENCE OF DIRECTION → ANGULAR MOMENTUM CONSERVATION.
If the Lagrangian is invariant under a transformation, then there is a conserved quantity.
Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point A to another B in the least time.
THE BRACHISTOCHRONE PROBLEM: