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Home , Curved space, Einstein field equations, Equivalence principle, General relativity, Karl Schwarzschild, Parallel (geometry)

A GRAND TOUR OF

GENERAL RELATIVITY

LECTURE 5

APR. 19, 2019 DR. GEORGE DERISE 1:30 – 3:30 PROFESSOR EMERITUS, TNCC THOMAS NELSON COMMUNITY COLLEGE ROOM 328. SPRING 2019

A QUICK SURVEY OF NON-EUCLIDEAN

PARALLEL POSTULATE

EUCLIDEAN GEOMETRY: Through a given P, not on a given L, there is one and only one line that can be drawn through P to L.

MODEL OF A GAUSS-BOLYAI-LOBATCHEVSKI NON :

ABSTRACT GBL GEOMETRY MODEL

ENTIRE OF A SADDLE POINT POINT ON THE SADDLE LINE OF THE SADDLE

GBL THROUGH A GIVEN POINT P, NOT ON A GIVEN LINE l, THERE ARE AT LEAST TWO LINES THROUGH P PARALLEL TO l .

MODEL OF A GAUSS-BOLYAI-LOBATCHEVSKI NON EUCLIDEAN GEOMETRY:

ABSTRACT GBL GEOMETRY MODEL

ENTIRE PLANE SURFACE OF A PSEUDOSPHERE POINT POINT ON THE PSEUDOSPHERE LINE GEODESIC OF THE PSEUDOSPHERE GBL PARALLEL POSTULATE HOLDS! MODEL OF A RIEMANNIAN NON EUCLIDEAN GEOMETRY:

BERNHARD 1826-1866 KARL FRIEDRICH GAUSS

86o 13' 58.366'' 53o 6' 45.642'' 40o 39' 30.165'' 180o 00' 14.173'' Can a bug living on a two dimensional surface determine the geometry of the surface?

INTUITIVE IDEA OF K=0 IN THE PLANE INTUITIVE IDEA OF CURVATURE 2 DIMENSIONAL Why are we doing this math?

IS THERE A “ OF ATTRACTION” BETWEEN A AND B ?

GENERAL RELATIVITY - “THERE IS NO FORCE” -IT’S JUST THE GEOMETRY

APPLE’S SURFACE- MODEL OF

ANT GOING ALONG A GEODESIC- LINE THROUGH SPACETIME OF A FREE PARTICLE STEM OF APPLE- BENDING OF SPACETIME BY A

LOCALLY THE APPLE IS

There is no experiment that will discern the difference between the effect of and the effect of .

GRAVITATIONAL MASS ~ INERTIAL MASS ...I know now that if I break my neck by falling off a cliff, my death is not to be blamed on the force of gravity (what does not exist is necessarily guiltless), but on the fact that I did not maintain the first curvature of my world-line, exchanging its security for a dangerous geodesic. Relativity- the General J.L. Synge

CONNECTING THE EQUIVALENCE PRINCIPLE WITH THE GEOMETRY OF SPACETIME:

THE OF THE EARTH AROUND THE IS A GEODESIC IN 4 DIMENSIONAL SPACETIME- I.E. THE SHORTEST 4 DIMENSIONAL SPACETIME BETWEEN TWO POINTS. (GEOMETRY). NEWTON: FORCE = MASS x ACCELERATION (PHYSICS) TELLS HOW TO , AND TELLS MATTER HOW TO MOVE. JOHN WHEELER GENERAL RELATIVITY

SPACETIME: 4 DIMENSIONAL RIEMANNIAN

THE CURVATURE OF THE 품흁흂 is related to THE MATTER- DISTRIBUTION OF SPACETIME

by EINSTEIN’S

푮흁흂 = ퟖ흅푻흁흂

CURVATURE OF SPACETIME ~ ENERGY OF MATTER

GEOMETRY ~ PHYSICS HILBERT GOT EINSTEIN’S FIELD BY USING AN PRINCIPLE 5 DAYS BEFORE EINSTEIN

GENERAL RELATIVITY EXPERIMENTAL VERIFICATION EXPEDITION -1919

GRAVITATIONAL LENSING: The of a massive object causes rays passing close to that object to be bent. Mass bends light. OF THE

POUND-REBKA EXPERIMENT 1960 HARVARD PHYSICS TOWER Top-bottom difference: 1 in 100 million

verified Einstein’s 1911 that gravity could change light’s frequency.

GRAVITATIONAL GPS

accuracy of 5 to 10 meters

24 satellites with atomic

Special Relativity predicts clocks on the satellites fall behind clocks on the ground by 7 microseconds per

General Relativity predicts clocks on the satellites get ahead of clocks on the ground by 45 microseconds per day.

combining these two relativistic effects: the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38) PHYSICS = GEOMETRY

GRAVITATIONAL : Disturbances in the curvature (fabric) of spacetime generated by accelerated that propagate as waves outward from their source at the .

First proposed by Henri Poincaré in 1905

Predicted by Einstein Theory of General Relativity-1916.

Gravitational waves transport energy as gravitational , a form of radiant energy similar to electromagnetic radiation.

LIGO: The Laser Interferometer Gravitational- Observatory (LIGO) is a large-scale physics experiment and observatory to detect cosmic gravitational waves.

The first direct observation of gravitational waves - September 2015. The waves given reached Earth as a ripple in spacetime that changed the of a 4-km LIGO arm by a ten thousandth of the width of a (proportionally equivalent to changing the distance to the nearest outside the by one hair's width.) Far field solution of Einstein’s The - of Einstein’s Field Equation on a wall of Museum Boerhaave, Leiden Gravitational lensing phenomena-deflection of light by an intervening mass (1873–1916) SCHWARZSCHILD HOLE SOLUTION

SCHWARZSCHILD METRIC VALID SOLUTION OF THE

BLACK HOLES A hole in space-time Black: even light can’t escape

2GM r 3KM SUN c2

Density= 20,000million tons/cubic cm NO HAIR : John Wheeler “ A has no hair.” A black hole has only three characteristics (1) mass (2) angular (3)

WILL THE EXPAND FOREVER? A CYCLIC UNIVERSE CYCLIC UNIVERSE R(t)

t

NO - SINGULARITIES HARMONIC OSCILLATING UNIVERSE

COSMIC MICROWAVE BACKROUND RADIATION (CMBR)

Remnant Electromagnetic radiation from the Big Bang Cosmic microwave background first predicted -1948; first observed -1965

NASA's Cosmic Background Explorer (COBE): 1989 - 1993

NASA-PRINCETON’S Wilkinson Microwave Probe (WMAP): 2003 - 2012

EUROPEAN SPACE AGENCY (ESA)’s Planck Space Observatory 2009 - 2013

41 COBE: Black-body curve of CMB First “baby pictures” of the Universe Intrinsic anisotropy of CMB-detecting early

WMAP: Mapped the pattern of tiny fluctuations in the CMB radiation (the oldest light in the Universe) Produced the first fine-resolution (0.2 degree) full-sky of the microwave sky Measured the fluctuations of density in the early universe that produced the first galaxies

Determined the universe to be 13.77 billion years old to within a half percent Nailed down the curvature of space to within 0.4% of "flat" Euclidean

Determined that ordinary atoms () make up only 4.6% of the universe Completed a census of the Universe - (matter not made up of atoms) is 24.0% , (cosmological const.) makes up 71.4% of the Universe

PLANCK SPACE OBSERVATORY: Mapped the of the CMB at microwave and infra-red frequencies Improved on WMAP Confirmation of the Universe having a 26% content of dark matter Validation of the simplest models of WHY INFLATION? PROBLEMS WITH THE STANDARD BIG BANG

WHY IS OUR UNIVERSE SO HOMOGENEOUS? (BETTER THAN 1:10,000)

WHY IS IT ISOTROPIC?

WHY ALL OF ITS PARTS STARTED EXPANDING SIMULTANEOUSLY?

WHY IS IT FLAT?

INFLATION MAKES THE UNIVERSE FLAT, HOMOGENEOUS AND ISOTROPIC

IN THIS SIMPLE MODEL THE UNIVERSE TYPICALLY GROWS 101000000000000 DURING INFLATION.

HAWKING RADIATION (1974)

BLACK HOLES ARE NOT ENTIRELY BLACK BUT EMIT SMALL AMOUNTS OF

BEKENSTEIN-HAWKING FORMULA

A S= ퟒ SU(3) x SU(2) x U(1) OF