CCOSMOLOGICAL MODELS ================= John Pazmino NYSkies Astronomu Inc nyskies@nyskies.org www.nyskies.org 1994 July 27 initial 2017 October 9 current Recent Astronomy Seminar ---------------------- The Recent Astronomy Seminar was a twice-monthly discussion group of astronomers in the New York area. It was conducted by the Amateur Astronomers Association in Yorkville, Manhattan, thruout the year, rain or shine. Topics were drawn from the current litterature and experiences of the members. Many sessions feature handouts, slides and videos, and computer demonstrations and simulations. In January 2005 the Seminar was converted to a 'members-only' function. These meetings were no longer announced thru NYC Events, NYSkies yahooogroup or other public medium. 1By summer 2005 the seminar skipped posting sessions for the coming fall season. and was terminated as an Association function. NYSkies Astronomy Seminar ---------------------- In March 2005 NYSkies began its own series of astronomy meetings for local astronomers. It is free and open to the public, the NYSkies Astronomy Seminar. The sessions convened in Chelsea, Manhattan, on the first and third Thursdays of each month. Topics are drawn from the current litterature and experiences of the members. Sessions may feature handouts, topical talks, slides and other visuals, and demonstrations and simulations. Notices of the meetings are in NYC Events, the NYSkies monthly roster of astronomy and related activities in New York, This was at first issued in the NYSkies yahoogroup and several astronomy Internet newsgroups. NYC Events, with the Seminar announcements, shifted to the NYSkies web on October 2007 but remained in the newsgroups until about 2010. With the global attraction of the web, the newsgroup posting of NYC Events was ended. The Seminar now meets, on first and third Fridays of every month, on 14th Street bordering Chelsea and Greenwich Village, Manhattan. Details about the NYSkies Astronomy Seminar are at www.nyskies.org/seminar.org In addition to NYC Events, meeting notices ar sent to astronomers thru a separate mailing list several days before each session. The notice describes the topics and sometimes offer late-breaking astronomy news. 'Cosmological Models' Paper ------------------------- This paper on cosmology is a living textbook based on the debates, comments, discussions, announcements at NYSkies Astronomy Seminar meetings, starting in March 2005. Prior to then, until the fall 2004 edition, it was released at the Recent Astronomy Seminar of Amateur Astronomers Association. Discs with files for the paper were distributed to the members only at the Seminar. Any astronomer may stop in at the next Seminar meeting and get the latest edition during the distribution season. Issuance by Internet email was limited due to the slow speed connections still in wide use then. Altho the paper is continuously revised, new discs were distributed only twice per year near the equinoctes. The first was handed out in September 1994 and continued until the treatise was uploaded into the new NYSkies yahoogroup in march 2001. 'Cosmological Models' Disc ------------------------ The computer disc for 'Cosmological Models' was a standard 90mm hi-density stiffy disc with 1.44 megabyte capacity for use in IBM operating systems. Some The fisc contents erre plain textfiles with no peculiar chars or sodes embedded in them. The files could be viewed and printed thru a word-processing software. The disc contained the complete paper with each chapter held in a separate textfile. The filenames were shown in the table of contents in the file '00100.txt'. You replaced just the revised files, as indicated by the filedates in the directory listing. New files whose dates match or precede those on your old disc can be disregarded. ' Cosmological Models' in NYSkies ------------------------------ The NYSkies yahoogroup opened in January 2001 for a rapid announcment service and discussion forum among New York astronomers. One of the earlier features of the NYSkies uahoogroup was the uploading in March 2001 of the 'Cosmological Models' disc into its article section. Then after the disc itself was no longer handed out. The yahoogroup collapsed in Septembr 2001, a follateeral vicitim of the World Trade Center attavcks. It was revived later in September 2001 with most of its contents restored, including the 'Csomological Models' disc. A notice in the yahoogroup called attention to new or revised files. Over the years the 'Cosmological Models' paper expanded to cover important, but poorly treated, subjects relating to cosmology. Along the way the files were increasingly disorganized and ell into severe need of massive reworking. In fall of 2017 this work bean by first combining associated short files into a single larger one and clarifying the notation in maths. The first new portions, now loaded into the NYSkies web, cover special relativity, general relativity, gravity, and blackholes. The progress is slow but steady. Announcements of new material are posted in the NYSkies yahoogroup. The files were revised or added irregularly since 2001. The initial date, posted above, of 1994 July 27 is that of the earliest surviving set of textfiles. When any one of the newly revamped files is modified, its modification date becomes the current date, entered above, for the entire treatise. The original collection of 'Cosmological Models' files is no longer updated. As they are gathered into the new chapters they are archived in their final state. Introduction ---------- This treatise on cosmological models does contain dense letterpress and maths. The paper aims to give the home astronomer a sound and proper tuition in cosmology, beyond the mish-mash of facts and stories so commonly offered to them. Cosmology, while attractive to home astronomers, is not a simple or easy subject to understand. The text and equations are an integral feature of learning cosmology. They do call for close attention. Conversance in first-year college maths and astronomy is presumed in order to follow this treatise of the cosmological models. The maths freely use algebra and some simple calculus, but very little trginometry. Due to typographic constraints, all maths are written in a BASIC or FORTRAN style without the fancy symbols of typeset works. .Formulae and equations are written as one line, sometimes with wrap to a second line, like extra-long web addresses. You may have to knit the lines together. Certain operations are treated like functions. For example '1der(x,y)' means 'first derivative of x relative to y'. Symbols are written out. 'SIGMA' means 'large-sigma' and 'sigma' means 'small- sigma'. When a derivation or conversion is discussed, each step is set out, not just the end result. Table of Contents -------------- This treatise consists of separate chapters, each a separate file. Because chapters may avail of mateial in previous chapters, the files should be studied in sequence within each series, between the '- - - ' separators. In the entries here only those with proper names, like 'Newotn's universe', are linked to actual files in the NYSkies web. Those with a numbered name, like '004000', are old files not in this web. Over time tte old filesy will be gathered into new files under proper names, updated, and cleaned. Eventually all files, minus those no longer useful, will be collected into the "Cosmological Models' book here. Please check back here from time to time for the new files. - - - - - - - - - -NEWTON'S UNIVERSE-- Newton's Universe - Early Problems - Impossible World - Gravitation under Newton - Definition of Force - Two Interpretations of Field StrengthEINSTEIN'S UNIVERSE-- Cosmological Principle - Newton versus Einstein Physics - The Lambda Force - The Acceleration of the Universe - Energy of the Universe - Friedmann Model - The Standard or Classical Model - Hubble Parameter - Hubble Time - The Redshift in Galactic Spectra - Expansion or Hubble Redshift - Time Dilation - Hubble Expansion vs Recession Velocity - What's Going On Here? - Milne & McCrea's Trick - 17th Century Cosmology? - MisinterpretationsCOSMOLOGY APPLICATIONS-- Scalefactor Function of Time - True Age of the Universe - Deceleration Parameter - Density Parameter - Radius of the Universe - Mass of the Universe - Is the Universe a Blackhole? - Proper or Einstein Distance - Hubble Horizon -- Enclosed Volume - Light Travel or Lookback Time -Inverse-Square Law - Spectroillumination - Hubble Expansion of lambda - Magnitude-Distance Relation - Angular Diameter - Angular Spectroillumination - - - - - - - - - - 06100 Electromagnetic Radiation -- Frequency versus Wavelength -- Haphazard Nomenclature -- Disparate Units of Measure -- Detection of EMR -- Miracle of Electromagnetic Radiation 06120 Ampere's Law -- Faraday's Law -- Lenz's Law -- Orthogonal Fields -- Lines of Force -- Potential Surface -- Inverse Square Law 06140 Gauss's Law for Charge -- Gauss's Law for Poles -- Gauss's Law for Mass -- Cosmic Implications -- Maxwell's Equations -- Waves -- Maxwell's Waves 06160 mu0 and epsilon0 -- mu0 -- epsilon0 -- Magnetic Field Strength -- Magnetic Pole Strength -- Refraction of Light -- Cherenkov Effect 06180 Interacting Fields -- Electromagnetic Wave -- Creation of EMW -- Speed of EMW 06190 Energy of a Field -- Energy in EMW -- Root Mean Square -- Electric Field Overwhelms -- Irradiation -- Sun's Irradiation -- Sun's EMR Disturbance -- Electric Power Damage -- Radiation Pressure -- Radiation Momentum 06200 Spectroirradiation -- Irradiation -- Inverse-Square Law -- Arcspectroirradiation -- [Spectro]irradiosity -- Radiation-Area Law 06300 Light Is Nothing But EMR -- The Grand Delusion of Light -- Spectrosensitivity -- Photometric Units -- Spectroillumination -- Color Temperature -- Irradiation versus Illumination 06400 Mechanism of EMR -- Blackbody Spectroirradiosity -- Two Planck Constants -- Stefan-Boltzmann Law -- Wien Law -- Photon-Temperature Law -- Density-Temperature Law -- Blackbodies in Nature -- Lowest Temperature in Nature 06500 Mass/Energy Ratio -- The Bigbang Photosphere -- Cosmic Background Radiation -- Time and Place of the Photosphere -- The Bigbang 06600 Behavior of Heat -- Second Law of Thermodynamics -- Limit on Energy Conversion -- No Work from Single Reservoir -- Potential Work 06610 Entropy -- Irreversibility of Heat Engines -- Sun as a Heat Engine -- Waste Energy in the Universe -- Total Accumulated Entropy 06700 Randomness -- Boltzmann's Entropy -- Clausius's Method -- Boltzmann's Method -- Equivalence of Clausius and Boltzmann -- Number Density as Entropy 06800 Bigbang versus Starlight Radiation -- Conservation of Mass -- Entropy from Starlight -- Thermal History 07000 Nucleus -- Isotopes -- Internal Structure -- Units of Measure -- Symbols -- Pseudoelements -- Avogadro Number -- Mass Defect -- Nuclear Size -- Compared to Solar System 07020 Radiosiotopes -- Decay Rate -- Halflife -- Alpha Decay -- Beta Decay -- Gamma Decay -- Electron Capture -- Other Decays -- Summary of Decays 07040 Ionizing Radiation -- Ionization Detectors -- Scintillation Detectors -- Track Detectors 07060 Radiodating -- Suitable Materials -- Suitable Decays -- Ratio of Isotopes -- Major Flaw 07080 The Melt -- The Stable isotope -- Formation of Minerals -- Crystallization -- As the Rock Ages -- Calculation of the Age 07100 The Early Universe -- The Singularity of the Bigbang -- Geometrical and Physical Cosmology -- Antimatter -- No Antimatter -- Grandfathered Matter -- Matter-Antimatter Ratio 07150 Abundance of the Elements -- Helium in the Universe -- Origin of the Helium -- Nucleogenesis -- Regimes of Element Creation 07200 Introduction to Atomics -- Table of Particles -- Table of Interactions -- Reaction Kinetics 07300 Initial Conditions -- Conservation Rules -- Melding the Reactions -- Interaction Flowchart -- Other Reaction -- Chains -- Limits of the Simulation 07400 Why Stop at Helium? -- The Mass 5 and 8 Gap -- The Relics of the Bigbang 08000 Observational Difficulties -- Distance versus Redshift -- Hubble Parameter -- Deceleration Parameter 08100 Difficulties with the Standard Model -- Age Problem -- History of Ages 08110 Flatness Problem -- delOMEGA vs Time 08120 Smoothness or Horizon Problem -- Horizons 08130 Missing or Dark Matter Problem -- Dark Matter -- Candidates for Dark Matter 09000 NonEuclid Geometries -- Geometric Curvature -- Angles of a Triangle -- Curvature of the Universe -- Nonzero k 09010 Gravitational Curvature -- Bending of Starlight -- Visualizing 4- Dimensional Space -- Curvature in Strong Gravity Fields -- Inside the Blackhole 09100 Preparing the Scenarios -- k = 0, q = 1/2, rho0 = rho@ -- k = -1, q < 1/2, rho0 < rho@ -- k = +1, q > 1/2, rho0 > rho@ -- Recapitulation 09200 Neutrinos -- Neutrinos from the Bigbang -- Neutrinos as Dark Matter -- Neutrinos Not the Final Answer 09300 Orbits in 3D Space -- Other Dimensions -- Anthropical Cosmology -- Life in the Universe 09400 Physical Constants -- Mass of the Electron -- Doubleheavy Electron -- Halfheavy Electron -- Is All This an Accident? -- Maybe this is Uniquely Our Universe? 09800 Fastest Communication by Light -- Four Dimensional World -- What Can We See? -- Who Can See Us? -- The Observability Zones 10000 Historical Models of the Universe -- Diversity of Cosmological Models 11000 Alfven-Klein Universe -- Alpher-Bethe-Gamow Universe -- Arp Universe -- Bondi-Gold (Steady State) Universe 11100 Brans-Dicke Universe -- deSitter Universe -- deWitt (Many-Worlds) Universe -- Dirac Universe -- Eddington Universe 11200 Einstein (Original) Universe -- Einstein-deSitter Universe -- Godel Universe 11300 Guth (Inflationary) Universe -- Hoyle-Narlikar Universe -- leMaitre Universe -- leMaitre-Tolman Universe -- Milne Universe -- Tolman (Oscillating) Universe 12000 Recent Observations -- Texture and Clumpiness -- Primordial Galaxies -- Keck Deuterium -- Tidal Movements -- Nearby Supernovae 12100 Quasars -- Microwave Relic Radiation -- Tully-Fisher Distances -- M87 Blackhole -- Cepheid Variables -- Dark Galaxies - - - - - - - - - -STEADY STATE UNIVERSE-- Steady State Universe - Furtherance of the Bigbang Theory - Age Problem with the Bigbang - Singularity Problem with the Bigbang - Perfect Cosmological Principle - Hubble Parameter - Redshift - Density of the Universe - Proper or Einstein Distance - Luminosity Distance - Angular Diameter - Curvature of Space - Deceleration Parameter - Comparison with Acceleration/Energy - Continuous Creation - Nature of New Matter - Formation of Galaxies - Minibangs - Cosmic Microwave Radiation - Helium Abundance -- No Cosmology? - Closing Remarks - - - - - - - - - -SPECIAL RELATIVITY-- Einstein's Physics of Relativity - Time and Space-- Spacetime -Natural Gravity - Inertial Platform or Frame - Impossibilty of Absolute Rest - The Speed of Light - Maxwell's Laws-- Michelson-Morley Experiment - Laws of Physics - The Term 'Speed of Light' -Comparing Clocks-- The Scenario - Equation of Motion - Home and Target Frame - Spacetime Interval - Four Roads to Follow -The Newton Road - Einstein's Mistake? - Behavior of Time - Why Is this Case Wrong? - Einstein's Solution - Time Dilation - The Barrier of c - The Fourth CaseRELATIVITY APPLICATIONS-- Doppler's Debacle - Absurd Doppler Speeds - Fizeau's Fixup -Frequency and Wavelength - The Historical Blunder - Reality versus Perception -Observed Time DIlation - Einstein and Doppler-Fizeau - The Low-Velocity Approximation - The Missing Step - Space Travel Near c - Twin Paradox - Simultaneous Events - Spacetime Interval for Simultaneous Events - Platforms Can Not Agree - Simultaneous in Space and Time - Lorentz Transformation - Addition of Velocities -Comparison with Newton - Fizeau's Experiments --Shift of PlatformsGENERAL RELATIVITY-- Energy and Mass - dePretto's Ideas - Rest Mass-- Conservation Law - Mass into Energy - Energy into Mass-- Electron-volt -Critiques - Atomic Bombs - Atomic Power - Recycling of Fuel - New York Els -Mass Increase - Early ideas - Relativistic Mass - Mass- Energy Equation --- No Real Increase of Mass - Invariant MassGRAVITY-- A Bit of Newton Physics - Ideal Spherical Body - Gravity Outside a Spherical Shell - Gravity Inside a Spherical Shell -Gravity Field within a Solid Globe - Range of Applicability - Nonspherical Bodies - No Defense Against Gravity -Gravity is Cumulative - Gravity Field Strength - A Useful Equivalence - Gravity Work and Energy - Gravitational Potential Energy - Gravity Well - Escape Velocity

BLACKHOLES-- Schwarzschild Blackhole - Idealized Blackhole - Spacetime with Mass - Schwarzschild Surface or Radius - Schwarzschild Spacetime Schwarzschild Blackhole - Idealized Blackhole - Space tEquation - The Safe Frame - No Change of Gravity Regime - Time Dilation versus Distance - Nonsymmetrical Nonreciprocal Relation - Tests of Schwarzschild Spacetime - Redshift of Spectral Lines - ercury's Orbit Precession - Bending of Starlight - Astronomers Neglect Relativity - Features of Schwarzschild Spacetime - Near the Schwarzschild Surface - Length and Mass near a Blackhole - Geometry near the Schwarzschild Surface - Thermodynamics and Blackholes - The Singularity - Newton Escapes the Singularity - Einstein Mandates the Singularity - - - - - - - - - - 15000 Introduction to Quantum Physics -- The Hydrogen Atom -- Quantized Orbital Motion -- Energy Levels of Hydrogen -- Spectrum Lines 15100 Waves and Particles -- The Uncertainty Principle -- Role of Humans -- Quantum Reality 80000 Angle Measure -- Degrees of Angle -- Radians of Angle --Triangles -- Ratios of Sides -- Trigonometric Functions -- Special Angles -- Alternate Functions 80010 Some Relations -- Sine/cosine -- sin^2 + cos^2 -- Law of Sines -- Law of Cosines -- Summary of Relations -- Trig Operations -- Small Angles -- Arclength -- How Small is Small? 80020 Angles in Other Quadrants -- The Quadrants -- Limits of Functions -- Inverse Function -- Arcfunction 80100 Vectors -- Specifying Vectors -- Adding Vectors -- Subtracting Vectors -- Multiplying Vectors -- Dot Multiplication -- Angle between Vectors Cross Multiplication -- Special Cases 80200 Logarithms -- Logs as Powers -- Exponential Notation -- Symbolism -- Finding a Logarithm -- Uses of Logarithms -- Inverse Logarithm -- Changing Bases -- Logarithmic Progression -- Log of Trig Functions 80300 Units of Measure -- The Meter -- Meter as Derived Unit -- Meter, Metre - The Stadion -- Columbus's Earth -- The Kilogram 80310 The Second -- Secular Acceleration -- Ephemeris Second -- Atomic Second -- Leapsecond -- The Offset -- Coordinated Universal Time -- GPS Time 80320 Systems of Units -- Gauss Units -- Electrostatics -- CGS System -- Heavyside-Lorentz System -- Special Names 80330 MKS System -- Systeme Internationale -- 4*pi -- Special names -- Prefixes -- Binary Prefixes 80340 Europe Slowly Adapts -- America Stands Down -- Oldstyle Measures -- Metrics Percolate In -- Home Astronomy Metrics -- Vernacular Metrics -- The New Millennium -- The Future 80400 Standard Time - US Standard Time -- Greenwich Mean Time -- Universal Time -- Timezones -- Zulu -- Specifying Local Time -- International Dateline 80404 Daylight Savings -- US Daylight Savings -- Arizona and Hawaii 80410 Hours of the Day -- Minutes and Seconds -- 12x12 and 24 -- 12 AM, 12 PM -- Planetarium Clocks -- 12-Hour Dial -- Time Notation 80420 The Week -- Days of the Week -- Order of the Days -- Sequence of Weeks 80430 Year Numbering -- Julian Calendar -- Leapyear -- Proleptic Julian Calendar -- Gregorian Calendar -- Acceptance of Gregorian Calendar -- Date Notation -- Dates on Other Worlds -- Day Counts 90000 Olber's Paradox -- Mach's Principle -- Proton Decay 91000 Blackholes -- Density inside a Blackhole -- Destruction of Identity -- Four Kinds of Blackhole -- No Vacuum Cleaner or Drainhole -- No Funnel or Well -- No Tidal Shredding -- No Remote Relativity 92000 Tidal Forces -- Roche Limit -- Applicability of the Roche Limit -- Roche and Schwarzschild Limits 99000 Cosmological Tables -- Table of beta = (1-(V/c)^2)^(1/2) -- 99020 Table of Useful Values -- Older Metric Units 99100 References -- 1920s -- 1930s -- 1940s -- 1950s -- 1960s -- 1970s 99120 References -- 1980s -- 1990s 99140 References -- 2000s 99200 Anceint elements -- Naming elements -- International names -- Numerical names -- Loose latin 99300 Table of heavy elements -- Transuuranium -- Name confusion -- Atomic address 99400 Chart of Nuclei 99500 Symbols Used in the Boxed Equations