Zero-energy space cancels the need for dark energy Tuomo Suntola, www.sci.fi/~suntola/, Finlandwww.sci.fi/~suntola/ Mathematics, Physics and Philosophy.

Slides:



Advertisements
Similar presentations
MEASURING DISTANCES IN ASTRONOMY Basic Principles: Geometric methods Standard candles Standard rulers [the last two methods relate quantities that are.
Advertisements

Stellar Deaths II Neutron Stars and Black Holes 17.
Extragalactic Astronomy & Cosmology First-Half Review [4246] Physics 316.
Chapter 11 – Gravity Lecture 2
Lecture 20 Hubble Time – Scale Factor ASTR 340 Fall 2006 Dennis Papadopoulos.
The Mathematics of General Relativity, Black holes, and Cosmology Chad A. Middleton Brown Bag Seminar Mesa State College February 12, 2010.
Developing a Theory of Gravity Does the Sun go around the Earth or Earth around Sun? Why does this happen? Plato } Artistotle } Philosophy Ptolemy }& Models.
July 2005 Einstein Conference Paris Thermodynamics of a Schwarzschild black hole observed with finite precision C. Chevalier 1, F. Debbasch 1, M. Bustamante.
Symposium on philosophy and the empirical sciences 16:15Welcome Jaakko Hintikka: Natural philosophy in quantum theory and quantum theory in natural philosophy.
PRESENTATION TOPIC  DARK MATTER &DARK ENERGY.  We know about only normal matter which is only 5% of the composition of universe and the rest is  DARK.
How do we transform between accelerated frames? Consider Newton’s first and second laws: m i is the measure of the inertia of an object – its resistance.
EPPT M2 INTRODUCTION TO RELATIVITY K Young, Physics Department, CUHK  The Chinese University of Hong Kong.
PRE-SUSY Karlsruhe July 2007 Rocky Kolb The University of Chicago Cosmology 101 Rocky I : The Universe Observed Rocky II :Dark Matter Rocky III :Dark Energy.
Black Holes Old ideas for black holes Theory of black holes Real-life black holes Stellar mass Supermassive Speculative stuff (if time)
Physics 133: Extragalactic Astronomy ad Cosmology Lecture 4; January
Lecture 1: Basics of dark energy Shinji Tsujikawa (Tokyo University of Science) ``Welcome to the dark side of the world.”
Cosmological Models II Connecting Hubble’s law and the cosmological scale factor What determines the kind of Universe in which we live? The Friedman equation.
Gravitation Applications Lecturer: Professor Stephen T. Thornton
Chapter 12 Gravitation. Theories of Gravity Newton’s Einstein’s.
Lecture 21 Cosmological Models ASTR 340 Fall 2006 Dennis Papadopoulos.
GRAVITY.
Hubble Diagram: Distribution of Galaxies. Hubble’s Law: v = H o d Velocity increases with distance.
1 The Origin of Gravity ≡ General Relativity without Einstein ≡ München 2009 by Albrecht Giese, Hamburg The Origin of Gravity 1.
Black holes: do they exist?
Chapter 26 Relativity. General Physics Relativity II Sections 5–7.
Imperial College, LONDON, SEPTEMBER, 2008 From local to global relativity Tuomo Suntola, Finland Physical Interpretations of Relativity Theory XI.
Cosmology: The Study of the Universe as a Whole Physics 360 Geol 360 Astronomy John Swez.
O n t h e T r a c k o f M o d e r n P h y s i c s Equation of motion to post-Newtonian order In 1918 J. Lense and H. Thirring, noted from the general relativity.
Dark energy: the greatest mystery of the universe Syksy Räsänen Department of Physics and Helsinki Institute of Physics Arkadia.
Module 3Special Relativity1 Module 3 Special Relativity We said in the last module that Scenario 3 is our choice. If so, our first task is to find new.
Advanced mechanics Physics 302. Instructor: Dr. Alexey Belyanin Office: MIST 426 Office Phone: (979)
From Ptolemy skies to FLRW cosmology Hierarchy of physical quantities and theory structures The Dynamic Universe: The overall energy balance – cosmological.
NS 1300 Dr. Hoge.  Can we slow light down?  Can we make things invisible?  Is it possible to travel faster than the speed of light?  Is faster than.
Bending Time Physics 201 Lecture 11. In relativity, perception is not reality Gravity affects the way we perceive distant events For example, although.
The Hubble law beyond the General Relativity L.M.Tomilchik B.I.Stepanov Institute of Physics of NAS of Belarus N.G.Kembrovskaya Belarusian State University,
Fundamental Principles of General Relativity  general principle: laws of physics must be the same for all observers (accelerated or not)  general covariance:
The Tully-Fisher Relation A relation between the rotation speed of a spiral galaxy and its luminosity The more mass a galaxy has  the brighter it is 
Extragalactic Astronomy & Cosmology Lecture GR Jane Turner Joint Center for Astrophysics UMBC & NASA/GSFC 2003 Spring [4246] Physics 316.
Special Relativity & Radiative Processes. Special Relativity Special Relativity is a theory describing the motion of particles and fields at any speed.
Black Holes Chapter Twenty-Four. Guiding Questions 1.What are the two central ideas behind Einstein’s special theory of relativity? 2.How do astronomers.
Space and Unsolved Mysteries. Black Holes Form from the death of a very large star ( more than 25 solar masses). A supernova occurs followed by a black.
Dipole of the Luminosity Distance: A Direct Measure of H(z) Camille Bonvin, Ruth Durrer, and Martin Kunz Wu Yukai
Type Ia Supernovae and the Acceleration of the Universe: Results from the ESSENCE Supernova Survey Kevin Krisciunas, 5 April 2008.
Cosmic Inhomogeneities and Accelerating Expansion Ho Le Tuan Anh National University of Singapore PAQFT Nov 2008.
RELATIVITY Based on Physical Processes B udapest 2009 by Albrecht Giese Hamburg, Germany 1 The Physical Causes of Relativity.
The dark side of the Universe: dark energy and dark matter Harutyun Khachatryan Center for Cosmology and Astrophysics.
Astro-2: History of the Universe Lecture 10; May
Physics 55 Monday, December 5, Course evaluations. 2.General relativity with applications to black holes, dark matter, and cosmology. 3.Hubble’s.
Special Theory of Relativity (STR) Speed of light (in vacuum): c = 300,000 km/s Constancy of the speed of light: Michelson & Morley experiment No signal.
The Meaning of Einstein’s Equation*
General Relativity and Cosmology The End of Absolute Space Cosmological Principle Black Holes CBMR and Big Bang.
Gravitation in 3D Spacetime John R. Laubenstein IWPD Research Center Naperville, Illinois APS April Meeting Denver, Colorado.
The general theory of relativity 100 years The Finnish Society for Natural Philosophy, The House of Sciences, Helsinki November 10, :15Prof. Tapio.
Universe Tenth Edition
1 The Re-Physicalization of Physics by Albrecht Giese Hamburg, Germany Puebla The Re-Physicalization of Physics.
British Society for the Philosophy of Science School of Computing & Technology, University of Sunderland. Physics Dept., Bauman Moscow State Technical.
Soichiro Isoyama Collaborators : Norichika Sago, Ryuichi Fujita, and Takahiro Tanaka The gravitational wave from an EMRI binary Influence of the beyond.
Black Holes A stellar mass black hole accreting material from a companion star 1.
Quantitative expression of Mach’s principle The Finnish Society for Natural Philosophy, The House of Science and Letters, Helsinki March 9, 2016 Tuomo.
Cosmology The Models and The Cosmological Parameters Guido Chincarini Here we derive the observable as a function of different cosmological.
Restructuring of the Scientific Picture Scientific Models and a Comprehensive Picture of Reality, The Finnish Society for Natural Philosophy, Helsinki,
Machian General Relativity A possible solution to the Dark Energy problem and an alternative to Big Bang cosmology ? Robin Booth Theoretical Physics Imperial.
Special Relativity without time dilation and length contraction 1 Osvaldo Domann
Relativistic Universe
The general theory of relativity 100 years
Introduction: Big-Bang Cosmology
2.1 Basics of the Relativistic Cosmology: the Dynamics of the Universe
Derek Kan Khalid Mansour Ian Nickles
Cosmological Expansion and Dark Energy
Expressing n dimensions as n-1
Presentation transcript:

Zero-energy space cancels the need for dark energy Tuomo Suntola, Finlandwww.sci.fi/~suntola/ Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Latest PhysicsWeb Summaries : Dark-energy teams win cosmology prize (Jul 17) Two independent teams of researchers who discovered that the expansion of the universe is accelerating have been awarded this year's Gruber Cosmology Prize. The prize, worth $500,000, has been given to the groups led by Saul Perlmutter and Brian Schmidt, who reported their discovery in Their work provided the first convincing evidence for the existence of "dark energy" -- a mysterious and so-far invisible entity that physicists believe works against gravity to boost the expansion of the universe. 2

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Latest PhysicsWeb Summaries : Dark-energy teams win cosmology prize (Jul 17) … an alternative way of wording the news: Two independent teams of researchers who discovered that the magnitudes of high redshift supernovae do not follow the prediction of the standard cosmology model … have been awarded … 3

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Latest PhysicsWeb Summaries : Dark-energy teams win cosmology prize (Jul 17) … an alternative way of wording the news: Two independent teams of researchers who discovered that the magnitudes of high redshift supernovae do not follow the prediction of the standard cosmology model … have been awarded … … a concept of dark energy working against gravitation between galaxies has been suggested to fix the problem. 4

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy +SN Ia observations Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) z  Magnitude versus redshift: Supernova observations 5

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy +SN Ia observations Standard model with  m = 1,   = 0 Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) z  Magnitude versus redshift: Supernova observations 6

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy +SN Ia observations Standard model with  m = 1,   = 0 Standard model with  m = 0.3,   = 0.7 Suggested correction:  m = 0.3   = 0.7 (dark energy) Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) z  Magnitude versus redshift: Supernova observations 7

Angular size of galaxies and quasars Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy z log (LAS) (a) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) 8

Angular size of galaxies and quasars Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy z log (LAS) (a)(b) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Euclidean Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) z

Angular size of galaxies and quasars Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy z  m = 1 log (LAS) (a)(b) (c) log (LAS) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Euclidean Standard model Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) 10

Angular size of galaxies and quasars Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy z z  m = 1  m = 0.3   = 0.7 log (LAS) (a) (d) (b) (c) log (LAS) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Euclidean Standard modelStandard model + dark energy Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) 11

Angular size of galaxies and quasars Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy z z  m = 1  m = 0.3   = 0.7 log (LAS) (a) (d) (b) (c) log (LAS) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Euclidean Standard modelStandard model + dark energy Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) Suggested explanation: high z galaxies are young; sizes are still developing (not supported by spectral data!) 12

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy … or could the observations reflect a more fundamental problem in the Standard Cosmology Model or Relativity Theory? … does the dark energy really solve the problem … 13

Standard Cosmology Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Solution of GR field equations by Friedman, Lemaître, Robertson, and Walker assuming - the cosmological principle - space-time metrics and the assumptions of general relativity - Lorentz transformation - relativity principle - equivalence principle - constancy of the velocity of light - local conservation of energy  galaxies conserve their dimension 14

Zero-energy space Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Solution of zero-energy condition in spherically closed space assuming - minimum volume for closing 3-space  the surface of a 4-sphere - conservation of total energy in all interactions in space - homogeneity as the initial condition  cosmological principle - absolute time and distance units 15

Zero-energy space Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy R4R4 mnmn FnFn 16 Solution of zero-energy condition in spherically closed space assuming - minimum volume for closing 3-space  the surface of a 4-sphere - conservation of total energy in all interactions in space - homogeneity as the initial condition  cosmological principle - absolute time and distance units

Zero-energy space Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy R4R4 mnmn FnFn contraction 17 Solution of zero-energy condition in spherically closed space assuming - minimum volume for closing 3-space  the surface of a 4-sphere - conservation of total energy in all interactions in space - homogeneity as the initial condition  cosmological principle - absolute time and distance units

Zero-energy space Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy R4R4 mnmn FnFn contractionexpansion 18 Solution of zero-energy condition in spherically closed space assuming - minimum volume for closing 3-space  the surface of a 4-sphere - conservation of total energy in all interactions in space - homogeneity as the initial condition  cosmological principle - absolute time and distance units

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance of motion and gravitation M”= M  Im 0 m Re  m 19

Re  Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance of motion and gravitation M” m Im  m 20

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance of motion and gravitation M” m Re  Im  m 21

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance in tilted space M” m Re  Im  m 22

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance in tilted space M” m Re  Im  m 23

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance in tilted space M” m Re  Im  m 24

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy balance in tilted space M” m Re  Im  m 25

The system of nested energy frames Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Hypothetical homogeneous space … zero-energy space appears as a structured system of nested energy frames … … where universal time and distance applies, … … the local state of rest is an attribute of the local frame, … … relativity is the measure of locally available share of total energy … 26

The effect of reduced local energy on clock frequency Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy space: 27

The effect of reduced local energy on clock frequency Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy space: Standard model (Schwarzschild): 28

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy c0c0 R4R4 R4R4 observer object D phys  O c0c0 (a) Optical distance of objects in zero-energy space 29 Physical distance of objects in zero-energy space

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy c0c0 R4R4 R4R4 observer object D phys  O c0c0 c0c0 R 4(0) observer emitting object  O c 0(0) R4R4 t t (0) (b)(a) 30 Optical distance of objects in zero-energy space Physical distance of objects in zero-energy space

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy zero- energy space D/R z (redshift) Optical distance in zero energy space 31 Zero-energy space:

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy  m = 0.3   = 0.7 zero- energy space D/R z (redshift)  m = 1   = 0 standard model Angular size distance Zero-energy space: Standard model: 32

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy 0,010, Zero energy space, standard rod (solid objects): z 0, ,01 Standard model: Angular size of standard rod  m = 0.3   = 0.7  m = 1   = 0 33

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy 0,010, z 0, ,01 Angular size of standard rod & galaxies and quasars  m = 0.3   = 0.7  m = 1   = 0 34 Zero energy space, standard rod (solid objects): Standard model: Zero energy space, expanding objects (e.g. galaxies, quasars): = Euclidean

Angular size of galaxies and quasars Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy z z  m = 1  m = 0.3   = 0.7 log (LAS) (a) (d) (b) (c) log (LAS) Suggested explanation: high z galaxies are young; sizes are still developing (not supported by spectral data!) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Euclidean, zero-energy space Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) Standard modelStandard model + dark energy Zero-energy space: complete agreement with observations 35

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Standard model (for k-corrected observations): Observed energy flux 36

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Standard model (for k-corrected observations): Observed energy flux 37

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Standard model (for k-corrected observations): Observed energy flux 38

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Standard model (for k-corrected observations): Observed energy flux Zero energy space (bolometric): 39

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Standard model (for k-corrected observations): Observed energy flux Zero energy space (bolometric): Zero energy space (for k-corrected observations in optimized multi-bandpass detection): 40

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Zero-energy space +SN Ia observations  Magnitude versus redshift: Supernova observations Zero-energy space 41

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Standard model with  m = 0.3,   =0.7 Zero-energy space +SN Ia observations  Magnitude versus redshift: Supernova observations Standard model with  m = 1,   =0 42

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy redshift (z)  m = 1   = 0 Standard Model zero-energy space Apparent magnitude (distance modulus)  =m-M Magnitude versus redshift observations 43

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy redshift (z)  m = 0.3   = 0.7  m = 1   = 0 Standard Model zero-energy space Apparent magnitude (distance modulus)  =m-M Magnitude versus redshift observations 44

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy redshift (z)  m = 0.1   = 0.9  m = 0.3   = 0.7  m = 1   = 0 Standard Model zero-energy space Apparent magnitude (distance modulus)  = m-M Magnitude versus redshift observations 45

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Schwarzschild space-time metric ct’ dd M ds r ds  r M r0r0 d0d0 Im 0   Im  Re  rr r ds r Zero-energy space geometry Local geometry of space 46

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy r/r c(Ze) Schwarzschild space-time Space geometry at local singularity Sgr A*: 47

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Schwarzschild space-time Zero-energy space Space geometry at local singularity r/r c(Ze) Sgr A*: 48

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Observed periodic emission at Sgr A* r/r c(Ze) Sgr A*: 17 min period* v orb = r/r c ·0.1 c Sgr A*: 49 *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ]

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Observed periodic emission at Sgr A* r/r c(Ze) Sgr A*: 17 min period* 27 min Orbital velocity at circular orbit according to Standard Model Sgr A*: 3*r c(Schwd) = limit for circular orbits in Standard model 50 *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ]

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Observed periodic emission at Sgr A* r/r c(Ze) Sgr A*: 17 min period* 27 min Orbital velocity at circular orbit according to Standard Model Proposed solution: spinning of black hole at 0.3 c Sgr A*: 3*r c(Schwd) = limit for circular orbits in Standard model 51 *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ]

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Observed periodic emission at Sgr A* r/r c(Ze) Sgr A*: 17 min period* *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ] 27 min Orbital velocity at circular orbit according to Standard Model 3*r c(Schwd) = limit for circular orbits in Standard model Orbits for black holes spinning at c Zero-energy space: Sgr A*: 52

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy Observed periodic emission at Sgr A* r/r c(Ze) 27 min Orbital velocity at circular orbit according to Standard Model 3*r c(Schwd) = limit for circular orbits in Standard model Orbits for black holes spinning at c Zero-energy space: 53

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy GR: Orbital velocity and the velocity of free fall 0 0, Velocity of free fall Orbital velocity

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy DU: Orbital velocity and the velocity of free fall Velocity of free fall Orbital velocity 0 0,

Conclusions … Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy There is a fundamental problem in the FLRW metrics – observed at the extremes: at large distances and at local singularities 56

Conclusions … Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy There is a fundamental problem in the FLRW metrics – observed at the extremes: at large distances and at local singularities the problem is related to the local nature of general relativity and the missing linkage between the energy of local systems and the total energy in space … 57

Conclusions … Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy There is a fundamental problem in the FLRW metrics – observed at the extremes: at large distances and at local singularities the problem is related to the local nature of general relativity and the missing linkage between the energy of local systems and the total energy in space … … and the linear sum of 2  and  2 terms in GR proper time – a consequence of the equivalence principle applied in space-time with time as the fourth dimension 58

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy … conclusions The zero-energy approach is a holistic analysis of zero-energy condition in spherically closed space 59

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy … conclusions The zero-energy approach is a holistic analysis of zero-energy condition in spherically closed space It shows the essence of relativity as the measure of locally available share of total energy, 60

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy … conclusions The zero-energy approach is a holistic analysis of zero-energy condition in spherically closed space It shows the essence of relativity as the measure of locally available share of total energy, … produces precise predictions to local and cosmological phenomena in closed mathematical forms, 61

Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Budapest, 7-9. September 2007 Tuomo Suntola, Zero-energy space cancels the need for dark energy … conclusions The zero-energy approach is a holistic analysis of zero-energy condition in spherically closed space It shows the essence of relativity as the measure of locally available share of total energy, … produces precise predictions to local and cosmological phenomena in closed mathematical forms, … and re-establishes the use of absolute coordinate quantities, time and distance, essential for human conception. 62