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