Zero-energy space cancels the need for dark energy. Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory

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1 Zero-energy spae anels the need for dark energy Tuomo Suntola, Finland Mathematis, Physis and Philosophy in the Interpretations of Relativity Theory 1

2 Latest PhysisWeb Summaries : Dark-energy teams win osmology prize (Jul 17) Two independent teams of researhers who disovered that the expansion of the universe is aelerating 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 Shmidt, who reported their disovery in Their work provided the first onvining evidene for the existene of "dark energy" -- a mysterious and so-far invisible entity that physiists believe works against gravity to boost the expansion of the universe. 2

3 Latest PhysisWeb Summaries : Dark-energy teams win osmology prize (Jul 17) an alternative way of wording the news: Two independent teams of researhers who disovered that the magnitudes of high redshift supernovae do not follow the predition of the standard osmology model have been awarded 3

4 Latest PhysisWeb Summaries : Dark-energy teams win osmology prize (Jul 17) an alternative way of wording the news: Two independent teams of researhers who disovered that the magnitudes of high redshift supernovae do not follow the predition of the standard osmology model have been awarded a onept of dark energy working against gravitation between galaxies has been suggested to fix the problem. 4

5 Magnitude versus redshift: Supernova observations 50 μ + SN Ia observations Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) 30 0,001 0,01 0,1 1 z 10 5

6 50 μ Mathematis, Physis and Philosophy in the Interpretations of Relativity Theory Magnitude versus redshift: Supernova observations + SN Ia observations Standard model with Ω m = 1, Ω Λ = RH μ = 5log 10 p Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) z 1 + 5log ( 1+ z) dz 0 ( 1 z) 2 ( 1 m z) z( 2 z + +Ω + ) Ωλ 30 0,001 0,01 0,1 1 z 10 6

7 50 μ Mathematis, Physis and Philosophy in the Interpretations of Relativity Theory Magnitude versus redshift: Supernova observations + SN Ia observations Standard model with Ω m = 1, Ω Λ = 0 Standard model with Ω m = 0.3, Ω Λ = RH μ = 5log 10 p z 1 + 5log ( 1+ z) dz 0 ( 1 z) 2 ( 1 m z) z( 2 z + +Ω + ) Ωλ 30 0,001 0,01 0,1 1 z 10 Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) Suggested orretion: Ω m = 0.3 Ω Λ = 0.7 (dark energy) 7

8 Angular size of galaxies and quasars log (LAS) (a) z Largest angular size (LAS), Open irles: galaxies Filled irles: quasars Colletion of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) 8

9 Angular size of galaxies and quasars Eulidean log (LAS) (a) z (b) z Largest angular size (LAS), Open irles: galaxies Filled irles: quasars Colletion of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) 9

10 Angular size of galaxies and quasars Eulidean log (LAS) (a) (b) Largest angular size (LAS), Open irles: galaxies Filled irles: quasars log (LAS) Standard model Ω m = 1 Colletion of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) () z 10

11 Angular size of galaxies and quasars Eulidean log (LAS) (a) (b) Largest angular size (LAS), Open irles: galaxies Filled irles: quasars log (LAS) Standard model Standard model + dark energy Ω m = 1 Ω m = 0.3 Ω Λ = 0.7 Colletion of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993) () (d) z z 11

12 Angular size of galaxies and quasars Eulidean log (LAS) (a) (b) Largest angular size (LAS), Open irles: galaxies Filled irles: quasars log (LAS) () Standard model Ω m = 1 Ω m = 0.3 Ω Λ = 0.7 (d) Standard model + dark energy Colletion 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 spetral data!) z z 12

13 does the dark energy really solve the problem or ould the observations reflet a more fundamental problem in the Standard Cosmology Model or Relativity Theory? 13

14 Standard Cosmology Solution of GR field equations by Friedman, Lemaître, Robertson, and Walker assuming - the osmologial priniple - spae-time metris and the assumptions of general relativity - Lorentz transformation - relativity priniple - equivalene priniple - onstany of the veloity of light - loal onservation of energy galaxies onserve their dimension 14

15 Zero-energy spae Solution of zero-energy ondition in spherially losed spae assuming - minimum volume for losing 3-spae the surfae of a 4-sphere - onservation of total energy in all interations in spae - homogeneity as the initial ondition osmologial priniple - absolute time and distane units 15

16 Zero-energy spae Solution of zero-energy ondition in spherially losed spae assuming - minimum volume for losing 3-spae the surfae of a 4-sphere - onservation of total energy in all interations in spae - homogeneity as the initial ondition osmologial priniple - absolute time and distane units R 4 m n F n 16

17 Zero-energy spae Solution of zero-energy ondition in spherially losed spae assuming - minimum volume for losing 3-spae the surfae of a 4-sphere - onservation of total energy in all interations in spae - homogeneity as the initial ondition osmologial priniple - absolute time and distane units F n m n R 4 Eg ontration 17

18 Zero-energy spae Solution of zero-energy ondition in spherially losed spae assuming - minimum volume for losing 3-spae the surfae of a 4-sphere - onservation of total energy in all interations in spae - homogeneity as the initial ondition osmologial priniple - absolute time and distane units E m R 4 m n F n E g ontration expansion 18

19 Zero-energy balane of motion and gravitation Im 0 E = p = m m m 0 p = m 0 0 E g GmM " = R" m Re 0 M = M Σ 19

20 Zero-energy balane of motion and gravitation m p ff ( δ ) Im δ p 0 p φ = m φ M E" g( δ ) m φ Re δ E" g ( 0) M 20

21 Zero-energy balane of motion and gravitation Erest( ) = os 0 pδ = 0m0 φ δ m Im δ p δ = m δ M m φ r 0 Re δ E" g( δ ) GM osφ = = 1 = 1 δ E" r g ( 0) δ = GM r M 21

22 Zero-energy balane in tilted spae E rest ( ) = E ( 0)( 1 δ δ rest ) m Erest( δ ) Im δ M m Re δ δ = GM r M 22

23 Zero-energy balane in tilted spae m M E rest ( 0,0) Erest( δ ) m m m Im δ p β Re δ M 23

24 Zero-energy balane in tilted spae E 2 = E 1 β rest δ, β δ ( ) rest( ) m E rest ( 0,0) Im δ β = v E δ β mv rest (, ) M m m Re δ M 24

25 Zero-energy balane in tilted spae E 2 = E 1 β rest δ, β δ ( ) rest( ) m E rest ( 0,0) E δ β mv rest (, ) Im δ p β = mv 2 1 β M m Re δ M E rest = E 1 δ 1 β δ, β 0,0 2 ( ) rest( )( ) 25

26 The system of nested energy frames Hypothetial homogeneous spae zero-energy spae appears as a strutured system of nested energy frames where universal time and distane applies, the loal state of rest is an attribute of the loal frame, relativity is the measure of loally available share of total energy n 2 ( ) 2 rest = i 1 i i= 1 E m δ β 26

27 The effet of redued loal energy on lok frequeny Zero-energy spae: f n = f 1 1 δ, β δ β i= 1 2 ( Z E) 0,0 ( i) i 27

28 The effet of redued loal energy on lok frequeny Zero-energy spae: f n = f 1 1 δ, β δ β i= 1 2 ( Z E) 0,0 ( i) i Standard model (Shwarzshild): 2 f = δ β δ β f, 0,0 1 2 ( GR) 28

29 Physial distane of objets in zero-energy spae Optial distane of objets in zero-energy spae 0 observer 0 objet D phys R 4 R 4 α O (a) Dphys = α R 4 29

30 Physial distane of objets in zero-energy spae Optial distane of objets in zero-energy spae 0 observer 0 objet t 0 R 4 observer D phys R 4 R 4 α t (0) α R 4(0) 0(0) emitting objet O (a) O (b) Dphys = α R 4 D opt = R R = R e = R α ( ) ( ) z 1+ z 30

31 Optial distane in zero energy spae 1 D/R zeroenergy spae z (redshift) Zero-energy spae: D= R 4 1 z + z 31

32 Angular size distane 1 D/R zeroenergy spae standard model Ω m = 0.3 Ω Λ = 0.7 Ω m = 1 Ω Λ = z (redshift) Zero-energy spae: D= R 4 1 z + z Standard model: R z H 1 D = Ω 2+ Ω z 0 2 ( z) ( mz) z( z) λ dz 32

33 Angular size of standard rod 100 θ rr 4 10 Standard model: Ω m = 1 Ω Λ =0 Ω m = 0.3 Ω Λ = 0.7 rs rs 1+ z θ = = D R z 1 H dz 0 ( 1+ z) 2 ( 1+Ω z) z( 2+ z) Ωλ m 1 Zero energy spae, standard rod (solid objets): rs rs 1+ z θ = = D R z 4 0,1 0,01 0,01 0, z

34 Angular size of standard rod & galaxies and quasars 100 θ rr 4 10 Standard model: Ω m = 1 Ω Λ =0 Ω m = 0.3 Ω Λ = 0.7 rs rs 1+ z θ = = D R z 1 H dz 0 ( 1+ z) 2 ( 1+Ω z) z( 2+ z) Ωλ m 1 Zero energy spae, standard rod (solid objets): rs rs 1+ z θ = = D R z 4 0,1 Zero energy spae, expanding objets (e.g. galaxies, quasars): 0,01 0,01 0, z 100 ( ) ( ) r z r0 1+ z 1+ z r0 1 θ = = = D R z R z 4 4 = Eulidean 34

35 Angular size of galaxies and quasars log (LAS) (a) (b) Eulidean, zero-energy spae Zero-energy spae: omplete agreement with observations r0 1 θ = R z Largest angular size (LAS), Open irles: galaxies Filled irles: quasars 4 log (LAS) () Standard model Ω m = 1 Ω m = 0.3 Ω Λ = 0.7 (d) Standard model + dark energy Colletion 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 spetral data!) z z 35

36 Observed energy flux Standard model (for k-orreted observations): F F D d 0 dlz ( 0) = D L 2 36

37 Observed energy flux Standard model (for k-orreted observations): 2 F d ( ) d D Lz 0 Az ( 0) = = 2 F d D 0 L DA ( 1+ z) 2 37

38 Observed energy flux Standard model (for k-orreted observations): d ( ) d ( ) d D Lz 0 Az 0 ( z 0) 1 = = = d0 L DA ( 1+ z) H z F F D R 1 ( 1+ z) dz 0 2 ( 1+ z) ( 1+Ωmz) z( 2+ z) Ωλ 38

39 Observed energy flux Standard model (for k-orreted observations): d ( ) d ( ) d D Lz 0 Az 0 ( z 0) 1 = = = d0 L DA ( 1+ z) H z F F D R 1 ( 1+ z) dz 0 2 ( 1+ z) ( 1+Ωmz) z( 2+ z) Ωλ Zero energy spae (bolometri): 2 2 ( z 0) 1 ( z 0) ( 1 ) F d d + z D = = 2 2 F d D 1 z R 0 + H z 39

40 Observed energy flux Standard model (for k-orreted observations): d ( ) d ( ) d D Lz 0 Az 0 ( z 0) 1 = = = d0 L DA ( 1+ z) H z F F D R 1 ( 1+ z) dz 0 2 ( 1+ z) ( 1+Ωmz) z( 2+ z) Ωλ Zero energy spae (bolometri): 2 2 ( z 0) 1 ( z 0) ( 1 ) F d d + z D = = 2 2 F d D 1 z R 0 + H z Zero energy spae (for k-orreted observations in optimized multi-bandpass detetion): 2 F d D ( z 0) 1 = F R z z d H ( 1+ ) 40

41 50 μ 45 Mathematis, Physis and Philosophy in the Interpretations of Relativity Theory Magnitude versus redshift: Supernova observations + SN Ia observations Zero-energy spae Zero-energy spae μ = R 4 5log 10 p ( z) + 5log z + 2.5log ,001 0,01 0,

42 50 μ 45 Mathematis, Physis and Philosophy in the Interpretations of Relativity Theory Magnitude versus redshift: Supernova observations + SN Ia observations Zero-energy spae μ = R 4 5log 10 p ( z) + 5log z + 2.5log Standard model with Ω m = 0.3, Ω Λ =0.7 Standard model with Ω m = 1, Ω Λ =0 35 RH μ = 5log 10 p z + 5log ( 1+ z) 30 0,001 0,01 0, ( 1 ) ( 1 ) ( 2 ) 0 + z 2 +Ωm z z + z Ωλ 1 dz 42

43 Magnitude versus redshift Apparent magnitude (distane modulus) μ =m-m zero-energy spae observations Ω m = 1 Ω Λ = 0 Standard Model redshift (z) 43

44 Magnitude versus redshift Apparent magnitude (distane modulus) μ =m-m observations zero-energy spae Ω m = 0.3 Ω Λ = 0.7 Ω m = 1 Ω Λ = 0 40 Standard Model redshift (z) 44

45 Magnitude versus redshift Apparent magnitude (distane modulus) μ =m-m observations zero-energy spae Ω m = 0.1 Ω Λ = 0.9 Ω m = 0.3 Ω Λ = 0.7 Ω m = 1 Ω Λ = 0 40 Standard Model redshift (z) 45

46 Loal geometry of spae Im 0δ Im δ t dϕ 0δ φ Re δ r 0δ ds ϕ r dϕ ds r r δ r ds ϕ ds r M M Shwarzshild spae-time metri Zero-energy spae geometry 46

47 Spae geometry at loal singularity Sgr A*: r 2GM 10 ( ) = 10 Shwarzshild 2 [ m] Shwarzshild spae-time 0 r r/r 10 ( Ze) (Ze) Sgr A*: r GM ( ) = = Ze 2 [ m] 0 47

48 Spae geometry at loal singularity Sgr A*: r 2GM 10 ( ) = 10 Shwarzshild 2 [ m] Shwarzshild spae-time Zero-energy spae 0 r/r (Ze) r ( Ze) Sgr A*: r GM ( ) = = Ze 2 [ m] 0 48

49 Observed periodi emission at Sgr A* Sgr A*: r 2GM 10 ( ) = 10 Shwarzshild 2 [ m] v orb β 0δ = 0δ 17 min period* v orb = r/r r/r (Ze) r ( Ze) Sgr A*: r GM ( ) = = Ze 2 [ m] 0 *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ] 49

50 Observed periodi emission at Sgr A* Sgr A*: r 2GM 10 ( ) = 10 Shwarzshild 2 [ m] 3*r (Shwd) = limit for irular orbits in Standard model v orb β 0δ = 0δ 17 min period* 27 min Orbital veloity at irular orbit aording to Standard Model 2r β orb = 1 3 r ( Shwd) 0 r/r (Ze) r ( Ze) Sgr A*: r GM ( ) = = Ze 2 [ m] 0 *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ] 50

51 Observed periodi emission at Sgr A* Sgr A*: r 2GM 10 ( ) = 10 Shwarzshild 2 [ m] 3*r (Shwd) = limit for irular orbits in Standard model v orb β 0δ = 0δ 17 min period* 27 min Orbital veloity at irular orbit aording to Standard Model 2r β orb = 1 3 r ( Shwd) Proposed solution: spinning of blak hole at r/r (Ze) r ( Ze) Sgr A*: r GM ( ) = = Ze 2 [ m] 0 *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ] 51

52 Observed periodi emission at Sgr A* Sgr A*: r 2GM 10 ( ) = 10 Shwarzshild 2 [ m] 3*r (Shwd) = limit for irular orbits in Standard model β = 0δ v orb δ 17 min period* 27 min Orbital veloity at irular orbit aording to Standard Model 2r β orb = 1 3 r ( Shwd) Orbits for blak holes spinning at Sgr A*: r 0 r/r (Ze) r ( Ze) GM ( ) = = Ze 2 [ m] 0 Zero-energy spae: β *Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ] ( δ ) r r = r r ( Ze) ( Ze) orb

53 Conlusions There is a fundamental problem in the FLRW metris observed at the extremes: at large distanes and at loal singularities 53

54 Conlusions There is a fundamental problem in the FLRW metris observed at the extremes: at large distanes and at loal singularities the problem is related to the loal nature of general relativity and the missing linkage between the energy of loal systems and the total energy in spae 54

55 Conlusions There is a fundamental problem in the FLRW metris observed at the extremes: at large distanes and at loal singularities the problem is related to the loal nature of general relativity and the missing linkage between the energy of loal systems and the total energy in spae and the linear sum of 2δ and β 2 terms in GR proper time a onsequene of the equivalene priniple applied in spae-time with time as the fourth dimension dr dt r dθ dt r sin θ dφ dt dτ = dt 1 2δ ( 1 2δ ) 2 β 55

56 onlusions The zero-energy approah is a holisti analysis of zero-energy ondition in spherially losed spae 56

57 onlusions The zero-energy approah is a holisti analysis of zero-energy ondition in spherially losed spae It shows the essene of relativity as the measure of loally available share of total energy, 57

58 onlusions The zero-energy approah is a holisti analysis of zero-energy ondition in spherially losed spae It shows the essene of relativity as the measure of loally available share of total energy, produes preise preditions to loal and osmologial phenomena in losed mathematial forms, 58

59 onlusions The zero-energy approah is a holisti analysis of zero-energy ondition in spherially losed spae It shows the essene of relativity as the measure of loally available share of total energy, produes preise preditions to loal and osmologial phenomena in losed mathematial forms, and re-establishes the use of absolute oordinate quantities, time and distane, essential for human oneption. 59