From local to global relativity


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1 Physical Interpretations of Relativity Theory XI Imperial College, LONDON, 115 SEPTEMBER, 8 From local to global relativity Tuomo Suntola, Finland
2 T. Suntola, PIRT XI, London, 115 September, 8 On board of Galileo ship Newtonian space defines no limits to space or physical quantities;  the velocity of an object increases linearly under the influence of a constant force  the state of rest is inseparable from the state of rectilinear motion dp F= = m a dt time c velocity kinetic energy ( v) dx v v v d m Ekin = dx= m d = m v dv= ½mv dt v dt c velocity
3 T. Suntola, PIRT XI, London, 115 September, 8 3 From Galileo ship to space craft Relativistic space:  increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration time v' dp F= = m a dt F' Rectilinear dp = = dt m ( 1 β ) 3 a c velocity Ekin = ½mv 1 Ekin = mc 1 = c Δm 1 v c kinetic energy c velocity
4 T. Suntola, PIRT XI, London, 115 September, 8 4 From Galileo ship to space craft Relativistic space:  increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration Mathematical description (SR): redefinition of coordinate quantities: dt ' = dt 1 β dr ' dr 1 β β = = vc time v' dp F= = m a dt F' Rectilinear dp = = dt m ( 1 β ) 3 a c velocity Ekin = ½mv 1 Ekin = mc 1 c m = Δ v 1 c kinetic energy c velocity
5 T. Suntola, PIRT XI, London, 115 September, 8 5 Gravitation in modified coordinates via equivalence principle Schwarzschild solution of GR field equations: dr ' = dr 1 β dr ' = dr GM 1 rc GM β ff ( Newton) = rc ct ds ϕ dϕ r' ds r' β ff= v ff /c dt ' = dt 1 β GM dt ' = dt 1 β rc M β ff ( Newton ) 1 β The (coordinate) velocity of free fall in Schwarzschild space goes to zero at the critical radius r ( ) c Schwd GM = c.5 β ff, Schwarzschild r GM c
6 T. Suntola, PIRT XI, London, 115 September, 8 6 In search of fundamental physical limits In his lectures on gravitation in early 196 s Richard Feynman [1] stated: If now we compare the total gravitational energy GM Σ /R to the total rest energy of the universe, M Σ c, lo and behold, we get the amazing result that GM Σ /R = M Σ c, so that the total energy of the universe is zero Why this should be so is one of the great mysteries and therefore one of the important questions of physics. and further []...One intriguing suggestion is that the universe has a structure analogous to that of a spherical surface... It might be that our threedimensional space is such a thing, a tridimensional surface of a four sphere
7 T. Suntola, PIRT XI, London, 115 September, 8 7 Zeroenergy balance in spherically closed homogeneous space R 4 m n F n Fn 3dimensional space
8 T. Suntola, PIRT XI, London, 115 September, 8 8 Zeroenergy balance in spherically closed homogeneous space E = c p = c mc m m E g V ( ) dv r = ρmg r m E g GmM " = R 4 GmM " = R 4 M" The balance of motion and gravitation. mc GmM " = R 4
9 T. Suntola, PIRT XI, London, 115 September, 8 9 Zeroenergy balance in spherically closed space Energy of motion Contraction Expansion Time Energy of gravitation
10 T. Suntola, PIRT XI, London, 115 September, 8 1 Zeroenergy balance in spherically closed space E = c p = c mc m dc c Δ t = year time E g GmM " = R"
11 T. Suntola, PIRT XI, London, 115 September, 8 11 The energy of motion in local space m E = c p = c mc m E g GmM " = R 4 M"
12 T. Suntola, PIRT XI, London, 115 September, 8 1 The energy of motion in local space Im m E = c p = c mc m Em = c mc ( ) E g GmM " = R 4 E g GmM " = R 4 Re M"
13 T. Suntola, PIRT XI, London, 115 September, 8 13 Buildup of kinetic energy maintaining the zeroenergy balance Em Im ( ) Re Im = c mc mc φ p φ ( Re) Ekin Re = c cδm Ekin = c mδc mc φ p ff mc local ( ) Global relativity (DU) : E = c Δ p = c cδ m+ mδc kin ΔE g ( global ) M E c m Local relativity (SR): kin = Δ
14 T. Suntola, PIRT XI, London, 115 September, 8 14 Rest energy in nested frames Im Im E rest( ) E rest ( ) m = m 1 β ( ) rest n n i= i n n i= ( 1 ) c = c δ i E = c p = c m c 1 δ 1 β rest n ( ) ( i) i n i=
15 T. Suntola, PIRT XI, London, 115 September, 8 15 The system of nested energy frames Hypothetical homogeneous space local galaxy group frame Milky Way frame Solar frame Earth frame n ( ) rest = 1 i 1 i i= E m c δ β Relativity of rest energy
16 T. Suntola, PIRT XI, London, 115 September, 8 16 The system of nested energy frames Hypothetical homogeneous space local galaxy group frame Milky Way frame Solar frame Earth frame n f = f 1 δ 1 β (,) ( ) local i i i= Relativity of characteristic frequencies
17 T. Suntola, PIRT XI, London, 115 September, 8 17 Satellite in Earth gravitational frame 1 f δ,β /f, GR DU β = δ f( ) = f, ( 1 δ) 1 β f, 1 δ β β δβ DU f( ) = f, 1 δ β f, 1 δ β β δβ GR 8
18 T. Suntola, PIRT XI, London, 115 September, 8 18 Free fall and orbital velocity in Schwarzschild space and in DU space β ff ( Newton ) Schwarzschild space:  the velocity of free fall goes to zero at the critical radius r ( ) c Schwd GM = c 1 β.5 Limit for stable orbits  velocity at circular orbit exceeds the velocity of free fall at r = 3r c(schwd) β β orb ( ) ( Schw ) ff Schw r GM c DU space:  the velocity of free fall goes to zero at the critical radius r ( ) cdu GM = c β 1.5 β ff ( Newton ) β ff DU ( )  velocity at circular orbit goes to zero at r = r c Slow orbits maintain the mass of the black hole! β orb ( DU ) r GM c
19 T. Suntola, PIRT XI, London, 115 September, 8 19 Orbital period near black hole DU DU P = c π r ( 1 δ ) 3 π r Schwarzschild P = ( = Newton ) c δ δ P min( DU ) 16π r = c c r /r c Schwd Sgr A*: M 3.7 million solar masses r c(du) 5.3 million kilometers DU 6 min. 4 Schwd r /r c Observed 17 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 45, 934 (3) ]
20 T. Suntola, PIRT XI, London, 115 September, 8 Distinctive characteristics of local and global relativity Local relativity (SR): Global relativity (Dynamic Universe): What is finite? Velocity in space Total energy Description of finiteness dt ' = dt 1 β dr ' = dr 1 β E total GM " = c p = R 4 Rest energy Erest = mc E rest = c mc ( ) = mc 1 δ 1 β i i i Kinetic energy Ekin = c Δm kin ( ) E = c Δ p = c cδ m+ mδc by local momentum via insert of mass equivalence by gravitation via tilting of space
21 T. Suntola, PIRT XI, London, 115 September, 8 1 Jump to Galileo ship characterized as a velocity frame Velocity of mass object on board v = v vship = v 1 v ship v Velocity of light on board? c c v ship h pλ = c= mλc λ characterized as a momentum frame Momentum of mass object on board p= mv= p 1 h v ship vship Momentum of light on board p= mλc= 1 c= p 1 λ c c (as reduced by the Dopplereffect) v ship v p λ h c = = h f λ The observed phase velocity is conserved c λ λ ( 1 β ) ( 1 β ) β β = = = = Tβ T T λ c
22 T. Suntola, PIRT XI, London, 115 September, 8 Jump to Galileo ship characterized as a velocity frame Velocity of mass object on board v = v vship = v 1 v ship v Velocity of light on board? c c v ship h pλ = c= mλc λ characterized as a momentum frame Momentum of mass object on board p= mv= p 1 h v ship vship Momentum of light on board p= mλc= 1 c= p 1 λ c c (as reduced by the Dopplereffect) v ship v p λ h c = = h f λ Michelson  Morley interferometer: no change in momentum in different arms zero result guaranteed
23 T. Suntola, PIRT XI, London, 115 September, 8 3 Distinctive characteristics of local and global relativity QM, SR : Dynamic Universe: Planck constant h 3 h= π e μ c= hc [ ] h kg m Quantum of radiation E h = hν Eλ = cc = c k c= cmc λ λ Energy momentum fourvector ( ) ( ) E = mc + pc energy momentum mass ( ) Im( ) ( ) ( ) ( ) ( ) m = ptot = + E c c mc c p ( ) ( Re( ) ) ( Im ) ( Re( )) kc = k c + k c φ φ φ k = k + k φ φ φ wave number kφ = kim( ) + k φ Re( φ)
24 T. Suntola, PIRT XI, London, 115 September, 8 4 Magnitude versus redshift: Supernova observations 5 μ ,1,1,1 1 z 1 Data: A. G. Riess, et al., Astrophys. J., 67, 665 (4)
25 T. Suntola, PIRT XI, London, 115 September, 8 5 Supernova observations: Predictions by FLRW and DU 5 μ 45 + SN Ia observations Dynamic Universe ( z) μ = μ +.5 log z 1+ 4 Standard model (FLRW) Ω m =.3, Ω Λ =.7 Standard model (FLRW) Ω m = 1, Ω Λ = 35 μ = μ + 5log 1+ ( z) z ( 1 ) ( 1 ) ( ) + z +Ωmz z + z Ωλ 1 dz 3,1,1,1 1 1 Data: A. G. Riess, et al., Astrophys. J., 67, 665 (4)
26 T. Suntola, PIRT XI, London, 115 September, 8 6 Angular size of galaxies and quasars, observations log (LAS) (d) z Largest angular size (LAS), open circles: galaxies, filled circles: quasars Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993)
27 T. Suntola, PIRT XI, London, 115 September, 8 7 Angular size of galaxies and quasars, observations / predictions log (LAS) Standard model Ω m = 1, Ω Λ = Standard model + dark energy Ω m =.3, Ω Λ =.7 (d) Dynamic Universe: Euclidean θ = r 1 R z z Largest angular size (LAS), open circles: galaxies, filled circles: quasars Collection of data: K. Nilsson et al., Astrophys. J., 413, 453 (1993)
28 Where is the antienergy of a localized object? 8 cmc
29 It is everywhere it is the gravitational energy of matter in the rest of space! 9 GM " m R" cmc GM " m Em + Eg = cmc = R"
30 Thank you for your attention. 3
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