Post on 28-Dec-2015
Zero-energy space cancels the need for dark energy
Tuomo Suntola, www.sci.fi/~suntola/, Finland
Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory
Budapest, 7-9. September 2007
1
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Latest PhysicsWeb Summaries 20.7.2007:
Dark-energy teams win cosmology prize (Jul 17)
http://physicsweb.org/article/news/11/7/15
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 1998. 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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Latest PhysicsWeb Summaries 20.7.2007:
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Latest PhysicsWeb Summaries 20.7.2007:
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
30
35
40
45
50
0,001 0,01 0,1 1 10
+ SN Ia observations
Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004)
z
m
Magnitude versus redshift: Supernova observations
5
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
30
35
40
45
50
0,001 0,01 0,1 1 10
+ SN Ia observationsStandard model with m = 1, = 0
Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004)
z
m
Magnitude versus redshift: Supernova observations
0 2
5log10 pc
15 log 1
1 1 2
H
z
m
R
z dzz z z z
6
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
30
35
40
45
50
0,001 0,01 0,1 1 10
+ SN Ia observationsStandard model with m = 1, = 0Standard 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
m
Magnitude versus redshift: Supernova observations
0 2
5log10 pc
15 log 1
1 1 2
H
z
m
R
z dzz z z z
7
Angular size of galaxies and quasars
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0.01 0.1 1 10 z
log
(LA
S)
0.001
(a)
Largest angular size (LAS),Open circles: galaxiesFilled 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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0.01 0.1 1 10 z
log
(LA
S)
0.001
(a) (b)
Largest angular size (LAS),Open circles: galaxiesFilled circles: quasars
Euclidean
Collection of data:K. Nilsson et al., Astrophys. J., 413, 453 (1993)
0.01 0.1 1 10 z0.001
9
Angular size of galaxies and quasars
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0.01 0.1 1 10 z
Wm= 1
log
(LA
S)
0.001
(a) (b)
(c)
log
(LA
S)
Largest angular size (LAS),Open circles: galaxiesFilled circles: quasars
Euclidean
Standard modelCollection 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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0.01 0.1 1 10 z 0.01 0.1 1 10 z
Wm= 1 Wm= 0.3WL= 0.7
log
(LA
S)
0.001 0.001
(a)
(d)
(b)
(c)
log
(LA
S)
Largest angular size (LAS),Open circles: galaxiesFilled circles: quasars
Euclidean
Standard model Standard 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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0.01 0.1 1 10 z 0.01 0.1 1 10 z
Wm= 1 Wm= 0.3WL= 0.7
log
(LA
S)
0.001 0.001
(a)
(d)
(b)
(c)
log
(LA
S)
Largest angular size (LAS),Open circles: galaxiesFilled circles: quasars
Euclidean
Standard model Standard 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 TheoryBudapest, 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 TheoryBudapest, 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 TheoryBudapest, 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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
R4 mn
Fn
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
R4 mn
Fn
gE
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
R4 mn
Fn mE
gE
contraction expansion
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance of motion and gravitation
M”= 0.776 M
Im0
m
0 0mp c
Re0
m
0 0 0mE c c mc p
"
"g
GmME
R
0c
19
Red
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance of motion and gravitation
M”
m
Imd
m
m p c
ff p
0p
"gE
0"gE
M
20
M
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance of motion and gravitation
M”
m
Red
Imd
m
m p c
0 0 0 cosrestE c c mc p
2
0 00
"cos 1 1
"g
g
E GM
E r c
0r
20 0
GM
r c
21
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance in tilted space
M”
m
Red
Imd
m
0 1rest restE E
restE
M
20 0
GM
r c
22
M
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance in tilted space
M”
m
Red
Imd
m
0,0restE
p restE
23
mc
mc
M
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance in tilted space
M”
m
Red
Imd
m
,restE mv
0,0restE
24
2
, 1rest restE E
mc
v
c
M
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy balance in tilted space
M”
m
Red
Imd
m
,restE mv
2, 0,0 1 1rest restE E
2
, 1rest restE E
0,0restE
21
m
vp
25
The system of nested energy frames
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 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 …
2 20 0
1
1 1n
rest i ii
E m c
26
The effect of reduced local energy on clock frequency
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zero-energy space:
27
20,0,
1
1 1n
i iZ Ei
f f
The effect of reduced local energy on clock frequency
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
20,0,
1
1 1n
i iZ Ei
f f
Zero-energy space:
2
0,0, 1 2GRf f
Standard model (Schwarzschild):
28
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
c0
R4R4
observer
objectDphys
O
c0
(a)
4physD R
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
c0
R4R4
observer
objectDphys
O
c0
c0
R4(0)
observer
emitting object
O
c0(0)
R4
t
t(0)
(b)(a)
4physD R 4 4 44 0 11optD
zR R R e R
z
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
zero-energy space
0.01
0.1
1
0.001
D/R4
0.01 0.1 1 10 100 10000.001 z (redshift)
Optical distance in zero energy space
31
4 1
zD R
z
Zero-energy space:
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
m = 0.3 = 0.7
zero-energy space
0.01
0.1
1
0.001
D/R4
0.01 0.1 1 10 100 10000.001 z (redshift)
m = 1 = 0
standard model
Angular size distance
4 1
zD R
z
Zero-energy space:
20
1
1 1 1 2
zH
m
RD dz
z z z z z
Standard model:
32
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0,01 0,1 1 10 100
Zero energy space, standard rod (solid objects):
z
0,1
1
10
100
4r R
0,01
Standard model:
4
1s sr r z
D R z
Angular size of standard rod
m = 0.3 = 0.7
m = 1 = 0
20
11
1 1 2
s s
zH
m
r r z
D R dzz z z z
33
4
1s sr r z
D R z
20
11
1 1 2
s s
zH
m
r r z
D R dzz z z z
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0,01 0,1 1 10 100z
0,1
1
10
100
0,01
Angular size of standard rod & galaxies and quasars
m = 0.3 = 0.7
m = 1 = 0
0 0
4 4
1 1 1r z r z rz
D R z R z
4r R
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
0.01 0.1 1 10 z 0.01 0.1 1 10 z
Wm= 1 Wm= 0.3WL= 0.7
log
(LA
S)
0.001 0.001
(a)
(d)
(b)
(c)
log
(LA
S)
Suggested explanation:high z galaxies are young; sizes are still developing(not supported by spectral data!)
Largest angular size (LAS),Open circles: galaxiesFilled circles: quasars
Euclidean,zero-energy
space
Collection of data:K. Nilsson et al., Astrophys. J., 413, 453 (1993)
Standard model Standard model + dark energy
Zero-energy space:complete agreement with observations
0
4
1r
R z
35
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Standard model (for k-corrected observations):
Observed energy flux
0
2
0L zD
d L
dF
F D
36
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Standard model (for k-corrected observations):
Observed energy flux
0
22
0 0
21
L z A zD
d L A
d dF
F D D z
37
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Standard model (for k-corrected observations):
Observed energy flux
0
22 20 0 0
2 22
20
1
11
11 1 2
L z A z zD
d L HA z
m
d d dF
F D RD zz dz
z z z z
38
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Standard model (for k-corrected observations):
Observed energy flux
0
2 20 0
2 2
11
1z zD
d H
d d zF
F D z R z
Zero energy space (bolometric):
0
22 20 0 0
2 22
20
1
11
11 1 2
L z A z zD
d L HA z
m
d d dF
F D RD zz dz
z z z z
39
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Standard model (for k-corrected observations):
Observed energy flux
0
2 20 0
2 2
11
1z zD
d H
d d zF
F D z R z
Zero energy space (bolometric):
0
20
2 2
1
1zD
d H
dF
F R z z
Zero energy space (for k-corrected observations in optimized multi-bandpass detection):
0
22 20 0 0
2 22
20
1
11
11 1 2
L z A z zD
d L HA z
m
d d dF
F D RD zz dz
z z z z
40
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
30
35
40
45
50
0,001 0,01 0,1 1 10
Zero-energy space+ SN Ia observationsm
Magnitude versus redshift: Supernova observations
Zero-energy space
45log10 pc
5log 2.5log 1
R
z z
41
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
30
35
40
45
50
0,001 0,01 0,1 1 10
Standard model with Wm = 0.3, WL=0.7
Zero-energy space+ SN Ia observationsm
Magnitude versus redshift: Supernova observations
0 2
5log10 pc
15 log 1
1 1 2
H
z
m
R
z dzz z z z
45log10 pc
5log 2.5log 1
R
z z
Standard model with Wm = 1, WL=0
42
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
redshift (z)
m = 1 = 0
Standard Model
30
35
40
45
50
55
60
65
0.01 0.1 1 10 100 1000
zero-energy space
Apparent magnitude
(distance modulus)
m =m-M
Magnitude versus redshift
observations
43
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 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
30
35
40
45
50
55
60
65
0.01 0.1 1 10 100 1000
zero-energy space
Apparent magnitude
(distance modulus)
m =m-M
Magnitude versus redshift
observations
44
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 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
30
35
40
45
50
55
60
65
0.01 0.1 1 10 100 1000
zero-energy space
Apparent magnitude
(distance modulus)
m = m-M
Magnitude versus redshift
observations
45
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Schwarzschildspace-time metric
ct’
dj
M
dsr
dsj
r
M
dsj
r0d
dj0d
Im0d
Imd
Red
rdr
dsr
Zero-energy space geometry
Local geometry of space
46
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420 r/rc(Ze)
Schwarzschild space-time
Space geometry at local singularity
10Schwarzschild 2
210 mc
GMr
c Sgr A*:
9Ze 2
0
5 10 mc
GMr
c Sgr A*:
47
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420
Schwarzschild space-time
Zero-energy space
Space geometry at local singularity
r/rc(Ze)
10Schwarzschild 2
210 mc
GMr
c Sgr A*:
9Ze 2
0
5 10 mc
GMr
c Sgr A*:
48
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420
Observed periodic emission at Sgr A*
10Schwarzschild 2
210 mc
GMr
c
r/rc(Ze)
Sgr A*:
17 min period*
vorb = r/rc ·0.1 c
00
orbv
c
9Ze 2
0
5 10 mc
GMr
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 TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420
Observed periodic emission at Sgr A*
10Schwarzschild 2
210 mc
GMr
c
r/rc(Ze)
Sgr A*:
17 min period*
27 min
Orbital velocity at circular orbit according to Standard Model
00
orbv
c
9Ze 2
0
5 10 mc
GMr
c Sgr A*:
3*rc(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) ]
Schwd
21 3orb
c
rr
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420
Observed periodic emission at Sgr A*
10Schwarzschild 2
210 mc
GMr
c
r/rc(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
00
orbv
c
9Ze 2
0
5 10 mc
GMr
c Sgr A*:
3*rc(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) ]
Schwd
21 3orb
c
rr
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420
Observed periodic emission at Sgr A*
10Schwarzschild 2
210 mc
GMr
c
r/rc(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
Schwd
21 3orb
c
rr
3*rc(Schwd) = limit for circular orbits in Standard model
Orbits for black holes spinning at c
Zero-energy space:
3
Ze Ze
0 1c c
orb
r r
r r
0orbv
c
9Ze 2
0
5 10 mc
GMr
c Sgr A*:
52
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
Zecr 1086420
Observed periodic emission at Sgr A*
10Schwarzschild 2
210 mc
GMr
c
r/rc(Ze)
27 min
Orbital velocity at circular orbit according to Standard Model
Schwd
21 3orb
c
rr
3*rc(Schwd) = limit for circular orbits in Standard model
Orbits for black holes spinning at c
Zero-energy space:
3
Ze Ze
0 1c c
orb
r r
r r
0orbv
c
53
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
GR: Orbital velocity and the velocity of free fall
2
2c Schwd
GMr
c
21 3orb
c Schwd
rr
0
0,5
1
0 5 10 15 20 25 30 35 40
Velocity of free fall
Orbital velocity
1c Schwd c Schwd
ff
r r
r r
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 7-9. September 2007
Tuomo Suntola, Zero-energy space cancels the need for dark energy
DU: Orbital velocity and the velocity of free fall
DU 2c
GMr
c
Velocity of free fall
0.52
1 1c DU
ff
r
r
Orbital velocity
3
0 1c DU c DU
orb
r r
r r
0
0,5
1
0 5 10 15 20 25 30 35 40
Conclusions …
Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 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 TheoryBudapest, 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 TheoryBudapest, 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 2d and b 2 terms in GR proper time – a consequence of the equivalence principle applied in space-time with time as the fourth
dimension
2 2 2 2 2 2 2 2 2
2 2 2
sin1 2
1 2
dr dt r d dt r d dtd dt
c c c
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Mathematics, Physics and Philosophy in the Interpretations of Relativity TheoryBudapest, 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 TheoryBudapest, 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 TheoryBudapest, 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 TheoryBudapest, 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.
www.sci.fi/~suntola/
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