Zero-energy space cancels the need for dark energy Tuomo Suntola, suntola/, Finlandsuntola/ Mathematics, Physics and Philosophy

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

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http://www.sci.fi/~suntola/

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.

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http://physicsweb.org/article/news/11/7/15





… 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 …

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… 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



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



30

35

40

45

50

0,001 0,01 0,1 1 10

+ SN Ia observationsStandard model with m = 1, = 0


z

m


0 2

5log10 pc

15 log 1

1 1 2

H

z

m

R

z dzz z z z

6



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)


z

m


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



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




0.01 0.1 1 10 z

log

(LA

S)

0.001

(a) (b)


Euclidean


0.01 0.1 1 10 z0.001

9




0.01 0.1 1 10 z

Wm= 1

log

(LA

S)

0.001

(a) (b)

(c)

log

(LA

S)


Euclidean

Standard modelCollection of data:K. Nilsson et al., Astrophys. J., 413, 453 (1993)

10




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)


Euclidean

Standard model Standard model + dark energy Collection of data:

K. Nilsson et al., Astrophys. J., 413, 453 (1993)

11




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)


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!)

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… 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



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

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Zero-energy space



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



R4 mn

Fn

16


assuming







Zero-energy space



R4 mn

Fn

gE

contraction

17


assuming







Zero-energy space



R4 mn

Fn mE

gE

contraction expansion

18


assuming









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




M”

m

Imd

m

m p c

ff p

0p

"gE

0"gE

M

20

M




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



Zero-energy balance in tilted space

M”

m

Red

Imd

m

0 1rest restE E

restE

M

20 0

GM

r c

22

M




M”

m

Red

Imd

m

0,0restE

p restE

23

mc

mc

M




M”

m

Red

Imd

m

,restE mv

0,0restE

24

2

, 1rest restE E

mc

v

c

M




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



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



Zero-energy space:

27

20,0,

1

1 1n

i iZ Ei

f f

The effect of reduced local energy on clock frequency



20,0,

1

1 1n

i iZ Ei

f f

Zero-energy space:

2

0,0, 1 2GRf f

Standard model (Schwarzschild):

28



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



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



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:



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



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



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




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!)


Euclidean,zero-energy

space


Standard model Standard model + dark energy

Zero-energy space:complete agreement with observations

0

4

1r

R z

35



Standard model (for k-corrected observations):

Observed energy flux

0

2

0L zD

d L

dF

F D

36





0

22

0 0

21

L z A zD

d L A

d dF

F D D z

37





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





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





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



30

35

40

45

50

0,001 0,01 0,1 1 10

Zero-energy space+ SN Ia observationsm


Zero-energy space

45log10 pc

5log 2.5log 1

R

z z

41



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


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



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



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


observations

44



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


observations

45



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



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



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



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) ]



Zecr 1086420


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


Schwd

21 3orb

c

rr



Zecr 1086420


10Schwarzschild 2

210 mc

GMr

c

r/rc(Ze)

Sgr A*:

17 min period*

27 min


Proposed solution: spinning of black hole at 0.3 c

00

orbv

c

9Ze 2

0

5 10 mc

GMr

c Sgr A*:



Schwd

21 3orb

c

rr



Zecr 1086420


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


Schwd

21 3orb

c

rr


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



Zecr 1086420


10Schwarzschild 2

210 mc

GMr

c

r/rc(Ze)

27 min


Schwd

21 3orb

c

rr


Orbits for black holes spinning at c

Zero-energy space:

3

Ze Ze

0 1c c

orb

r r

r r

0orbv

c

53



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



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 …



There is a fundamental problem in the FLRW metrics – observed at the extremes: at large distances and at local singularities

56

Conclusions …




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 …




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

258



… conclusions

The zero-energy approach is a holistic analysis of zero-energy condition in spherically closed space

59



… conclusions


It shows the essence of relativity as the measure of locally available share of total energy,

60



… conclusions



… produces precise predictions to local and cosmological phenomena in closed mathematical forms,

61



… conclusions



… 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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Zero-energy space cancels the need for dark energy Tuomo Suntola, suntola/, Finlandsuntola/ Mathematics, Physics and Philosophy