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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Observations support spherically closed dynamic space without dark energySPIE Conference 5866, THE NATURE OF LIGHT: WHAT IS A PHOTON?
San Diego, August 1-2, 2005
Tuomo SuntolaSuntola Consulting Ltd., Tampere University of Technology, Finland
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Photon – the minimum dose of electromagnetic energy
The energy given by Planck’s equation
20hE hf cλ λ
= =
T. Suntola: Photon – the minimum dose of electromagnetic radiation SPIE, San Diego, August 1-2, 2005
describes the energy of one wavelength of radiation emitted by a single transition of an electron in a point source
in dynamic space where the line element in the fourth dimension is
4 id dt= ⋅s c
A. Einstein,Cosmological considerations1917
pages 187 to 188
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
24A rπ=
2 rπ2r
24A rπ=24A rπ=
r
Closing of two-dimensional surface
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Closing of two-dimensional surface
Closing of three dimensional volumecreates a surface of a 4-sphere
xR4
y z
24A rπ=
2 rπ2r
24A rπ=24A rπ=
2 33 2A V rπ= =
r
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Closing of two-dimensional surface
Closing of three dimensional volume creates a surface of a 4-sphere
xR4
y z
24A rπ=
2 rπ2r
24A rπ=24A rπ=
2 33 2A V rπ= =
r
αAB
AB
O
rAB
R4
4AB ABr R α= ⋅
Distance in spherically closed volume
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
αAB
AB
O
rAB(t0)
R4
4AB ABr R α= ⋅
AB
O
rAB(t1)
R4
αAB
A
B
O
rAB(t2)
R4
αAB
t
Distance in spherically closed expanding volume
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
αAB
AB
O
rAB(t0)
R4
4AB ABr R α= ⋅
AB
O
rAB(t1)
R4
αAB
A
B
O
rAB(t2)
R4
αAB
t
4 44 4 0
4 4
AB ABrecession AB AB AB AB
dr dR r cv c c r H rdt dt R R
α α= = ⋅ = ⋅ = ⋅ = ⋅ = = the Hubble law
Distance in spherically closed volume expanding at velocity c :
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
αAB
AB
O
rAB(t0)
R4
4AB ABr R α= ⋅
AB
O
rAB(t1)
R4
αAB
A
B
O
rAB(t2)
R4
αAB
t
4 44 4 0
4 4
AB ABrecession AB AB AB AB
dr dR r cv c c r H rdt dt R R
α α= = ⋅ = ⋅ = ⋅ = ⋅ = = the Hubble law
Distance in spherically closed volume expanding at velocity c :
4 id dt= ⋅s c
10
2
4 0
2 sing
GmME dR
π φ φπ φ
Σ= − ∫
D=φR4
R4
dM
Im(x0,y0,z0)
mφ
Gravitation in spherically closed space
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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2
4 4 40
2 sin "0.776gGmM GmM GmME d
R R R
π φ φπ φ
Σ Σ= − = − ⋅ = −∫
D=φR4
R4
dM
Im(x0,y0,z0)
mφImR4
M”=0.776 MΣ
4
"g
GmMER
= −
m
Gravitation in spherically closed space
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
24 4 4 4 4mE v v m mv= = =p v
12
ImR4
M”=0.776 MΣ
4
"g
GmMER
= −
m
The balance of motion and gravitation
24
4
" 0m gGmME E mv
R+ = − =
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
24 4 4 4 4mE v v m mv= = =p v
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ImR4
M”=0.776 MΣ
4
"g
GmMER
= −
m
24
4
" 0m gGmME E mv
R+ = − =
84
m3 10s
v c⎡ ⎤≈ ± ⋅ = ±⎢ ⎥⎣ ⎦
[ ] [ ]9 264
211
2
27 27( )2 2
14 10 l.y. 1.32 10 m
Nm6.67 10kg
kg kg5 10 5 10 0.55m m c Friedmann
R
G
ρ ρ
−
− −
= ⋅ = ⋅
⎡ ⎤= ⋅ ⎢ ⎥
⎣ ⎦⎡ ⎤ ⎡ ⎤= ⋅ = ⋅ = ⋅⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
4 4ids c dt= 2m restE mc E= =
The balance of motion and gravitation
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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Energy of gravitation
Energy of motion
Time
−
Contraction Expansion
∞ ∞
∞
−∞
The cycle of physical existence
The rest energy of matter is gained against release of gravitational energy in a contraction phase …
… and paid back to gravitation in the expansion phase after singularity
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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Gravitational energy
Rest energy
Time
ExpansionContraction
Singularity
The balance of motion and gravitation
mE
gE
24 4 4 4 4mE c c m mc= = =p c
4
"g
GmMER
= −
24
4
" 0m gGmME E mc
R+ = − =
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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Conservation of the energies of motion and gravitation
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
m
Im0
Re0
04
"" igGmME
R= −
0 0 0 0"mE c c mc= =p0 0m=p c
M”
" ?gEΔ =
17
Conservation of the energies of motion and gravitation
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
m
M
M”
φRδ
0δc
Im0
Re0δ
Imδ
Reδ
δc
Rphysical
R0δ
ffv
M”ρ = Μ”−Μ ≈ M”
( ) ( )4 200,0 ffmE c mc p= +
( ) 24
"" 1 igGmM GME
R c R δδ⎛ ⎞= − −⎜ ⎟⎝ ⎠
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The effects of gravitation and motion on the energetic excitation of mass
R4
m
Im
vc
β =
M”
( )2
0 1gE c mcβ β= −
R4
0c
m
M
0 cosc c φ=
ffv
φ
M”M”
( ) 00,mE c mcδ =
( ) ( )2 20 0 0, 1 1 1IE c mc c mcδ β β δ β= − = − −
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
hypothetical homogeneous space
apparent homogeneous space for frame M2
M1
M2M3
R1
The system of cascaded energy frames
( ) ( )2 20,
1
1 1i i
n
i iresti
E mcβ δ δ β=
⎡ ⎤= − −⎣ ⎦∏
apparent homogeneous space for frame M3
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
0restE c mc=
0c
The system of cascaded energy frames
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Extragalactic space
Acceleratorframe
Milky Way frame
Ion frame
Solar frame
Earth frame
Hypothetical homogeneous space( ) ( ) 0 00 0,0I restE E c mc= =
( ) ( ) ( ) 20 1 1XG XGI XG restE E δ β= − −
( ) ( ) ( ) 21 1MW MWI MW I XGE E δ β= − −
( ) ( ) ( ) 21 1S SI S I MWE E δ β= − −
( ) ( ) ( ) 21 1E EI E I SE E δ β= − −
( ) ( )21 AI A I EE E β= −
( ) ( ) ( )2 2(0,0)
1
1 1 1n
Ion rest i iI Ion I Ai
E E Eβ δ β=
= − = − −∏
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
4 2 2 22
2 30 28
en e
e m Z ZE m cn nh
αε
= =
22
1, 20 1 2
1 12n n ef Z m c
h n nα ⎡ ⎤
= −⎢ ⎥⎣ ⎦
22 2
1, 21 2
1 12n n ef Z m c
h n nα ⎡ ⎤
= −⎢ ⎥⎣ ⎦
Balmer’s formula for characteristic frequencies:
( ) ( ) ( ) 2, 0 ,0 1 1I If fβ δ β δ δ β= − −
( ) ( ) ( ) 2, 0,0
1
1 1n
i iI Ii
f fβ δ δ β=
⎡ ⎤= − −⎣ ⎦∏
Characteristic frequencies of hydrogen like atoms
Physical and optical recession velocities
R4c0(t0)
Im2m1
α
Im1
22
c0
m2
( ) 0 04 1rec opt
D zv c cR z
= =+
( ) ( )0 0 ln 1rec physv c c zα= = +
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Propagation of light in dynamic space
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R4 = 1 (observer)
z=0.5
z=1
z=2
z=5
0.67
0.5
0.33
0.17
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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0,01 0,1 1 10 100Redshift
q0=0
q0=0,5
0,1
1
10
100
0,01
Dynamic Universe standard rod
Standard model
DU
4
1
s
zr R zθ +=
( )( )
( )( )22
0F
0 0 0
1
1 1 1 2s H
q zr R q z q q z
θ +=
+ − − + +
Angular size of standard rod & expanding objects / redshift
0 4r Rθ
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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0,01 0,1 1 10 100
Dynamic Universe standard rod
Dynamic Universe expanding objects
(e.g. galaxies)
Redshift
q0=0
q0=0,5
0,1
1
10
100
0 4r Rθ
0,01
Standard model
DU
4
1
s
zr R zθ +=
DU
4
1
sr R zθ
=
( )( )
( )( )22
0F
0 0 0
1
1 1 1 2s H
q zr R q z q q z
θ +=
+ − − + +
Angular size of standard rod & expanding objects / redshift
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Angular size of standard rod & expanding objects / redshift
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0,01 0,1 1 10 100
Dynamic Universe standard rod
Dynamic Universe expanding objects
(e.g. galaxies)
Redshift
0,1
1
10
100
0,01
DU
4
1
s
zr R zθ +=
DU
4
1
sr R zθ
=
0 4r Rθ
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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Angular size /redshift in radio sources (expanding objects)
A. Sandage: The Deep Universe:Fig. 4.4. Kapahi’s (1987, Fig.7) data for the median angular sizes (arcsec) and redshift for his radio-source sample compared with the predictions of the standard model for various q0values (without evolution).
q0 = 0
Steady state
Tired light
DU / Euclidean
q0 = 0.5 (Einstein-deSitter)
Median angular size[arcsec]
redshift0.1 1
10
100
Red curves and observations:
Blue curve: The DU prediction.
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Apparent magnitude of standard candle / redshift
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( )
( )2 1e
obs
FF
z z=
+
( )0 5 log 2.5 log 1z zμ μ= + + +
Distance modulus vs. redshift for Riess et al’s gold dataset and the data from the HST. The triangles represent data obtained via ground based observations, and the circles represent data obtained by the HST. The optimum fit for the standard cosmology equations is shown in red, and the optimum fit for the equation μ = μ0 + 5 log( z) + 2.5 log (z + 1) is shown, slightly below, in blue.
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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Radioactive dating
-15 -10 -5 0
time ( x 109 years )
-15 -10 -5 0
DU
Q/Q(0)
Q/Q(0)
1
1
0
0
DU
linear decay
linear decay
The effect of the declining rest energy on the geological age estimate based on radioactive dating
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
Background radiation: 360° light path
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( )
( )( )
( )
2 6444 0
4 00
4 0
2
26 10 light years535.5
2 750000 years3
1 534.5
RR R e
Rt
c
z e
π
π
−= ≈ ≈ ⋅
= ≈
= − =
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
ACKNOWLEDGEMENTS
The presentation of this paper in the symposium “The Nature of Light: What is a Photon?” in SPIE 2005 conference in San Diego 2005 has been supported by the Foundation of the Finnish Society of Electronics Engineers. The author expresses his gratefulness to the Foundation and the Society.
Acknowledgement is also due to Bob Day for his detailed analysis of the magnitude versus redshift data of supernova observations.
Theoretical Basis of the D
ynamic U
niverse Tuom
o Suntola
http://www.sci.fi/~suntola/
http://www.amazon.com/
33
1. Space is spherically closed through the fourth dimension.
2. There is a zero-energy balance between the total energies of motion and gravitation in the structure. The zero-energy balance is conserved in all interactions in space.
3. Initially space is at rest with infinite dimensions, i.e. the energies of motion and gravitation are zero. Initially mass, as the substance for the expression energy, is unstructured and uniformly distributed in space.
Basic assumptions
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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1. The inherent energy of gravitation is defined in “exclusive space” space as
2. The inherent energy of motion is defined as the energy equivalence of inherent momentumin “environment at rest” as
3. Force is defined as a the negative of the gradient of energy − as the measure of “a natural trend towards minimum potential energy”
Basic definitions
( )g iGmME
r= −
( ) ( )m i iE v= p
ˆdEdr
= −F r
=“Vis viva” ( “living force”, Leibniz 1695)
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
35
Energy of gravitation
Energy of motion
Time
−
Contraction Expansion
∞ ∞
∞
−∞From emptiness at infinity in the past … … to emptiness at infinity in the future.
The cycle of physical existence
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
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The effects of gravitation and motion on the energetic excitation of mass
R4
0c
m
M
0 cosc c φ=
ffv
φ
M”M”
( ) 00,mE c mcδ =( ) ( )4 2
00,0 ffmE c mc p= +
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005
37
The effects of gravitation and motion on the energetic excitation of mass
R4
0c
m
M
0 cosc c φ=
ffv
φ
M”M”
( ) 00,mE c mcδ =
( ) ( ) ( ) ( )0 04
" 1 cosg g gGM m GMmE E E
R Rδ δ φ⎡ ⎤
= − − = − =⎢ ⎥⎣ ⎦
42"
MR GMRM Rc
δ = =
( )0gE
( ) ( )4 200,0 ffmE c mc p= +
T. Suntola: Observations support spherically closed dynamic space without dark energy SPIE, San Diego, August 1-2, 2005