From Ptolemy skies to FLRW cosmology Hierarchy of physical quantities and theory structures The Dynamic Universe: The overall energy balance – cosmological

•From Ptolemy skies to FLRW cosmology

•Hierarchy of physical quantities and theory structures

• The Dynamic Universe: The overall energy balance – cosmological and local consequences

• Conclusions

The Finnish Society for Natural Philosophy: Models in physics and cosmology, Helsinki 27-28.9.2010 T. Suntola

The Dynamic Universe - from whole to local

Friedman

From Earth centered to everywhere-centered universe


m F a

Claudius Ptolemy († 168)

Nicolaus Copernicus († 1543)

Johannes Kepler († 1630)

Galileo Galilei († 1642)

Isaac Newton († 1727)

Bohr

De BrogliePlanck

Dirac

Schrödinger

Heisenberg

Aristarchus

Aryabhata

2' 1dt dt v c

2' 1dr dr v c

Minkowski

Albert Einstein († 1955)

time

velocityc

velocity

time

c

Contemporary physics

Hierarchy of physical quantities and theory structures

rv

Dynamic Universe

tds

distance [m]time [s]

dt

mE gE

p

Zero-energy balance

Erest(0)

- Redefinition of time and distance- Constancy of the velocity of light- Relativity principle- Equivalence principle- Cosmological principle- Lorentz invariance

QM basis: Resonant mass wave structures

3 20 00 2 kgmh e h cm h

Cosmology


distance [m]time [s] substance [kg]

m

Spherically closed homogeneous space

Re: Kaarle ja Riitta Kurki-Suonio, Fysiikan merkitykset ja rakenteet

Conservation of total energy in local structure buildupRelativity and gravitation

are expressed in terms of modified metrics

Cosmology

Celestial mechanics

Relativity is expressed in terms of locally available energy

ThermodynamicsElectromagnetismCelestial mechanics

Relativity between object and observer Relativity between local and the whole

- Maxwell equation- Planck equation Dirac / Klein-Gordon- QM basis: Schrödinger equation

Erest(local) Eg(local)

Ekin ECoulomb Eradiation

4

The Dynamic Universe

• Spherically closed space, zero-energy balance of motion and gravitation

• Buildup of total energy in spherically closed homogeneous space


5

In search of the structure of space …

Einstein 1917, ”Cosmological considerations of the general theory of relativity”


In search of a finite structure …

Feynman ” Lectures on gravitation in 1960’ ”

“...One intriguing suggestion is that the universe has a structure analogous to that of a spherical surface. If we move in any direction on such a surface, we never meet a boundary or end, yet the surface is bounded and finite. It might be that our three-dimensional space is such a thing, a tridimensional surface of a four sphere. The arrangement and distribution of galaxies in the world that we see would then be something analogous to a distribution of spots on a spherical ball.”

… If now we compare the total gravitational energy Eg= GM 2tot/R to the total rest

energy of the universe, Erest = Mtotc 2, lo and behold, we get the amazing result that GM 2

tot/R = Mtotc 2, 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. After all, what would be the use of studying physics if the mysteries were not the most important things to investigate”

… and energy balance in space …


gE

contraction

Energy of gravitation

Energy of motion

time

Contraction Expansion

expansion

20mE M c

2

4g

GME

R

Zero-energy balance of motion and gravitation


" 0.776M M

20 0 0mE c c m mcp c

0c


4

"g

GME m

R


20

4

"GMc

R

4

"g

GME m

R

" 0.776M M

20 0 0mE c c m mcp c

0c


0c

20

4C

cF m

R

24

"g

GMF m

R


20

4

"GMc

R


• Mass as wavelike substance for the expression of energy

• Unified expression of energy


Quantum as the minimum dose of electromagnetic radiation

“A radio engineer can hardly think about smaller amount of electromagnetic radiation than emitted by a single oscillation cycle

of a unit charge in a dipole.“

1. We solve Maxwell’s equation for the energy of one cycle of radiation emitted by a single electron transition in a dipole

2. We apply the solution to a point source as a dipole in the fourth dimension

3. We apply the result for a unified expression of energies


i

Br

E

E

0z

2 4 2 420 0 0 0

ave 2 2sin

1232s s

dEP c dS dS

dt cr c

E

22 2 2 4 4

2 3 20 0 00

16 22

12 3

N e z f zPE N e c f

f cf

0 , 1z N

3 2 2 200 02

hE e c f hf h cf c m c

kg

The energy of one wavelength of radiation emitted by a dipole


20

3 30

1 1 1

2 1372 2 1.1042 4

e

h

h

Unified expression of energy

00 0 0

hE c cc c m c

p

Coulomb energy

ic ic

1 2 0 0c 0 1 2 0 0 c4 2

q q hE c c N N c c c m c

r r

00 4 0 0rest

m

hE c c mc c c

p

A unit cycle of radiation

The rest energy of mass

0 00 0 0kin tot

m

h hE c c m c c m c c c

pKinetic energy


14


• Conservation of energy in the buildup of local structures in space

• The system of nested energy frames



M”= 0.776 M

m

0 0 00"mE c c mc p

0

""

"g

GmME

R


Conservation of energy in interactions in space

M”= 0.776 M

Im0

mRe0

0restE

m

0

""

"g

GmME

R

0"gE


0 0 00"mE c c mc p

M”= 0.776 M

Im0

mRe0

17

Im

Re

restE

0

"cos 1 "

"g

g

g

EE

E

m

0restE

0"gE "gE 0

""

"g

GmME

R


0 0 00"mE c c mc p


M”= 0.776 M

m

18

m

M

r

cos 1 " 1 1g

GmME

r

"gE

0 1rest restE E

0" " 1g gE E

0

""

"g

GmME

R


0 0 00"mE c c mc p


M”= 0.776 M

19

Im0

mRe0

m

0

""

"g

GmME

R

0"gE

mc


0 0 00"mE c c mc p


M”= 0.776 M

Im0

mRe0

m

0

""

"g

GmME

R

0"gE "gE

mc mv

21mc v c mc

21mc v c

0 2

11

1totE c mc

v c


0 0 00"mE c c mc p


M”= 0.776 M

21

Im0

mRe0

0restE

m

0

""

"g

GmME

R

0"gE

m c

0restE

"gE

restE

mv mv

0totE c c m m

rp v m m

totp c m m


0 0 00"mE c c mc p


The system of nested energy frames

Hypothetical homogeneous space

2

0 00,0restE m c

20,0 1 1XG XGrest XG restE E

21 1MW MWrest MW rest XGE E

21 1S Srest S rest MWE E

21 1E Erest E rest SE E

21 Arest A rest EE E

21 Ionrest Ion rest AE E 2

(0,0),1

1 1n

rest i irest n ni

E E


Clocks in DU space

Substitution of the rest energy of electron

into Balmer’s equation results in characteristic frequencies

of atomic clocks

2,4 0

1

1 1n

i irest n resti

E E

20,0

1

1 1n

local i ii

f f




20,0

1

1 1n

local i ii

f f

0,0f




2, 0,0DU: 1 1local localf f

2

, 0,0GR: 1 2local localf f


0,0 localf

, localf

Satellite in Earth gravitational frame (ECI frame)

2 2 40 0

2,0 ,0

11 1

2 281 1 1DUf f f

2 2 4

0 02

,0 ,0

11

2 8 2

11 2 1GRf f f

0

0.2

0.4

0.6

0,8

1

0 0.2 0.4 0.6 0.8

GR DU

2 = 1

f, /f

Near-Earth clocks


Experiments with atomic oscillators


- Hydrogen ions in canal-ray tube (Ives & Stilwell) 1939

- Mössbauer experiments with centrifuges in 1960th

- Mössbauer experiments in tower in 1960th

- Cesium clocks in airplanes (Hafele & Keating) 1971

- Hydrogen maser to 10 000 km, Scout D (Vessot) 1976

- GPS satellite system 1980 –

- TAI, International Atomic Time laboratories

- Lunar Laser Ranging, annual perturbations

Properties of locally tilted space

Basis of celestial mechanics in GR space and in DU space:

- the velocities of orbital motion and free fall- perihelion advance- orbital periods in the vicinity of black holes

Shapiro delay, bending of light near mass centers


Free fall and orbital velocity in Schwarzschild space:

0

0.5

1

40 30 20 10 02

GMr

c

Limit for stable orbits

orb Schw

Free fall and orbital velocityin DU space:

c DUr

40 30 20 10 02

GMr

c

ff Newton

orb DU

0

0.5

1

slow orbits

ff DU

M ff Newton

0ff

M

31orb DU

2 1 1 2ff DU

ff Schw

2 1 2ff Schwd

1 2

1 3orb Schwd

ff Schw


ff Newton

Dynamic UniverseGR, WeberGR, Berry

Gravitational factor r/rc = 20Eccentricity e = 0.5

Development of elliptic orbit in GR and DU



GR DU

Dj

2

2

2 2

1

1 sin 3 cos cos 31

a er

GMe e e e

c a e

D j

20 0

0 20

1 6 1 cos

1 cos 1

ca e err

e e

Equation (5.37) in J. Weber’s book:

The increase of the orbital radius and the perturbation of the elliptic shape are due to term 3j in the nominator

DU equation for elliptic orbits:



Dj

2

2

2 2

1

1 sin 3 cos cos 31

a er

GMe e e e

c a e

Rotation of Mercury perihelion direction by j = 45 occurs in about 0.5 million years

D j (0)

20 0

0 20

1 6 1 cos

1 cos 1

ca e err

e e

Equation (5.37) in J. Weber’s book:

The increase of the orbital radius and the perturbation of the elliptic shape are due to term 3j in the nominator

DU equation for elliptic orbits:


GR DU

Orbital period near black hole

0

20

40

60

0 4 8 1062 r /rc

min.

Observed 16.8 min rotation period at Milky Way Center, Sgr A* [R. Genzel, et al., Nature 425, 934 (2003) ]

0 4 8 1062 r /rc

Schwarzschild

2

c DU

r cP

r

r

3

2

1c DU c DU

r cP

r r

r r

DU:

Sgr A*: M 3.7 million solar massesrc(DU) 5.3 million kilometers

http://www.youtube.com/watch?v=k7xl_zjz0o8&NR=1


http://www.youtube.com/watch?v=k7xl_zjz0o8&NR=1

34

Geometry of local dents, Shapiro delay, bending of light


The 4D depth profile of the planetary system

Distance from the Sun (light minutes)

0 100 200 300 400

MercuryVenusEarthMars

JupiterSaturn

Uranus

Neptune

Pluto

Sun

dR" x 1000 km

50

100

150

200


The velocity of light in the vicinity of the Earth

-2.9

-3.0

-3.1

-3.2

Sun Moon

Earth

Dc [m/s]

c0d

c(Earth)

Distance from the Earth x 1000 km

-400 -200 200 400

-2.8

0 00 0 0

1 1 ee

GMc c c

r c c


Shapiro delay of radio signal

GR:

DU:

DA DB

Md

, 3 2

2 4Δ ln

A B

A BD D

GM D DT

c d

, 3 2

2 4Δ ln 1

A B

A BD D

GM D DT

c d


Mariner 6 and 7 experiments

10 20 25

Sivuaminen

50

5 150

Mariner 6

Mariner 7

100

150

200

250

Conjunction

Distance from Earth [light minutes]

10 20 25

Conjunction

50

5 150

Mariner 7

100

150

200

250

Mariner 6

Shapiro delay [s]

GR prediction Sun

Earth

Mariner

8.3 min

14.2 min

Sun


Mariner 6 and 7 experiments

Earth

Mariner

8.3 min

14.2 min

Sun

10 20 25

Conjunction

50

5 150

Mariner 7

Sun

Distance from Earth [light minutes]

100

150

200

250

Mariner 6


Shapiro delay [s]

DU prediction

40

Observation of electromagnetic radiation


Signal transmission from Earth satellite

0 0 LL L L v TLT

c c c c

0

1 L

TT

v c

Sagnac delay

Sagnac effect in satellite communication

O

Lωr

h

rΦ

B

A

C

ψ

drBO

At0

Bt1

drr

Bt0

rA(t0)→B(t1)

ψ

2

2Δ ABO

ω Earth

ωAT

c

0

ˆ

1

ABAB tAB

B

Tc β r

r r


Observation of radiation in a moving frame

Sagnac delayed signal Doppler shifted radiation

0 1

1v Dopplerv

TT T

v c f

0

1v Doppler

L

v c

0c

v

vc


0

1SagnacL

TT

v c

0

1SagnacL

LL

v c

0 0 0v v vc f f c Phase velocity in moving frame

Observation of radiation in a moving frame


v0

0

1opt SagnacL

LL L

v c

Momentum in observer’s frame 0 0

0

1v v vv

h h v

c

p c c

0 0 0v v vc f f c Phase velocity in moving frame

Momentum in propagation frame 00 0

0

h

p c

v

2

0Re Re

0

1½

1

h

p c

Im

0ReRe

0ReRe

½

½

IC

IC

h

h

p c

p c

Internal (rest) momentum External momentum

Re –

Re +

c

0Re Re Re2

0 1eff

hm

p p p c v

c

Mass object as Compton resonator

0

20 1

C

h

m

20

Re Re0

1½

1

h

p c

The double slit experiment

0 0external

dB

h h

p v c

Absorption patternMass object


Hydrogen atom: Electron energy minima as resonant mass wave states

2

,0 0

1 1restZ n

n ZE E

k r k r

0 0 0

2

h h nћp c c c

r n r

22

min 1 1tot

ZE mc

n


2 2 2 20tot

Z ћE c mc p mc c

r

2 222

2

Z Zmc R hc

n n

r/r0

Kinetic energy Coulomb energy

22 20 0

2Coulomb

Ze Z ћE c c

r r

2 200 0

0rest

hE c ћ k c

Cosmological properties of spherically closed space


t

FLRW cosmology Dynamic Universe

GR / FLRW space and DU space

0c

4R


Expanding and non-expanding objects in DU-space.

Electromagnetic objects, like atoms, conserve their dimensions

R0R0

R0(1)

emitting object

R0(2)

t(2)

t(1)

Gravitational systems expand with the expansion of space

The wavelength of electromagnetic radiation propagating in space increases in direct proportion to the expansion


Annual increase of the Earth to Moon distance

50

GR DU

Measured 38 mm 38 mm

Expansion of space 0 28 mmTidal interactions 38 mm 10 mm

Lunar Laser Ranging


t

51

FLRW cosmology Dynamic Universe

Light path


Virtual image Distances

GR / FLRW space and DU space

Light path

Angular size of galaxies and quasars

0.01 0.1 1 10 z0.001

log

(LA

S)

Standard model

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

Dynamic Universe:

Euclidean 0

4

1r

R z

0

20

11

1 1 2

z

Hm

rz dz

R z z z z

FLRW cosmologyWm= 1

DU: Euclidean

log

(LA

S)

galaxiesquasars


DistancesVirtual image

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


30

35

40

45

50

0,001 0,01 0,1 1 10

m

Magnitude versus redshift: Supernova observations

Zero-energy spaceDU space

4

2

5log10 pc

2.5log1

R

z

z

Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004)

0 2

5log10 pc

15 log 1

1 1 2

H

z

m

R

z dzz z z z

+ SN Ia observations


Magnitude versus redshift

How does the dark energy hypothesis change the angular diameter prediction?


Angular size of galaxies and quasars

0.01 0.1 1 10 z

log

(LA

S)

0.001

log

(LA

S)

Standard model

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

Dynamic Universe:

Euclidean 0

4

1r

R z

0

20

11

1 1 2

z

Hm

rz dz

R z z z z

FLRW cosmologyWm= 1WL= 0

Wm= 0.3WL= 0.7

Suggested explanation: high z galaxies are young; sizes are still developing (not supported by spectral data!)

galaxiesquasars DU: Euclidean


From Earth centered to 4-sphere centered universe


Claudius Ptolemy († 168)

Nicolaus Copernicus († 1543)

Johannes Kepler († 1630)

Galileo Galilei († 1642)

Isaac Newton († 1727)

Aristarchus

Aryabhata

R4

M”

Gottfried Leibniz († 1716)

20 0 0

0

"GMm c m

R

0c

Heraclitus († 475 BCE)

kr

k0

Re

Dk

k0

Im

0 0m h ћ k

2 20 0,

1

1 1n

i irest n ni

E m c

Albert Einstein († 1955)

Bohr

De BrogliePlanck

Dirac

Schrödinger

Heisenberg


- Offers a holistic – from whole to local approach for describing physical reality

- Relies on a few fundamental postulate

- Covers a wide range phenomena - from microstructures to cosmological dimensions – in a unified formalism

- Produces accurate predictions with straightforward mathematics and clear logic

- Produces a comprehensive picture of physical reality


Development paths of physics and astronomy

2000

0

-1000

Aryabhata

Local approaches / reductionism

System of nested energy frames

Unified expression of energy

DYNAMIC UNIVERSE

Aristarchus

Earth centered universe

Ptolemaios

Local system linked to the

whole

QUANTUM MECHANICS

RELATIVITY THEORYFLRW-COSMOLOGY

Holistic approaches / emergent processes

Logos: intelligence, concluding

EuclidPlato

AristotelesSokrates

Parmenides

Atomists Epikuros

LeucippusDemokritos

AnaxagorasAnaximanderApeiron

Galilei

Space-time

Local system independent of the whole

Mach

Newton

MaxwellKant

HubbleLorentz

PlanckHeisenbergDirac

SchrödingerEinsteinMinkowski

Wrigth LaplaceDe Broglie

HeraclitusLogos: law of nature

Zeno

Brahman

Manifestation via buildup of

opposites

Zero-energy

Ibn ash-Shatir

Leibniz

KopernikusKepler

Friedman

TAO: yin, yang

Nous

1000

Bohr


Documents

From Ptolemy skies to FLRW cosmology Hierarchy of physical quantities and theory structures The Dynamic Universe: The overall energy balance – cosmological