imperial college, london, 12-15 september, 2008 from local to global relativity tuomo suntola,...
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Imperial College, LONDON, 12-15 SEPTEMBER, 2008
From local to global relativity
Tuomo Suntola, Finland
Physical Interpretations of Relativity Theory XI
T. Suntola, PIRT XI, London, 12-15 September, 2008 2
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
On board of Galileo ship …
T. Suntola, PIRT XI, London, 12-15 September, 2008 3
dm
dt
pF a
c velocity
time
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
On board of Galileo ship …
T. Suntola, PIRT XI, London, 12-15 September, 2008 4
dm
dt
pF a
2
0 0 0
½v v v
kin
d m dE d m d m v dv mv
dt dt
v xx v
c velocity
time
c velocity
kinetic energy
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
On board of Galileo ship …
T. Suntola, PIRT XI, London, 12-15 September, 2008 5
Relativistic space:
- increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration
From Galileo ship to space craft …
c velocity
time
c velocity
kinetic energy
c velocity
time 'v
T. Suntola, PIRT XI, London, 12-15 September, 2008 6
Relativistic space:
- increase of velocities are limited to the velocity of light which breaks the linear linkage between force to acceleration
c velocity
From Galileo ship to space craft …
kinetic energy
dm
dt
pF a
2½kinE mv
Rectilinear 32
'1
d m
dt
pF a
2 2
2
11
1
kinE mc c mvc
c velocity
time 'v
T. Suntola, PIRT XI, London, 12-15 September, 2008 7
c velocity
kinetic energy
2' 1dt dt 2' 1dr dr v c
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:
From Galileo ship to space craft …
dm
dt
pF a
2½kinE mv
Rectilinear 32
'1
d m
dt
pF a
2 2
2
11
1
kinE mc c mvc
T. Suntola, PIRT XI, London, 12-15 September, 2008 8
Schwarzschild solution of GR field equations:
2
2
2ff Newton
GM
rc
2' 1dr dr
Gravitation in modified coordinates … via equivalence principle
ct’
dj
M
dsr'
dsj
r'
T. Suntola, PIRT XI, London, 12-15 September, 2008 9
Schwarzschild solution of GR field equations:
2
2
2ff Newton
GM
rc
2
2' 1
GMdr dr
rc 2' 1dr dr
ct’
dj
M
dsr'
dsj
r'
Gravitation in modified coordinates … via equivalence principle
T. Suntola, PIRT XI, London, 12-15 September, 2008 10
Schwarzschild solution of GR field equations:
2
2
2ff Newton
GM
rc
22
2' 1
GMdt dt
rc 2' 1dt dt
2
2' 1
GMdr dr
rc 2' 1dr dr
ct’
dj
M
dsr'
dsj
r'
Gravitation in modified coordinates … via equivalence principle
bff=vff/c
T. Suntola, PIRT XI, London, 12-15 September, 2008 11
Schwarzschild solution of GR field equations:
The (coordinate) velocity of free fall in Schwarzschild space goes
to zero at the critical radius 0
0.5
1
0 10 20 30 40 2
GMr
c
,ff Schwarzschild
ff Newton
2
2
2ff Newton
GM
rc
2
2c Schwd
GMr
c
22
2' 1
GMdt dt
rc 2' 1dt dt
2
2' 1
GMdr dr
rc 2' 1dr dr
ct’
dj
M
dsr'
dsj
r'
Gravitation in modified coordinates … via equivalence principle
bff=vff/c
T. Suntola, PIRT XI, London, 12-15 September, 2008 12
Hypothetical homogeneous space
The system of nested energy frames
local galaxy group frame
Milky Way frameSolar frame
2 20 0
0
1 1n
rest i ii
E m c
Earth frame
“Relativity of rest energy”
T. Suntola, PIRT XI, London, 12-15 September, 2008 13
Hypothetical homogeneous space
The system of nested energy frames
Milky Way frameSolar frame
Earth frame
20,0
0
1 1n
local i ii
f f
local galaxy group frame
“Relativity of characteristic frequencies”
T. Suntola, PIRT XI, London, 12-15 September, 2008 14
Satellite in Earth gravitational 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
T. Suntola, PIRT XI, London, 12-15 September, 2008 15
Satellite in Earth gravitational 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
T. Suntola, PIRT XI, London, 12-15 September, 2008 16
0 0kinE c c c m m c p2kinE c m
Local relativity: Global relativity (Dynamic Universe):
Distinctive characteristics of local and global relativity
by local momentum via insert ofmass equivalence
by gravitation via tilting of space
2restE mcRest energy
Kinetic energy
0
2 20 0 1 1
rest
i ii
E c mc
m c
Description of finiteness
2' 1dt dt
2' 1dr dr
Total energyVelocity in spaceWhat is finite ?
04
"0total
GME c
R p
T. Suntola, PIRT XI, London, 12-15 September, 2008 17
Velocity of mass object on board
Jump to Galileo ship …
0 00
1 shipship
v
v
v v v v
Velocity of light on board ?
characterized as a velocity frame …
0 ship c c v
T. Suntola, PIRT XI, London, 12-15 September, 2008 18
Velocity of mass object on board
Jump to Galileo ship …
0 00
1 shipship
v
v
v v v v
Velocity of light on board ?
Momentum of mass object on board 00
1 shipvm
v
p v p
characterized as a velocity frame …
characterized as a momentum frame …
0 ship c c v
T. Suntola, PIRT XI, London, 12-15 September, 2008 19
Velocity of mass object on board
Jump to Galileo ship …
0 00
1 shipship
v
v
v v v v
Velocity of light on board ?
Momentum of mass object on board 00
1 shipvm
v
p v p
Momentum of light on board
(as reduced by the Doppler-effect)
00
0 0 0
1 1ship shipv vhm
c c
p c c p0hm
p c c
characterized as a momentum frame …
00
hc h f
p
characterized as a velocity frame …
0 ship c c v
T. Suntola, PIRT XI, London, 12-15 September, 2008 20
Velocity of mass object on board
Jump to Galileo ship …
0 00
1 shipship
v
v
v v v v
Velocity of light on board ?
Momentum of mass object on board 00
1 shipvm
v
p v p
Momentum of light on board
(as reduced by the Doppler-effect)
00
0 0 0
1 1ship shipv vhm
c c
p c c p
0 0
0 0
1
1c c
T T T
0hm
p c c
characterized as a momentum frame …
00
hc h f
p
characterized as a velocity frame …
The observed
phase velocity is conserved
0 ship c c v
T. Suntola, PIRT XI, London, 12-15 September, 2008 21
Momentum of mass object on board 00
1 shipvm
v
p v p
Momentum of light on board
(as reduced by the Doppler-effect)
00
0 0 0
1 1ship shipv vhm
c c
p c c p
0 0
0 0
1
1c c
T T T
0hm
p c ccharacterized as a momentum frame …
00
hc h f
p
Phase velocity, group velocity, observed frequencey
T. Suntola, PIRT XI, London, 12-15 September, 2008 22
0 0
0 0
1
1c c
T T T
Phase velocity, group velocity, observed frequencey
Mk
A(k+3)
A(k+2)
A(k+1)
B(k+1)
B(k+1)A(k+2)
A(k+1)
0
0 1
ˆ
1
ABAB t
ABA t B t m
j Bj k
T Tc
r
r r
T. Suntola, PIRT XI, London, 12-15 September, 2008 23
0 0
0 0
1
1c c
T T T
Phase velocity, group velocity, observed frequencey
Mk
A(k+3)
A(k+2)
A(k+1)
B(k+1)
B(k+1)A(k+2)
A(k+1)
0
0 1
ˆ
1
ABAB t
ABA t B t m
j Bj k
T Tc
r
r r
Propagation and observation of electromagnetic radiation
B
B
0 1 AAc c C
C
A
A
0 1 BBc c 0 1 CCc c
2
, 1 AA Af f
21B BBf f
, 1A A A rβ
, 1
B A
B AB
rβ
,1 BB A B A
f f rβ
,A
, , ,A A A
A
c f
c
, , ,
, 1 1
A A A A
AB A C AA A A A
c f ff f f
r rβ β
, 21
A
A
A
B
AB AA
c
c
,B Bc c
, 1
C A
C AC
rβ
C
AC AA
c
c
2
, 1 CC Cf f
,1 CC A C A
f f rβ
,C Cc c
0A t
1C t
Propagation and observation of electromagnetic radiation
C
C
A
A
00
1n
iBi
c c
,A
1
00
0
1
1
C t
A C nA t
i ri
T drc
0A t 1C t
,C A
r
1
00
0
1
1
C t
A C nA t
i ri
T drc
1/ 32 / 3
2 / 3
4
1/ 61/ 3
1/ 31 24
3 2
3 2
g
g
GI Mt
R
GI Mt
R
00
"GMc
R
T. Suntola, PIRT XI, London, 12-15 September, 2008 26
0 0
0 0
1
1c c
T T T
Phase velocity, group velocity, observed frequencey
c0
B
A
0
0 1
ˆ
1
ABAB t
ABA t B t m
j Bj k
T Tc
r
r r
0 1A Ac c
CB
A
Frequency observed
BA
0 1B Bc c 0 1C Cc c
T. Suntola, PIRT XI, London, 12-15 September, 2008 27
Propagation and observation of light
Milky Way frame
Earth
Hypothetical homogeneous space
00
1n
local ii
c c
Bending of light path- D is increased due to local bending of space- DT is increased (Shapiro delay)- c is reduced- l is reduced- f = c/l is conserved- p = h0 f is conserved- redshift of wavelength D l /l = DD /D
2
1
2
1
1 1 1
11 1 1
n
Bj Bj jBj kB
received A B m
Ai Ai iAi k
ff f
z
r
r
Af
Bf
T. Suntola, PIRT XI, London, 12-15 September, 2008 28
Velocity of mass object on board
Jump to Galileo ship …
0 00
1 shipship
v
v
v v v v
Velocity of light on board ?
Momentum of mass object on board 00
1 shipvm
v
p v p
Momentum of light on board
(as reduced by the Doppler-effect)
0hm
p c c
characterized as a momentum frame …
00
hc h f
p
characterized as a velocity frame …
Michelson - Morley interferometer: no change in momentum in different arms – zero result guaranteed
0 ship c c v
00
0 0 0
1 1ship shipv vhm
c c
p c c p
T. Suntola, PIRT XI, London, 12-15 September, 2008 29
Local relativity: Global relativity:
Distinctive characteristics of local and global relativity
2 22 2E mc pc Energy –momentum four-vector
2 2 22 2 20 0 0
2 22
0 0 0Im Re
2 22
0 0 0Im Re
m totE c c mc c p
k c k c k c
k k k
p
Planck constant h 3 20 01.1049 2h e c h c
energy
momentum
mass
wave number 2 2 2
Im Rek k k
0 kg mh
Quantum of radiation
E h 00 0 0 0
hE c c c k c c m c
T. Suntola, PIRT XI, London, 12-15 September, 2008 30
Mass object as a closed energy structure (resonator)
0 0internal kp c
Internal (rest) momentum
T. Suntola, PIRT XI, London, 12-15 September, 2008 31
Mass object as a closed energy structure (resonator)
0 0internal kp c
Internal (rest) momentum
Re 0 0 Re½ k p c
Re 0 0 Re½ k p c
Back wave
Front wave
T. Suntola, PIRT XI, London, 12-15 September, 2008 32
Mass object as a closed energy structure (resonator)
0 0internal kp c
Internal (rest) momentum External momentum
Re 0 0 Re½ k p c
Re 0 0 Re½ k p c
Re Re 0 p p p
Back wave
Front wave
T. Suntola, PIRT XI, London, 12-15 September, 2008 33
Mass object as a closed energy structure (resonator)
20 0 1internal k p c
Internal (rest) momentum External momentum
Re 0 0 Re½ k p c
Re 0 0 Re½ k p c
Re Re 0 p p p
Back wave
Front wave
T. Suntola, PIRT XI, London, 12-15 September, 2008 34
Mass object as a closed energy structure (resonator)
20 0 1internal k p c
Internal (rest) momentum External momentum
2
Re 0 0 Re
1½
1k
p c
2
Re 0 0 Re
1½
1k
p c
0 0 0Re Re 2 21 1
k m
p p p v v
v
Back wave- Doppler shift
Front wave+Doppler shift
T. Suntola, PIRT XI, London, 12-15 September, 2008 35
Mass object as a closed energy structure (resonator)
20 0 1internal k p c
Internal (rest) momentum External momentum
v
0 0 0Re Re 2 21 1
k m
p p p v v
Unified expression of energy
2 2 00 0 0
hE N h N cc c c m c
p
Coulomb energy
A cycle of radiation
The rest energy of matter
B
q2q1
r
ic
FEM
ic
21 2 0 0c 0 0 0 c4 2
q q hE c c N c c c m c
r r
00 0rest
m
hE c c c mc
20 02h e c h c
0 kgmhIntrinsic Planck constant
T. Suntola, PIRT XI, London, 12-15 September, 2008 36
0mE c p
2
0
3
2
1 1
2 1.1049 2 137.036
e
h c
T. Suntola, PIRT XI, London, 12-15 September, 2008 37
2
0 0 Im 0Im 1 ComptonI k k p c
2
Re 0 0 Re
1½
1k
p c
Im
20 0 Re ReRe ½ 1 0I k p c c
2
Re 0 0 Re
1½
1k
p c
Internal (rest) momentum External momentum
Re –
Re +
c
Re Re 0 0 Re 021k k
p p p c c c
Mass object as a closed energy structure
T. Suntola, PIRT XI, London, 12-15 September, 2008 38
2
0 0 Im 0Im 1 ComptonI k k p c
2
Re 0 0 Re
1½
1k
p c
Im
20 0 Re ReRe ½ 1 0I k p c c
2
Re 0 0 Re
1½
1k
p c
Internal (rest) momentum External momentum
Re –
Re +
c
Re Re 0 0 Re 021k k
p p p c c c
The double slit experiment
0 0external k k p c v
20 0 1internal k p c
Mass object as a closed energy structure
Absorption pattern
T. Suntola, PIRT XI, London, 12-15 September, 2008 39
Signal transmission from Earth satellite
0 0 Lv TL L LLT
c c c c
0
1 L
TT
v c
Sagnac delay
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