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Dynamics, Relativity and the Equivalence Principle in
the ‘once-given’ Universe
C. S. Unnikrishnan
Gravitation Lab,
Tata Institute of Fundamental Research,
Homi Bhabha Road, Mumbai 400005, India
E-mail address: [email protected]
Website: www.tifr.res.in/~filab
Moriond 2015: Gravitation
Topics:
1) Experimental tests of the PREDICTIONS of the General Theory of
Relativity
2) Experimental tests of the FOUNDATIONS of the General Theory of
Relativity: Equivalence Principles and Special Relativity
3) SOME missing physics
1) Implications for the General Theory of Relativity
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Testing The General Relativistic Theory of Gravity
1. Tests of ‘electric gravity’: Redshift, Time dilation, Deflection, Shapiro delay
-3
-6
10 ®10
2. Tests of Gravitomagnetism: Lense-Thirring and Geodetic spin precession
20%
3. Gravitational waves
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0.3%
Equivalence Principle
Universality of Free Fall  Weak Equivalence Principle; Universal ratio
of gravitational and inertial mass
Einstein’s Equivalence Statement:
Gravitational field ‘g’ and
acceleration ’-a=g’ are equivalent
g
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Einstein Equivalence Principle
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g
5
F -F )
(
dT =
T = gd T / c
1
2
2
c2
From gravitational redshift to time dilation:
Frequency is the number of waves ‘per second’. The number detected
is the same as the number of waves emitted at the source – however,
the unit ‘second’ is different at different points in these frames and
hence the measured frequency is different.
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Gravitomagnetism : uniquely relativistic consequence of GR-like theories
The real gravitational field near the earth
GM
w » 2 W » 5´10-14 rad / s
cr
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Testing Foundations
1. The Weak Equivalence Principle (WEP)
2. Einstein Equivalence Principle and the Strong Equivalence Principle
3. The Principle of Relativity
4. Dynamics: The Special Theory of Relativity
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A serious problem with the foundations of fundamental theories
Universe with all its matter content and gravity existed ages before we
started making our theories…
All our fundamental theories of the physical world were completed well before we
acquired ANY significant knowledge about the physical universe, its content and its
long term evolution.
In particular, the theories of relativity and dynamics (including QM) as well as the
theory of gravity were developed assuming an EMPTY universe.
However, the gravitational potentials of the matter in the universe is a billion (109)
times larger than our local potentials, and if these have any say in dynamics, then we
have completely missed that out in our theories. All our experimental tests, in contrast,
are in the unavoidable presence of cosmic gravity.
So, empirical evidence includes all cosmic gravitational effects, whereas fundamental
theories, as constructed, do not – A reconsideration becomes essential.
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The necessary paradigm change
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300 Million
Light years
(up to Coma)
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10 Billion
Light years
U 

All Galaxies
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G  (4 R 2dR) / R  2 G R 2 H
Moving through the Universe and its CMB marker
Absolute velocity
Absolute (universal) time
Same as average T
(1/105)
Every observer can decide whether he is moving or not, and all clocks
in the universe can be synchronized to this temperature.
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Universe with matter and radiation
There is ONE special frame in which V=0
In all other frames,
SPACE is anisotropic in the frame of a moving observer.
There is a large current of matter (the charge of gravity)
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é g = -1 g = 0
0
0
00
01
ê
0
0
ê g10 = 0 g11 = 1
ê
0
g 21 = 0 g 22 = 1
0
ê
ê
0
0
0
g33 = 1
ë
ù
ú
ú
ú + L(vr : x,t) ®
ú
ú
û
é g = -1 g = 0
0
0
00
01
ê
0
0
ê g10 = 0 g11 = 1
ê
0
g 21 = 0 g 22 = 1
0
ê
ê
0
0
0
g33 = 1
ë
ù
ú
ú
ú
ú
ú
û
Isotropic space remains isotropic after Lorentz transformations on coordinates
Clear conflict with real anisotropic space from matter current
A physical and logically consistent boost transformation should have
returned an anisotropic homogenous metric, reflecting the symmetry of
the transformed space.
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A maximal Lorentz violation from a vector-like (part of a modified metric
tensor field) generated by the motion of the laboratory through the real
matter-filled universe. The anisotropic current and the gravi-magnetic
potentials are physical and large ~v/c.
Physics – dynamics and relativity – indeed has a preferred frame and
universal time.
There are important consequences for even laboratory experiments
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ds = -dt + a (t){dx + dy + dz }
2
2
2
2
2
2
In a frame moving through this matter filled universe, there is
a large matter-current and space is ANISOTROPIC
x' = x -Vt, t ' = t ®
é g ' = -(1- v 2 / c 2 ) g ' = v / c
0
0
00
01
ê
'
'
g
=
v
/
c
g
=1
0
0
ê
10
11
ê
'
'
0
g
=
0
g
=1
0
21
22
ê
ê
0
0
0
g33' = 1
ë
ù
ú
ú
ú
ú
ú
û
Galilean boost gives the physically consistent metric – flat and anisotropic
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é g ' = -(1- v 2 / c 2 ) g ' = v / c
0
0
00
01
ê
g10' = v / c
g11' = 1
0
0
ê
ê
'
'
0
g 21 = 0
g 22 = 1
0
ê
'
ê
0
0
0
g33 = 1
ë
ù
ú
ú
ú
ú
ú
û
Both time dilation and length contraction follows from this anisotropic
transformed metric, with ‘absolute velocity’ (velocity relative to the cosmic
frame) in the Lorentz factors instead of relative velocities.
GPS/atomic clock data strongly support time dilations with
‘absolute’ velocities. It is in fact the most accurate estimates of
such time dilations.
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 gU  1017 m2 / s2
 gE  108 m2 / s2
300 Million
Light years
(up to Coma)
2
v
1  v2 2
1 c
U
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F gU » c !
2
U 
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10 Billion
Light years

All Galaxies
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G  (4 R 2dR) / R  2 G R 2 H
Dynamics and Relativity from Cosmic Gravity (Cosmic Relativity)
Principle of Relativity as unobservability of this ‘gauge’ potential.
Same as statement of Lorentz/Galileo Invariance or invariance under boosts.
NEWTON’S LAW FROM COSMIC GRAVITY
It is already relativistic and ‘gravito-magnetic’
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NEWTON’S LAW FROM COSMIC GRAVITY
It is relativistic and ‘gravito-magnetic’
EQUIVALENCE PRINCIPLE FROM COSMIC GRAVITY
If dynamics respects Newton’s law it respects Equivalence principle as well!
The result that Newton’s law of motion and the WEP have exactly the same
cosmic gravitational origin and physical content implies that all test systems
that follow Newton’s law in any experiment (even in non-gravitational fields)
also obeys the WEP, to the same accuracy!
C. S. Unnikrishnan, Int. Jl. Mod. Phys. (2014) WAG 2014
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A very serious prediction:
No differential time dilation in accelerated frames!
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10 m
This test will return a positive result, obeying EEP – There
will be a redshift in an accelerated frame, as there is in a
real gravitational field.
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10 m
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However, this test will return a null result, violating EEP – There will
be no differential time dilation in an accelerated frame, while there is,
in a real gravitational field.
But the test is intermingled with the issue of the nature of the relative
velocity of light and clock synchronization. Galilean relative velocity of light
is the only way one can get a redshift and no differential time dilation.
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Is the genuine one-way velocity of light relative to an inertial observer
Galilean or Einsteinien?
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Is light Galilean or Einsteinien?
DT =
(
2L
2
c 1- v / c
2
)
-
2L
c 1- v 2 / c 2
The Michelson-Morley interferometer experiment compared the TWOWAY speed of light in two orthogonal directions
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Time delay
(fixed L in rest frame)
Vel. of reference source/detector
L vo
dt = 2
cs cs
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4.0E-18
3.0E-18
2.0E-18
T ( s)
1.0E-18
0.0E+00
-0.1
-0.05
0
0.05
0.1
-1.0E-18
-2.0E-18
-3.0E-18
Velocity (m/s)
The relative one-way velocity of light is Galilean to first order
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Cosmic Gravito-magnetic Effects
Universe in rotating frame
Currents of mass generates a vector potential.
‘A’ changes direction…
Centrifugal force is clearly of cosmic gravitational origin
(Mach, Sciama…)
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Cosmic Gravito-magnetic Effects
Universe in rotating frame
Currents of mass generate large vector potential
And its ‘curl’ is a strong gravito-magnetic field
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In the interferometer frame: Mass current with curl  Gravitomagnetic field
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Atom Interferometer Gyroscope and Cosmic Gravity
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Cosmic Gravity and Spin Physics
SPIN (both classical and quantum) will couple to this because spin and
angular momentum are currents of the charge of gravity – mass currents
Results:
1) Spin-Statistics Connection
2) Spin valves in chiral molecules (experiments)
3) Fractional quantum Hall effect
4) Geometric Phases in chiral transport (experiments)
Unnikrishnan: Relativity and Dynamics in the once-given Universe (in prep.)
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An Ampere Experiment in Electromagnetism
The flip of the magnetic moment is due to a reversed current-current
interaction or reversed magnetic field, now written as
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An ‘Ampere Experiment’ in Gravity
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All our theories are constructed and TESTED in the background gravity of
the entire matter in the universe. There are no experimental tests in the
absence of this cosmic gravity, and there will not be any that can avoid it.
Therefore, ALL theories have to incorporate this EVER-PRESENT
gravitational background a priori, in the relevant equation itself.
Einstein’s equation is INCOMPLETE and needs an important correction.
1
(U )
(M)
Rik - gik R - k Tik = k Tik
2
Warning:
Removal gives the wrong theory
So the 'vacuum' Einstein equation is
1
Rik - Rg ik - k Tik(U ) = 0 and not Rik = 0
2
This incorporates Mach’s principle, and more, into theory of gravity
It is now clear why Einstein could not do it, as he regretted, before ‘seeing’
the real
universe.
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Gravitation
The Centenary Einstein Equation
1
(U )
(M)
Rik - gik R - k Tik = k Tik
2
Machian, Galilean, and fully relativistic
The only input is the observed ~isotropic and ~homogeneous universe
with near-critical density
No assumptions of relativity principle, equivalence principle, or geodesic
principle – all are derived from cosmic relativity. On close and careful
experimental scrutiny, special relativity has to be replaced by cosmic
relativity as the only consistent choice for the basis of GR.
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The case of the asymmetric clocks:
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V
Time contraction for leftward clock!
Experiments do show that the relative rate of clocks depend not on
their relative velocity, but on their absolute velocity (GPS data).
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Is light Galilean or Einsteinien?
DT =
(
2L
2
c 1- v / c
2
)
-
2L
c 1- v 2 / c 2
The Michelson-Morley interferometer experiment compared the TWOWAY speed of light in two orthogonal directions
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L
T 

2 L
c 1 v / c
L
2
2


2 L
c 1  v2 / c2
NO SIGNAL WAS SEEN
Lorentz-Fitzgerald: There is ether, as a special preferred frame
L  L 1  v / c
2
L  L
2
c  c  v and c  v
c  c 1  v / c
2
2
Anisotropic length contraction, anisotropic speed-of-light
Einstein: There is no ether, no real length contraction and no preferred
frame, but isotropic speed of light
L= ® L, c= = c
L^ ® L, c^ = c
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