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REVISITING NEWTON’S LAWS Possible Modification and Cosmological Consequences
Amitabha GhoshIndian Institute of TechnologyKanpur
POINTS TO BE PRESENTED
Unresolved Issues Possible Modification Results Ultimate Consequences
NEWTON’S LAWS
amF i a
F im
2r
mmGF appleearth gg
F
Fr
PROBLEMS WITH THESE LAWS
Ambiguity
Mystery
Paradox
AMBIGUITY
amF i
amF i
The frame of reference ?
valid if ‘a’ is measured in an inertial frame of reference
What is an inertial frame ?
In which is valid
MYSTERY
Why ?
gi mm
This has remained as one of the biggest mystery in mechanics
PARADOX
Because the outer universe can be considered to be composed of concentric spherical shells and each of these shells produces ZERO force on the particle
Grm
rmGrF
34
/.34 23
But O has been chosen arbitrarily. Hence F is arbitrary
F
r
m
O
d
MACH’S PRINCIPLE
George Berkeley 1717Ernst Mach 1883
Interpretation of Mach’s Principle1. The inertial properties of an object are
determined by the presence and distribution of mass-energy throughout all space
2. The geometry of space-time and ,therefore, the inertial properties of every infinitesimal test particle are determined by the distribution of mass-energy throughout all space
F
a
MACH’S PRINCIPLE
amF i
gi mm F
a
Pmg
QUANTIFYING MACH’S PRINCIPLEModel of Inertial Induction
Fi +Gravitational Pull = F
arc
mmGFi 2
21
Fi
a
m1 m2
r
aFi
m2
m1
Fi is the force due to inertial induction proposed by D.W.Sciama (1953)
r
F F+e1 -e2
r
F F+e1 -e2
a
arc
ee
r
eeF
221
221
2
21
r
eeF
LAWS OF MOTION FROM INERTIAL INDUCTION
Fi
am
ma
ar
rdrc
Gm
ar
dv
c
Gm
marc
GmF
HcR
Universe
UniverseObservable
i
ol
101
1..
4
.
0
0
22
2
22
Actually the result should be ideally Fi=ma
SOME ISSUES
Does Mach’s Principle involve instantaneous action-at-a-distance?Does the interaction depend on relative acceleration only?
Let us have a look at our universein the large scale
PICTURE OF THE UNIVERSE
Plot of one Million Gallaxies in the universe
Universe is homogeneous; quasi static and infinite
A mean rest frame of the universe exists
APPLICATION OF THE PROPOSED MODEL
Universal Interaction In which the interaction with the matter present in the rest of the universe is considered
Local Interaction In which the interaction with the nearby matter is considered. Effect of the interaction with the far away matter is negligible
Assumptions regarding the matter present in the universe: The universe is infinite and homogeneous in the large
scale The universe is quasi static The universe is non evolving as a whole
EXTENSION OF MACH’S PRINCIPLE:A Simple Model
Fa
m1 m2
r
F
v
221
r
mGmF
Newton’s static gravitation
arc
mGm2
21
Mach’s Principle as modelled by Sciama
2
2221 v
rc
mGm
Extension ofMach’s PrincipleAs proposed byGhosh
INTERACTION OF A PARTICLE WITH THE REST OF THE UNIVERSE
Integrating over dm1 for thewhole universe
UniverseUniverseUniverse r
dmG
c
ama
r
dmGv
c
mvdm
r
rGmF 1
221
2
2
12
ˆˆ
ˆ
vc
mvˆ0
2
2
r
Gdma
c
ma 12
ˆ
k -
It is nothing but a drag
dF
v
dm1
a
r
m rarc
dmGmrv
rc
dmGmr
r
dmGmdF ˆˆˆ
212
221
21
Drop in energy for traversing a distance ‘dr’
drcE
dE
Edrc
FdrdE
rc
rc
eGG
eErE
0
)0()(
Attenuation of Gravity
EG 21
21
mmEr
Gravitational Force
(energy of graviton)
Ec
cc
E
cF
2
2Cosmic drag
Using this expression for G on the RHS of the expression for FWe get
amvc
mvF
ˆ
2
INERTIAL INDUCTION OF A MASS PARTICLE WITH THE REST OF THE UNIVERSE
mac
mvF
2
rceGG
0
1180 102.1 sxG
m
v
a
F
EXTENSION OF MACH’S PRINCIPLE:Detailed Model
Newton’s Static Gravitation
rurr
GmdMFd ˆ
31 m
dM
rur
1Fd
Accl. Dependent+ Inertial Induction (Mach’s Principle)
forf
forf
forf
uafrc
GmdMFd r
1)(20)(
01)(ˆ)(
23
a
3Fd
forf
forf
forf
ufvrc
GmdMFd r
1)(20)(
01)(ˆ)(2
222
v
2Fd
Vel. Dependent+ Inertial Induction (Extension of Mach’s Principle)
PHENOMENOLOGICAL MODEL OF DYNAMIC GRAVITATIONAL INTERACTION
All masses are relativistic gravitational masses though the subscript g has been dropped
rrr uafrc
GmdMufv
rc
GmdMur
r
GmdMFd ˆ)(ˆ)(ˆ
22
223
The total force on m due to the interaction with the whole universe
0 0
12
11
222
22
0
2
0 12
12
1
0
2
022
22
.ˆ.ˆ
cos)(.sin2.ˆ2
cos)(.sin2.ˆ2
drarrc
Gmudrrv
rc
Gmu
rc
drdamfrGu
rc
drdmfvrGuF
av
a
v
dfdf )(cossin4)(cossin42
0
2
0 where
amdrGrc
umvc
umadrGrc
umvGdrc
v
av
0
1122
0
1122
02
ˆ
)1.....(ˆˆ
v
This is nothing but a drag on m moving at a velocity w.r.t. the Mean Rest Frame of the universe
Drop in energy for traversing a distance ‘dr’
drcE
dE
Edrc
FdrdE
rc
rc
eGG
eErE
0
)0()(
Attenuation of Gravity
EG 21
21
mmEr
Gravitational Force
(energy of graviton)
Ec
cc
E
cF
2
2Cosmic drag
20
0
112
0
02
GdrGr
c
c
GGdr
c
Using this
Substituting in (1) the total force on a particle of gravitational mass m moving with velocity and acceleration w.r.t. the mean rest frame of the universe (which is assumed to be quasi static)
av umaG
umvc
GF ˆˆ
2020
But has been written asvumvc
Gˆ20
vumvc
ˆ2
Hence c
G
c 0
Or, 0G
v
a
in
Finally using this
amumvc
F v
ˆ2
Cosmic Drag Newton’s Second Law
The Magnitude of Cosmic Drag
To determine the magnitude of the cosmic drag the value of is necessary, which depends on the nature of and .
It can be shown that and
satisfy the necessary condition. With these functions .
Using the average matter density of the universe
cos.cos)( f cos.cos)( f
327107 kgm
1181021.1 s
)(f )(f
COMPARATIVE MAGNITUDES OF INERTIAL
INDUCTION TERMS
Local Interaction – Velocity-dependent Inertial Induction is much more significant
Universal Interaction – Primary contribution is from acceleration-dependent Inertial Induction. All moving bodies are subjected to a cosmic drag due to velocity dependent
inertial induction.
REDSHIFT OF PHOTONS
Redshift of light (or electromagnetic wave) will be used frequently. So, a brief introduction is presented below.
The wavelength of the photon increases means that it is shifted towards red. The function
and by the loss of photon energy (called the tired light effect).
ObserverSource
z
is called the redshift.
zc
vrecession The redshift is caused by a recession of the source (called the Doppler effect )
CONSEQUENCES OF UNIVERSAL INTERACTION: Cosmological Red Shift without Universal Expansion
A photon of energy E is subjected to cosmic dragc
E
Hence dxc
EdE
Since the above relation becomeshE dxcd )(
Using the initial condition 0
xc )(exp0
r
dx
c
hE
When the above relation is linearized as follows:
Thus the redshift of an object at a distance r becomes
The exact expression is
1)( xc
xc
0
0
0
xc
0
rc
z
rcez
1
Or,
When the gravitational potential energy of a particle of rest massm is determined using this model
it comes out as -4/3 mc² !!!
GENERAL RESULTS FROM THE PROPOSED MODEL
A Mean Rest Frame Exists. This removes the ambiguity about the frame of reference
The force law is derived from the gravitational interaction establishing the exact equivalence between the gravitational and inertial masses
The gravitational constant decreases exponentially with distance. This removes the gravitational paradox
The gravitational potential energy of a particle of rest mass m comes out as -4/3 mc². Indications are there that the total energy content in the universe is zero.
So all the three major problems of Newton’s laws are resolved
INTERACTIONS OF LOCAL NATURE
Interaction of light with matterInteraction of matter with matter
PHOTON – MATTER INTERACTION
LOCAL PHOTON – MATTER INTERACTION
Rc
MGz
20
0
R
M
GRAV. PULL
000
Rc
MGz
20
0
67.1
R
M
GRAV. PULL
INERTIAL DRAG
00 0
EXCESS REDSHIFT IN WHITE DWARFS
)sin3
11(~ 2
220
0
Rc
GM
Rc
GMz
)sin3
12(~ 2
2
Rc
GM
Rc
GM2
The gravitational redshift of the photons emerging from the surface of a star is given by the following equation:
Since white dwarfs are very high density stars the gravitational redshifts of the light from such stars are much higher than normal stars. The added magnitude of the redshift due to velocity dependent inertial induction will make the star to appear more massive if the whole magnitude is assumed to be due to just gravitational redshift.
R
M
0
Rc
GM
Rc
GMz
22 3
2~ With the proposed theory
Method No. of stars Mean mass
Photometry 110 0.55 ms
Photometry 31 0.60 ms
Binary stars 7 0.73 ms
Two-colour Diagram 40 0.60 ms
Two-colour Diagram 35 0.45 ms
H-line profiles 17 0.55 ms
All together 240 average ma = 0.60 ms
Gravitational red shift (conventional) 83 average mr = 0.80 ms
Gravitational red shift (considering VDII)
83 average m`r = 0.50 ms
According to conventional theoryRc
GMz
20
0 ~
G
RczM
2
~
G
RczM
2
5
3~
So
PHOTONS GRAZING MASSIVE OBJECTS
0
r
M
c c
0
0
z 13
4exp
20
rc
MG=
Typical object M r z
Typical star ~Mo ~ro ~10-6
Typical white dwarf ~Mo ~ro/80 ~10-4
Typical neutron star ~2Mo ~10km ~0.5
Jupiter ~2Mo/100 ~ ro/100 ~10-8
Black Hole ~1Conventional theories do not predict any resultant red shift of photons.
OBSERVATIONAL RESULTS FOR GRAZING REDSHIFTS
UNEXPLAINED EXCESS REDSHIFT AT THE SOLAR LIMB
'
''SUN
R
Because of granulation effect the solar matter oozes out of the surface in the form of bubbles. It expands sideways and then again sinks below the surface. The redshift of the coming out of the sun and reaching earth can be expressed in the form of an equivalent Dopplerian velocity of recession
sin2.0cos)sin3
12(636.0 2 eqv Km/s
OBSERVATIONAL RESULTS OF EXCESS REDSHIFT IN THE SOLAR LIMB
Thus in all the three cases of photon-matter interaction the proposed model produces correct results
It resolves the unexplained mass discrepancy in whiteDwarfs
It explains the unexplained redshift of light grazing past the sun
It resolves the long standing issue of excess redshift in The solar spectrum at the limb
MATTER-MATTER INTERACTION
TRANSFER OF ANGULAR MOMENTUM
F
FResultant forceSpin
As a result of the velocity dependent inertial induction the spinning body is subjected to a resisting torque and it slows down. Loss of angular momentum
The resultant force pushes the body forward causing a gain in its orbital angular momentum. Gain in angular momentum
NO SUCH TRANSFER OF ANGULAR MOMENTUM FROM ONE BODY TO ANOTHER IS POSSIBLE IN CONVENTIONAL MECHANICS
SECULAR RETARDATION OF EARTH’S ROTATION
22106
rad s2
23103.1
moon rad s2
Conventional explanation of thisSecular retardation is tidal friction due to the moon
MECHANISM OF TIDAL FRICTION
Moon
Earth
Ocean
Torque due to tidal friction
Force due to gravitational pull of the tidal bulge
According to this theory the moon should have been so close to the earth 1000 million years ago that both the earth and the moon should have been destroyed because of mutual gravitational pull. But though there is sedimentological evidence
of tidal phenomenon for last 3000 million years there is no sign of any close approach
SUN
2
2
.
c
R
r
mGM
s
s
2
2
.
c
R
r
mGM
s
s R
R
T
mNT 161075.4 !!!!.105.5~ 222
srad
Furthermore there is NO close approach problem of the moon
EARTH
R
SECULAR ACCELERATION OF PHOBOS
MARS
Phobos
phobos
mars
marsphobos
Observed23 .deg106.0~
yrphobos
The calculated value of Using the proposed theory~0.46X10 -3 deg yr-2 !!!!
phobos
SECULAR RETARDATION OF DEIMOS
In a similar manner the secular change in the orbitalSpeed of the other satellite Deimos can be calculated.We get the following theoretical result:
Deimos
=-4.94x10-23 rad s-2
The observation is very inaccurate for Deimos. TheFollowing observational result is available which is Very approximate:
Deimos
=-2.46x10-23 6x10-23 rad s-2
SECULAR RETARDATION OF MARS
Interaction with the sun produces a secular retardationof the spin of Mars. The magnitude can be calculated asdone in case of the Earth and we get a magnitude asfollows:
221025.1
Mars rad s-2
Still no observation has been made to detect anysecular retardation of Mars. Perhaps because itis not expected to be present in the absence ofany sizable satellite that can absorb the loss ofangular momentum of Mars. Phobos and Deimos are like specs of dust in comparison to the Moonand transfer of any noticeable angular momentumwill throw them out of the solar system. However ifever a secular retardation of Mars is detected therewill be no other explanation but the inertial induction
TRANSFER OF SOLAR ANGULAR MOMENTUM At present the sun consists of 99.9% of the total mass of the solar system but only 0.5%
of the total angular momentum of the solar system is possessed by the sun!!!
Onset of main sequence - 107 yrs
Main sequence period- 4.6x109 yrs
Collapse - 106 yrs
Conventional mechanisms are active & prominent only during this pre-main- sequence period
Velocity-dependent inertial induction is operating during the whole period
Taking the angular momentum of the original cloud as 1044kg.m2.s-1(from other existing estimates) and taking the mass of the detached disc as ~2% (estimated from the existing evidences) the present solar angular momentum comes out as 1.4x1041kg.m2s-1 when a transfer mechanism based on inertial induction is considered. This value is 1.5x1041kg.m2s-1.This model also agrees with the observed phenomenon of old stars being slow rotators and vice versa
A number of other unexplained phenomena can be nicely explained using the proposed model. This modelalso removes the problem of large proportion of darkmatter in clusters of galaxies. The required massdistribution in spiral galaxies resulting in flat rotationcurve also comes out as a result of the proposed inertial induction.
It is indeed very surprising that so many unconnectedphenomena are explained by this theory though thereare NO free adjustable parameters in the model
CONCLUSIONS
The proposed theory of “Extended Mach’s Principle” based on themodel of “Velocity Dependent Inertial Induction” leads to a numberof interesting consequences and results as presented below in aconsolidated format
Model of the universe: Infinite, non-evolving and non expanding satisfying the Perfect Cosmological Principle
Consequences of universal interaction Consequences of local interaction
1.Exact equivalence of gravitational and inertial mass2.No ambiguity about the frame of reference3.No gravitational paradox4.Law of motion modified; a small cosmic drag acts on all bodies moving with uniform velocity5.Cosmic drag produces the cosmological redshift6.No need of large amount of dark matter
1.Excess redshift of photons grazing massive bodies explained2.Excess redshift at the solar limb explained3.Mass discrepancy of white dwarf stars resolved4.A mechanism for angular momentum transfer without physical contact is obtained. It explains- (i) Secular retardation of the earth’s spin without close approach problem (ii) Secular acceleration of Phobos and Deimos (iii) Longstanding problem of solar angular momentum transfer is resolved 5.Mass distribution in spiral galaxies explained
The diurnal and annual variations of the anomalous redshift in the signals from Pioneer 10 and 11 alsomatch very nicely (both in magnitude and phase) with the predictions from this theory
Final Recommendation and Comments
The secular change in the spin rate of planetmars should be detected if any. That can yielda positive decision either in favour or againstthe hypothesis of “velocity dependent inertial
induction”.
As planet mars played the most crucial centralrole in transforming old astronomy into
the modern one , it can again help to decide the nature of our
universe
REFERENCES
1. A.Ghosh, Pramana-Jr.of Physics,v23,p-L671(1984)2. A.Ghosh, Pramana-Jr.of Physics,v26,p-1(1986)3. A.Ghosh, Pramana-Jr.of Physics,v27,p-725(1986)4. A.Ghosh,S.Rai,A.Gupta, Astrophysics & Space Science,v141,p-1(1988)5. A.Ghosh, Earth, Moon & Planets,v42,p-169 (1988)6. A.Ghosh, Apeiron, no.9-10 (1991)7. A.Ghosh, Progress in New Cosmology: Beyond the Big Bang (Proc. Of the 13th Krakow Int. Summer School on Cosmology, Lodz, Poland, 1992), Plenum Press (1993)8. A.Ghosh, Physics Education (India),v11,p-417 (1995)9. A.Ghosh, Apeiron, v2, p-38 (1995)10.A.Ghosh, Astrophysics & Space Science,v227, p-41(1995)11.A.Ghosh, Origin of Inertia, Apeiron, Montreal (2000) Affiliated East West Press, New Delhi (2002)
THANK YOU
