Einstein’s Tests of General Einstein’s Tests of General Relativity through the Eyes of Relativity through the Eyes of
NewtonNewtonJames Espinosa James Espinosa
Department of PhysicsDepartment of PhysicsUniversity of West GeorgiaUniversity of West Georgia
OutlineOutline
I.I. Experimental OverviewExperimental OverviewII.II. Newtonian PhilosophyNewtonian PhilosophyIII.III. Gravitational RedshiftGravitational RedshiftIV.IV. Ritzian Emission TheoryRitzian Emission TheoryV.V. Precession of MercuryPrecession of MercuryVI. Bending of StarlightVI. Bending of StarlightVII. ConclusionsVII. ConclusionsVII. Future WorkVII. Future Work
Experimental OverviewExperimental Overview1845 – Urbain LeVerrier observes a 35'' per century
excess precession of Mercury's orbit
Modern accepted value is 43.11" ± .45" per centuryWould take over 3,000,000 years to complete a circle
1915 - Einstein's General Relativity predicts 1915 - Einstein's General Relativity predicts 42.9" precession42.9" precession
1919 – Eddington measures deflection of 1919 – Eddington measures deflection of starlight during total solar eclipse – 1.75”starlight during total solar eclipse – 1.75”
1960 – Pound and Rebka measure a 1960 – Pound and Rebka measure a redshift of 2.5 x 10redshift of 2.5 x 10-15-15
Newtonian PhilosophyNewtonian Philosophy•Absolute space and time•Atomic Hypothesis•Determinism•Three laws of motion•Action-at-a-Distance•“The whole burden of philosophy seems to consist in this- from the phenomena to investigate the forces of Nature and then from these forces to demonstrate the other phenomena”- Newton•Unification of Force is implicit
Historical InterludeHistorical Interlude
Gravitational RedshiftGravitational Redshift 1784 - Rev. John Michell proposes using 1784 - Rev. John Michell proposes using
gravitational redshift to measure the mass of gravitational redshift to measure the mass of starsstars
Bending of StarlightBending of Starlight 1785 – Henry Cavendish calculates the 1785 – Henry Cavendish calculates the
deflection of light due to Sun’s gravity, getting deflection of light due to Sun’s gravity, getting half the value of the modern value.half the value of the modern value.
Precession of MercuryPrecession of Mercury 1875 – Tisserand uses gravitational version of 1875 – Tisserand uses gravitational version of
Weber’s law to arrive at correct value.Weber’s law to arrive at correct value.
Gravitational RedshiftGravitational Redshift
+=
21c
ghEE topbottom
+=
21c
ghEE topbottom
+=
21c
ghEE topbottom
211c
gh
E
E
h
hz
top
bottom
top
bottom
bottom
top +====+ν
νλλ
15105.25.22 −=∆=⇒= xzmhλλ
From Pound & Rebka (1960)…
Unification SchemeUnification Scheme
GravityThermodynamicsAtomic PhysicsElectromagnetism
Force TransmissionForce Transmission
Ballistic methodBallistic method
Action-at-a-distanceAction-at-a-distanceMedium methodMedium method
EtherEther
Medium PictureMedium Picture
Waves move outward at velocity c, independent of source velocity
Ballistic PictureBallistic Picture
Particles move outward at velocity c+v’
Ritzian Emission TheoryRitzian Emission Theory( ) ( ) ( ) ( )
−⋅+−
⋅−⋅−−
−+=→ 22222
2
2
2
20
2112 ˆ
2
1ˆˆ
2ˆ
4
13
4
31
4a
c
rvrv
c
krra
c
rrv
c
k
c
vk
r
QQF
πε( ) ( ) ( ) ( )
−⋅+−
⋅−⋅−−
−+=→ 22222
2
2
2
20
2112 ˆ
2
1ˆˆ
2ˆ
4
13
4
31
4a
c
rvrv
c
krra
c
rrv
c
k
c
vk
r
QQF
πε( ) ( ) ( ) ( )
−⋅+−
⋅−⋅−−
−+=→ 22222
2
2
2
20
2112 ˆ
2
1ˆˆ
2ˆ
4
13
4
31
4a
c
rvrv
c
krra
c
rrv
c
k
c
vk
r
QQF
πε
( ) ( ) ( ) ( )
−⋅+−
⋅−⋅−−
−+=→ 22222
2
2
2
20
2112 ˆ
2
1ˆˆ
2ˆ
4
13
4
31
4a
c
rvrv
c
krra
c
rrv
c
k
c
vk
r
QQF
πε
Explains:•Electrostatics•Magnetostatics•Electrodynamics•Radiation/Optics•Radiation Reaction
Gravitational VersionGravitational Version
G
MQ
→
→
04
1
πε
−+= ...
4
31
2
221
11 c
vk
r
MMGaM
G
MQ
→
→
04
1
πε
−+=→ ...
4
31
2
221
12 c
vk
r
MMGF
Insert into Newton’s 2nd Law
Precession of MercuryPrecession of Mercury( ) ( )
dt
dr
dt
dx
rc
k
dt
dr
c
k
dt
dy
dt
dx
c
k
r
x
dt
xd22
2
2
22
232
2
2
1
4
13
4
31
++
−−
+
−+−= µµ
( ) ( )dt
dr
dt
dy
rc
k
dt
dr
c
k
dt
dy
dt
dx
c
k
r
y
dt
yd22
2
2
22
232
2
2
1
4
13
4
31
++
−−
+
−+−= µµ
−+=
−
dt
dyx
dt
dxy
dt
dr
rc
k
dt
dyx
dt
dxy
dt
d222
)1(µ
µ≡
=+= 222 yxr Ugly… But not a tensor!
Angular Momentum
rc
k
edt
dyx
dt
dxy
22
)1( µ
α+−
=
−
+−=
rc
k
dt
dr
22
2
)1(1
µαφ
Mercury Cont’dMercury Cont’dAdd higher order terms to make equation of motion integrableAdd higher order terms to make equation of motion integrable
+−+
+
2
2
2
2
2222
2
2
1
2
1
dt
yd
r
y
dt
xd
r
x
rc
kx
rc
k
dt
xd µµ
+−+
+
2
2
2
2
2222
2
2
1
2
1
dt
yd
r
y
dt
xd
r
x
rc
ky
rc
k
dt
yd µµ
dt
dy
dt
dx,Multiply each by , add, integrate to find first integral of motion
constant 22
11
2
)1(
2
1
2
11
2
)1(
2
1
2
1
22
22
2
2
2
2
2
22
==−
−−−
−
−+−
+
βµµ
µ
rcdt
dr
cr
k
dt
dy
cdt
dx
cr
k
dt
dy
dt
dx
Mercury Cont’dMercury Cont’d
++++++−×
−+
=
++
+++
−+−=
ββµµµαµ
µβµµµαφ
α
2)1(2)2(
2
)1(1
122
)12(1
2
2
)1(1
222
22
2
2222
22
4
2
rc
k
rrc
k
rrc
k
rc
k
rc
k
rrc
k
rd
dr
r
pr
=1
∫ ++−
−−
=−ABppC
c
pkdp
22
2
0
4
)1(1
µ
φφ
22
22
2222
)2(1
)1(2
2
c
kC
c
kBA
αµ
αβµ
αµ
αβ +−=++==
ABppCc
k
ACB
Bpc
c
k ++−−+
+−
++=− 22222
2
22
2
0 4
)1(
4
2arcsin
4
)5(1
µα
µφφ
let
++22
2
4
)5(1by but , revolution a halfafter by not advances
c
k
αµππφ
Mercury Cont’dMercury Cont’dIf N is the number of revolutions per century, the angle of precession isIf N is the number of revolutions per century, the angle of precession is
22
2
2
)5(
c
Nk
απµδ += )1(
122 ea −
=αµ
200
0
0
century
revs. 414.9378
.206 Planet ofty eccentrici
Au .38703 Sun &Planet between distance averages
km29.77 speed orbital
Au 1 Sun &Earth between distance average
va
N
e
a
v
a
=
=
=≡=≡
=≡
=≡
µ
Na
a
c
v
e
k 0
2
02 )1(2
)5(
−+= πδ
ka
a
v
c
N
e =−
−5
)1(2
0
2
0
2
πδ
k = 7 results in a precession of 43.1” per century
…On to the Bending of Starlight…
Bending of StarlightBending of Starlight( ) ( )
dt
dr
dt
dx
rc
k
dt
dr
c
k
dt
dy
dt
dx
c
k
r
x
dt
xd22
2
2
22
232
2
2
1
4
13
4
31
++
−−
+
−+−= µµ
( ) ( )dt
dr
dt
dy
rc
k
dt
dr
c
k
dt
dy
dt
dx
c
k
r
y
dt
yd22
2
2
22
232
2
2
1
4
13
4
31
++
−−
+
−+−= µµ
−++
−
ryyxx
rc
x
r
xx
rc
µµµµ
3232
Add higher order terms to x-component to make equation integrable
Similar term for y-component
Energy Conservation Equation
( ) ( ) 22222
2
2
22
2
1constant2/
21
2
1
21
2
1
2
1 ωµµµ ==−
−−+
−++
•
rcc
r
r
k
c
v
r
kv
Bending of StarlightBending of StarlightAngular Momentum Conservation EquationAngular Momentum Conservation Equation
++=
22
11
c
khJ
µρ
parameterimpact , 1
, where ≡== br
bh ρω
Angular Deflection Equation
Using b = 1 solar radius (6.96x108 m) and k=7
2
4
bc
GM S=∆θ = 1.75”
ConclusionsConclusions
• Ritz's Theory explains both observations if the constant Ritz's Theory explains both observations if the constant
k has the value 7.k has the value 7.
• Explanations of the precession of Mercury,the bending Explanations of the precession of Mercury,the bending of starlight and gravitational redshift do of starlight and gravitational redshift do notnot require require
the General Theory of Relativity.the General Theory of Relativity.
Future WorkFuture Work
Gravitational LensingGravitational LensingGravitational WavesGravitational WavesUnify Gravity and ElectromagnetismUnify Gravity and Electromagnetism
Many Thanks to:
Mr. Gary Hunter
Dr. Julie Talbot
UWG’s Student Research Assistant Program
G.R. Parameters vs. Our ParametersG.R. Parameters vs. Our Parameters
k=7k=7