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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