Extinction Shift PrincipleExtinction Shift Principle

Discourses&

Mathematical Illustrationspertaining to the

under the Electrodynamics ofGalilean Transformations

Edward Henry Dowdye, Jr., Ph.D., PhysicsFounder Pure Classical Physics Research

Member American Physics Society

NPA

Definition of Extinction ShiftExtinction Shift

On Galilean Transformations of VelocitiesOn Galilean Transformations of Velocities

Definition of Extinction ShiftExtinction Shift

On Galilean Transformations of VelocitiesOn Galilean Transformations of Velocities

On Rectilinear Motion of the PhotonsOn Rectilinear Motion of the Photons

• All transformations are strictly carried out under Galilean Transformations of VelocitiesGalilean Transformations of Velocities

• All calculations are performed strictly in

Euclidean Space GeometryEuclidean Space GeometryNo AD HOC assumptions requiredNo requirements of a medium (no ether)No curvilinear coordinates requiredNo distortions of the standard coordinate system of

space and time required

• All Photons and Gravitons move strictly alongRectilinear PathsRectilinear Paths

Extinction Shift PrinciplePure Classical Physics . Euclidean Space . Galilean Transformations

The Photon and its Measurability

• All Laws of Nature are totally invariant under Galilean Transformations

in Euclidean Space

from Reference Frame - to - Reference Frame

• All transformations are describable in a single set of Principal Axioms

• The exact mathematical equivalence of both Special and General Relativity is accomplished from the above premises alone

Extinction Shift PrinciplePure Classical Physics . Euclidean Space . Galilean Transformations

The Photon and its Measurability

Extinction Shift PrincipleExtinction Shift Principle

Principal AxiomsPrincipal Axiomsof theof the

Real WorldReal World

Hypothetical ObserverHypothetical Observerversus theversus the

ObserverObserver

Observer's Observation {in his own frame} Observer

0 1( ) vc

011( ) 2v

c

c + v

0

5v

Hypothetical

Observer c + v

0

2v

Hypothetical

Observer

c + v

0

v

Ordinary

Observer

US

0

0

US

0 1( ) 6vc

0 1( ) 2vc

c - v

c + 6v

c

US

Primary Soure of waves

v

Hypothetical Observer versus Real World Observer

c + v

0

v

US Shuttle

Space Detective extinguishes moving with velocity c + v.He always observes the extinction shifted length and the velocity crelative to the shuttle. Neither the true undisturbed wavelength nor the true undisturbed velocity c + v is measurable!

US

Hello ground control! Just got one! It scattered at the wavelength " ". Its speed was " C "

Space Detective Hunts Down Photon

Interference Lense

'

c

scatteredextinction shifted photon

0

'

undisturbed photon

0

ADVANCEDHypothetical Observer

0

SOME CREATURE JUST KILLED A PHOTON OF LENGTH " " ITS SPEED WAS " C+V " RELATIVE TO ALL THAT INTERFERENCE

'

Hypothetical Observer versus Real World Observer

Equivalent WavesEquivalent Waves

IndistinguishabilityIndistinguishabilityofof

Primary Soure of waves

v

Equivalent Waves and the Ordinary Observer

The Ordinary {Real-World} Observer can make no distinction between Equivalent Waves or Photons!

c v cc v c

B eforeIn terferen ce

A fterIn terferen ce

c + v

c+v

c

c + v

c+v

Ordinary

Observer

c

c

c + v

c+vOrdinary

Observer c

c

c

Mathematical Proof Mathematical Proof

Principal AxiomsPrincipal Axioms applied toapplied to

ElectromagnetismElectromagnetism

Principal AxiomsPrincipal Axioms applied toapplied to

GravitationGravitation

On GravitationOn GravitationThe very same principal axioms of the logical addition of velocities also apply to the exchange of gravitons between particles of mass! The motion of a particle through the field set up by a different particle under the gravitational influence of the first, has a direct representation under the electrodynamics of Galilean Transformations of Velocities, abiding strictly by the rules of rectilinear motion in Euclidean Space!!!

MM motion of Gravitons

from M

c

v

mm

motion of m

G g = field of m

c

vc'

= field of M

Gravitational LensingGravitational LensingSignificant FindingsSignificant Findings

Fundamental Facts supported by Observational EvidenceFundamental Facts supported by Observational Evidence

on

Significant FindingSignificant Finding

Solar Gravitational Gradientinteracts directly with

Solar Plasma Limbwhich interacts directly with

Electromagnetic Waves

The Observational Evidence

• The gravitational gradient field of the sun acts directly on the plasma limb of the sun.

• The plasma limb of the sun acts directly on the electromagnetic waves propagating along a minimum-energy or a least-time path within the plasma limb as would be defined by the gravitational gradient field of the sun.

• The gravitational gradient field of the sun acts only indirectly on the electromagnetic waves that are being deflected by the plasma limb.

All electromagnetic waves propagating in the plasma-free vacuum space appear to be unaffected by the gravitational gradient field of the sun and of the stars

The Observational EvidenceAll electromagnetic waves in the plasma limb

propagate along a minimum-energy path

VSUN

Earth1.00 AU

Venus0.72 AU

Mercury0.38 AU

Earth1.00 AU

VEARTH

VSUN = 14.14 VEARTH

grav

itatio

nal p

oten

tial

VS

UN

distance r

The Gravitational Potentialof the SUN and of the EARTH at a given point of reference

where the point of reference is near Earth’s Surface

VSUN = 14.14 VE

where the point of reference is anywhere in space

The Gravitational Potential Gradientof SUN compared to EARTH along Earth’s Orbit

R 4G MR c 2

r R R

R

M

2R

r R R

Gaussian Sphere of 2 Solar Radii

Gaussian Sphere of 3 Solar Radii

Gaussian Sphere of 4 Solar Radiii

Sun

thin plasma rim

The Observationsas function of

Impact Parameterin empty vacuum space

R 4G MR c 2

r R R

R

r R12 R 2

M

2R

r R13 R 3

r R14 R 4

r R R

Gaussian Sphere of 2 Solar Radii

Gaussian Sphere of 3 Solar Radii

Gaussian Sphere of 4 Solar Radiii

Sun

thin plasma rim

General Relativitypredicts as function of

Impact Parameterin empty vacuum space

42

G MR c

22

2 G MR c

12

2 G MR c

GeneralRelativity

integrated effect

Gauss Law

22

2 G MR c

12

2 G MR c

Sg dA 4 GM 2

2GMg R

gA ( )(4 R ) 4 GM

22GM

1 Rc

MINIMUM ENERGY PATH or MINIMUM TIME PATH

PRINCIPAL OF RECIPROCITY

Gravitational Light Bendingas function of

Impact Parameterin

Plasma Free Vacuum Space

R 4G MR c 2

r R R

R

r R12 R 2

M

2R

r R13 R 3

r R14 R 4

r R R

Gaussian Sphere of 2 Solar Radii

Gaussian Sphere of 3 Solar Radii

Gaussian Sphere of 4 Solar Radiii

Sun

thin plasma rim

General Relativityas function of

Impact Parameterin empty vacuum space

R 4G MR c 2

r R R

R

M

2R

r R R

Gaussian Sphere of 2 Solar Radii

Gaussian Sphere of 3 Solar Radii

Gaussian Sphere of 4 Solar Radiii

Sun

thin plasma rim

The Observationsas function of

Impact Parameterin empty vacuum space

1 .7 5 a rc s e c o b s e rv e d

N o le n s in g o b s e rv e d

R 2 R3 R

N o le n s in g o b s e rv e d

A light bending effect due to the sun’s gravitational field, should, as theoretically predicted by General Relativity, take place at the Gaussian sphere, 2R, yielding 1/2 of 1.75 arcsec, at the Gaussian sphere, 3R, yielding 1/3 of 1.75 arcsec.This should be noticeable for nR using modern technical means.

As Function of the Impact Parameter

The focal length F and the radius R of the sun are expressed in the same units. The light rays from a distant star of 1 solar mass M and 1 solar radius R will come to a focus at a distance of roughly 550 astronomical units, assuming a convergence angle of 1.75 arcsec. It has been a long desire of astrophysicists, SETI study groups and the International Academy of Astronautics, to send instruments to large astronomical distances to exploit the light bending focal length of the sun’s rim.

550 AU

1.75 arcsec

The Focal Lengthof the

Solar Plasma Rim

Distance h(RSUN ) above Rim

r = RSUN + h

Acceleration

gSUN

1/r 2 Effect

Acceleration m/s2

1/r 2 Effect

Observed Lensing

Predicted by General Relativity

1/R EffectR = RSUN + h

h = 1.0, r = 2.0 RSUN 0.25 gSUN 68.5 m/s2 none 0.88 arcsec

h = 0.5, r = 1.5 RSUN 0.44 gSUN 121.8 m/s2 none 1.17 arcsec

h = 0.2, r = 1.2 RSUN 0.69 gSUN 190.3 m/s2 none 1.45 arcsec

h = 0.1, r = 1.1 RSUN 0.83 gSUN 226.4 m/s2 negligible or none 1.59 arcsec

h = 0, r = 1.0 RSUN 1.00 gSUN 274.0 m/s2 1.75 arcsec 1.75 arcsec

Distance / Rsun

0.10

0.05

0

no lensing observed

negligible or no lensing observed

The Shapiro DelayA Frequency Dependent Transit-Time Effect

noticeable transit time delay as a function of the impact parameter of the microwave beam relative to the sun

no bending of optical, IR or UV waves due to the electron density profile

THE OBSERVATIONAL EVIDENCE

SOLAR  PLASMA  INDEX  OF  REFRACTION

r(Rsun) Ne( cm^-3) Ne / Nc Ne / Nc n=1-½Ne/Nc 1 / n 1 / n 1 / n2.2GHz 8.8GHz 8.8GHz 2.2GHz 8.8GHz Optical

200 5.4606E+00 9.0985E-11 5.6866E-12 1.0000000000 1.0000000000 1.0000000000 1.0000000000

150 1.0124E+01 1.6869E-10 1.0543E-11 1.0000000000 1.0000000001 1.0000000000 1.0000000000

100 2.4386E+01 4.0632E-10 2.5395E-11 1.0000000000 1.0000000002 1.0000000000 1.0000000000

50 1.1282E+02 1.8798E-09 1.1749E-10 0.9999999999 1.0000000009 1.0000000001 1.0000000000

40 1.8640E+02 3.1059E-09 1.9412E-10 0.9999999999 1.0000000016 1.0000000001 1.0000000000

30 3.5868E+02 5.9763E-09 3.7352E-10 0.9999999998 1.0000000030 1.0000000002 1.0000000000

20 9.1538E+02 1.5252E-08 9.5327E-10 0.9999999995 1.0000000076 1.0000000005 1.0000000000

15 1.7986E+03 2.9968E-08 1.8730E-09 0.9999999991 1.0000000150 1.0000000009 1.0000000000

12 3.0559E+03 5.0919E-08 3.1824E-09 0.9999999984 1.0000000255 1.0000000016 1.0000000000

11 3.7631E+03 6.2702E-08 3.9189E-09 0.9999999980 1.0000000314 1.0000000020 1.0000000000

3 9.2431E+04 1.5401E-06 9.6257E-08 0.9999999519 1.0000007701 1.0000000481 1.0000000000

THE OBSERVATIONAL EVIDENCE

No Gravitational Light Bending OccursAt Astronomically Large Impact Parameters

in empty vacuum space

THE QUESTION IS

Where are the Einstein Rings?

No Gravitational Light Bending on the Rays of Star Light atAstronomically Large Impact Parameters

in empty vacuum space

Distance h(RSUN ) above Rim

r = RSUN + h

Acceleration

gSUN

1/r 2 Effect

Acceleration m/s2

1/r 2 Effect

Observed Lensing

Predicted by General Relativity

1/R EffectR = RSUN + h

h = 1.0, r = 2.0 RSUN 0.25 gSUN 68.5 m/s2 none 0.88 arcsec

h = 0.5, r = 1.5 RSUN 0.44 gSUN 121.8 m/s2 none 1.17 arcsec

h = 0.2, r = 1.2 RSUN 0.69 gSUN 190.3 m/s2 none 1.45 arcsec

h = 0.1, r = 1.1 RSUN 0.83 gSUN 226.4 m/s2 negligible or none 1.59 arcsec

h = 0, r = 1.0 RSUN 1.00 gSUN 274.0 m/s2 1.75 arcsec 1.75 arcsec

Distance / Rsun

0.10

0.05

0

no lensing observed

negligible or no lensing observed

From the BookDiscourses & Mathematical Illustration pertaining to the 

Extinction Shift PrincipleSolved Problems on GRAVITATION

Solar Light Bending (in Plasma Atmosphere of Sun)Here, it is found that, due to the gravitational gradient of the plasma of the sun, the very same light bending equation of

is derived using pure classical assumptions only. Exactly 1.75 arcsec of light bending in the plasma atmosphere of the sun is predicted by this Extinction Shift Principle because of pure classical reasons only. The significant finding here is that for nearly a century of intense observations, an indirect interaction between the gravitational field of the sun and the rays of light of the stars has been observed, not a direct interaction as predicted by General Relativity. The mere fact that this effect is observed for a century only in the plasma atmosphere of the sun is in itself a direct violation and thus an astrophysical discount and disproof of the light bending rule of General Relativity. Recall that Relativity claims gravitational light bending effect should occur in the vacuum space just slightly above the solar rim of the plasma as well as in the solar plasma atmosphere.

Integrated Effect of the Gravitational Gradient Field

(Potential) of mass M

r Rr G M

rr R

rG M

Rdr

2

Max Velocity v 2 G MR

Light Ray Frequency ' ( ) ( ) 0 021 1 2

vc

2

2G M

R c

Light Ray Wavelength

' ( ) ( ) 0

10

2 11 1 2vc

2

2G M

Rc

' ( ) 021 2

G MR c

Number of Wavelengths per unit

Length

n G MR c

1 1

1

1 2

01 0

21 ' ( )( )

v2

c2

Redshift

Redshift

Energy along path of light as function of

Gravitational Potential 0

21 2( )G Mrc

Change in Energy

per unit length

dd r

G Mr c

02

2 2

02

2 2G M

r cR

Deflection Angle

upon approach

ap p

GMr cr

r RG M

R c

a pp dr

2 22 2 2

Deflection Angle

upon receding

re cG M

r cr R

rG MR c

r e c dr

2 22 2 2

Net Deflection Angle rec a ppG M

R c4

2

rec a p pG MR c

42

less than1 arcsec

Telescope

Observed and Recorded by Modern Astrophysics since 1992

If the light bending rule of General Relativity were actually correct then occasional distortions in the images of the stellar objects moving about Sagittarius A* will most likely have been observed and recorded; given modern Astrophysical means.

As Predicted by General Relativity: Not Currently Observed

Direct Gravitation-Electromagnetism Interaction

THE PREDICTION OF GENERAL RELATIVITY

No Direct Gravitation-Electromagnetism Interaction

THE OBSERVATIONAL EVIDENCENo Gravitational Light Bending Occurs

in Empty Vacuum Space

R

M

2R Gaussian Sphere of 2 R

Gaussian Sphere of 3 R

Gaussian Sphere of 4 R

Black HolesBlack HolesEmission Theory

R

THE OBSERVATIONAL EVIDENCEat the

Galactic Center

Einstein Ring CalculationEinstein Ring Calculation

DL DSL

DS

24

1 2 approach recede

GMRc

Assume : : 1:1:2L SL SD D D

R2

Einstein ring of radius

1M

1

4G MR c 2 1 2

RD

RDL SL

4G Mc 2

R R2 1D

1D

2 D DD DL SL

SL L

L SL( ) ( )

T O T A L g en era lcase

R

D4G Mc D

D DD DL

2L

L SL

SL L

2G Mc D2

L D DL S L

From symmetry we have

Solving for the radius of the impact parameter of the light ray and thus the radius of the Einstein Ring expressed in radians we have

and finally

Radius of the Einstein Ring

Note that the angle of deflection for the approach segment, one half of the total gravitational effect, is exactly equal to the radius of the solved Einstein ring expressed in radians and is given as   

This is a rarely covered fundamental on in modern academic textbooks. The accumulative effect must sum the effects on the light ray upon approach and receding the gravitating mass.

From above, the total accumulative effect is thus

22GM

1 Rc

2

p

a(1 e )1 eCos( )r( )

R r( ) p

2 2 2 2

1 eCos( )2GM 2GM1 Rc c a(1 e )c

[ ]

E. H. Dowdye, “Time resolved images from the center of the Galaxy appear to counterGeneral Relativity”, Astronomische Nachrichten, Vol. 328, 2, pp. 186-191 (2007)

Published online at: http://www3.interscience.wiley.com/search/allsearch

2

2GMg R

gA ( )(4 R ) 4 GM

Sg dA 4 GM

22GM

1 Rc

2

p

a(1 e )1 eCos( )r( ) R r( )

p

2 2 2 2

1 eCos( )2GM 2GM1 Rc c a(1 e )c

[ ]

SUMMARY

• The gravitational gradient field of the sun acts directly on the plasma limb of the sun.

• The plasma limb of the sun acts directly on the electromagnetic waves propagating along a minimum-energy or a least-time path within the plasma limb.

• The gravitational gradient field of the sun acts indirectly, not directly, on the electromagnetic waves propagating in the plasma limb of the sun.

SUMMARY

All electromagnetic waves in the plasma limb propagate along a minimum-energy path

All electromagnetic waves propagating in the plasma-free vacuum space appear to be unaffected by the gravitational gradient field of the sun and of the stars

SUMMARYThe severe dependency of the observedgravitational deflection of microwaves

on the IMPACT PARAMETER

is solid evidence light bending rule ofGeneral Relativity is violated.

THERE IS STILL THE BURNING QUESTION

Where are the Einstein Rings?

SUMMARY

SUMMARY

Where is Einstein at Sagittarius A*?

"Wenn die Lichtgeschwindigkeit auch nur ein bißchen von der Geschwindigkeit der Lichtquelle abhängig ist, dann ist meine ganze

Relativitätstheorie und Gravitationstheorie falsch.“

"If the velocity of light is only a tiny bit dependent on the velocity of the light source, then my whole theory of Relativity and Gravitation is false.“

{Quotation of A. Einstein from a letter to Erwin Finley-Freundlich: August 1913}.

Nobel Prize Physicist Dr. Albert Einstein receivesa Lincoln University honorary degree for his accomplishments during his visit in 1946.

http://www.lincoln.edu/sesquicentennial/legacy.html

Extinction Shift PrincipleExtinction Shift Principle

Discourses & Mathematical Illustrations pertaining to the

under the Electrodynamics ofGalilean Transformations

www.extinctionshift.com

Significant Findings on Gravitational Lensing

www.extinctionshift.com/SignificantFindings.htm

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