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GENERAL THEORY OF RELATIVE MOTIONS

 E. A. ROBINSON
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Copyright © 1969 by Edwin A. Robinson

 

ABSTRACT
General Theory Of Relative Motions is a new approach to interpreting classical Doppler phenomena with the introduction of four laws of relative motion, five different transformation equations to account for relative motion, and much geometry to explain relative motions, tables to demonstrate agreement with the Principle of Reciprocity, the Principle of Detailed Balance, and the Principle of Causality. All are in agreement with each other and are provable or disprovable, and all are in complete agreement with logic and nature in other spectrums.

SYMBOLS USED
C Velocity of electromagnetic or sound waves.
S Source.
O Observer.
Sv Source velocity.
Ov Observer velocity.
tf Transform factor.
Stf Source transform factor.
Otf Observer transform factor.
l’ Wavelength alteration.
fo Laboratory frequency.
h Index of refraction found by C’/C.
h Plank's constant.
lo Laboratory wavelength.
ls Wavelength altered by source motion.
lo Wavelength altered by observer motion.
lr Wavelength under refraction (internal).

Eq’ Quantum energy alteration.
X Longitudinal axis.
Y Lateral axis.
Z Vertical axis.

 

INTRODUCTION
New concepts are introduced to describe the mechanical operation of the Doppler effect, and which successfully explains the null result found in the Michaelson-Morley experiment without resorting to time dilation or length contraction principles. It offers new transformation equations, four new laws, geometric proofs, agrees with Maxwell's electromagnetic wave theory, Fresnel’s convection theory, Keppler’s laws, and Newton's laws. The main five conservation laws are not violated, the constancy of the velocity of light is assured and there is complete agreement with de Sitter's arguments in this respect. It demonstrates the necessity of separately describing source and observer motion in equations by showing that the source alters wavelengths by a factor derived by the reverse of the addition or subtraction of velocities, and the observer alters wavelengths by a factor obtained by the inverse of the addition or subtraction of velocities. The same laws, equations, and geometry may be used to describe Doppler phenomena in any spectrum and operates from stationary to carrier propagation velocity.

SOME INSTRUMENTATION LIMITS
An optical spectroscope is capable of systematically separating the various wavelengths of light and placing them on a scale or screen perpendicular to the longitudinal (X) axis. The wavelengths we see in the spectroscope are only those within the range covered by our optic detectors or photographic emulsions and grating spacing. It is incapable of indicating differences from standard, such as an apparent increase in velocity accompanied by an apparent or real increase in wavelength. It will present a standard spectrum for various parameter combinations. It is also incapable of indicating a complete spectrum shift except for omissions (dark lines), emissions (bright lines), or superimposition, reinforcements, or artificially filled in omissions (transmissions). Except for these cases it will not indicate when two or more complete spectra overlay.

An interferometer is capable of indicating light wave interference due to real or apparently altered velocity or wavelength by comparing two beams of light on a screen or in a telescope so that they may affect each other. It suffers blindness under certain conditions.

A photometer or light meter is designed to indicate the brightness or intensity or amount of light falling on its cell, also within limits. It is because of its construction more sensitive to some wavelengths than others, and is restricted in its reliable presentation. This can be somewhat overcome by changing or adding cells according to formulae.

DOPPLER EFFECT – NEW CONCEPTS
The usual method of accounting for motions of source and observer while transmitting or receiving, is to put both source and observer velocities into the same equation and thereby account for the changing gap between the two. The following will demonstrate the error of this method.

The wave is formed first at the source, then carried by the wave carrier to the observer, then altered by the observer motion. So these must be treated separately to understand the basics, because the source alters the wavelength according to reverse addition or subtraction of velocities due to source motion, and the fact that the wave always travels ²away² from the source. Then it is carried to the observer. The wavelength is always ²approaching² the observer from the front, rear, or at angles, so due to observer motion while receiving a wavelength an intercept problem exists. These in-line transformations may be solved by algebra.

The following pages treat source and observer motions basically, and finally use the equations to show a null result on the interferometer for an interferometer motion of ½ C.

One point is a little difficult to understand at first, that is the concept of the reflector altering the incident wavelength as an observer, and the reflected wavelength as a source. A relay with a receiver, tape recorder, and transmitter, helps to explain what happens when a beam of light is received and reflected by a reflector or relay.

SOURCE MOTION
The electromagnetic wave carrier propagates a wavelength in all directions at C, and no motion of source or observer can alter this propagation velocity in a real way. However, when source and observer motion and wave propagation is studied separately it can be demonstrated that observer motion will cause an ²apparent² alteration to C.

If the source and observer are stationary, the source (transmitting) oscillates at the proper frequency to create a wavelength 1² long –

The wavelength is created in all directions spherically and propagated outwards from the source, (Fig. 1). If the source moves to the left at ½ C while it forms the wavelength, the wave front will be in the same place as it is in Fig.1 when the wave rear is completed ½² to the left (Fig. 2), that is 1² + ½² = 1 ½², so the wavelength is now 1 ½² long on the source 180° X axis.

If the source moved to the right at ½ C while forming the wave, the wave front would be 1² to the right of the starting point, but the source would be ½² to the right while completing the wave rear, (Fig. 3), therefore, 1² – ½² = ½², so the wavelength would be ½² long.

 

Fig. 3

Since the wave propagation is always away from the source the wavelength is altered in a real way by source motion according to addition or subtraction of velocities. No intercept problem exists here. Propagation velocity is never altered really or apparently. Wavelength only is altered according to source motion.

OBSERVER MOTION
When a stationary observer receives a wavelength, the length of the wave is exactly the same as when it was formed and transmitted. Also, there is no apparent change in carrier propagation velocity.

Fig. 4

The 1² wave is carried to the observer at C (or any other carrier velocity). However, if the observer moves to the right at ½ C an intercept problem exists. The wave front is received and the observer starts timing and measuring. The wave rear would catch up with the observer in double the time that it would if the observer was stationary. (i.e.- instead of 1 sec. It would take 2 sec.)

Fig. 5

Or, looking at this same condition on a 1 foot scale –

Fig. 6

 

If the observer is at the 1" mark and the source is at the 0" mark the same instant the observer receives the wave front and at the same instant the observer starts moving to the right at ½ C. The rear end of the wave would be at the 2" mark the same instant the observer arrived at the 2" mark, so the wavelength would appear to be twice as long as a standard wavelength. Again, if it took the wavelength 1 sec. to travel each 1" span, the observer begins timing when he receives the wave front, so, in 1 sec. the observer is at the 1 1/2" mark and the wave rear is at the 1" mark, and in 2 sec. the observer is at the 2" mark when the wave rear is at the 2" mark. Therefore, this becomes an intercept problem to determine wavelength (or apparent wavelength) alteration on the observer’s 180 deg. X axis. This can be solved with algebra. Note – this apparent wavelength alteration is due to observer motion causing an apparent alteration to carrier propagation velocity.

The formulae to solve for the four basic in-line source or observer conditions would be chosen from one of the four main transformation equations in this theory (further on), it in turn produces a transform factor which is used by multiplication or division to adjust any transformable quantity depending on whether the quantity varies in reverse, direct, or inverse, proportion to the addition or subtraction of velocities.

With the forgoing examples of source and observer influence in mind, consider the following motions.

 

Fig. 7

Fig. 8

For simplicity, let C = 2, and Sv and Ov = 1. The conditions of the wave leaving the front of the source are exactly the opposite as for the wave approaching the rear of the observer. Also the conditions of the wave leaving the rear of the source are exactly the opposite as for the wave approaching the front of the observer. Therefore, if this is truly the case, each of these opposite transform factors should cancel, and the equations to solve for the transform factors should be exactly the opposite or inverse one from the other. This is the case.

To demonstrate, to obtain the Stf for the 0 deg. X axis of the source –

Eq. 1

The opposite is the Otf for the 180 deg. X axis of the observer –

Eq. 2

The remaining two motions work the same way. The Stf for the 180 deg. X axis of the source –

 

Eq. 3

The inverse is the Otf for the 0 deg. X axis of the observer –

Eq. 4

By these examples it is demonstrated how for source action the result of the equations amount to addition or subtraction of velocities (reverse) (1 – ½ = .5 or 1 + ½ = 1.5), and for the observer it becomes an intercept of velocities (2 / 1 = 2 or 2 / 3 = `.6

The above equations would not break down at C (to agree with the Principle of Causality) so to get the same results properly and so the equations are sound mathematically, logically, and agree with the principles of physics that are established safeguards, they must be stabilized. The four main transformation equations (T.E. #1, T.E. #2, T.E. #3, and T.E. #4) are the correct ones to use for such as the previously described circumstances for in-line operations. They also agree with the four laws of relative motion, T.E. #4 is the inverse of T.E. #1, and T.E. #3 is the inverse of T.E. #2, and the laws and transformation equations agree with the geometric transformation methods for the X axis (where they begin and end). The initial relation, Sv / C or Ov / C must be retained as such, however the symbol C in the rest of each may be changed to the quantity of a l, a time, etc, and this will still produce the tf.

To use the equations (T.E. 1, 2, 3 ,4) four examples are given now to demonstrate the changes to a 24m l emitted from the front or rear of a S which is moving at ½ C, and to a 24m l which is received from the front or rear of an O which is moving at ½ C.

Use T.E. #1 –

Fig. 9

Substituting quantities: ( 300 000 - [( 150 000 / 300 000 ) x 300 000] ) / 300 000 = .5

The tf obtained by subtraction of velocities is .5, so the l of 24m is 24 x .5 = 12m.

 

Use T.E. #2 –

Fig. 10

Substituting quantities: ( 300 000 + [( 150 000 / 300 000) x 300 000]) / 300 000 = 1.5

The tf thus obtained by addition of velocities is 1.5, so the l of 24m now becomes 24 x 1.5 = 36m.

Use T.E. #3 –

Fig. 11

Substituting quantities: 300 000 / ( 300 000 +[(150 000 / 300 000) x 300 000 ]) = .`6.

_

The tf thus obtained is used now to alter the l, 24 x .6 = 16m.

Use T.E. #4 –

Fig. 12

 

Substituting quantities – 300 000 / ( 300 000 – [( 150 000 / 300 000 ) x C ]) = 2.

By the same procedure, 24 x 2 = 48m.

To obtain Stf s for angles between 0 deg. and 180 deg. X axis the geometric addition or subtraction of velocities is used, and to obtain Otf s for angles off the 0 deg. and 180 deg. X axis the geometric intercept of velocities is used. These are both described in full a little further on. Mathematical equations are adjusted to replace the geometric methods when possible for more accuracy. The cosine is added to handle the angular operations to the X axes.

INTERFEROMETER RESULTS EXPLAINED
On the following illustrations, follow mathematically the laboratory 24mm wavelength as it is altered first by the S then by the O and it will become clear why the Michaelson-Morley interferometer failed to show anything but a null result due to wavelength change. However, the Sagnac and Michaelson-Gale interferometer experiments produced fringe displacement due to wave phase differences (see p19), because the experiments are designed in a way which brings one wave train to the target out of phase with the waves of the other beam. The laws should be noted here. Also, there is no change to a wavelength due to S or O motion when it is transmitted or received 90 deg. off the X axis.

 

Fig. 13 (refraction is treated separately further on)

 

 

 Fig. 14

 

 

Fig. 15

 

 Fig. 16

 

 

In each of the four cases (90 deg. variations in direction) the various gaps remain constant. Michaelson and Morley assumed the beams would lose time travelling upstream and gain time travelling downstream, relative to the mirrors. I agree. The wavelengths are determined in a real way by S motion and by O motion, Apparent changes in propagation velocity mean nothing whatever to the final result BUT CAN CAUSE THE TWO BEAMS TO REACH THE TARGET OUT OF PHASE. It is a fact that wavelength changes are not always accompanied by apparent velocity changes due to basics. The interferometer screen shows real and apparent wavelength changes only and due to basics can display no apparent velocity changes except by phase shifts. However, it can display phase shifts between two beams of waves due to apparent differences in velocity caused by the beams moving in different directions through the wave carrier at V = C and relative to the moving interferometer.

The Michaelson-Morley experiment used 2nd order effects and are therefore scalar. 1st order effects are necessary as the Michaelson-Gale experiment. Scalar effects are not capable in theory of giving required data concerning the one way velocity of electromagnetic waves.

BASIC MOTIONS USING THE SLIDE RULE

Mathematical examples of four basic motions along the source and observer in-line X axis using the slide rule.

Fig. 17

 

 

 

 

 

GEOMETRIC TRANSFORMATION
Fig. 20

Geometric method of solving for source angular transform factors.

  1. Draw a circle of r = 1 l (enlarged or reduced for convenience). S is at center at A.
  2. Draw X axis.
  3. Locate F on AG line to represent Sv / C.
  4. Draw line AC on tf angle desired.
  5. Draw line CD perpendicular to AC. (This line always runs forward from C).
  6. Draw line from point F parallel to line AC until it meets line CD. (This line never moves off F when AC and FE are drawn on a new angle).
  7. The linear measurement AC represents 1 l at C.
  8. The distance AF represents the distance the S moves during transmission of 1 lo of distance AC.
  9. FE represents the actual l transformation due to S motion, but when AC is referred to as 1, FE becomes a tf. (i.e. - .43, 1.26, etc.).
  10. Note – there is no alteration to l perpendicular to the X axis.
  11. Note – in-line transformations follow in-line transformation equations for S.
  12. This geometry represents reverse addition or subtraction of velocities and agrees with the laws.

GEOMETRIC TRANSFORMATION (ALTERNATE METHOD)
Fig. 21

Geometric method of solving for source angular transform factors.

  1. Draw a circle of r = 1 l (enlarged or reduced to scale). S at center.
  2. Draw X axis.
  3. Locate B on AG line (or E on AH line) to represent Sv / C.
  4. Draw small circles as shown of d = AB.
  5. Draw line AD on tf angle desired.
  6. AD represents 1 l, so subtract AC from AD to get l' or tf. (on the rear, add AJ to AF).
  7. Note that no alteration to l occurs perpendicular to the X axis.
  8. Note that in-line transformations follow in-line equations for source.

 

GEOMETRIC TRANSFORMATION;

 Fig. 22 

 

Geometric method of solving for observer angular transform factors.
  1. Draw circle of r = 1 l (altered to scale), O at center at A.
  2. Draw X axis.
  3. Locate F between A and G to represent Ov / C.
  4. Draw line AC at desired transform angle.
  5. Draw line CD perpendicular to AC.
  6. Locate BE parallel to AC so full scale measure on line BE is identical to fractional scale measure on line AB.
  7. Linear measure of BE or AB will represent the l' for that particular reception angle at that particular Ov.
  8. The rear angular transforms are found the same way, but instead of being a fraction of 1 (line A to F), it would be 1 (A to F) plus a fraction more, or 2 plus a fraction more, etc.
  9. Note that perpendicular to the X axis there is no alteration to the l regardless of Ov up to lim : C, full-scale measure and fractional scale measure are both 1. Also on 0 deg. and 180 deg. X axis the in-line transformation equations are used. This geometric method also (as well as source geometric transformation method) predicts the results obtained by the in-line transformation equations.

 

 

When a source emits a wave, the wave whether very directional, circular, or spherical, will be carried away from the source at the standard velocity of the carrier, molecular (sound etc.), or electromagnetic (light, radio, etc.), which will be modified by density, temperature, structure of the medium. The length of the wave is mechanically determined by the oscillator or other cause in the source (frequency) and by any motion of the source. On the forward side of a moving source, the transmitter is chasing after the wave front as it forms the rest of the wave. On the rear side the wave front and transmitter are moving in opposite directions as the rest of the wave is formed. Source motion does not affect the carrier propagation in any real or apparent way whatsoever. It does change the wavelength physically in a real way. After the wave length is determined and formed by the carrier propagation velocity, transmitter frequency, and source motion, that wave length will be propagated unchanged unless acted upon by another force, interference, or blocked completely or partially as by an observer, and will (I suggest) be deenergized with distance as per luminosity, absolute brightness, and spectrum red shifting.

Whatever the angular velocity transformation factor from an observer maintaining a steady gap from a source on a parallel track, the source angular velocity transform factor will be such that they reduce to standard wavelength regardless of velocity, lim 0 to C when source leads, and lim 0 to C when observer leads.

To match a moving and rotating source the observer must match the rotational velocity or balance it by constantly altering the gap to compensate for a different rotational velocity, or select the mathematical null to base measurements on.

From the previous illustration and solution (Fig. 23) it can be seen that when source and observer X axes (and space tracks) are parallel and the gap between them is constant, the observer will always detect a standard lab. condition wavelength from the source regardless of the source’s angular position at any point on the observer’s projected sphere. It is possible to balance source X axis angle and source velocity so the observer will detect the same wavelength for each, so the observer must balance the source angular velocity factors against the certain source motion (in radians for example) to obtain the true source X axis location, velocity, and distance. When using this method in astronomy, it must be checked against distance obtained from parallax measurements, absolute luminosity measurements, proximity to nearby cephids, and any other method, which will help to confirm the distance.

 

Of special interest

 

It is demonstrated that when the gap between S and O is constant regardless of velocity or 90 degree angular relationships on the three axes, the S and O wavelength transformation factors "together" return the wavelength to standard laboratory conditions. Therefore, rather than geometrically solve for both S and O tf’s for each change in angle and/or velocity, it is sufficient to establish the S transform factor, then obtain the Otf’s from the slide rule (scale C and C1) or by computer for more accuracy, and used with the D scale (or computer) to solve real or apparent wavelength changes.

 

Three O angular transforms to show the geometrics a little clearer.

Note that the transforms operate from minimum on the front to zero on the Y or Z axis to maximum on the rear as the pivot at the O is rotated through 180°.

 

  Fig. 24

 

Source transform factors 0 deg. - 180 deg. X axis at .5C.

Observer transform factors from 0 deg. - 180 X axis at .5C.

Fig. 25

 

 

Comparison between S and O transformations for the same velocity.

Fig. 26

 

LAWS OF RELATIVE MOTION
The transform factors are derived by use of the transformation equations and are used by multiplication or division according to standard mathematical practice to alter laboratory quantities due to source and/or observer motion. They are valid for use with any national or international system of measure.

Addition or subtraction of velocities is by basic arithmetic only.

First law of relative motion.
Due to source motion, the transform factor varies in reverse proportion to the addition or subtraction of velocities.

Second law of relative motion.
Due to observer motion, the transform factor varies in inverse proportion to the addition or subtraction of velocities.

Third law of relative motion.
Any given source transform factor will be exactly cancelled by the diametrically opposite observer transform factor for synchronized constant velocities, parallel X axes, and rectilinear paths.

Fourth law of relative motion.
Motion of a reflector, relay, or refractor, will alter the incident transform factor as an observer, and the reflected transform factor as a source.

 

TRANSFORMATION FORMULAE
T. E. #1 – S 0 degree X axis tf due to source motion –

T. E. #2 – S 180 degree X axis tf due to source motion –

T. E. #3 – O 0 degree X axis tf due to observer motion –

T. E. #4 – O 180 degree X axis tf due to observer motion –

T. E. #5 – Quanta energy transformation due to source or observer motion –

 

When T.E. #1, T.E. #2, T.E. #3, or T.E. #4, are used in wave mechanics, insert the cos q (as shown in these examples) into the T.E.s, and the formulae will now give the tf for any angle. For example: #1 will handle wavelength alteration due to S motion, from 0 deg. X axis to 90 deg. (measured from the forward X axis). T.E. #2 will handle alterations from 180 deg. S X axis to 90 deg. (measured from S rear X axis). The formulae for O motion is handled the same way.

Example-

 Example-

 

 

Note – If Eq is measured by a moving O, the hf takes care of the Eq' automatically. If a prediction is required for a certain velocity and its effect on a lab. measurement, the Eq' would be predicted by hf / tf.

Also – If a moving S radiates wavelengths, the frequency he measures is the lab. value, but the wavelength a stationary O will measure is altered. Therefore, the moving S must adjust the frequency and thereby the Eq, by the Stf to give the desired wavelength and Eq.

USE OF T.E.s #1 AND #3 FOR ALL QUADRANTS IN WAVE MECHANICS

Once the use of the four transformation equations to explain and predict Doppler phenomena in wave mechanics for in-line operations, and the use of the cos q for angular functions, is understood, it is possible to do this by using only T.E. #1 and/or T.E. #3 by using the value for cos q as a calculator presents it, and by measuring angles from 0 deg. to 360 deg. continuously in the same direction.

For example:

When using T.E. #1 for S, or T.E. #3 for O, conditions, from 0 deg. X axis to 90 deg., insert the positive (+) value for the cos q.

When using T.E. #1 for S or T.E. #3 for O conditions from90 deg. to 180 deg., insert the negative (-) value for the cos q.

This allows the operator to measure the q (continuously) from 0 deg. to 360 deg. and use only two transformation equations instead of four. A calculator would give the proper value for the cos q, but when tables and slide rule are used the operator must measure each quadrant in the correct direction (from forward or rear X axis) and insert the correct sign for the cos value.

Note – In T.E. #1, T.E.#2, T.E. #3, and T.E. #4, C represents both the velocity of light and the velocity of sound. Also, in place of C, any quantity may be used for special purposes, such as wavelength, time, period, distance, force, etc.

The tf is a factor used by multiplication to alter a wavelength, time, period, distance, or by division to alter a uniform constant speed, or force, or kinetic energy.

T.E. #6 – Stf from known wavelengths, for source 0 deg. or 180 deg. X axes –

Stf = ls / lo

  T.E. #7 – Sv for 0 deg. X axis from Stf –

Sv = C – (C x Stf)

T.E. #8 – Sv for 0 deg. X axis from lo and ls –

T.E. #9 – Sv for 180 deg. X axis from Stf –

Sv = ( C x Stf ) – C

T.E. #10 – Sv for 180 deg. X axis from lo and ls –

Sv = [ C ( ls / lo ) ] – C

 

 Table of velocities and transform factors to illustrate agreement with Principle of Reciprocity, Principle of Detailed Balance, and Principle of Causality, for in-line X axes.

Following the arrow in each table between Stf and Otf describes Reciprocity.

Switching top and bottom table for the same velocity describes Detailed Balance.

The zeros at each end of each table agree with Causality (breakdown of equations), and total cause and effect are demonstrated along each line.

 

BASIC SOURCE / OBSERVER MOTIONS

 

C – Apparent increase due observer motion.

l - Real increase due source, apparent decrease due observer. (Spectroscope would show no change).

f - Real decrease due source, apparent increase due observer, will appear standard.

Result- necessary to measure C' not relying on adaptations of f or l.

 

C – Unaffected.

l - Real lengthening due source.

f - Real decrease due source. The number of source vibrations/sec. remain the same, but the l is increased due source recession which lowers the f for the same propagation velocity.

Result – red shift.

 

C – Unaffected by source, apparent decrease due observer.

l - Real lengthening by source, apparent lengthening due observer.

f - Apparent decrease due source (as in b), apparent decrease due observer.

Result – large red shift.

 

C – Apparent increase due observer.

l - Real decrease due source, apparent decrease due observer.

f - Increase due source, apparent increase due observer.

Result – large blue shift.

 

C – Unaffected.

l - Real decrease due source.

f - Increase due source.

Result – blue shift.

 

C – Apparent decrease due observer.

l - Real decrease due source, apparent increase due observer.

f - Standard.

Result – measure C'.

 

C – Apparent increase due observer.

l - Apparent decrease due observer.

f - Apparent increase due observer.

Result – blue shift.

 

 

 

C – Apparent decrease due observer.

l - Apparent increase due observer.

f - Apparent decrease due observer.

Result – red shift. (Linear shift is larger for the same Ov than in g).

SPECTRUMS – IDENTICAL ASPECTS
Various directions and velocities cause apparent changes in the velocity, wavelength, and therefrom the frequency, of sound due to observer motion, and real changes in wavelength, and therefrom the frequency, due to source motion. The velocity of sound propagation remains constant under standard conditions and is only altered by molecular density, structure, temperature, etc.

If a car is moving away from an observer with the horn blowing, the sound still travels from car to observer at the constant velocity of sound governed only by the conditions of the molecular wave carrier. Because the car’s horn is oscillating while moving away, the real (not apparent) wavelength is lengthened rearward resulting in a lower pitch. An observer ahead of the car would witness the reverse in wavelength and pitch, but the velocity of sound would be the same for both directions. If the car’s velocity was equal to the velocity of sound (for prevailing atmospheric conditions) the energy buildup travelling with the forward edge of the car would hit the observer in a larger compression wave, instead of the usual waves due to the horn, and the observer would hear a sonic boom. The waves due to the horn become absorbed in the compression wave buildup. This sonic boom is due to the car pushing the molecules at their maximum velocity for prevailing conditions and is a mechanical function of the car’s structure and the air’s molecular structure at that velocity and has nothing whatsoever to do with the operation or non-operation of the horn.

When a source moves through a carrier as it is emitting energy waves, the waves vary from the standard lengths radially on any single plane from shorter wavelengths ahead of the moving source to longer wavelengths in the rearward direction. Fig. 102 shows the wave pattern when the source is in motion. See also Fig. 34. Motion of the source alters the wavelengths front and rear from the Y axis (lateral) as addition or subtraction of velocities. Observer motion "apparently" alters wavelengths by intercept of velocities. (Fig. 97, `.6 & 2 sec.). The Doppler effect will always convert algebraically to real conditions by removing the effect of observer motion, and from there to standard laboratory or at rest conditions by removing the addition or subtraction of velocities and thereby removing the effect of source motion. The `.6 sec. intercept in the train and lightning hypothesis of Fig. 97 converts to standard velocity of light as does the 2 sec. hypothesis. In the first case, the light traveled a shorter distance, and when the time and distance are converted to speed, it becomes the standard velocity of light. The same applies to the longer distance in the 2 sec. case, but, the `.6 and 2 sec. times are due to "apparent" velocity or wavelength alteration due to observer motion. This apparent change due to observer motion comes from using an alteration in time without using the proper change in distance.

The motion of a source will cause a real alteration of wavelength because of the mechanical connection between source and carrier, but the carrier propagation velocity is constant and can not be altered in a real way by the motion of the source or observer. The motion of the observer will cause an apparent alteration of wavelength and propagation velocity due to real altered distance and time. The energy wavelengths are imposed on the carrier by the source and are not altered by motion of the observer, but the distance and time of intercept gives the illusion of changed wavelength and propagation velocity due to observer motion only.

Light from a star we approach at 20 km/sec. will travel from a planet used as a shutter to the eyepiece of a telescope at a greater apparent velocity than light from a flashlight 20 cm away (when basing judgement on wave length alteration or interference) because the flashlight and telescope gap is fixed. No relative motion, 3rd law applies, hence, no visible Doppler effect. Source and observer changes convert to standard because of a constant gap. See table of velocities and transform factors. In the sound or electromagnetic spectrums, with a constant gap between source and observer regardless of direction, or velocity, the wavelength is intercepted as standard in a static carrier, because the apparent wavelength alteration due to observer motion cancels real wavelength alteration due to source motion, and a standard wavelength is presented. Fig. 98 of source, carrier, and observer, (ignoring possible carrier motions to simplify conditions), and the relationships of all including various motions and propagation velocities become very clear.

The longitudinal axis of wavelengths, distance, and time, undergo in some cases real alterations, and in others apparent alterations, due to real motions of source and observer relative to the carrier. "If" a carrier motion exists it would add to real and apparent alterations. For the longitudinal axis, if the distance alteration is ignored (because it would have to be computed from observer velocity also) the time alteration would represent the apparent propagation velocity alteration due to observer motion.

Energy can be transmitted one wave alone as from an atom, or one vibration of a car’s horn, or with a continuous wave after wave quantity, with wavelengths according to source oscillating frequency and carrier propagation velocity under standard conditions, or with altered energy presentation according to departure from standard. Also, it would be possible to, in each type of carrier, form a compression wave or single energy wave ahead of a source which is moving at the carrier propagation velocity.

As no real or apparent change in wavelength or velocity of sound will be detected for various directions inside a moving aircraft which encloses the source and detector or observer at a constant gap, but the complete Doppler phenomena will be experienced for sound entering or leaving the moving aircraft, so the Michaelson-Morley experiment is invalid for the performance claimed, because being set up on the earth with fixed gaps, we would be as enclosed in a moving aircraft with no relative motion between source and observer, except that in the aircraft there is no flow of wave carrier over the instruments. (The result and analogy is the same even if there were). It will be essential to use solar system worlds or satellites and motions such as planetary-stellar occultation as gigantic instruments and shutters to measure apparent changes in C. (See Figs. 95, and section ²C' Apparent). But for wavelength, the apparent changes are read in a spectroscope. Remove the apparent wavelength alteration due to observer motion and observer X axis position, and real wavelength changes due to source motion and source X axis angle remain. Determine the wavelength alteration due to source, and time for the source to traverse a given arc, and source distance and velocity can be computed. This can be checked against the luminosity scale and nearby cephids to be sure of the distance.

When a wavelength is measured mathematically, the time or distance or velocity must be measured from the front of the wave to the rear of the wave as it travels past any given point, and compared to standard.

The sound and electromagnetic spectrums exhibit most of the same effects. They both show the Doppler effect in exactly the same manner, convection coefficients, standard propagation constants, they both obey the same fundamental time – distance – speed formula, both obey the same fundamental propagation velocity – frequency – wavelength formula, both show the same type of source motion influence, both show the same type of observer motion influence. Olaf Romer has already measured an apparent alteration to C for the electromagnetic spectrum (see section ²C' Apparent) so I would say that in this respect also both spectrums are similar in operation. It is very logical to believe that if a standard wave length which is being transported at the standard propagation velocity of the carrier can be apparently altered by observer motion, then it should also be possible to measure the same apparent change to the carrier propagation velocity which caused its transport from one point to another point.

 

Acknowledgements

I wish to express my gratitude to the many intellectual honest men of history who did much of the early work that this theory is based upon.

Also, a special thanks to Professor J. A. McCorquodale, Engineering Department, University of Windsor, who assisted with the intercept principle by providing the match line which he passed to me by private communication.

To Ernest Mach for stating the principle known as Mach's Principle, i.e. Concepts and statements, which are not empirically verifiable, should have no place in a physical theory.

Especially to the God of our fathers who said:

1 Cor 11:14

14 Doth not even nature itself teach you, ………………………………………………………….?

(KJV)

Gal 6:4

4 But let every man prove his own work, and then shall he have rejoicing in himself alone, and not in another.

(KJV)

1Thes 5:21

21 Prove all things; hold fast that which is good.

(KJV)

2 Cor 13:1

CHAPTER 13

1 This is the third time I am coming to you. In the mouth of two or three witnesses shall every word be established.

(KJV)