TUTORIAL NOTE 18


Welcome to the Second 'Semester' of Ten Tutorial Notes, which teach the mathematical basis of Aether Science theory.

MICHELSON-MORLEY REVISITED

© Harold Aspden, 1999

At this stage in these Tutorials I propose to review an aspect of aether theory from the viewpoint of the null result of the Michelson-Morley Experiment. Most physicists put this on a par with their belief in Einstein's theory in their blind acceptance that the aether, as something in space that regulates the speed of light, simply cannot exist.

In a sense, therefore, this Tutorial No. 18 could be the most important in claiming the attention of the teaching sector of the physics community. Relativity and the Michelson-Morley Experiment are not of much interest to those involved in applied physics nor does what one learns at university about those subjects have any bearing upon the daily pursuits of most physicists. However, that omnipresent aether is ever active in regulating the physical forces which are harnessed by the physics community and, inevitably, the failure to see what is there has its price in retarding progress.

I will begin by quoting a section from page 67 of my book Physics Unified [1980e]:
"Such rigidity (a reference to the aether having a kind of crystal structure) might then permit us to make an analogy with solid materials by imparting to the vacuum medium a pressure modulus or energy density modulus P, which relates to the propagation speed c1 by the formula:
c1 = (P/ρ)1/2 ............(59)
where ρ is the mass density of the lattice. Here c1 is referenced on the universal frame.

In undisturbed space remote from matter c1 will equal c, but, where we have a body of the lattice in linear motion at velocity v, some of the lattice substance will be shed to establish the counterflow at velocity u and ρ in (59) will thereby be reduced, making c1 larger than c. Write:
n = c/c1 ...............(60)
where n is the refractive index in this region. Then, from (59) and (60) we see that n2 is proportional to the mass density of the lattice.

We expect linear momentum of the vacuum medium to be zero and this means that if the proportion k of the lattice is shed to provide the balancing flow the following relation holds:
uk + v(1-k) = 0 .............(61)
Also:
n2 = 1 - k .............(62)

Combining (61) and (62), we have:
u(1 - 1/n2) = v ...............(63)

If you consider this then you will understand that I am suggesting that 19th century physics offers a explanation as to why the Michelson-Morley Experiment failed to detect motion of the Earth through the aether. The experiment was merely one aimed to advance our knowledge of physics by testing the standard assumption that there exist an aether which offers a single absolute frame of reference relative to which the speed of light in vacuo is constant. It was not a test to prove the existence or not of a real aether! It was a test to verify or disprove an assumption made by the physics community.

A little consideration should tell you that if one can measure motion relative to the unseen aether then that aether has a subtle way of communicating momentum. A little further consideration, having regard to a later experiment performed by Michelson, one which did detect rotation using the same optical techniques as those of the Michelson-Morley Experiment, should tell you that the aether can absorb (or shed) angular momentum in its interaction with matter.

These are clues as to the real nature of the aether which are provided by experiments.

So you may now understand how equation (61) as quoted above was formulated. It was a statement that the aether when disturbed by being dragged along by body Earth reacts to keep its net linear momentum zero. As to the angular momentum aspect and rotation of body Earth or of the sun, do keep in mind that cosmological phenomena pose anomalies such as 'why is it that the solar system as a whole has a very substantial net angular momentum?'

Now, as this point, I ask you to consider whether what I have quoted above amounts to a theoretical explanation of the Michelson-Morley experiment based on aether theory. I submit that it does if we can be satisfied by importing the standard pre-Einstein physics of the material world into the aether scene.

However, though the Fresnel drag coefficient derived as equation (63) has been verified by experiment, its traditional theoretical derivation is, I believe, partly dependent upon empirical evidence. It has the merit, however, of being firmly of record in accepted physics in the 19th century and so, if we can explain the Michelson-Morley Experiment based on Fresnel drag and aether theory, then Einstein's Principle of Relativity, with its time warp problems, does not merit consideration.

Our task, however, is to justify what we observe as general phenomena in physics by developing a viable theory giving account of those phenomena. We find that the speed of light in passage through matter varies slightly with frequency. This we know has a theoretical explanation owing to the fact that the oscillations set up in the dielectric system have to contend with the natural frequencies, the resonant modes, of the atomic structure of that matter form.

Using the cgs system of units the standard theory by which the speed of propagation of electromagnetic waves in matter is explained indicates that the refractive index n, the ratio of the speed of light in vacuo to that in matter, is given by a formula:
n2 = 1 + D
where D is a summation of terms representing an oscillating system each component of D having a different natural oscillation mode and being also a function of the wave frequency.

When there is no matter present n2 reduces to that value of unity but, hidden in the meaning of that unity term, is the oscillating system of the aether itself.

We can formulate a simple harmonic oscillatory state by equating the restoring force of an electric displacement with an inertial reaction and, assigning the Compton electron frequency as the natural frequency of this oscillation. The standard electromagnetic wave theory then tells us that the unity dielectric constant of the vacuum (the aether) is implied by such an equation, namely the aether has a mode of oscillation that is at the Compton electron frequency. Indeed, this is why the vacuum can shed energy by creating electrons and positrons, a feature of the theory of quantum electrodynamics.

With that in mind let us come back to that phenomenon by which light in passage through matter travels at different speeds as a function of frequency, the phenomenon of frequency dispersion. This is seen by many physicists as a reason which precludes acceptance of theory which likens the aether to the matter form.

Light suffers no frequency dispersion in its passage through the vacuum. Note, however, that by 'dispersion', I mean change of speed as a function of frequency. I do not intend this to mean that the frequency of an electromagnetic wave in transit through the vacuum has to be constant as well as the speed of propagation being constant.

Indeed, the challenge we face is that of justifying an aetherial property by which electromagnetic waves travel at constant speed and yet are progressively attenuated in frequency in linear proportion to the distance travelled, such a situation not involving frequency dispersion.

A discerning reader may see that I am intent here on revealing an aether property by which, not only the null result of the Michelson-Morley Experiment can be explained, but also the cosmological redshift, currently interpreted as signifying the expansion of our universe.

Look again at that quotation above from my book Physics Unified. Ignore the derivation of equation (63), the Fresnel drag term, but keep in mind equations (60), (61) and (62). We know that the speed of light in matter involves a refractive index n that exceeds unity. However, in the vacuum there is no matter present, but we can have aether in motion if some of that aether is in counter-motion to assure balance of its linear momentum as prescribed by equation (61). Equation (62) conforms with the theoretical derivation of the refractive index of the matter form in terms of its electrical properties in relation to the mass properties of the electric charges involved in their oscillations in responding to electromagnetic waves in transit. As applied to the aether, we have that factor k in equation (62) providing the link.

Now we know that that factor n tells us something about the speed of light. We also know from the way in which equation (62) is derived by standard theory that it is n, and not n2, that emerges in the linear relationship between the velocity of light c and the velocity c1. They are related by an expression that is the square root of a physical quantity. They have direction and so are vectors, a property lost from sight once we square the relationship to obtain equation (62). Note the difference between an electric field and electric field energy density. One is a vector and one is a scalar quantity. We well know the difference in using the electric field concept in advancing our ideas in physics. So let us not confuse the issue in dealing with the speed of light issue. Our interest is in n, not n2. So we will take note that c/n is the speed of light in matter having n as a refractive index, but now apply this formula to the velocity of light in the aether, given that the aether moves bodily at velocity v as a structure whilst a component shed by it moves rapidly in reverse a velocity u to hold net linear momentum at the zero value. That is the condition implied by equation (61).

So, what is c/n? Can we combine equations (60), (61) and (62) to determine c/n? To explore this we may use a little algebra to show that, ignoring second-order terms owing to v being small relative to c:
1/n = 1 + k/2
and:
k = -v/u

It then follows that:
c/n = c - vc/2u


This may seem a little confusing, given that we need to know the value of u to proceed, but here I draw your attention to what was discussed in Tutorial No. 8 where it was argued that the aether comprises a structured system of aether particles, quons, which were all moving collectively in circular orbits at that Compton electron frequency and had a quantum of angular motion which corresponds to their motion in orbit at a speed c/2 so as to move at a speed c relative to the gravitons that moved in counter-balancing orbits.

What then happens when those aether particles come out of orbit and adopt a migrant form to move linearly through the residual aether structure to provide that balance of linear momentum? Whatever their form they must keep the mass balance and the momentum balance and that means that they travel at the speed c/2, meaning that u has the value c/2. So, with 2u replaced by -c, consider the equation we have just derived.

You can see that it tells us that the speed of light in a region of aether sharing the motion at velocity v is c+v in the direction of that motion, that is simply c relative to the moving system. Given that this is a vector expression and not a scalar quantity we may also say that the speed of light is c relative to that moving system, even though its motion is not in the same direction as the light. Therefore we have deduced by aether theory the condition observed in the Michelson-Morley Experiment.

Now, although I am writing this for publication in 1999, I wish to point out that I discovered this aspect of my theory 24 years ago and reported it in a slightly different way at pages 11-12 in my 1975 book Gravitation. So this is not a new thought. It was published in that work alongside two other topics as part of a trio of references to the 'unfortunate errors of omission in nineteenth century physics' (Abstract of chapter 1 at page 1 of the book).

I next address the other topic concerning light passage through the aether, that of the frequency attenuation with no dispersion.

Note that equation (61) above really declares that the aether reacts to linear motion effects to set up displacement of two components in opposite directions, conserving dynamic balance and avoiding momentum unbalance. Instead of probing this property in terms of mass deployment we can look at it from another angle, especially so far as concerns its disturbance by the passage of those electromagnetic waves. Maxwell's theory tells us about the undulating lateral displacement of charge accompanying the passage of a wave. He overlooked the need for a secondary wave action which provides the dynamic balance.

We can have dynamic balance in an inertial sense. We do not have the balance of the electric field action, but we must have two components in that electric wave. I have discussed this in a publication in Wireless World [1982a] and formulated it in formal physical terms in a scientific paper of record [1984e]. Equations (3) and (4) of the latter paper define this:
E = E1 - E2
dE/dt = (E1 - E2)F(E1/E2)
where t is time and F is a function of the ratio of E1 and E2.

The rate of change of the amplitude of an electromagnetic wave can be codified in this way in terms of the strengths of two electric field components, E1 and E2, at a point in space under consideration. To explain what this means in physical terms, first take note that the aether, owing to its adaptable fluid crystal type properties, comprises basically a system of charges, quons, which share a universal jitter motion. This is a quantum oscillation in two dimensions, a condition needed to assure dynamic balance with the graviton system. Superimposed on this motion there is, when an electromagnetic wave is being propagated, a lateral oscillation of those quon charges. Now whereas the quon lattice structure is adaptable in sharing the motion of matter present, as we see from our account of the null result of the Michelson-Morley Experiment, the quons also are compliant in a dynamically balanced sense in adopting a component of motion having the frequency of oscillation of that electromagnetic wave.

This latter component of motion is represented by the composition of two lateral displacements indicated by the electric field E1 and E2. They act in opposition to give the net field effect that we sense as the electric field of the wave. They are seated in different systems of charge, because the quons exist in a background of heavier aether charges, virtual muons as well as gravitons, and there is on-going transmutation of form as energy is conserved in their quantum-electrodynamic interplay.

The overall result, however, is the dynamic balance of the two components of the electromagnetic wave in its transit through aether. In contrast with its motion through matter it cannot call upon the substance of that matter acted upon by the presence of the electric field oscillations to provide the inertial reaction. This difference is vital when we come to judge why it is that light suffers frequency dispersion in passage through matter but not in passage through the structure constituting the aether.

Hence we find that an electromagnetic wave in transit through the aether is represented by those two field equations presented above.

The function F is the key to our understanding of electromagnetic wave phenomena in the vacuum medium. Ask yourself why it is that waves coming from opposite directions can crash into one another and emerge seemingly unscathed. They involve energy and energy is a scalar quantity which can be pooled with other energy so as to be conserved. However, why is it that the energy of the two waves, in being deployed between them, does not cause some change affecting those waves?

At a point P in space the local passage of a wave can only be sensed by what occurs at that point. Whatever controls the physical action at P cannot look with human eyes to see what electrical signal is coming next at P or what has been there and is now receding from P. So logic says that Nature must codify the essential data concerning that electromagnetic wave in a dual form active at P. This means the value of E, its strength and direction, plus its instantaneous rate of change dE/dt. Hence the two equations. However, as can be seen by dividing E into dE/dt, the physical information at P includes also the value of F(E1/E2). F is a function of the amplitudes of E1 and E2.

The aether determines the function F by adapting itself so as to be always responsive in its reaction to the superimposed lateral motion occasioned by the passage of the wave in just such a way as to keep in tune with the frequency of that wave. It adapts its resonance mode by allowing the electric field E of the wave to separate it into two opposed displacement states, corresponding to E1 and E2, respectively.

Thus, expressing the wave frequency f in terms of the Compton electron frequency fo, we can determine K as:
K = (f/fo)2
where K is equal to E/E1, which is 1 - E2/E1. This gives E2 = 0 when f equals fo.

E1 becomes progressively larger relative to E as the frequency is reduced and, indeed, E2 also becomes progressively larger, but that ratio which determines k will keep the aether in tune with the frequency. This means that there is no frequency dispersion. One has, in effect, a near analogy with a result achieved artificially in electrical telegraphy by Oliver Heaviside who devised the distortionless telegraph line. He made the properties of the line, the combination of inductance, capacitance, leakance and resistance, such that the signal in transit did not suffer the normal distortion.

For a sinusoidal planar wave the amplitude of dE/dt is 2fE or 2(fo)k1/2(E1 - E2), which is the second of the above equations, because k is a function of (E1/E2).

This insight into the process by which the aether transmits electromagnetic waves without dispersion occurring as between the different frequencies involved offers a surprise, because the dual displacement feature gives scope for a differential effect if there is some pseudo-matter present in space that can absorb energy from the wave. It seems likely that almost all of the energy loss will come from the E2 component so that, with E1 constant, E1/E2 will change if the waves are obstructed in some way in their passage through very tenuous space containing no structured matter form. For example, if the aether of outer space devoid of matter is trying to create bare particles such as electrons and protons and these exist sporadically, then that can be sufficient to alter that ratio E1/E2.

Now, as can be seen, if the electric fields E1 and E2 arise from charges of opposite polarity moving in opposite directions, then E2 is a negative quantity and this means that a reduction of the displacement will mean an increase in E2 and that implies a decrease in E. The energy density of the wave is proportional to E2 or (KE1)2, which means that (1/W)dW can be written as (2/K)dK and with fo constant this tells us that (2/fo)df is (1/K)dK. Taken together, these relationships allow us to write:
(1/f)df/dx = (1/4W)dW/dx
where x is distance travelled by the wave.

In short, we have the remarkable situation where our dual displacement feature has explained the zero frequency dispersion property of the aether whilst at the same time telling us that there will be a progressive reduction of wave frequency with distance travelled if energy is absorbed from the wave by non-structured particles, the odd electron and proton, that might be distributed throughout space.

From this it is a small step to see that if the aether is trying to create protons and electrons which come into being sporadically but decay back into the energy sea of the aether, the condition for aether-matter equilibrium having been reached, then we can predict something that has mistakenly been interpreted as evidence of a doppler effect occasioned by an assumed ongoing expansion of the universe. More than this, however, if we can estimate the rate at which those obstructing particles are being produced, then we can estimate the value of the Hubble Constant.

This is indeed possible and it is the subject of that paper [1984e]. It is a topic already introduced in these web pages. See Lecture No. 11.

However, our task in this Tutorial No. 18 has been to show why the Michelson-Morley Experiment did not prove the non-existence of the aether, as so many physicists believe. If you, the reader, still wish to hold faith in a belief that the universe is expanding and doing so in accordance with Einstein's philosophy by which time is distorted as a kind of fourth space dimension, then my words have fallen on deaf ears and I leave you to your destiny. Otherwise, please do take note of what I have been saying in these Tutorials and pay due attention to my other commentary in these web pages.

I shall now move on to the next Tutorial No. 19, where we shall discuss the mystery of 'the fourth dimension'.

To progress to the next Tutorial press:


Tutorial No. 19

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