Stasis theory is a natural consequence of the concept that magnetic fields form in response to the relative movement of electric fields through one another. A moving charge generates a magnetic intensity defined at a point in space by its velocity with respect to the average velocity of other charges weighted according to their relative field strengths at that point. This weighted average is found from the summation over all of the electrons, up quarks and down quarks in the universe.
Where the velocities of charges are measured relative to some frame of reference S and the result is the stasis vector which gives the velocity (in S) of the background presence of the electric fields of all the charges in the universe. The stasis vector should be subtracted from the velocity of a charge to obtain its locally absolute velocity.
Since light is an electromagnetic phenomena, the basic electromagnetic interactions by which it is propagated take place against stasis.
In the early stages of the theory stasis was only calculated in an approximate manor using the expression:
where the sum was performed over stars and planets. This gives us a reasonable idea of what is happening on the scale of the solar system. For greater accuracy, we would need to allow for the different ratios of protons to neutrons in the various heavenly bodies.
It was always tacitly assumed that the earth dominated local stasis: full stop. This simplistic view failed to address the questions of the earth's axial rotation, the composition of bodies and the effect of proximity on the integrals. This paper addresses these problems.
The composition factor is determined by the distribution of elements within each massive body. If we assume that each proton has an associated electron, the total charge, not taking sign into account is twice as much for a proton as a neutron.
If we take a simple example of a planet made of iron and a sun made of hydrogen, then the ratio of charge per unit mass is given by:
Notice that we have conveniently assumed that each atom of iron contains 26 protons and 30 neutrons. We can generalise this to an atom of atomic number Z and atomic weight A.
For hydrogen, this is making it convenient to take hydrogen as the base line and define the composition factor for an isotope as:
We can then define the composition factor of a massive body as:
The ability to influence stasis is dependent on the inverse square law and in this respect it is similar to gravity. When we integrate over the volume of a sphere to determine its gravitational field, we have to resolve the force from the volume element into the direction of the radius vector. This has a desirable effect on the integration and we find that gravity works as if the whole mass of a body were concentrated at its centre of gravity greatly simplifying further calculations. Unfortunately, stasis does not work in this way. The integral does not include the cosine ratio present in the case of gravity and the integral is far more complex. The result is that near to a sphere:
We can define the proximity factor b as:
where R is the distance from the centre of the sphere and a is the radius of the sphere. This fearsome looking expression can be expanded into a power series in which rapidly converges to 1 as R increases.
We shall derive this result latter. The behaviour of can be seen in this table.
On an interstellar scale, or within a planetary system, we can identify a number of spherical massive bodies which influence stasis. Within an inertial reference frame in which the the velocities of the bodies are mesured.
In most situations which we shall be concerned with, stasis will be dominated by one local massive body. It is helpful to define the "local dominance" of a massive body at a point as:
For a point on the surface of the earth, the local dominance is about kg of hydrogen per metre squared. (Based on the composition factor for iron, A = 56, and on g = 9.81)
We can then calculate the dominance of local objects on this basis. By assuming that the object is of uniform composition, its local dominance may be found by:
The simplest situation is that of the centre of a cannon ball of radius a. Let us start by calculating the volume integral of for a sphere. The area of a spherical shell is , so taking a spherical shell of thickness as our volume element.
For a big cannonball of 10cm radius, this is 7.23 units compared the 160,000,000,000 units of the earths local dominance. The importance of this result cannon be over emphasised, for it enables us to state with confidence that the nearness of local objects has has no significant effect on the calculation of stasis on earth. Even if we have a large local object such an 8000 m high mountain. Simply consider a 4000 m radius sphere of rock, guess at and and the effect of the mountain will be less the value we calculate.
Over the ocean, we can find a similar mass of low density water beneath us, The effect will be less than that of the mountain. We are safe in the assumption that in the presence of a massive body such as the earth, local variations due to mountains, oceans and man made structures will have little effect on stasis.
From the formula , we can produce a table showing how the local domonance of the earth varies with height. These figures are accurate only in respect to each other, because the exact consistency of the earth is not known. The units of D are mega tonnes of hydrogen / metre squared.
The local dominance of the sun is around 0.085 units. The speed of the earth relative to the sun is 30,000 m/s and we can readily calculate its effect on stasis at the earths surface by using the following calculation.
The moon has a mass of kg and an orbital velocity of 1023 m/s and an orbital radius of m. This gives it a local dominance in the region of the earth of about:
The contribution to the stasis vector of the moon at the centre of the earth is therefore:
The natural inertial frame for a planet is based on the instantaneous orbital velocity of the planet with the axes fixed in direction relative to the stars. In this frame, the surface of the earth has a tangential velocity of where is the latitude and the unit vector points east. The rotation of a sphere defines the locus of its axis of rotation and its equatorial plane from which latitude can be measured. If we take a point P at a distance R from the centre of a rotating sphere and latitude , we can with difficulty calculate the effect on stasis.
Everything depends on the way in which we divide the sphere into volume elements. We will take segments of a ring about the line joining P to the centre of the sphere. The volume element is then:
The co-ordinates of a point on the ring are:
The velocity of the point due to the angular velocity of the sphere is:
This is not the time to panic for this velocity must integrated around the ring and the terms containing will vanish.
The effect on stasis of the rotating sphere is given by which is somewhat complex so we will examine its integrals separately.
Now the limits on r can be found from the diagram to be and the limits of are found from the fact the the length ranges from zero to a, the radius of the circle giving 0 and as limits.
By expanding the brackets, we can reduce this integral to the sum of two integrals, one of which we have to do anyway. This halves the number of terms in the integral so that they only cover the four page widths!
Now is the time to panic. Mathcad can be coaxed to perform these integrations. I say coaxed, because it has one or two rules for simplifying expressions which are not helpful. It likes to write as introducing imaginary numbers and it does not recognise that .
For those with an interest in the diabolical:
The only reasonable way to deal with such expressions is to let Mathcad do the work of turning them into a numerical table. On the basis that , the contribution to stasis from the rotation of the earth may be calculated with a value for s from the following table.
The equation can be most meaningfully expressed thus:
Notice that we do not perform the obvious cancellation because we need to know the magnitude of the denominators in order to combine stasis vector components. This formula gives us the component of stasis due to the rotation of the earth. We need the denominator to determine the component of stasis due to the sun. This process has been simplified by introducing the concept of local dominance in which we multiply the volume by the density and composition factor.
If we now define the rotational proximity factor:
We can write the rotational effect of a spherical body as:
The stasis vector at any point in a system of massive spherical bodies, taking their rotation into account is:
We can simplify the formula for the rotational effect by performing the division to give:
to show how the two proximity factors combine.
This is a modern version of the Michelson Morley experiment. It sought to prove the validity of the Special Theory of Relativity against the Lorentz theory that motion through the aether causes objects to contract in the direction of that motion.
The experiment used a laser and a Fabry Perot interferometer with a 30.5 cm spacer between the mirrors. The fringes were detected by a sensor which controlled a servo mechanism altering the frequency of the laser to hold the the fringes in a constant position. The apparatus measured the changes in the frequency which the experimenters interpreted as being due to changes in the length of the interferometer. The wave length of the laser is 3.39 µm and that scale, the length of the interferometer varied quite a lot due to temperature and stress. Like Michelson and Morley, they were looking for a Lorentz contraction due to the earth's orbital velocity of 30,000 m/s. Throughout all their attempts to eliminate and account for variations in the frequency, a frequency shift of around 17 Hz persisted. They referred to it as "this persistent spurious signal (17 Hz amplitude at 2f)". The "2f" referring to to the fact that this occurs at twice the speed of rotation of the table. They said that the variation remained "with an approximately constant phase in the laboratory".
Instead of investigating this effect, they simply averaged it out over 12 and 24 hour periods.
Let us now take the standpoint that there is a difference between the east to west and the west to east speeds of light. This is precisely the way in which the time dilation of a light clock is worked out in many texts and the way in which the the Michelson Morley experiment is analysed. The effect of east west alignment of the interferometer is a third order effect and may be neglected, but the effect of north south orientation reduces the effective speed of light to . The wave length must remain constant under the control of the servo, so we can write.
When we substitute the observed 17 Hz anomaly into this we get v = 186 m/s.
The experiment was conducted at Bolder, Colorado where the latitude is 40°. The result predicted by the stasis theory is 176.6 m/s in an easterly direction measured in a frame of reference moving with the centre of the earth and fixed in direction relative to the stars. Since the laboratory has twice this velocity in this frame, the component of the stasis vector, due to the rotation of the earth, relative to the laboratory is 176 m/s in a westerly direction. The stasis theory also predicts a component of 15.9 m/s in the opposite direction to the earth's orbital velocity. This direction varies throughout the day and throughout the seasons.
It must be emphasised that all of Brillet and Hall's measurements take place against a background noise many times greater than that they are trying to measure. The data in their paper has been averaged over periods of 12 and sometimes 24 hours to average out the noise. The 17 Hz anomoly was simply part of that noise. It remains to be seen whether or not they and the university archivists have recorded their data for posterity. If they kept records as they performed the experiment, then it should be possible to look for some of the vital data missing from their paper.
The alternative is to perform the experiment again, grouping and averaging the data so as to look for the effects predicted by the stasis theory.