Hidden Variables

[Keith Wakelam]

DARK MATTER AS A HIDDEN VARIABLE

ABSTRACT

You wouldn’t believe how much of science depends on imagination

Complex Numbers were announced to the world by Cardano (1501-1576), he regarded them as useless. Was he right? They were used successfully to measure power in out of phase AC current. Then Minkowski invented spacetime as x,y,z,ict, The ‘i’ being the square root of minus one and therefore imaginary. Making time a 4th dimension was done without rigorous proof (such as might have been accepted in philosophical circles), but Einstein seized upon the idea, and so we were lead into schemes of up to eleven dimensions, covering different aspects of atomic phenomena. Complex numbers also form an essential framework of Quantum Theory but are they just a device to obscure the fact that we are dealing with David Bohm’s hidden variable or Dirac’s infinite sea of negative energy states? Now Dark Matter offers the answer.

To every thing there is a reason and a purpose to everything under the sun.

Einstein’s use of time as a dimension was mistaken .We just live now.

Time is related to entropy, the conversion of useful energy into waste heat. The Weak Force of radioactive decay. Everything happens in the moment ‘now’, there just isn’t enough energy to have everything happening continuously throughout a time dimension of four thousand million years, and an unspecfied future. Then the idea that nothing can exceed the speed of light is no longer true now we know about ‘non-locality’.

Heisenberg’s Uncertainty Principle Δ x Δ p = h/2π can be challenged in one or two instances where measurement is not dependent on illumination by electromagnetic waves. For example, the track of a particle in a Cloud Chamber. It might be said that the width of the track illustrates uncertainty, but the curvature of the track gives an exact measure of momentum. In the case of the neutron uncertainty in the measurement of its momentum depends of the assumption that it is a single particle and not a close group of proton, electron and neutrino. The fine structure of atomic spectra due to spin does not reflect uncertainty. Computer screens carry fine detail. If there are ways of by-passing uncertainty then the principle is at stake. Einstein remarked ‘God doesn’t play dice with the Universe.’

Schroedinger’s Wave Equation = ihδΨ(x,t)/δt is forced to contain a complex function, The whole of Quantum Mechanics is therefore based on imagination. Amazingly the solutions to this equation are invariably correct, integral negative powers of e, the base of Naperian Logarithms give eigenstates and exact quantum numbers corresponding to energy states like the Balmer Series. Such accuracy is extraordinary. Does it suggest that some real hidden variable underlies the imaginary solution? The Ptomelaic sys tem of epicycles, afferents and deferents gave accurate forecasts of the eclipses of the Moon and Sun yet it did not represent reality. The hidden variable was the force of gravity.

Existing theory maintains that there is no such thing as ether. It was regarded anyway as a neutral transmission medium. But we now have Dark Matter to contend with. As there are four states of matter – solid, liquid, gaseous, plasmic, it is logical to suppose that there are at least three states of Dark Matter somewhat analogous to ordinary matter. Being invisible and intangible it can also be supposed that Dark Matter, like a neutrino, only possesses spin. Spin – spin coupling is therefore the only form of interaction possible between Dark Matter particles. The hot form of Dark Matter is most likely gaseous, in the cooler form there could be two forms of spin coupling – end to end and side to side, making long strings. Then in the cold, solid form the strings make a lattice. In the realm of Dark Matter temperature is on a different scale, since if we are to believe Dirac, Dark Matter particles are of negative energy. What this may imply is that these particles are bound internally with such a high degree of force that they depart from the Kelvin scale, they are on the flip side of absolute zero and cannot return past it unless given a large amount of Photon energy, as with photoproduction of particle pairs.

Each form of Dark Matter would support some kind of activity, one cannot imagine a hidden state just sitting there and doing nothing. But their activity is real, since spin coupling does not involve any imaginary, complex maths. The forces generated by these various states of Dark Matter would vary from strong to weak as with normal matter. Strong for the lattices and strings and very weak for the gaseous state. The lattices can be seen as imposing restrictive barriers, but allowing a small proportion of the impacting particles through its gaps. The strings can be seen as allowing communication along their length very efficiently (as lines of force), but being so thin that they can pass between particles in a normal solid. They would obey Fermi/Dirac statistics, terminating on particles they encountered. Being of two types, side to side and end to end they can be identified as conveyors of electric and magnetic force.

The gaseous constituents of Dark Matter at the high energy end of the spectrum would not form orbitals around atoms, but because of the huge difference in density that would probably exist between hot and cool states (as with steam and water) turbulence would undoubtedly exist at boundaries between the two states. Some turbulence might also exist within the gaseous regions such as is found in atmospheres surrounding the earth, sun and planets. These could be of cyclonic or anti-cyclonic nature, spurred by the rotation of their primaries.

One next has to consider whether the neighbourhood of particles or atoms is condusive to heating or cooling Dark Matter, thus giving rise to the cyclonic or anti-cyclonic disturbances. The atomic nucleus, being the place associated with its mass, might be considered the colder part of the atom and therefore capable of producing a cyclonic disturbance of the Dark Matter. Bands of the cyclone formed of it would therefore circulate around the nucleus corresponding to the quantum energy levels, except that these would be real levels where thick bands of Dark Matter conspired to urge electrons around in their orbits and the thickness of the banding would determine a measure of uncertainty. As the temperature gradient diminishes out from the nucleus the bands would move close together to merge completely at the Bohr radius of the atom. The spacing of these bands conforms to the negative roots of ‘e’ the same as the eigenstates of the Schroedinger Wave equation. This gives an entirely different picture of the atom to the one currently in vogue. It does not consist for the most part of empty space but is a three dimensional vortex of furious activity out to its boundary which appears to be a higher temperature skin and is where its anti-cyclonic vortex ceases to exist.

To continue with this highly speculative picture one must now imagine that the space around atoms is filled with Dark Matter at a still lower (negative energy) temperature corresponding to zero point energy, so that atomic spin produces a weak cyclonic disturbance around the atom. This cyclone is not constrained electromagnetically and so expands like a figure 6, very much as an atmospheric hurricane or tornado and the orbits of planets.

Ref. The Power of the Vortex, Keith Wakelam 1991