Chapter Six

Quantum Potential Interpretation and Many Body Problem

6.1 Quantum Potential Interpretation

The same idea is depicted in a slightly different terminology in Quantum Potential Interpretation. Bohm (D. Bohm: A Suggested Interpretation of the Quantum Theory in Terms of 'Hidden' Variables, II and I. Phys.Rev. 85 (1952) 166.) and DeBroglie (L. DeBroglie: "Nonlinear Wave Mechanics" Elsevier Science, Amsterdam (1960).) on the other hand assume a causal or ensemble interpretation.

According to Bohm (1892-1987), the wave function supplies an additional potential - the Quantum-Potential. This potential, when inserted into the Hamilton-Jacobi-equation of classical physics, leads to well-determined trajectories of the individual particles. Thus there is a second wave that determines a precise position for the particle at any particular time. In this theory, there is some 'hidden variable' that determines the precise position of the photon.

For the case of the double-slit-experiment, each particle has a well-defined trajectory and passes through one of the two slits. However the particles do produce interference pattern because it is guided by the quantum potential. Thus classical trajectory depends on the quantum potential, which is dependent on the external situation. It is not possible, to predict or to select a specific trajectory for the particle by controlling physical conditions such as the slit width or source distance or screen distance.

This theory was thwarted when John von Neumann (1903-1957) a well-known mathematician in 1932 proved that this theory was impossible. John Bell (1928-1990) in 1966 discovered that the proof had holes. According to Bell there is a definite possibility of a quantum guiding potential and possible hidden variables -- but only if particles could communicate faster than light (this is called 'nonlocality').

In 1982 at the University of Paris, Aspect and his team discovered that under certain circumstances subatomic particles such as electrons are able to instantaneously communicate with each other regardless of the distance separating them. But we cannot use this method to communicate.

Bohm's theory was that the second wave was indeed faster than light, and moreover it did not get weaker with distance but instantly permeated the entire universe, acting as a guide for the movement of the photon. This is why it is sometimes called the 'pilot wave'.

"Classical physics provided a mirror that reflected only the objective structure of the human being who was the observer. There is no room in this scheme for his mental process that is thus regarded as separate or as a mere 'epiphenomenon' of the objective processes. ... [Through the] mirror [of quantum physics] the observer sees 'himself' both physically and mentally in the larger setting of the universe as a whole. ... More broadly one could say that through the human being, the universe is making a mirror to observe itself." -- Bohm and Hiley, The Undivided Universe, pg. 389

In this beautiful approach, the trajectory of the path is determined by the state function, which in turn is determined by the situation. Again we are presented with the total unity of the virtual and the visible. We cannot distinguish God’s decrees and purposes apart from the unfolding drama of human reaction and history. God changes his plan depending on the historical development and history develops according to God’s plan. Do we have evidence for this? I believe that the whole Biblical history is just that. If God wanted to implement salvation in his own way without regard to history, it would have been simple, direct and instantaneous. There would have been no worsening of sin or suffering nor there was any necessity of cross. It is this intertwining of the Quantum potential with the situation that causes the process development.

Quantum physics tells us the atomic "particles" of which we are made are not the ultimate physical reality. There is an ultimately physical reality with infinite latent potentialities which are realized in context in interactions. These potentialities are described by the "wavefunction" or "state function"

In the view of Bohm, subatomic particles such as electrons are not simple, structureless particles, but highly complex, dynamic entities. Their motion is determined not only by the external classical forces, but also by more subtle forces which are not perceptible by senses. These are the quantum potentials. The quantum potential pervades all space and provides direct connections between quantum systems. In 1959 Aharonov-Bohm (AB) discovered the where electrons were able to sense the magnetic field of nearby regions even when they were in the region of zero field. It confirms that we cannot really isolate a system from the rest of the cosmos. We now have sufficient proof for nonlocal effects in the EPR paradox and subsequent experiments, which we will discuss later.

Jean-Paul Vigier and several other physicists at the Institut Henri Poincaré in France, explain the quantum potential in terms of fluctuations in underlying ether. He explains it in terms of a stream with disturbances as follows:

“On this stream, one may see an ever-changing pattern of vortices, ripples, waves, splashes, etc., which evidently have no independent existence as such. Rather, they are abstracted from the flowing movement, arising and vanishing in the total process of the flow. Such transitory subsistence as may be possessed by these abstracted forms implies only a relative independence or autonomy of behavior, rather than absolutely independent existence as ultimate substances. (Page 48). “We must learn to view everything as part of "Undivided Wholeness in Flowing Movement." (Ibid., p. 11.) “

(David Bohm, Wholeness and the Implicate Order, Routledge & Kegan Paul, London, Boston, 1980.)

Bohm suggests that the whole universe can be thought of as a kind of giant, flowing hologram, or holomovement. What we notice in mundane world is only a projection from higher dimensional levels of reality. Just as a hologram records the entire image in every part of the film, the image of universe is reflected in every point matter. Bohm suggests that the quantum potential is itself organized and guided by a super quantum potential, representing a second implicate order, or super implicate order ad infinitum. Higher implicate orders organize the lower ones, which in turn influence the higher.

6.2 The Hartree and Hartree-Fock Approximation

The Hartree Fock Approximation is what is known as a Self-Consistent Field Method (SCF). The original Hartree method considers the total wavefunction of the system as a product of independent one particle wave function. For the electrons, for example, the wavefunction is an antisymmetrized determinantal product of one-electron orbitals known to scientists as the "Slater" determinant. The Hartree method allows us to to change the 3N dimensional equation into a 3 dimensional equation for each electron . This equation depends on the wavefunctions of the other electrons but can be solved in a self consistent way using the variational principle and iterating. Schrödinger equation is transformed into a set of Hartree or Hartree-Fock equations. The method of approximation is to start with the simple superposition principle (use a product wave function of individual particles) without interaction. This is equivalent to totally independent individuals. One particle is then taken and the potential in which it moves is calculated by freezing the distribution of all other particles and treating their averaged interaction as potential. The solution to this will give the first approximation. It is then repeated in sequence for all particles over and over allowing for all forms of interactions.

There are two broad categories of such approaches: those based on perturbation theory and those based on the variational principle. The main problem of the Hartree-Fock and DFT methods is the underlying treatment of electron correlation.

6.3 Born-Oppenheimer Approximation

The Born-Oppenheimer approximation is the first of several approximations used in solving Schrödinger equation for manybody systems. In the case of an atom it separates electron and nuclear motion based on the idea that nuclear mass is so much larger than electron mass that the nuclei are basically "fixed" particles. This equation shows the full Hamiltonian for a molecular system.

This can then be converted into the corresponding Schrödinger Equation.

Then the Hamiltonian for the nucleus will contain the vibrational energy added to effective potential energy due to the presence of the electronic system surrounding it.

The translation of this concept into theological terms is direct and straightforward. In theology the fixed factor is God. However in the experiential realm of human existence the Saguna Brahman (God who is knowable and known) interacts with each of the beings. Thus the behavior of the God in human history is controlled by human reaction to God and to other beings and to the created cosmos as a whole. The same is true of every being. Every human state is defined not only in terms of the internal state of the being but also in terms of the interaction of the cosmos, co-created beings in every plane as well as with God. We can look upon the whole – which includes God, Man, Creatures and Cosmos as a whole in all its dimensions – as one system. We cannot isolate each individual and attribute an absolute constant property. Even though for convenience we can identify and separate the Ego of each, ultimately we are all bound together inseparably and that includes God as the major factor.

We are influenced by God. Even the small changes in the nucleus make a lot of changes in the system. But the changes in each of the other particles, however small or weak in interaction, do produce a change in the overall state of the system. It does not change the nucleus much, but there is a still a change.

God is influenced by the behavior of his independent conscious creation. This is evidenced in the incarnation and the cross. The whole idea of conscious being in the cosmos seems to be like a network totally interconnected. If one of the strands is made weak or broken the entire strand will readjust to form a new setup.

or as Greek Kaballa portrays it

Why we can consider nucleus as a point is simply because the nucleons are bound together with extreme binding forces produced by strong nuclear interaction forces in contrast to weak interaction between electrons.

Thus one of the descriptions of God is “Rock”- something that is heavy and therefore stable and unchanging.
Psa 18:31 For who is God, but the LORD? And who is a rock, except our God?--
Psa 19:14 Let the words of my mouth and the meditation of my heart be acceptable in thy sight, O LORD, my rock and my redeemer.

Many Body Problem in Theology

The problem of many free will consciousness in a cosmos is very much similar to the Many body problem in Quantum theory. Most theological structures agree that Man (and probably many others like angelic hierarchies) are together in this cosmos with total free will interacting with each other. Thus in order to set up a solution it will be necessary to build a state function that represent the system. As a first approximation we could assume that they are separable. In that case we could make the first approximation of the state as a product of the independent state functions of each being. However this does not take into consideration the interaction between these various beings. I have developed a graphical method of dealing with these many body functions in 1969 to simplify these Hartree or Hartree Fock equations. This interaction model for four independent beings can be drawn as follows.

Replace this with this:

As we can see the whole interaction field will be enormously complicated when the number of beings increase. Add to this the societies and clubs with resonant interests forming a group that interact, family, churches etc. The only alternative is to consider the various methods of approximation. One simple method would be to find a single field to represent the interactions. This is the quantum potential interpretation. Second is to develop an average interaction field out of the large interactions. The nearer and more important interactions can be considered or asymptotically approximated. This is the Hartree and Hartree-Fock methods and the Born Openheimer method. In general we assume the important impact of God and the near relations and events to explain our behavior. The general potential thus derived is called society. Thus it is often said, the individual is created by the society.

The way we can influence the individual in a mission field is also seen here. It can be a one to one method – a direct evangelistic mission. Door to door evangelism and one to one evangelism falls in this group. There is a more effective evangelism in corporate influence. This is through church groups. Individuals get involved with the small groups where the influence is maximized in the field. There is however a limit to the size of the group depending on the radius of effective interaction. A group bigger than the radius of interaction will be counter productive. In fact factional disharmony can harm the process.