Chapter Four

Lessons from the Particle Waves

4.1 The Strange Case of an Isolated Particle in unbound universe

Consider the Free particle Schrodinger Equation  for a particle of energy

which has the solution of the form 

This  give a moving wave. If we stop the time at some instant we will get the following static wave form.

Here we know its energy exactly; but we have no idea where it is and where it came from and which way it is going.  It has no defined position.  This is due to uncertainty principle which says
Dp Dq ³ h/4p
Since we know the momentum p exactly ( = 0) we have infinite uncertainty in position ( = infinite). Again for a given value of k both +k and  -k, give the same energy . 

It  really doesn't know "if it is coming or going?". Taking the probability interpretation of Born the probability of finding the particle at any one instant is given below

There are many points in the space where it has a probability of 1.  The particle is at several places at the same time.  In time this distributes and over half the period of the wave it is everywhere.  It is an omnipresent particle.  This surprising result is because it is an isolated particle and is in unbounded space. An isolated particle with definite energy cannot be localized in an unbound universe!

They have no direction or purpose.  They in fact represent the potent (Omni or not), Omnipresent Monad. However when it becomes a composite body it gets meaning and purpose as we show below. I have actually used this argument in order to indicate that God the Absolute (Nirguna Brahman as defined in Indian theology) has no purpose and cannot be known. Because of this Nirguna Brahman do not engage in creation or redemption. Such a God is as good as non-existent.

4.2  Effect of Coherent Particle System

Suppose now we have a large number of particles which are coherent – which means each wave is in phase with all the others.  Then for all practical purposes we still have a  multiple particle which act as one particle - Many in One.  Thus a number of personalities that are in coherence, act as one Unit, each enhancing and supporting the other.    We still have the same waveform with higher wave amplitude.  It is as though we only have one single particle of a larger mass m. They still do not localize and is in no way different from a single particle.

Thus even a totally coherent group of gods do not make a difference because they have no personalities to express.

After all how do we define mass and particle without extensions.  They will remain as mathematical imaginations.  Indeterminacy is vital to the reality of existence .  At least  for experiencing the particle we need extensions. A point will remain imaginary unless it is a circle of infinitely small radius.  This is also seen in the visibility of line spectra.  If the energy levels were discrete and the transitions gave rise to a single discrete frequency in spectra, these will be totally incapable of being seen unless we have a blurring senser.   Fortunately each spectral line is given a width due to Lamb Shift so that we can see it.

4.3  Effect of Binding the Particle   

If we now place this single particle in a bounded box, reflection of the same wave results in what is known as the standing waves.  These waves are quantized. This transformation is a transition from the Nirguna Brahman – the God who is unknown and unknowable to Saguna Brahman. The unknowable when restricts himself into a boundary become one with a form. Then this God has properties that are measurable or knowable. Again this is similar to incarnation. The eternal God enters the finite dimensions of human existence brings along with it its own restriction. Thus the incarnate Jesus had limitations with regard to space and time. While he was capable of superceding these restrictions, Jesus as incarnate man never seems to have violated this self imposed restriction. “Having found himself in the form of man, he humbled himself.”

With the probability function as:

This is produced by a self-reflection process at the boundaries. Thus it is the boundaries that has produced the properties that we can see. Only those quantized waves will sustain while all the other modes will decay and vanish. This state will remain without decay as long as the system is isolated from the rest of the cosmos.  The motion is unabated unless external interference occurs.

4.4 Particle in 3D and Degeneracy

When we extend the problem to 3 Dimensions the particle in a 3D box exhibits degeneracy because of its 3 freedoms of motion. Each possible state has a threefold degeneracy.

If we stretch any one axis this degeneracy is broken. Thus in an unbounded space it reduces to omnipresence.

God appears in our finite bounded world as degenerate beings and with specific properties. It is the same Nirguna Brahman appearing as Saguna Brahman by restricting Himself.

4.5  Effect of Many non-Coherent Particles

However in the infinite space, if there are several waves that are not in phase or not coherent, these waves interfere with each other and wave packets are formed.

 Look what happens as we add more are more waves with varying phases in the universe which is still considered unbound.

1 Wave 4 waves 16 waves

32waves 128waves

If there are an infinite number of particles of varying energies we have a localized particle.

Localization and individual direction of motion develops when large number (ideally infinite number)  of non-coherent waves fall on each other.

The Motion is as follows:

Every mathematics students knows how to get these waves given a wave form using Fourier Analysis

Thus it is the lack of coherence within us that gives us the location – the feeling of I – the definition of Ego. In reality we are one with the rest of the cosmos. When the creation is in resonance with the creator we in fact part-take of the divinity with Him. But the entry of sin into the cosmos through the free beings produced a separation – separate beings in the creation each striving and competing with each other resulting in the decaying world. Competition and survival of the fittest really do not produce more efficient systems but a decaying dying system.

The purpose of incarnation was to bring back the coherence and oneness of mind in resonance with the Divine. In other words, it was to bring back Love into the beings. The plan of Jesus in this regard was to start groups of willing beings to come together in oneness of mind. This was his Church on which he places the whole responsibility of redeeming the cosmos as a whole. In fact the whole creation is waiting for the appearance of the “Sons of God” so that through them the redemption can be obtained. Church is essentially is worshipping community.

1Co 10:16 The cup of blessing which we take, does it not give us a part in the blood of Christ? and is not the broken bread a taking part in the body of Christ?

1Co 10:17 Because we, being a number of persons, are one bread, we are one body: for we all take part in the one bread.

1Co 12:12 For as the body is one, and has a number of parts, and all the parts make one body, so is Christ.

1Co 12:13 For through the baptism of the one Spirit we were all formed into one body, Jews or Greeks, servants or free men, and were all made full of the same Spirit.

Eph 4:4 There is one body and one Spirit, even as you have been marked out by God in the one hope of his purpose for you;

Eph 4:5 One Lord, one faith, one baptism,

Eph 4:6 One God and Father of all, who is over all, and through all, and in all.