(A.K.Balamurugan) - About my name

We know the existence of the universe formed out of the fundamental particles. Is there anything new to know about the existence of the fundamental particles? Yes.

The existence of fundamental particles is swinging on both sides of non-existence. If asked what non-existence is and what are on the either side of non-existence, it is one existence compensating the other so that the net existence is nil.

This fact is interpreted from the nature of the wave functions that describe the particles. I am introducing a new interpretation of quantum mechanical wave functions. I will refer to this as the new picture and the other interpretations as old pictures in this article. We know that the modulus square of the wave function describes the probability of existence of the particle. By existence, we mean all the attributes of existence viz, mass, charge ... (And even space and time?). Modulus square is the sum of the square of the real part and the negative of the square of the imaginary part. Is it done so to get a positive real quantity? I suppose that this is what has concealed the intended fact. To get the correct picture, I consider the squares of the real and imaginary parts of the wave function separately without changing the sign. These two parts represent the two types of existences of the particle. The squares of these two parts give the probability of finding these two existences separately. Thus, each particle has two components existing in two mutually opposite states. These two states of a particle vary simultaneously and sinusoidally with respect to time and in many cases with respect to space also. Since all the matter in the universe have components existing in such mutually opposite states, there is no way to say that either of the two states is more unique than/familiar than/preferred to the other. Hence, I see both existences equivalent. The opposite signs of the existences imply that all the attributes of these existences are opposite in nature to each other. The attribute, for example, mass, of these two components of the particle are mutually opposite to each other.

Let us examine the concepts with the help of a real world particle, an electron in a hydrogen atom. Its wave function is of the form R(r)f(l,m)exp(iωt). If we consider an electron with the magnetic quantum number, 'm' equal to 0, the square of the real part of the wave function is [R(r)f(l,0)cos(iωt)]^{2} and the square of the imaginary part is -[R(r)f(l,0)sin(iωt)]^{2}. Thus, these two existences mutually complement each other in magnitude to make the sum of their absolute values constant. Thus by adding the first one and the negative of the second one, we get the monotonous independence from time. The two components represent the same single electron, but we have to consider them as different components of the same electron. The graphical view of this for an s-electron is presented in Illustration 1. The two tints, blue and orange, represent an existence each, say, positive and negative existences respectively. The combined view of these two existences is given in Illustration 2. The intermediate tints in this illustration mean the combination of the two existences in varying ratios and the extreme colours mean the presence of one and only one existence.

*Illustra**tion 1: The two existences** of an s-electron*

* Illustration 2: Combined view of the existences (The swinging of s-electron's existence)*

If we consider an electron with magnetic quantum number, 'm', not equal to zero, then the probability functions of its two existences show azimuthal variation also in addition to the temporal variation. The probability functions of the positive and negative existences have the factors [cos(mϕ+ωt)]^{2} and -[sin(mϕ+ωt)]^{2} respectively. The combined effect of both the existences is illustrated in Illustration 3 analogous to the Illustration 2 of the s-electron. There is an exciting feature in this picture that the probability distributions of the two existences revolve around the nucleus, which is analogous to the logically expected classical revolution.

*Illustration** 3:* *The time dependance of a p-electron*

The new picture gives an interesting interpretation about the spin of the electrons. In the old interpretations, there is not a clear conceivable account of the spin of the electrons. The new picture explains the spin of the electron as its swinging between the two types of existences with time. As expressed in the beginning, the two existences have opposite properties attributed to them, If space is one among those properrties, the positive existence is occupying positive space, while the other existence is occupying the opposite (negative) space. Thus, an electron occupies either positive space or negative space or parts of these two spaces depending on the time. However, at any time, the remaining space is available for another electron to occupy. Thus, if ψ is the wave function of the first electron, then, iψ is the wave function of the other electron occupying the counter-space. In the case of the s-electron discussed above, the spins of two 1s electrons is shown in Illustration 4. The second electron swings between the two states in the opposite direction to that of the first one. This is how two electrons with the same n, l and m values are allowed to exist together but with opposite spins.

*Illustration** 4: **Two s-electrons spinning in opposite directions*

Analyzing an electron with non-zero 'm' value, in a similar way, reveals more facts that are interesting. The existence-state of this electron shows azimuthal variation unlike the s-electrons. When the azimuthal part in the positive state swings towards the negative state with time, the other azimuthal part in the negative state swings towards the positive state at the same time. This swinging of states with time, gives the two spatially varying states the classical appearance that they are revolving around the nucleus. The orbital revolution of two p-electrons with the same n, l and m values but with opposite spins is shown in Illustration 5. If we imagine an opaque screen in front of this illustration, with a small window in it, we will see through this window, the spinning similar to that found in Illustration 4 that is for an s-electron. The exciting scene of revolution is the outcome of the spin of the electron. The two electrons show revolution in the same direction since their 'm' have the same sign. If the sign of 'm' is changed, the direction of revolution will change.

This revolution represents motion in the scale of an elementary particle. By extending this picture to any more complex or even macroscopic systems, it should be possible to attribute the motion found in that system to the spin of the particles constituting that system.

*Illustration 5: p-electrons spinning in opposite directions*

Hence, in compliance with the old picture, a spinning electron cannot be thought of as a spherical ball of charge revolving around its own axis. The spin is the consequence of the time dependence of the system.

According to this picture, the time average existence of matter and hence that of the universe is nil. However, the material universe is existing because the time really exists and along with it, the created matterial universe also exists. The time average being zero indicates that the matter is created from some 'nothing' so that the net existence is conserved to that 'nothing'. In Hindu shastras, it is referred to as 'Maya'. In scientific discussion, I do not think it is inappropriate to talk about God. The shastras say that God created the universe from Maya. This theory complies with the Shastras.

Thus, the conservation to zero is found to be more logical than conservation to some unknown and huge (infinite?) existence (if the existence is thought of to be having a single existence polarity)

The unknown matter, called as dark matter, I believe, should also have a similar existence, although it is not discovered what it is, and if it is existing.

Can these two components of existences be the antimatter to each other? If these can satisfy the requirement of existence of antimatter in the universe, they are available in nature in perfectly equal abundance. By the way, we do not have to think that the antimatter of the universe is missing and to look for them as if they exist isolated somewhere in the astro-space. I do not think that positron is the antimatter of electron. Hence, we do not have to look for matter constituted by anti atoms to exist in equal abundance to mattter constituted by normal atoms. The opposite existences discussed in this article have to be considered as matter antimatter pairs. They satisfy the expectation that matter and antimatter should exist in equal abundance.

Can this picture help in removing the controversial concept of sea of negative energy particles proposed by Dirac?

P.S. I created this document using OpenOffice and LibreOffice. They support Gif animations whereas MS word doesn't. Hence to view the animations of the gif images inserted in this document, please use a compatible 'Office' software. I used GIMP to create the gif animations used in this document. I thank these and other opensource software communities for the help I receive through their products.