Conjectures on quantum mechanical wave functions
A.K.Balamurugan
There are some existing questions such as, how do particles get mass?[2], and where mass comes from [3]. Taking these questions as addressing the existence of mass rather than how mass manifests, can this composite picture be a part of answer to this question? That is, since the net mass of any particle according to this picture is zero, the particle's mass (and hence the particle) should have come into existence from some 'vacuum'. Although the net mass of a particle is said to be zero, while in existence the particle behaves as it has its conventionally considered mass. The main implication conveyed through the ‘two mutually opposite components’ picture is that the particles are created from nothing and at suitable (but unknown) conditions may disappear. (The Higgs hypotheses are not involved in these discussions.)
Conventionally, the sum of real part squared and the negative of imaginary part squared at any point in space and time is interpreted as the probability of finding the particle at that point of space and time. If the probabilistic nature has to be preserved, in the composite picture, the real part squared represents the probability of finding the mass component of the particle and the negative of imaginary part squared represents the probability of finding the negative mass component of the particle. It is interesting to view according to this picture that the mass – negative mass pair of an electron in an atomic orbital with m ≠ 0 appears to revolve around the nucleus as in the classical model. The direction of revolution reverts with change in the sign of m that is also compatible with the classical picture.
The measurable angular momentum of an electron with m = 0 is zero. Hence as expected, no revolution of this electron is seen. But the wave function continuously and sinusoidally becomes real and imaginary. This implies that the particle's mass continuously and sinusoidally becomes positive and negative. Although for m ≠ 0 cases, the electron's two components appear to move with time, to maintain a uniform criterion as with m = 0 cases, it can be interpreted that the particle's two components sinusoidally transform mutually into each other with time. But the net effect is that the mass and negative mass shift with time. This scenario has to be tested viz., whether this 'scene' of motion is seen in general for systems having complex wave functions and a measurable momentum. The simple problems like particle in a box have real solutions. However they are not physically realizable systems because the potentials involved in these problems, like an ideal square potential or any one-dimensional potential, are hypothetical. Hence they are not discussed here.
This picture redefines the law of conservation of mass that the apparent mass is not conserved and the actual mass is conserved to zero, considering the space and time together. The apparent mass is the mass in the conventional sense and the actual mass is the sum of the mass and negative mass components of all particles. The statement that the apparent mass is not conserved supports and is supported by the LENR (Low Energy Nuclear Reactions) [4] observations. Considering the mass equivalence of energy, probably the total energy is also conserved to zero. Zero appears to be more unique than the unknown quantity of mass and energy to which the classical law of conservation could refer to. And according to LENR, the conservation of mass is questioned.
This mass – antimass (negative mass) pair appears to be more truly matter – antimatter pair than the pairs like electron – positron pair. But it is to be explored whether the former pair can replace the latter in Physics.
To conclude, it is conjectured that the matter (mass) seen in the world is elementarily composed of two components of masses with mutually opposite signs. Both signs appear to be nearly equivalent. While a particle is in existence, it behaves as carrying the conventionally considered mass. But this mass – antimass picture implies that matter is created from nothing and annihilate into nothing under suitable but currently unknown conditions. The other implications of the conjecture are to be explored.
References
[1] Bondi, H. "Negative Mass in General Relativity," Reviews of Modern Physics, Vol. 29, No.3, July 1957, pp. 423-428
[2] ‘Approaching the altar of the 'god particle', Ideation online, Spring 2008
[3] ‘Is jiggling vacuum the origin of mass?’ , New Scientist, 13 August 2005 , issue 2512
