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REVISING WAVE FUNCTION

JUlia Implant flowers009

The wave function of sub-atomic particles” was introduced in response to the Heisenberg uncertainty principle. The uncertainty principle asserts that we cannot be certain about the precise location and momentum of a particle simultaneously. The concept maintains that objects have particle-like and wave-like properties at the same time. Different models have been introduced to explain this paradoxical concept. Max Born postulated that wave function does not represent an actual wave but the probability of finding a particle in a particular place.

wave of probability

Another postulate introduced by Schrodinger describes the wave function as packet of waves that represent the object. There is another explanation called the pilot wave model introduced by Louis de Broglie and further developed by David Bohm, it proposes that there is no duality; rather, particles are guided by a pilot wave. The pilot wave model maintains that each particle follows a trajectory, which is guided by a special wave. In this section, I adopt the above model and take wave function to be the actual motion of a particle along a modified sin wave.

pilot wave and wave packet

My conjecture is in line with De Broglie-Bohm’s approach, where particles in space-time have well-defined positions and trajectories at every instant. The wave-particle approach is closer to objective reality which is somehow paled by the other two models. The De Broglie-Bohm’s model was criticized for being non-local. Here, I make the assumption that particle’s trajectories in space-time are interrupted. Particles periodically hit the non-local singularity as they travel along their trajectory. Therefore the experimentally confirmed non-local features are explained.

Electron in Relativistic quantum electrodynamics

An electron, is supposed to be point-like (i.e., it has no volume). According to classical physics, the energy associated with its electrostatic field increases as we get closer to it, becoming infinite when the distance vanishes. However, infinity is not defined in space-time. Here, mass/energy equivalence (E = mc2) comes to the rescue. The quantum field theory suggests that as the distance decreases and the energy equals 2mc2 of the mass of the electron, an electron-positron pair is formed that consumes the extra energy. Of course, in closer distances, the energy is much greater. But not to worry: an infinite number of electron-positron pairs can be formed then annihilated, so that we end up with the energy of just one electron. In short, the electron is comprised of a “seed,” with a heavy blanket of infinite positrons and another heavy layer of infinite electrons on top of that. Yet infinite electrons and positrons need infinite space. What are we to do about this? Here again, renormalization comes to the rescue. The gigantic electron is not observed. This situation is not normal, so we must close our eyes and normalize the results. This means ignoring such a blanket altogether. The Schrodinger equation for wave function is as follows:


Ψ (x,t) = A exp[ i ( kx-Δt )]

Without going to the details, I just want to draw your attention to the A in the equation. A is called the normalization constant. Its role is to insure the probability of finding a particle somewhere in space-time. Without A we need to deal with i and the imaginary domain. With A we can manipulate the equation by arbitrarily changing its value to any number that suits our perception of normal.

Here, I propose a model where the electron is exposed to an entity with infinite energy. The model attributes the huge energy of electron field to this entity.

   
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