Singularity and Tonomura Double Slit Experiment

Richard Feynman tried to explain the paradox by claiming that each electron will follow all possible trajectories before it hits the screen. With Feynman interpretation electron has to have infinite speed. Infinite speed, is only possible in a non-local arena. Alternatively, we may assume that electron is flowing in a field with no time dimension. Only in these situations, speed conflict is resolved. Either non-locality or being not time-bound can explain the results more logically than assuming that electron travelled along all possible trajectories before hitting the screen. This way the electron can come from everywhere and nowhere. Using the verb come applies to travel in space. Maybe it is better to use appear and accept that in this experiment electron pops in and out of space-time universe.

To analyse the above experiment and explain the non-locality two different speculations can be followed. The first one is that space and time are not real. Alternatively we can take space and time as real and assume a nonlocal sub-structure media to accommodate the result and represent the non-locality aspect.

Roger Penrose offers the mathematics equation for two-slit experiment by using complex numbers . He writes;

“They (mathematical equations of double split experiment) can be represented on a two-dimensional plot with the purely real numbers running along the x-axis, and the purely imaginary numbers running up the y-axis, the imaginary axis.” ^{[13]}

To introduce the mathematics of the double slit experiment, Roger Penrose has to use imaginary dimension along real dimension. He could not find any real dimension in our space-time universe, which can help him to mathematically explain the phenomenon. One can assume that if complex numbers represent particle functions, then particles themselves have to have an imaginary (out of space-time) phase. Maybe we can postulate that here, electron immerses in a non-local arena or proposed singularity. Again, we can imagine complex numbers (with its potentiality component) in our mind. But quantum behaviour is happening all over the world in every moment, even if, our mind is not with it. There should be another being out there to accept the image, to be able to accommodate the imaginary dimension of complex numbers. Can we suppose that singularity is the all-pervasive entity that accommodates the imaginary portion of the transaction.

### Abstract World of Mathematics

Roger Penrose uses the Argand Diagram (presented in the Complex Number chapter) to discuss quantum mechanics behavior.

“The fact that these numbers are built into the foundation of quantum theory often makes people feel that theory is a rather abstract and unknowable kind of thing, but once you get used to complex numbers, particularly after playing around with them on the Argand diagram, they become very concrete objects and you do not worry so much about them.” ^{[14]}

Therefore, Professor Penrose is suggesting staying in the abstract world of mathematics and viewing imaginary portion of quantum physics as a component of Argand diagram which is plotted in a piece of paper.

If we try to understand the meaning of complex numbers with our space-time knowledge, we will face a concrete wall. Therefore, professor Penrose chose to take refuge in mathematical domain. We tend to take imaginary number as an abstract mathematical entity and give ourselves comfort. From school times we got to the habit of using numbers as abstract entities. Erroneously, we are have performed mathematical calculations and ignore their relation with physical reality. We cannot stay in this refuge for long. Our father Adam didn't accept the confinement. We cannot do it either. We have to explore, find and assign a tangible and deterministic reality to notions of imaginary and of complex numbers. On the other hand because mathematics are so precise in calculating the Newtonian physics, electromagnetism, GTR and quantum mechanics, if in some parts it does not match our perception of reality, one could suspect that our perception might be wrong or incomplete.

In our model, because, there is no dimension in singularity an electron can move radially -- in and out of space-time universe, but yet cover the whole angular range, because singularity is everywhere and nowhere. An electron being at the same time in singularity, can defy 'steel ball' or ‘Classical’ interpretations of stationary orbital as perpetual motion in our space-time universe. In this explanation an electron does not need to follow the laws of classical physics.

Information field theory offers another explanation for strange results of double slit experiment. In mathematics any element added to the field changes the whole calculations and drastically alters the outcome. In the informational field theory we do not deal with individual components. New conditions creates a totally different system. If we take the experiments environment as a whole field then tampering with slits (altering the data) changes the whole system and therefore a drastic outcome is expected. ^{[15]}

But then this interpretation requires a pervasive informational field. I have assumed singularity as such a field.

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