State Reduction and Dream Elucidation

Copenhagen interpretation of quantum mechanics first suggested by Neils Bohr, has gained popularity against the other theories despite its very strange sketch. It talks about how an observer would collapse superposition of particle properties into a definite and objective state. Arnold Mindell compares these phenomena with fantasy and its overlapped states versus a definite state found in consensus reality. He claims:

“Another method of marginalizing experience occurs when you start thinking about the meaning of the fantasy, while in the midst of the fantasizing. Thinking about it stops the fantasy.”¹⁴ and we are back to one state world that we call reality.

Singularity and State Reduction

Lee Smolin believes that we are seeing the same universe from different angles. At the beginning of this paper I was trying to draw an entity with zero dimension where the image of all of the points in our world can drop in it and stay superimposed. Some place where different events can happen simultaneously because the notion of time is not present. May be we don't have to speculate in remote and strange thought domains.Multiple universes and multiple histories do not sound very logical. Rather we can assume an intimate proximity and relationship between macrocosm and singularity. With this assumption, multiple states stay in one arena, which has the capability to accommodate them. This way we do not have to mix it up with activities, which are allowable in space-time and macrocosm. Otherwise, it leads to confusion and we will be dragged into an in-deterministic physics that nobody knows how to deal with it.

Dr. Walker rejects the measurement error interpretation by reasoning that our measuring device is only another sub-atomic particle, which according to Schrödinger’s equation entangles with the particles under observation. This should add to complexity of superposition, not state reduction. At the beginning we explored the similarities between mind and proposed singularity. The necessity to utilize complex numbers in order to explain quantum behavior suggests that elements in imaginary world participate in determining quantum physics. Previously, I took the imaginary portion, to represent the effect of the proposed singularity.

My conjecture is that the physical world is made of separate and discrete parts and bodies. But the duality nature of the existence connects and interacts each part through the universal consciousness.The universal consciousness is extended through our bodies as well and this is how we are connected and mingled with the whole.

Tonomura Double Slit Experiment:

Feynman's Sum over Paths Approach

In Thomas Young’s double-slit experiment a beam of light is directed towards a barrier with two slits that diffract the beam. A screen is installed behind the barrier that shows light and dark rows or the so-called interference pattern.This is the basic experiment, which shows the wave property of light.In 1920, Albert Einstein received the Nobel Prize for introducing the photon as a packet of light energy. Thereafter, light has been considered as a particle wave function. Photon is the particle portion of light.

Tonomura Double slit experiment is almost a similar experiment but with a very strange result. In this experiment, electrons are fired one by one in time intervals of ten seconds. Interestingly, the interference pattern appears in the screen similar to the one when a bunch of electrons is fired towards both slits simultaneously. The experiment has been repeated by many researchers. Brian Greene explains how the strange results were first observed:

“In 1920 Davisson and Germer ...were studying how a beam of electron bounces off a chunk of nickel. The nickel crystals in such an experiment act very much like the two slits in the double slits experiment of Thomas Young... Their experiment therefore showed that electrons exhibit interference phenomena... even if the beam of fired electrons was thinned so that, for instance, only one electron was emitted every ten second, the individual electron still built up the bright and dark bands.”¹

In order to explain the electron two-slit paradox the Late Physicist Richard Feynman proclaimed:

“Each electron that makes it through to the phosphorescent screen actually goes through both slits. Feynman argued in traveling from the source to a given point on the phosphorescent screen each individual electron actually traverse every possible trajectory simultaneously…It goes in a nice orderly way through the left slit. It simultaneously also goes in a nice orderly way through the right slit. It heads toward the left slit, but suddenly changes courses and heads through the right. It meanders back and forth, finally passing through the left slit. It goes on a long journey to Andromeda galaxy before turning back and passing through the left slit on its way to the screen. And on it goes- the electron, according to Feynman, simultaneously sniffs out every possible path connecting its starting location with its final destination.”¹

Of course, this is not his personal opinion. Different experiments suggest the above conclusion. The so-called Diffraction Grating Mirror works with the same principle.

Broken Mirror
The reflection angles do not match. However, a detector placed out of range can still register a signal.⁵²

In addition, the above explanation is obviously against the Special Relativity that limits the velocity to light speed. If the electron is going back and forth in different ways, it should have infinite fold time speed of light, which is contradicting the known space-time physics.

Singularity and Tonomura Double Slit Experiment

To have an infinite speed, the particle has to perform in a non-local arena. A better explanation can be reached, if we accept that the electrons are acting in a field with no time dimension. In this situation, speed conflict is solved but the paradox is still not completely resolved. One has to delete the notion of space and distance out of this experiment as well. This way the electron can come from everywhere and nowhere. Using the verb come applies to travel in space. It is better to use appear and accept that in this experiment electrons pop in and out of space-time universe.

On above interference experiment, Feynman tried to explain the paradox by claiming that each electron will follow all possible tracks before it hits the screen. We can claim that here, the electron follows the non-locality characteristic of the proposed singularity.Either non-locality or being not time-bound can explain this effect more logically than assuming that electron traveled along all possible trajectories before hitting the screen. Roger Penrose offers the mathematic equation for two-slit experiment by using complex numbers for quantum state. Roger Penrose writes:

“They 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.”⁵

To introduce the mathematics 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. Again, we can imagine the complex numbers in our mind. But quantum two-slit behavior 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 there to do it for us?

One can assume that if complex numbers represent particle functions, then particles themselves have to have an imaginary (out of space-time) phase.

Abstract World of Mathematics

Roger Penrose uses the Argand Diagram (presented in the Complex Number chapter) to discuss the complex numbers 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.”⁵

Therefore, Professor Penrose is suggesting staying in the abstract world of mathematics and viewing the imaginary number as a component of Argand diagram which is drawn in front of us.

If we try to understand the meaning of complex numbers with our space-time knowledge, we will face a concrete wall. Therefore, we choose to take refuge in mathematical domain. We tend to take imaginary number as a mathematical entity and give ourselves comfort.From school times we have learned how to use numbers as abstract entities. We are used to perform mathematical calculations and ignore their relation with objective reality. We cannot stay in this refuge for long. Our father Adam didn't. We cannot do it either. We have to explore, find and assign a tangible and deterministic reality to imaginary and notion 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.