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Singularity and State Reduction

At the beginning of this essay I have assumed the presence of 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 in this entity the notion of time is not present. I have assumed that space-time universe and this entity are like two sides of the same coin. The coin being the existence.

Von Neumann 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 behaviour 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 dual nature of the existence connects and interact 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 permits the light to go through. 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 demonstrates the wave property of light.

On the other hand, in 1920, Albert Einstein received the Nobel Prize for introducing the photon as a particle (packet of light energy). Currently, light has been considered to have double character. It is assumed to have a particle and a wave property. Photon is the particle trait of light.

Tonomura Double slit experiment is almost similar to Young experiment but with a twist. In this experiment, instead of photons, electrons are fired one by one in time intervals of ten seconds. Interestingly, the interference pattern appears in the screen even there was just one electron in the system at a time. Just like there are bunch of electrons 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.”  [10]

The experiment shows that electron acts like a wave. Then we ask; how can one electron wave creates interference with itself?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.”  [11]

Of course, this is not his personal opinion. Many physicists share the above conviction. Feynman’s explanation is obviously against the special relativity that limits the velocity to light speed. If the electron is going back and forth to remote distances along the way, it should have infinite fold time speed of light, which is contradicting the known space-time physics. Infinite speed is only possible in a non-local arena. Here we either have to drop locality or the notion of time or both.

Information/ Interference Complementarity


George Greenstein and Arthur Zajong mention another very interesting complementarity relation in their book “The Quantum Challenge”. They explained the complementarity between information and interference pattern in double slit experiment (see the explanation under the same subtitle in this chapter). Referring to moveable slit modification of the experiment, they wrote:

“Wootters and Zorek have returned to Einstein's modification of the classic double-slit interference experiment, and analyzed it from the stand point of partial information…The slits are free to move. After particle has passed through, we measure the slit's momentum… if the slits are moving downward, the particle must have passed through slit 2…
Wootters and Zorek noted that the above conclusion is not in fact entirely certain. The same motion of the slits would also be observed had the particle passed the wrong slit --if the initial slit momentum had been large and downward…
They evaluated the probability of the initial slit momentum being large enough to yield such an erroneous conclusion, and so obtained an expression of the probability that we had obtained path information. Using the same wave function, they also calculated the resulting pattern of arrival at the final screen. It turned out to be a partially smeared-out interference pattern” [12]

Their experiment showed that if they had certain knowledge about the slit that particle passed through, there were no interference on screen. There will be a single band that reflects particle nature. But as the uncertainty about the passage of particle through one of the slits, increased a better interference were developed. This reflects wave nature of it. Why does our knowledge about the apparatus operation change the interference pattern on the screen to a band? What does our attention have to do with the shape formed on the screen? The experiment suggests that consciousness has a fundamental role in shaping the physical reality.

It is interesting that in any complementary pairs, one is either spatial or mass type, and the other is either energy or informational type. The two characteristic that we hypothesized for proposed singularity. On the other hand complementarity displays itself at ultra-micro scale. We may assume that this demonstrates duality and merge at the boundary of space-time and singularity? The fuzzy states of fundamental elements in boundaries of space-time were discussed in Boundaries Chapter.

Greene, Brian R. The Elegant Universe. Vintage Books, 2000. 
Greene, Brian R. The Elegant Universe. Vintage Books, 2000. 
Greenstein, George and Arthur G. Zajong. The Quantum Challenge. Jones and Bartlett Publishers, 2001. 
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