프로그래밍과 경제

Oh YeungJong

Many people who know well that Feynman's famous statement, "I think I can safely say that nobody understands quantum mechanics" will think it foolish or crazy if they hear someone arguing that he actually understand quantum mechanics and here I dare to insist that. 

One of the most weird things in QM is the wave-particle duality which can be seen in the famous double slit experiment with electrons. In the experiment, electron known as a particle act like wave when it is not observed but act as particle when observed. There are no ultimate single consensus on how single electron can move to show diffracted pattern on the final screen and how the measurement of electron's property can breakdown diffraction pattern on the final screen. 

Here I will try to provide another interpretation to understand several reasonable scenarios which will make readers to understand it much intuitive way. Comparing with the Copenhagen interpretation there will be several differences in my interpretation. For example, CI assume the existence of super-positioned particle to understand wave like behavior of single particle but I don't need such concept. All we can see is just particle form of it and wave like form is just illusion created by movement of a particle of which details will be provided later in this series. I also think that every movement act in deterministic way as Einstein tried to cling to but with one exception: Uncertainty in number realization which also will be given in following article. In my view, randomness arise only at the stage of realization for any number or state of a particle. 

 I am not a math guy so there will be fewer mathematical stuffs or equation in this scenario. Instead mentioning lots of equation, I will do my best to describe several concepts or intuitions in simple basic sentences so that even high school students with basic knowledge in Mathematics can understand.

As always can be seen in other proves somewhat related to some form of philosophy, let me adopt few assumptions which are required to get a complete understanding all weirdness seen in Feynman's double slit experiment . Layer I will explain why these assumptions were necessary.

Assumptions or Axioms

1. The dynamical system of every subatomic entity such as light, electron and etc is basically chaotic dynamics showing unique features including deterministic behavior and sensitivity to the initial condition and I call it Statically Distributed Periodic System.

2. Any measurable state of a dynamical system which is realized must be re-synchronized with the realized single value so that everyone can see the very same single state out of infinitely many possibilities. 

3. Some sort of wave field relative to the moving object is generated and propagated in every outer direction centering at everywhere discontinuity of matter or energy exist. Best candidate for the its wave function seems to be Bessel function of which wave length is related to the one of particle moving nearby within close distance from the center of wave field.

With the above 3 assumptions, I dare to insist that almost every weirdness in quantum mechanics can be understood in much intuitive manner and details will be provided in the following series.

To summarize my interpretation, Current Quantum mechanics is correct but not enough to understand all weirdness. To fill the gab between precise prediction and better understanding of QM, we need to adopt three concepts or new ways of thinking: 1. Statically Distributed Periodic function as a governing rule of every subatomic entity. 2. Randomness in realization of any value or state of a particle. 3. Existence of force field generated at the edge between matter and emptiness.

To be continued...

It is well known that any subatomic entity including light and electron has both wave and particle like properties but no one can see both of them simultaneously. Wave-particle duality is quite different property with everything experienced in our real life, simply unbelievable thing.

But I will argue that the weirdness can be easily understood in much intuitive way if you can find similar pattern found in the Realization uncertainty introduced in my previous post here.

Similar patterns

1. Measurement of subatomic entity and realization of irrational number are same in that ideal entity which reside only in human mind is realized in physical form which can be compared with other same kind of form.

For a subatomic entity, before measurement, it can have multiple possibilities and after measurement, all possibilities disappear suddenly and instantaneously but except one candidate appear.

As for irrational number, to find out similar behavior, let me take an example related to number quantization issue in digital computer. No computer existing in the world can compute any irrational number without error due to limit in number resolution. All computer can output is finite number only and impossible to represent true value of any irrational number. It means that for any irrational number there is always quantization error for to be it expressed with finite memory or bits. 

Picture 1 shows that given number representing resolution, there is a relative decision problem to make a much suitable position somewhere between mr and (m+1)r due to limitation of finite memories or bits so called resolution limit. It is obvious that it is impossible to express a number with infinite number of digits with finite digits. It is possible to increase number precision by adding more bits but even with increased precision, it is impossible to express infinite number of digits including floating points. Same difficulty prevent human to get exact same value in real life and true form of all irrational number can be imagined and handled only in human mind. Without a realized form for the irrational number, there is no way to compare with other irrational number. Comparing two numbers is only possible when they are represented in realized form.

Picture 1. number realization is like picking a position within a range of quantization error due to limit in finite bits to store number. For a given resolution r, Any point on the line between mr and (m+1)r such as (mr +r/2) and (mr+r/4) can be selected as an approximated value for the target number n. Once decision is made, then only single point will be used and effective as like we can see only one particle once measured.

Everyone will agree that any irrational number is single value and is impossible to have multiple values. On the other hand, to realize an irrational number, it is possible for someone to pick a position somewhere between mr and (m+1)r and there are infinite number of possibilities.

Below table shows summary of similarity between particle and number based on the above description. Especially it is very important to know that the whole range of many possibilities is actually dependent to the observer or measure. It is relative metric which can be varied over different person who measure it or pick. If two persons having different number resolution without common rule for choice of realizing form for the irrational number want to realize it, than the quantization error is also different.

The possibility density function for the number realization would be varied upon persons who realize it with his own decision. If normal computer will quantize it, one possible candidate for the density function would be delta function peaky at a low end, mr as seen in Picture 1. In normal case it would be normal distribution function with peak at the center of quantization error range. But again, it all depend on user's own decision. Synchronization or advance promise on what is the common rule for choices is a must for getting all agreed single output for object as the same way computer is constructed.

This topic also related to the sensitivity to the initial condition for a Chaos system. Chaos system is a deterministic system but extremely sensitive to the change in initial condition. If there is a tiny little error in the initial value, the final evolving result will be differ greatly and that is why prediction is impossible for a chaos system. 

Conclusion

For a subatomic entity such as light, electron etc, the particle form appears only when it is observed and measured, in other word realized. There is no wave-like form we can sense but it disguise in wave-like form if it is not realized. If we think about the process for number realization and apply it to wave-particle duality, then we can find that both shared the vary same mechanism: before realization many possibility given to us and after realization only one value is defined.

Definition

Realization: Being defined as a physical form comparable with other same type out of something unmeasured or unobserved by any means yet.