Realization uncertainty is the source to cause weirdness in wave-particle duality.

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.

 

	before	triggering event	After
Wave-particle	Many possibilities	measurement or observe	singe particle
Irrational number	Many possibilities ,	pick any finite number	Finite single value. Ex)3.1415926

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.