### The quantum world is fundamentally, inherently random. All measurements of quantum systems confirm this fundamental claim as a fact. It is ...

The quantum world is fundamentally, inherently random. All measurements of quantum systems confirm this fundamental claim as a fact. It is this random nature that distinguishes our naturally experienced world, the macro-world, which we perceive as deterministic, from the quantum nature of the micro-world, which we experience as inherently random. One of our fundamental philosophical questions about nature is how the deterministic macro-world comes into being, how it emerges from the probabilistic randomness of the quantum world.

Perhaps it will help answer this question, help solve this mystery, and perhaps bring us closer to understanding how our reality works if we examine the actual nature of randomness of the quantum world.

We typically do not distinguish between different kinds of genuine randomness in general, randomness is randomness. However, when we think about randomness, we can actually distinguish between two typically different types of genuine randomness, dependent and independent kind of randomness.

Consider a random event as independent randomness if the random occurrence of the random states of a randomly behaving system is not influenced by the internal states or configuration of the randomly behaving system. Such a random system with independent random behavior is, for example, a blind selection from a well-mixed set of balls.

*Ignore the fact that the system presented as an independent random example is actually part of the deterministic macro world, so if all circumstances were known precisely when the selection was made, the system considered random would actually be deterministic. The system chosen as an example is a thought consideration, the analysis of the type of randomness is not affected by considering that the mixing and selection of the balls occur under unknown deterministic or real nondeterministic conditions. *

The characteristic of such random behavior, which can then be called independent randomness, is that the randomly formed states, actually which ball is selected, are independent of the internal structure of the randomly behaving system. In this example, no matter which ball is selected, the resulting random state is in no way influenced, affected, or formed by the potentially existing relationship between, or the arrangement of the balls, by the actual structure of the system.

Dependent randomness occurs when the random states of a randomly behaving system are influenced by the internal configuration of the system, when the internal structure of the system affects the resulting random state. Such a dependent random system is, for example, a roll of a dice.

*The example of throwing dice also serves as an illustrative example. Again, ignore the fact that this system is part of a deterministic macro world, so if all the circumstances in the situation were known exactly, the system, the throwing of the dice, which we consider random, would actually be deterministic. The system is also a thought consideration, and the analysis of the type of the nature of the randomness is not affected by the circumstances that the throwing of the dice occurs under unknown deterministic or real nondeterministic conditions.*

This type of random behavior, which we can call dependent randomness, is characterized by the feature that the random states that occur, which side the dice lands on, depend also on the internal structure of the system. Whichever side is rolled, the resulting state is physically not independent of the other possible states, as the resulting state is fundamentally influenced by the physical structure of the dice.

Both examples of random systems exhibit generally random behavior, but the two types of randomness are fundamentally and objectively different.

According to what randomness the quantum world behaves? The question may seem philosophical, but understanding the physical foundations of the quantum world certainly requires an answer to this question that is consistent with reality. In fact, understanding quantum nature may depend fundamentally on whether the behavior of the quantum world is independent or dependent randomness.

How can the two different types of inherent randomness be distinguished on the basis of behavior?

There is a characteristic difference in behavior between dependent and independent randomness, which is manifested in the statistics of actually realized random states. Because the occurrence of states of independent random behavior does not depend on the internal structure, relationships, arrangement of the randomly behaving system, the occurrence of random states cannot be related to the unique specialities of the system, so the statistics of the occurrence of random states is independent of the actual inside characteristics of the system. The occurrence of states of dependent random behavior is dependent on the internal structure of the randomly behaving system, therefore the occurrence of random states can be related to the specific characteristics of the internal structure of the system, therefore the statistics of the occurrence of random states is dependent on the actual unique specialities of the system.

So, defined by this difference, what kind of randomness does the quantum world have? Let's examine the statistics of the measurements of the inherently random quantum world. The statistics produced by measurements of quantum randomness clearly follow a sinusoidal function, which is indicative of a dependent type of randomness, as opposed to the distribution statistics of an independent type of randomness, which can be characterized by a linearly behaving function. The quantum world definitely functions according to dependent randomness.

However, the actual validity of this statement, that quantum randomness is a dependent type of randomness, also fundamentally affects the interpretation of the Bell inequality violation, since the Bell inequality violation serves as a proof to demonstrate the non-local nature of the quantum world. Why?

We consider the experimentally proven violation of Bell inequality as an actual fact of the quantum world. We use this fact to state that the quantum world cannot function according to local reality, i.e. the states of spatially separated particles behaving according to the laws of the quantum world cannot be determined only by locally present interactions - at least for particles in the entangled state - but also requires supposedly existing effects beyond the limit that allows causality.

This statement, based on the experimentally proven Bell inequality violation, is a fundamental statement of the natural philosophy about the quantum world. According to it, the quantum world cannot be local in nature, no local interactions or any present intrinsic property - known or yet unknown (hidden) variables - are possible that could realize the experimentally verified behavior, the compliance of entanglement in the quantum world.

However, the problem with the statement that the quantum world is non-local in nature as a consequence of the Bell inequality violation, the reasoning of this logical justification is actually based on comparison of two fundamentally different kinds of randomness, the dependent and the independent randomness. The setting of the Bell inequality essentially belongs to a system behaving according to an independent type of randomness, while the actual measurement proving the inequality violation is performed on a system of the quantum world behaving according to a dependent type of randomness.

The random statistics of the Bell inequality are not the same as the random statistics of the quantum world, and therefore the two types of randomness, and systems that produce different types of random behavior, cannot be and should not be related or compared to each other at the same time. Therefore, the existence of the violation of Bell inequality is not a valid basis for the statement of the invalidity of locality and/or the existence of distant effects in the quantum world. Therefore, if we cannot consider the Bell inequality violation as a proof that the quantum world is non-local in nature, we can and must continue to search for physical structures and settings that do not violate locality, but are suitable to provide the behavior of the quantum world.

If the randomness of the quantum world is dependent randomness, where the internal structure of the system influences the statistics of the possible random states of the system, it follows - as is also often stated - that quantum particles in entangled states actually form a single coherent system, in fact they are one coherent structure. Thus, understanding how the quantum world works does not necessarily require an understanding of how it is possible for spatially separated entangled particles to influence each other, but rather allows us to find an answer to the question of how entangled particles can actually form a system without violating local reality.

Although the approach to the two situations, i.e. the existence of (distant) interactions between components and behavior as a coherent structure, seems similar in the case of the quantum world, there is a fundamental difference. It is not only possible to behave as a system if the constituent parts of the system are in possible ongoing contact with each other, it is also possible to behave as one structure if at some point in the history of the system there is a causal relationship between the constituent parts, and then the constituent parts can continue their lifetime undisturbed, since until one of the constituent parts of the system is affected by an effect that does not apply equally to the whole system.

*An example of such a structure, which is not directly causally related but forms a single structure, is a banknote torn in half. Wherever we find a half banknote, we can immediately know that another half banknote physically exists or has existed somewhere, because it is printed as one, and we can even precisely determine the characteristics of the missing half as a banknote as well.*

This type of behavior typically applies to systems where there is no continuing relationship between the components, but the immediate causal state existed earlier, and the components of the system were able to maintain this shared state later in the life history of the components that are no longer causally connected.

But this description exactly corresponds to the behavior of entangled quantum particles. The birth of quantum particles in an entangled state always occurs under conditions of causality, in a causally coupled part of space, and the state of entanglement can indeed only persist until, and would break, if the entangled particles were subjected to some different external influence.

Thus, considering the behavior of entangled quantum particles, it is not the only possibility to assume that the existence and presence of distant effects can explain the behavior corresponding to the quantum measurement, as it would be the necessary consequence in the case of the beyond doubt validity of the Bell inequality violation.

However, unlike a torn banknote, the quantum world is a dynamic structure. A measurement of a single particle of the components of an entangled system shows inherent (yet dependent) randomness. Understanding the behavior of entangled quantum particles, and thus understanding the foundations of how the quantum world functions, may therefore require finding a suitable solution to the question of what form of structure is possible that allows entangled particles to behave as a coherent system without the presence of distant effects (or originally set mutually agreed behavioral variables), and at the same time, possess inherent genuine randomness. A possible solution to this problem is proposed in the thoughts.

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