What are hidden variables and the significance of Bell's Theorem?

[Ed Quanta]

I have found a site that derives Bell's inequality
The number of objects which have parameter A but not parameter B plus the number of objects which have parameter B but not parameter C is greater than or equal to the number of objects which have parameter A but not parameter C.

And I follow this derivation alright, but I have seen examples where this inequality is violated when the objects we imply this inequality to things in the quantum world like the spin of an electron for orientations of different angles. Now, what I read is that these violations are not really violations due to the fact that Bell's theory is based on the assumptions that logic is valid and that hidden variables exist locally. What are hidden variables exactly? And what is the significance of Bell's Theorem?

Note* I know this is similar to the post earlier on Bohmian mechanics but I wanted to take a step backwards for a moment before even beginning to look into Bohm's Implicate Order ideas.

 

[selfAdjoint]

A hidden variable theory is one that claims the weirdness of QM is due to neglecting some unknown factor(s), which cannot be observed at present, but which by their dynamics account for the quantum effects without breking with classical physics. Bell showed that for any such theory which also respects relativity, any local hidden variable theory, the inequality would be strict, but quantum mechanics predicts equality.

 

[R0man]

Hidden variables refer to theoretical, unobservable properties or quantities that are thought to determine the behavior of a system. These variables are not directly measurable, but are believed to exist in order to explain the seemingly random behavior of particles in quantum mechanics.

Bell's Theorem, also known as Bell's Inequality, is a mathematical proof that attempts to address the long-standing debate in quantum mechanics about the existence of hidden variables. The theorem shows that if hidden variables do exist, they must violate certain inequalities, which have been experimentally confirmed to be true in quantum systems.

The significance of Bell's Theorem lies in its implications for our understanding of the fundamental nature of reality. It challenges the traditional view that particles have definite properties and behaviors, and suggests that there may be underlying factors or variables that we cannot observe or measure. This has led to the development of alternate theories, such as Bohmian mechanics, which attempt to explain the behavior of particles in a way that is consistent with Bell's Theorem.

Furthermore, Bell's Theorem has also sparked continued research and experimentation in the field of quantum mechanics, as scientists seek to further understand and test the implications of the theorem. It has also played a crucial role in the development of quantum computing and other technologies that rely on the principles of quantum mechanics.

In summary, Bell's Theorem highlights the limitations of our current understanding of the quantum world and challenges us to question our assumptions about the nature of reality. It continues to be a topic of interest and debate in the scientific community, and has opened up new avenues for exploration and discovery in the field of quantum mechanics.