Maximal identical configuration symmetries

[Loren Booda]

Quantum mechanics: classical indistinguishability?

What is the quantum number correspondent to the maximal symmetry shared by any two real physical configurations in observable spacetime? For instance, any two protons have a high probability of sharing an identical set of quantum numbers, whereas any two simple crystals are much less likely to, yet only two DNA molecules in the cosmos might match mutually and exactly between the quantum numbers which describe each.

It follows that there exists an upper bound within our finite universe where at most two macroscopic configurations of identical quantum numbers occur with equal likelihood. Consider this cosmic limit for identical sets of quantum numbers to enumerate the symmetry of the correspondence principle, to demarcate the quantum from the classical.

Do you find significance in the fact that beyond a certain complexity, statistics requires unique forms of physical entities? That is, does the correspondence principle rely upon the distinguishability of macroscopic quantum configurations?

 

[AndyW]

I find this topic of quantum mechanics and classical indistinguishability to be quite fascinating. The quantum number that corresponds to the maximal symmetry shared by two real physical configurations in observable spacetime is known as the spin quantum number. This number describes the intrinsic angular momentum of a particle and is a fundamental property of quantum systems.

In terms of the upper limit of identical quantum numbers in our finite universe, it is important to note that the concept of indistinguishability only applies to identical particles, such as protons or electrons. In the case of DNA molecules, they are unique and not identical, so the concept of indistinguishability does not apply.

I do find significance in the fact that beyond a certain complexity, statistics requires unique forms of physical entities. This is because as systems become more complex, the number of possible configurations and combinations increases, making it less likely for two identical configurations to occur. This is known as the law of large numbers in statistics.

The correspondence principle does rely on the distinguishability of macroscopic quantum configurations. In classical mechanics, two objects with identical properties can be distinguished by their location or trajectory. In quantum mechanics, identical particles cannot be distinguished in this way, but they can be distinguished by their spin or other quantum numbers. This is why the concept of indistinguishability is important in understanding the boundary between the quantum and classical worlds.

Overall, the concept of classical indistinguishability plays a crucial role in our understanding of quantum mechanics and the correspondence principle. It highlights the fundamental differences between the quantum and classical worlds and helps us to better understand the behavior of particles at the microscopic level.