Associativity problem with observables

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In summary, the question is regarding the non-commutativity of observables in quantum mechanics and whether or not this leads to non-associativity. The speaker also mentions that adding a fourth observable worsens the problem. However, the speaker also notes that non-commutativity does not necessarily mean non-associativity in other mathematical concepts such as non-Abelian groups and matrices.
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zetafunction
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let be A , B and C three non-commuting observables

my question is how can one solve the problem with associative property ? i mean

[tex] (AxB)xC [/tex] will in general be different from [tex] Ax(BxC) [/tex]

and if we had 4 A, B ,C ,D instead of three the problem is even worse , how can anyone deal with it ?? i mean since the observable do not commute and we can not apply the associative property is there any ambiguity in QM ?? or similar ??
 
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  • #2
Non-commutativity does not imply non-associativity, so I do not really see your problem here... (for example a non-Abelian group is still associative; the same goes for matrices).
 

FAQ: Associativity problem with observables

1. What is the associativity problem with observables?

The associativity problem with observables refers to the issue of how different observables interact and combine with each other in a given system. This can be a challenging problem to solve because the interactions between observables can be complex and difficult to predict.

2. How does the associativity problem impact scientific research?

The associativity problem can have a significant impact on scientific research, as it can make it difficult to accurately model and understand complex systems. It can also lead to unexpected results and hinder the development of new theories and technologies.

3. What are some strategies for addressing the associativity problem with observables?

One strategy for addressing the associativity problem is to use mathematical models and simulations to simulate the behavior of observables in a system. This can help researchers better understand the interactions between observables and predict their behavior.

4. How can the associativity problem be relevant in different scientific fields?

The associativity problem can be relevant in a wide range of scientific fields, including physics, chemistry, biology, and even social sciences. It can impact our understanding of everything from chemical reactions and biological systems to economic and social systems.

5. Are there any potential solutions to the associativity problem with observables?

While the associativity problem may never be fully solved, there are ongoing efforts to develop new mathematical tools and techniques that can help address the issue. Additionally, interdisciplinary collaborations and the sharing of data and knowledge between different scientific fields can also aid in tackling this problem.

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