What is the mathematics behind quantum entanglement?  by The Doctor  Quora Question Review
This document contains a review of the answer by The Doctor on the question in Quora: "What is the mathematics behind quantum entanglement?"
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https://www.quora.com/Whatisthemathematicsbehindquantumentanglement
 The text in italics is copied from the article.
 Immediate followed by some comments
Contents
Reflection
1. Answer Review

Entanglement has been predicted because of the mathematics behind quantum mechanics, so it certainly doesn't “go against” mathematics, whatever that may mean.

You cannot predict anything physical, purely by using mathematics. The same with Thought experiments, you cannot understand the physical reality, by using thought experiments.

The math behind it is linear algebra. A quantum system (like a particle) is represented by a vector space and (unit) vectors in this space represent the different possible physical states the system can be in.


Two interacting systems can be represented by a tensor product of their respective vector spaces, which forms a new, bigger vector space.


The clue is, this bigger vector space contains more than just all combinations of the states that are available to the two subsystems on their own. It contains new states, in which the two systems have no physical state of their own. Such a state is entirely one of the combined system. Those states are called entangled.

That is typical the problem with this top down or bottom up approach. How do you relate the final conclusion with the physical reality?

That's the math.

































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Reflection 1  Question Review
The word 'behind' in the question: "What is the mathematics behind quantum entanglement?" is tricky.
The reality is, that when you perform experiments with photons, the result of the experiments can be, that the two photons are correlated. The question to answer is: why are these photons correlated? This requires a physical explanation, which involves the details of the process that takes place during the reaction that creates the two photons.
When the frequency of both case photons can be measured and the reaction can be repeated a more mathematical approach is possible.
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Created: 28 May 2024
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