Coupling spin and momentum

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In our quest for a local and realistic model of quantum mechanics, we have discussed spin in recent posts. We introduce now an additional quantity and mechanism, which will play a fundamental role in spin entanglement.
In my earlier 2020 arXiv paper, this "spin-flip mechanism" has been introduced and described as reproduced below.


The following figure help explaining the spin-flip probabilities mentioned above. Remember that spin is defined as


where s0 is the source spin and M is the spin propensity.

As shown in the figure 1d above, jumps of spin propensity occurring across an external reset cannot induce spin flips. Therefore, there is no spin-flip energy associated to an ER. 

How is this spin-flip energy manifested? Naturally, into momentum. This momentum transfer can be described as

 
where V denotes here the momentum propensity. We can also represent this transfer as a "force". Indeed, for small values of spin-flip energy, we get

 
In summary, it happens that spin propensity has an influence on momentum propensity. This coupling between spin and momentum will play an important role to determine coincidences and correlation statistics for entangled particles, as will be discussed in future posts.


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