Tuo Liu

Tucson, AZ 85745

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news

Sep 12, 2024	My research has been featured in the UA Health Sciences!
Jan 08, 2023	Website Created!

latest posts

Dec 04, 2024	a post with image galleries
Jul 12, 2024	Statistics Notes
Jul 12, 2024	Machine Learning Notes

selected publications

PhysRev

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

A. Einstein^*†, B. Podolsky^*, and N. Rosen^*

Phys. Rev., New Jersey. More Information can be found here , May 1935

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In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.