In the News (from Cornell University Library): “A central question in our understanding of the physical world is how our knowledge of the whole relates to our knowledge of the individual parts. One aspect of this question is the following: To what extent does ignorance about a whole preclude knowledge of at least one of its parts?
“Relying purely on classical intuition, one would certainly be inclined to conjecture that a strong ignorance of the whole cannot come without significant ignorance of at least one of its parts. Indeed, we show that this reasoning holds in any non-contextual hidden variable model (NC-HV).
“Curiously, however, such a conjecture is false in quantum theory: We provide an explicit example where a large ignorance about the whole can coexist with an almost perfect knowledge of each of its parts. More specifically, we provide a simple information–theoretic inequality satisfied in any NC-HV, but which can be arbitrarily violated by quantum mechanics. Our inequality has interesting implications for quantum cryptography.”
My Comment: From the perspective of Kabbalah, there is no paradox because the part and the whole are equivalent. Everything from micro to the whole is built on the principle of a hologram where any part contains information about everything. In other words, any part and the whole are made up of ten Sefirot. Our egoistic mind cannot connect the parts and the whole, recognizing that a part is equal to the whole. However, in the spiritual world, this condition is fundamental and understood on the first spiritual degree.