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Dara Stepanek Thermodynamics, Quantum Mechanics, and General Relativity HW #20 Due: Friday 5/13 1. What is absolute zero? Why was it a different flavor of physics from what Newton offered? 2. What is the zero-point energy? How can this force of nothing exist? 3. Heisenberg’s Uncertainty Principle (HUP) says ΔxΔp ≥ ђ/2. Given the General Uncertainty Relation ΔAΔB ≥ |<[A, B]>|, prove HUP. Things to recall and/or note: - The right side of the inequality reads “the absolute value of the expectation value of the commutator of the operators A and B”. - The expectation value of a commutator implies that it is acting on a function. - The commutator [A, B] = AB-BA. - Bold-faced variables are operators. - X=x and P=-iђ(d/dx). - ђ is just a constant and i is imaginary. 4. Mathematically describe a black hole. 5. Give the mathematical analogy we used in class to explain why quantum mechanics and relativity yield different or meaningless results for the exact same problem.