Heisenberg's Uncertainty Principle: A Quantum Revolution in Physics, Study notes of Physics

Download Heisenberg's Uncertainty Principle: A Quantum Revolution in Physics and more Study notes Physics in PDF only on Docsity! Modern Physics THE FAR SIDE By GARY LARSON — Fall 2008, Dr. Starovoitova Lecture 11 SE Data scent retest | “iOhhhhhhh . .. Look at that, Schuster... Dogs are 30 cute when they try to comprehend quantum mechanic.” Review Lecture 10 • Matter waves, De Broglie relations • Electron diffraction • Waves: λ , ω, T, and k • Fourier series and Fourier integral 11.2. Heisenberg’s microscope Heisenberg pictured a microscope that obtains very high resolution by using high-energy gamma rays for illumination. The microscope can resolve objects to a size of ∆x, which is related to the wavelength λ of the gamma ray, by the expression: ∆x = λ / (2sinA) Momentum before: p=h/ λ 1)Momentum after: p'x + (h sinA ) / λ' 2)Momentum after: p''x - (h sinA ) / λ'' p'x + (h sinA ) / λ' = p''x - (h sinA ) / λ'' p''x - p'x = ∆px ~ 2h sinA / λ Since ∆x ~ λ/(2sinA) and ∆px ~ 2h sinA / λ , ∆x ∆px ~ h 11.3. Implications “I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it.” “In the sharp formulation of the law of causality-- "if we know the present exactly, we can calculate the future"-it is not the conclusion that is wrong but the premise.” Heisenberg, in uncertainty principle paper, 1927 11.4. Quantum wave function Ψ A wave function is a mathematical tool used in quantum mechanics to describe any physical system. It is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics describe how the wave function evolves over time. “Quantum coral” shows electron wave functions (sort of…) 11.5. Indeterminacy Suppose you measure the position of the particle and find it at point C. Question: Where was it right before the measurement? 1) The realist position (at C) - Einstein 2) The orthodox position (wasn’t really anywhere) - Bohr 3) The agnostic position (refuse to answer) - Pauli C 11.5. Indeterminacy • “The position of the particle was never undeterminate, but was really unknown to the experimenter…” - d’Espagnat • “Observations not only disturb what has to be measured, they produce it… “ – Jordan • “One should no more rack one’s brain about the problem of whether something one cannot know anything about exists all the same, than about the ancient question of how many angels are able to sit on the point of a needle…” - Pauli 11.5. Indeterminacy Orthodox position: (Copenhagen interpretation) A quantum particle doesn't exist in one state or another, but in all of its possible states at once. It's only when we observe its state that a quantum particle is essentially forced to choose one probability, and that's the state that we observe.