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U NCERTAINTY P RINCIPLE II: C IRCUMVENTIONS by Robert Nemiroff Michigan Technological University

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Physics X: About This Course Pronounced "Fiziks Ecks" Reviews the coolest concepts in physics Being taught for credit at Michigan Tech o Michigan Tech course PH4999 o Aimed at upper level physics majors o Light on math, heavy on concepts o Anyone anywhere is welcome No textbook required o Wikipedia, web links, and lectures only

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U NCERTAINTY P RINCIPLE : H EISENBERG ' S M ICROSCOPE H EISENBERG ' S M ICROSCOPE A particle (blue) sits at the focus of a microscope. Shooting long wavelength photons at it will determine the particle's position only crudely but the low recoil will create only a small uncertainty in its momentum. This is a simple example of a direct measurement that cannot break the uncertainty principle.

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U NCERTAINTY P RINCIPLE : E INSTEIN ' S S LIT A photon goes through a slit in a wall. Einstein: By measuring both the resulting momentum of the photon AND the wall, one might determine the photon's momentum arbitrarily well, violating the uncertainty principle. Does this work?

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U NCERTAINTY P RINCIPLE : E INSTEIN ' S S LIT E INSTEIN ' S LIT Bohr: No -- there will be uncertainty also in the wall's measured position. When everything is accounted for, the uncertainty principle sill holds.

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U NCERTAINTY P RINCIPLE : E INSTEIN ' S B OX Einstein: A box filled with photons has a shutter that opens at a very precise time. A photon leaves. The box is then re-weighed to find out the photon's precise energy. Doesn't this violate the energy-time uncertainty principle (ΔE t > h)?

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U NCERTAINTY P RINCIPLE : E INSTEIN ' S B OX E INSTEIN ' S B OX Bohr: No. When the photon leaves, the reduced gravity does make the box sag. However, the uncertainty of the clock position in the gravity field includes GR gravitational slowing, so that an uncertainty in the position of clock leads to an uncertainty of the slowing of the clock which leads in an uncertainty in time. The uncertainty principle holds.

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T HE "O THER " U NCERTAINTY P RINCIPLE : E NERGY VERSUS T IME E NERGY VERSUS T IME ΔE Δt > h / 4 π Not exactly like "regular" uncertainty principle: time is not like position. Δt really refers to the measured lifetime of a given state with energy E known to accuracy ΔE. Effective definition: A state that exists for only a time Δt cannot have an energy better defined than ΔE.

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T HE "O THER " U NCERTAINTY P RINCIPLE : E NERGY VERSUS T IME E NERGY VERSUS T IME Can conservation of Energy be violated for short times Δt? No -- but which energy state a particle is in can remain unknown. More on this when virtual particles are explored.

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