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Exploring Uncertainty: Heisenberg's Principle in Quantum Physics

Discover the fundamental limit in measuring particles precisely through Heisenberg's Uncertainty Principle. Learn how position and momentum become elusive in quantum mechanics, affecting our understanding of the microscopic world. Dive into the intriguing realm of probability and indeterminacy in physics.

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Exploring Uncertainty: Heisenberg's Principle in Quantum Physics

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  1. Can we measure exactly where this projectile is every second?

  2. Physics has a lower limit on what we can ever know • You can’t see electrons because…… • Even if you could, the effect of bouncing an electron off an atom is ………

  3. The minimum uncertainty product DpDx for any experiment is around Planck’s constant That’s still pretty exact: around 10 millionth of billionth of a billionth of a billionth of a meter, or a Joule or a second 10-34Js

  4. In Young’s double-slit experiment, Dxand Dp (the electron’s displacement and the momentum, respectively) can only be analyzed by probability. • Werner Heisenberg won the Nobel Prize in physics for the following relationship: • DpDx≥ h/(2p)

  5. HEISENBERG UNCERTAINTY DpDx ≥ h/(2p)≈10-34Js • It’s impossible to know both the position and momentum of a particle with arbitrary precision at any given time. • If position is known precisely, so that Dx 0, then Dpx ∞ • Similarly, if Dpy0, then Dx ∞

  6. HEISENBERG EXAMPLE: • If the speed of an electron is 35 m/s, with an uncertainty of 5%, what is the minimum uncertainty in the object’s position? • Dpx= 0.05 mev = 0.05 (9.11x10-31 kg)(35 m/s) = 1.59x10-30 kg*m/s • Dy = h/(2pDpx) = (6.63x10-34J*s) 2p(1.59x10-30 kg*m/s) = 6.64x10-5 m

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