Goodbye Determinism Hello Heisenberg Uncertainty Principle

Goodbye Determinism Hello Heisenberg Uncertainty Principle

Planck introduced Planck’s constant, h, which is the proportionality factor between energy and the frequency of radiation. Bohr noticed that Planck’s constant had units of angular momentum, so he guessed that this was the minimum angular momentum that an electron could have to remain in a stable orbit. He showed that the atom goes from a high energy state to a lower one, proportional to this constant.

Here’s how to derive the uncertainty principle: In the double slit experiment, when monochromatic light goes through two slits we get an interference pattern just like if it was a wave. A single slit produces a similar diffraction pattern where we see a central very high peak, and very faint peaks elsewhere.

The width of the slit represents the uncertainty in position, because the electron could be anywhere along the slit. The distance to the interference pattern represents the momentum. The uncertainty in the momentum is represented by the distance from the center of the pattern to the first interference pattern.

Louis de Broglie showed that the wavelength, lambda for a particle with mass is equal to h/p, where h is Planck’s constant, and p is the momentum. Using trigonometry, we can get a series of equations showing how the uncertainty in position and uncertainty in momentum are equal to h. This is essentially what the uncertainty principle is.