2 minute read

Heisenberg’s uncertainty principle is an important discovery in quantum mechanics. It’s the principle of the uncertainty of what we know about a particle’s position and momentum. It was discovered in 1927 none other than Werner Heisenberg. This brilliant discovery is only one of the many principles that govern our quantum world.

Plank’s Constant

Planck’s constant is a very small number which is the limit to how small energy packets (quanta) can be. It acts as a “law” of the size of things in the quantum realm. It is expressed as $h \approx 6.626 \times 10^{-34}$ Joule-seconds. The reduced Planck’s constant, $\hbar$ (h-bar), is Planck’s constant divided by $2 \pi$. This constant is like the “center of attention” in quantum mechanics, as it is used in many equations such as in the Schrodinger equation. It is also used in the equation for the energy of a photon: $E = hf$. However, in our cases, its just a constant. It’s nothing you need to worry about.

Uncertainty Principle

Heisenberg’s uncertainty principle, discovered in 1927 by Werner Heisenberg, states that one cannot simultaneously know the exact position and the exact momentum (speed) of a particle. This equation is written as $\Delta x \Delta p \ge \frac{\hbar}{2}$ where $\Delta x$ is the uncertainty in the position, $\Delta p$ is the uncertainty in momentum, and $\hbar$ is the reduced Planck’s constant. If you know a particle’s position, $\Delta x \to 0$ (there is no uncertainty). But then, to keep the statement true, the momentum would have to be uncertain ($\Delta p \to \infty$). If both uncertainties were 0, you would get the result that $0 \times 0 = \frac{\hbar}{2}$ which is false.

Real-Life Example

We see things when light (photons) bounce off of objects. Since atoms are so small, we would need very small wavelengths to see them. The wavelength is Planck’s constant over momentum ($\lambda = h/p$), so if the wavelength is shorter, the photons would have more momentum. Once the photons hit the particles, they will reach higher speeds. We would know the position, but the speed would be uncertain.

Conclusion

As you can see, the uncertainty principle is a great demonstration of how strange the quantum world is. It is truly amazing how things that work at the microscopic scale are different that what we see. All these principles of quantum mechanics - they are all different that classical physics. That makes them unique.

Updated: