### Equation #11: Heisenberg’s Uncertainty Principle

“Anyone who is not shocked by Quantum Mechanics has not quite understood it”-Niels Bohr

I agree Mr. Bohr, QM does blow your mind. The uncertainty principle is one of those things that prove that our perception of the world is limited. Anything in the universe can be both wave and particle at the same time and that puts a limit to how accurate our measurements can be.
What that means in our context is that, if you try to measure the velocity(or momentum) of a particle as well as its position at the same instant, you cannot have exact values of both. If you measure position accurately, the value of velocity will have some uncertainty associated with it and vice a versa.

The reason we don’t observe this phenomenon in everyday life is is that the uncertainty values are very, very tiny. A person moving with a velocity of say, 5 km/hr (+or – 0.05 km/hr) and weighing 60 kg will have the uncertainty in position = 1.8 * 10-35 meters! That’s smaller than the radius of an atomic nucleus. However, when you go into the realm of lightweight, superfast entities(like subatomic particles), the uncertainties get larger and can have a significant effect on the macroscopic properties of an object.

The uncertainty principle applies to a number of pair of observables other than momentum and position. Most common example is that of energy-time which explains the working of Strong force, according to some theories.

It is important to understand that this fundamental limit is not due to experimental errors, rather a phenomenon of nature itself.

You cannot predict, even theoretically, the exact values of two so called “incompatible” quantities simultaneously.

For uncertainty principle in action, see