A Simple Way to Derive the Heisenberg Uncertainty Principle

Here is a simple way to derive the Heisenberg Uncertainty Principle. It also shows why the princlple exists for momentum and position; and energy and time. Kinetic energy is the basis for the uncertainty principle. We start with that premise in step 1). (Where E=energy; m=mass; v=velocity.)

In steps 2) through 5) we use dimensional analysis to arrive at ET=PL. Energy times time equals momentum times position. (Where M=mass.)

At steps 6) and 7) we realize that ET is h-bar (Planck's constant). Since E (kinetic energy) has a 1/2 factor, we divide h-bar by 2. That brings us to 8), the Uncertainty Principle for momentum (p) and position (x).

Since ET=PL and PL = h-bar/2, it follows that ET=h-bar/2 (step 9). Step 10) is the Uncertainty Principle for energy (E) and time (t).