Heisenberg’s Uncertainty Principle. Why, exactly, can you not know both the velocity and position of a particle?

Question

Heisenberg’s Uncertainty Principle. Why, exactly, can you not know both the velocity and position of a particle?

In: 146

Answer 1

Let’s look at a baseball you throw. First, let’s take a picture of a single instant in time. We know exactly where the baseball is, but from that picture we have no idea how fast it’s going (or even the direction).

Now suppose instead of an image, we use a radar gun to measure the speed of the ball. To do this, the ball has to move from one place to another. So now we know the speed, but there is some uncertainty in the position of the ball because our speed measurement isn’t instantaneous (it is an average over some period of time).

You can’t have zero uncertainty in both position & momentum for this system because one value (momentum) requires measurement over some time period and the other value changes during that time period (position).