Chapter 28, Problem 4Q

To determine

Why a baseball has well-defined position and speed, but an electron does not.

Answer to Problem 4Q

Solution:

A baseball has well-defined position and speed because macroscopic objects like baseballs have large mass and momentum as compared to an electron.

Explanation of Solution

The Heisenberg Uncertainty Principle is stated as:

$\begin{array}{l}△x△p\ge \frac{h}{2\pi },wherehisPlanck\text{'}sconstant\\ \Rightarrow △x△v\ge \frac{h}{2\pi m}(△p=m△v)\end{array}$

For a baseball, mass is of the order of a few grams. Thus, the uncertainty limit is extremely low, to the order of 10^-30. This is small enough that it can be neglected, and we seldom measure quantities to that precision. Accurate predictions can be taken while not coming close to the limit of error.

But for an electron, $m_e\approx {10}^{-31}$, so uncertainty limit comes to the order of ${10}^{-3}$, which is very significant. Thus, precise measurements come close to the Uncertainty limit.