Heisenberg Uncertainty


PHF Hall of Fame
Apr 2009
Boston's North Shore
I mentioned Griffiths before. Here I'd like to quote exactly what he wrote. In his text on particle physics he wrote

In general, when you hear a physicist invoke the uncertainty principle, keep your hand on your wallet.
What comes before that is lengthy but will quote all of it upon request. He gives a back of the envelope derivation using the time-energy uncertainty principle which he follows by saying
If you find that argument compelling, I can only say that your gullible.
The author does reference this article which he mentions after mentioning that different writers use different definitions of uncertainty, some of which are unjustified. The article is

The standard deviation is not an adequate measure of quantum uncertainty by Jan Hilgevoord, American Journal of Physics, 70, 983 (2002);

is online at


May I ask you where you got your notions of what uncertainty is?

When I was an undergrad I had a great professor who always made sure I knew what certain important terms meant. One day he asked me what uncertainty was. I thought I knew but when I couldn't describe it other than by repeating "Its what I'm not certain of" or something just as lame I realized that I didn't really know the answer to his question. So I looked it up and learned exactly what it meant. I then realized that it has nothing to do with experimental error because the spread of the probability function tells you the likelihood, and thus "uncertainty" of where a particle is measured. That means its totally dependent on the wave function itself and has nothing to do with experimental error.

Its unfortunate that so many students and physicists don't really know what it means. Some authors actually describe uncertainty "after" the position has already been measured, which is quite wrong since after its been measured you know exactly what the value is. Uncertainty describes only what a measurement will be.

That said I'd like to remind everyone of a counter example which is never used to elaborate uncertainty and why I used dice as an example. If the original quantum state of the spin of an electron is a superposition of up and down then the uncertainty is nonzero even though there are only two possible finite values one can measure. One measured there is zero uncertainty in whether its spin up or spin down.