There I go again, mistating the facts. Facts are neccesary of course, but I am more attracted to ideas, from which future facts can sometimes arise.
In my previous post I said the quantity in brackets in the People Aren't Perfect lab handout (my doubly previous post) is the standard deviation. Nope. It's just the old ordinary average, somewhat like Mr. Ordinary Smith in Alfred Hitchcock's movie Stage Fright, which I watched last night and enjoyed very much.
This isn't the first time I've blundered slightly in regard to the standard deviation. In my very first post on 14 August 2010 I couldn't remember what the thingy Larry put on the board related to the uncertainty principle is called (this is in the classroom dream sequence in A Serious Man).
In my second post, I remembered what it's called--hell yes, the standard deviation--but really didn't correctly state the way it's used in Heisenberg's uncertainty principle. I said "the product of the standard deviation of position and the standard deviation of momentum cannot be smaller than Planck’s constant divided by 4π."
Here's the better way of stating the uncertainty principle for position (that is, location) and momentum (mass times speed) of a particle, which I copied from the Hyperphysics website: "The position and momentum of a particle cannot be simultaneously measured with
arbitrarily high precision. There is a minimum for the product of the
uncertainties of these two measurements."
So, you see, in the Uncertainty Priniciple, we are talking about the uncertainties in measurement, and the fact (well it hasn't been disproved) that these uncertainties cannot be made arbitrarily small as was the thought-to-be case in classical physics. When you quantify this mathematically, the uncertainty is expressed as the standard deviation, and the product of the standard deviation of x (location) with the standard deviation of p (momentum) cannot be smaller than, ta-da!, 5.27285863 × 10-35 joule seconds.
As you can see the units are "energy times time," and the uncertainty principle applies to actual energy and time measurements the same way it does to position and momentum measurements. Yep, x times p has units of energy times time, or if you break it down to basic units, kilogram-(meter squared)/ second. This particular combination of units is called "action" by physicists. (You can supply your own pun here.)
As you can see the units are "energy times time," and the uncertainty principle applies to actual energy and time measurements the same way it does to position and momentum measurements. Yep, x times p has units of energy times time, or if you break it down to basic units, kilogram-(meter squared)/ second. This particular combination of units is called "action" by physicists. (You can supply your own pun here.)
By the way, if you have one of those T-shirts or bumper stickers from the Mean Eyed Cat bar in Austin that says "MEAN," you should not forget that this word is synonomous wtih "average." So that same message would be written mathematically as <your name here>.
Next time: back to the People Aren't Perfect lab, and how the standard deviation can be written in a simpler form using the average of the square minus the square of the average, which is what Larry puts on the board (incorrectly at first; see my 14 Aug 2010 post) in the classroom dream sequence.
