"The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa."
--Heisenberg, uncertainty paper, 1927
The uncertainty principle says that we cannot measure the position $ (X) $ and the momentum $ (P) $ of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other.
i.e. $ \Delta X $ . $ \Delta P $ $\geq $ $ \frac{\hbar}{2} $
Multiplying together the errors in the measurements of these values (the errors are represented by the triangle symbol in front of each property, the Greek letter “$\Delta$”) has to give a number greater than or equal to half of a constant called: $“ \hbar ”$ (h-cut).
Planck’s constant is an important number in quantum theory, a way to measure the granularity of the world at its smallest scales and it has the value $ 6.626 * 10^{-34}$ Joule-Second. More in detail Click here.
A website called “How Stuff Works” I was looking at explained it in very simplistic terms:
Imagine that you’re blind and over time you’ve developed a technique for determining how far away an object is by throwing a medicine ball at it. If you throw your medicine ball at a nearby stool, the ball will return quickly, and you’ll know that it’s close. If you throw the ball at something across the street from you, it’ll take longer to return, and you’ll know that the object is far away.
The problem is that when you throw a ball — especially a heavy one like a medicine ball — at something like a stool, the ball will knock the stool across the room and may even have enough momentum to bounce back. You can say where the stool was, but not where it is now. What’s more, you could calculate the velocity of the stool after you hit it with the ball, but you have no idea what its velocity was before you hit it.
This is the problem revealed by Heisenberg’s Uncertainty Principle. To know the velocity of a quark we must measure it, and to measure it, we are forced to affect it. The same goes for observing an object’s position. Uncertainty about an object’s position and velocity makes it difficult for a physicist to determine much about the object.
More in detail Click here.
Uncertainty relations or uncertainty principle?
Let us now move to another question about Heisenberg's relations: do they express a principle of quantum theory? Probably the first influential author to call these relations a ‘principle’ was Eddington, who, in his Gifford Lectures of 1928 referred to them as the ‘Principle of Indeterminacy’.
In the English literature the name uncertainty principle became most common. It is used both by Condon and Robertson in 1929, and also in the English version of Heisenberg's Chicago Lectures (Heisenberg, 1930), although, remarkably, nowhere in the original German version of the same book (see also Cassidy, 1998).
Indeed, Heisenberg never seems to have endorsed the name ‘principle’ for his relations. His favourite terminology was ‘inaccuracy relations’ (Ungenauigkeitsrelationen) or ‘indeterminacy relations’ (Unbestimmtheitsrelationen). We know only one passage, in Heisenberg's own Gifford lectures, delivered in 1955-56 (Heisenberg, 1958, p. 43), where he mentioned that his relations "are usually called relations of uncertainty or principle of indeterminacy".
But this can well be read as his yielding to common practice rather than his own preference. Read more...»
Click for Next:
- Heisenberg recalls his Early thought on Uncertainty Principle(2):
- Mathematical Expression of Uncertainty Principle(3):