Heisenberg recalls his Early thought on Uncertainty Principle:

 

"The problem of language here are really serious. We wish to speak in some way about the structure of the atoms. But we cannot speak about atoms in ordinary language."

                                     - Werner Heisenberg

  

We had understood the mathematical scheme, and we also had understood that certainly we need the discrete energy levels, and the quantum jumps, and so on. But we could not even explain how such a thing as an orbit of an electron in a cloud chamber comes about, because they would see the orbit, but still we had no notion of the orbit in our mathematical scheme.

 

And at that time I remembered a long discussion which I had with Einstein about a year [before] - it was my first meeting with Einstein - I had given a talk on quantum mechanics in the Berlin colloquium. And Einstein had taken me to his room, and he first asked me about this idea which I had said in my lecture, that one should only use observable quantities in the mathematical scheme.

 

And he said, he understood the ideas of Mach, Mach's philosophy, but whether I really believed in it, he couldn't see. Well, I told him that I had understood that he has produced his theory of relativity just on this philosophical basis, as everybody knew. Well, he said, that may be so, but still it's nonsense. And that of course was quite surprising to me.

 

Then he explained that what can be observed is really determined by the theory. He said, you cannot first know what can be observed, but you must first know a theory, or produce a theory, and then you can define what can be observed...

 

And could it not be the other way around? Namely, could it not be true that nature only allows for such situations which can be described with a mathematical scheme? Up to that moment, we had asked the opposite question. We had asked, given the situations in nature like the orbit in a cloud chamber, how can it be described with a mathematical scheme? But that wouldn't work, because by using such a word like "orbit", we of course assumed already that the electron had a position and had a velocity. 

 

But by turning it around, one could at once see that now it's possible, if I say nature only allows such situations as can be described with a mathematical scheme, then *you can say, well, this orbit is really not a complete orbit. Actually, at every moment the electron has only an inaccurate position and an inaccurate velocity, and between these two inaccuracies there is this uncertainty relation. And only by this idea it was possible to say what such an orbit was.

 

From "The Development of the Uncertainty Principle", an audiotape produced by Spring Green Multimedia in the UniConcept Scientist Tapes series, © 1974. More in detail Click here.

Click for Next:

- The Heisenberg Uncertainty Relation(1)

- Mathematical Expression of Uncertainty Principle(3)

The Heisenberg Uncertainty Relations:

"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...»

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                          - Heisenberg recalls his Early thought on Uncertainty Principle(2):
                          - Mathematical Expression of Uncertainty Principle(3):