Busting Myths About Heisenberg's Uncertainty :: Episode 3

Aah! Finally, we come to our actual topic of discussion! But you see all that previous discussion (check out Episode 1 here) was necessary to build you up for this final stage. (If you have skipped all of the above, I would recommend you at least skim through them fast so that your concepts are all brushed up and shining clean.)

In its most general form, the Uncertainty Principle states that one cannot devise an experiment to tell which of the alternatives a system takes without disturbing the interference phenomenon exhibited by the system.

This is equivalent to saying that the Measurement Principle holds. How? Well, if you try to measure and find out which of the alternatives nature 'actually' takes, you will find that it takes just one, but then you will end up with no interference because the wave-function has collapsed to a Dirac-delta spike at that one particular alternative because of your act of  measurement.

I am sure you are wondering why I am talking about the Measurement Principle instead of uncertainties in position and momentum and the relation between them. Well, have some patience my friend. It is in fact equivalent. You need to understand the general principle first, then you will appreciate the particular case better.

NOTE: I intend to elaborate on this point, but right now I lack enough time to complete this text. Once I am done, I'll post an UPDATE to this entry. COMING SOON!

However, I want you to go through this video carefully which summarizes all of the ideas I have discussed so far, and gives you a fair sketch of the uncertainty principle.

WARNING: Heisenberg himself was wrong about the minimum limit to which one can reduce the uncertainties because he tried to "explain" the principle in terms of causal mechanisms such as optical effects as in his gamma-ray microscope which led him to conclude that the limit was h, Planck's constant. Be warned though, such an explanation does not exist. Do not indulge yourself in giving a classical picture to these things. They don't have one. They are purely quantum-mechanical phenomena. The true quantum limit is more than 6 times as low as that predicted by Heisenberg originally. It is half the reduced Planck's constant.

More on this later when I am ready with an UPDATE! Cheerio! :)